High quality group iii nitride crystal, method of making, and method of use

Abstract

Embodiments of the present disclosure include techniques related to techniques for processing materials for manufacture of group-III metal nitride and gallium based substrates. More specifically, embodiments of the disclosure include techniques for substrates with very narrow x-ray rocking curves using a combination of processing techniques. Merely by way of example, the disclosure can be applied to growing crystals of GaN, AlN, InN, InGaN, AlGaN, and AlInGaN, and others for manufacture of bulk or patterned substrates.

Description

Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01HIGH QUALITY GROUP III NITRIDE CRYSTAL, METHOD OF MAKING, AND METHOD OF USEBACKGROUNDField

[0001] This disclosure relates generally to techniques for processing materials for manufacture of gallium-containing nitride crystals and substrates and utilization of these crystals and substrates in optoelectronic and electronic devices. More specifically, embodiments of the disclosure include techniques for growing large area crystals using a combination of processing techniques.Description of the Related Art

[0002] Gallium nitride (GaN) based optoelectronic and electronic devices are of tremendous commercial importance. The quality and reliability of these devices, however, is compromised by high defect levels, particularly threading dislocations, grain boundaries, and strain in semiconductor layers of the devices. Additional defects can arise from thermal expansion mismatch, impurities, and tilt boundaries, depending on the details of the growth of the layers.

[0003] Progress has been made in the growth of large-area gallium nitride crystals with considerably lower defect levels than heteroepitaxial GaN layers. Progress has also been made in reducing the dislocation densities in free-standing, bulk gallium nitride crystals below 105cm-2. However, the crystalline quality of demonstrated bulk gallium nitride crystals remains significantly inferior to that of semiconductor-grade crystals with other compositions, including silicon, gallium arsenide, indium phosphide, and silicon carbide. Various techniques have been introduced to improve the crystalline quality of thick gallium nitride layers that originated from heteroepitaxial layers on a substrate such as sapphire, but challenges still remain.

[0004] In addition, characterization methods that have been widely applied to quantification of crystalline quality suffer certain limitations in their ability to distinguish between gallium nitride crystals having varying crystalline quality.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01

[0005] Due to at least the issues described above, there is a need for crystals substrates that have a lower defect density and are formed by techniques that are scalable to large diameters and improve the crystal growth process. Also, from the above, it is seen that techniques for improving crystal growth and better characterizing crystal quality are highly desirable.SUMMARY

[0006] In some embodiments, the disclosure describes a free-standing crystal, comprising a group III metal and nitrogen, wherein the free-standing crystal comprises: a wurtzite crystal structure; a first surface having a maximum edge-to-edge dimension in a first direction; and a second surface on the opposite side of the crystal from the first surface that is separated from the first surface in a second direction that is orthogonal to the first direction and to the first surface, wherein: the first surface is characterized by a root-mean-square surface roughness less than about 50 micrometers and an average concentration of threading dislocations below about 104cm’2; the first surface is further characterized by an x-ray rocking curve quality metric Q having a value greater than about 25, where Q is defined as~ 100 100 108

[0007] Q - Si=i FWHM(i)+FWQM(i)+FWEM(i)

[0008] where 100 / FWHM( / ), 100 / FWQM( / ), and 100 / FWEM( / ) are the average values of the quantities 100 divided by the full-width-at-half-maximum (FWHM), 100 divided by the full-width-at-quarter-maximum (FWQM), and 100 divided by the full-width-at-eighth-maximum (FWEM), respectively, of the th reflection at each of at least five points that are distributed approximately uniformly over the central 40 to 80% of the area of the first surface, and / =1 corresponds to the rocking curve for a symmetric reflection rocking about a first axis that is parallel to the first direction, i=2 corresponds to the rocking curve for the same symmetric reflection rocking about a second axis, orthogonal to the first axis and to the second direction, / =3 corresponds to the rocking curve for an asymmetric reflection, and the FWHM, FWQM, and FWEM values are in units of arc-seconds, and the x-ray rocking curves are measured using incident slit dimensions of at least 1 millimeter highAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01by 2 millimeters wide and receiving slit dimensions of at least 1 millimeter high by 1 millimeter wide.

[0009] In some embodiments, the x-ray rocking curve quality metric Q value of the free standing crystal ranges from about 25 to about 40.

[0010] In some embodiments, the first surface of the free standing crystal has a crystallographic orientation within about 5 degrees of (0001) or (000-1), the / '=1 rocking curve corresponds to a symmetric reflection chosen from one of (002), (004) or (006) rocking about an a-axis, the 1=2 rocking curve corresponds to the same symmetric reflection rocking about an orthogonal m-axis, and the i=3 rocking curve corresponds to an asymmetric (201 ) reflection.

[0011] In some embodiments, the first dimension of the free standing crystal is at least 45 millimeters.

[0012] In some embodiments, the first dimension of the free standing crystal is at least 95 millimeters.

[0013] In some embodiments, the root-mean-square roughness of the first surface of the free standing crystal is less than about 1 nanometer.

[0014] In some embodiments, the first surface of the free standing crystal is characterized by an average concentration of threading dislocations that varies periodically by at least a factor of 1.2 in a third direction, the period of the variation in the third direction being between about 1.5 millimeters to about 20 millimeters.

[0015] In some embodiments, the first surface of the free standing crystal is further characterized by an average concentration of threading dislocations that varies periodically by at least a factor of 1.2 in a fourth direction, the fourth direction being orthogonal to the third direction and the period of the variation in the fourth direction being between about 1.5 millimeters to about 20 millimeters.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01

[0016] In some embodiments, the first surface of the free standing crystal is characterized by an average concentration of threading dislocations that varies periodically by at least a factor of 2 in a third direction, the period of the variation in the third direction being between about 1.5 millimeters to about 20 millimeters and wherein the first surface is further characterized by an average concentration of threading dislocations that varies periodically by at least a factor of 2 in a fourth direction, the fourth direction being orthogonal to the third direction and the period of the variation in the fourth direction being between about 1.5 millimeters to about 20 millimeters.

[0017] In some embodiments, the first surface of the free standing crystal is characterized by average impurity concentrations of: oxygen (O) between 1×1016cm-3and 5×1019cm-3; hydrogen (H) between 1×1016cm-3and 8×1019cm-3; and at least one of fluorine (F) and chlorine (Cl) between 1×1015cm-3and 1×1019cm-3.

[0018] In some embodiments, a ratio of the impurity concentration of H to an impurity concentration of O of the free standing crystal is between about 0.3 to about 10.

[0019] In some embodiments, the x-ray rocking curve quality metric Q of the free standing crystal has a value greater than about 40.

[0020] In some embodiments, the disclosure describes a method for fabricating a freestanding crystal, the method comprising: providing a first seed crystal obtained by slicing a crystal that had been formed by at least three previous growth / wafering cycles and had an as-grown (000-1 ) surface on which less than 1 % of its area had trenches having a local width between about 250 micrometers to about 5 millimeters and a local depth between about 500 micrometers to about 10 millimeters, less than 10% of its area comprised depressions having a depth greater than about 5 micrometers to less than about 100 micrometers, and the balance of its area having a root-mean-square surface roughness between about 0.1 nanometers to about 20 micrometers; applying a pattern to the (000-1) face of the first seed crystal, the pattern having a minimum parallel separation of at least 1.25 millimeters; placing the patterned, first seed crystal within an outer position of a sealable container, such that most or all of the first seed crystal isAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01positioned in an outer position with respect to a cylindrical boundary having a diameter between about 70% and about 95% of an inner diameter of the sealable container; growing the first seed crystal to form a first boule having a thickness of at least 3 millimeters by an ammonothermal method; and forming at least a second crystal from the first boule by slicing at a distance at least one millimeter above a highest coalescence region within the first boule.

[0021] In some embodiments, the method of fabricating a free standing crystal further comprises: placing a second seed crystal, the second seed crystal comprising at least a portion of the second crystal, within an outer position of a sealable container, such that most or all of the second seed crystal is positioned in an outer position with respect to a cylindrical boundary having a diameter between about 70% to about 95% of an inner diameter of the sealable container; growing the second seed crystal to form a second boule having a thickness of at least 3 millimeters by an ammonothermal method; and forming at least a third crystal from the first boule by slicing at a distance at least one millimeter above a highest coalescence region within the first boule.

[0022] In some embodiments, the method of fabricating a free standing crystal further comprises: slicing off an a-corner from the second crystal or the third crystal, forming an a-edge on the second or third crystal having an orientation within about 10 degrees of a {11-20} a-plane; performing ammonothermal growth on the seed crystal with the a-edge, forming a 100%-laterally-grown a-wing having a width between about 1 millimeter to about 50 millimeters and lateral facets comprising one or more of m-plane facets and semipolar {10-1-1} facets; removing the 100%-laterally-grown a-wing, forming a free-standing- 100%-laterally-grown a-wing; and performing ammonothermal growth on the free-stand ing- 100%-late rally-g rown a-wing.

[0023] in some embodiments, the method of fabricating a free standing crystal further comprises the pattern applied to the (000-1) face of the first seed crystal having a minimum parallel separation of at least 2 millimeters.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01BRIEF DESCRIPTION OF THE DRAWINGS

[0024] So that the manner in which the above recited features of the present disclosure can be understood in detail, a more particular description of the disclosure, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only exemplary embodiments and are therefore not to be considered limiting of its scope, may admit to other equally effective embodiments.

[0025] FIGs. 1A, 1B, 1C, 1D, 1E, 1F, 1G, 1H, 11, 1J, 1K, 1L, and 1 M are top views of arrangements of openings in a patterned mask layer on a seed crystal or a substrate according to an embodiment of the present disclosure.

[0026] FIGs. 2A, 2B, and 2C are simplified diagrams illustrating an epitaxial lateral overgrowth process for forming a large area group III metal nitride crystal, according to an embodiment of the present disclosure.

[0027] FIGs. 3A, 3B, 3C, 3D, 3E, and 3F are simplified diagrams illustrating an improved epitaxial lateral overgrowth process for forming a large area group III metal nitride crystal, according to an embodiment of the present disclosure.

[0028] FIGs. 4A and 4B are simplified diagrams illustrating a method of forming a free-standing ammonothermal group III metal nitride boule and free-standing ammonothermal group III metal nitride wafers.

[0029] FIGs. 5A, 5B, 5C, and 5D are simplified diagrams illustrating x-ray rocking curve data according to embodiments of the present disclosure.

[0030] FIGs. 6A and 6B are simplified diagrams showing locations on a free-standing group III metal nitride wafer for characterization by x-ray rocking curve measurements.

[0031] FIG. 7 is a simplified diagram illustrating a method for preparing an analysis sample from a free-standing crystal according to an embodiment of the present disclosure.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01

[0032] FIGs. 8A, 8B, and 8C are simplified diagrams showing locations of seed crystals within a crystal growth apparatus according to an embodiment of the present disclosure.

[0033] FIG. 9 is a simplified diagram illustrating growth sectors and coalescence boundaries in a sectioned sample from a laterally-grown ammonothermal group III metal nitride boule according to an embodiment of the present disclosure.

[0034] FIGs. 10A, 10B, and 10C are simplified diagrams illustrating a lateral crystal growth process according to an embodiment of the present disclosure.

[0035] FIGs. 11 A and 11 B are simplified diagrams illustrating a method for measuring dislocation density as a function of position across a crystal according to an embodiment of the present disclosure.

[0036] FIG. 12 is a simplified diagram showing regions of smooth and rough surface morphology on a boule formed by one or more methods disclosed herein, according to an embodiment of the present disclosure.

[0037] To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures, it is contemplated that elements and features of one embodiment may be beneficially incorporated in other embodiments without further recitation.DETAILED DESCRIPTION

[0038] According to the present disclosure, techniques related to techniques for processing materials for manufacture of group-ill metal nitride and gallium-based substrates are provided. More specifically, embodiments of the disclosure include techniques for growing large area substrates using a combination of processing techniques. Merely by way of example, the disclosure can be applied to growing crystals of GaN, AIN, InN, InGaN, AIGaN, and AllnGaN, and others for manufacture of bulk or patterned substrates.

[0039] Threading dislocations in GaN are known to act as strong non-radiative recombination centers which can severely limit the efficiency of GaN-based LEDs andAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01laser diodes and also impact the performance of power electronic devices, for example, by increasing leakage current and reducing lifetime. In high-power applications, GaN-based devices suffer from decreased efficiency with increasing current density, known as droop. There is evidence suggesting a correlation between dislocation density and the magnitude of droop in LEDs. For GaN-based laser diodes there is a well-documented negative correlation between dislocation density and mean time to failure (MTTF), which appears to be due to impurity diffusion along the dislocations. One of the primary advantages of using bulk GaN as a substrate material for epitaxial thin film growth is a large reduction in the concentration of threading dislocations in the film. Therefore, the dislocation density in the bulk GaN substrate will have a significant impact on the device efficiency and the reliability.

[0040] It is well known that the concentration of threading dislocations can be reduced by performing lateral epitaxial overgrowth (LEO) techniques. Examples of these techniques, as applied to ammonothermal GaN growth, may be found in U. S. Pat. Nos. 9,589,792 and 11,705,322 and in U. S. Pat. Appt No. 2023 / 0295839. However, certain classes of defects in bulk GaN crystals used as seeds, such as multiple crystallite domains with tilt boundaries between them, may not be removed using conventional LEO techniques.

[0041] A number of characterization methods have been widely used to characterize crystals, wafers, and seed crystals of bulk group III metal nitride crystals such as gallium nitride, including crystals grown using LEO techniques. X-ray diffraction, specifically, the full-width-at-half-maximum (FWHM) of x-ray rocking curves (XRC), about specific reflections, such as (002), (004), (006), or (201), has been widely applied as a characterization tool for high quality GaN crystals. A schematic example of such an XRC is shown in FIG. 5A for a case with only a single grain present within the illuminated area of the x-ray beam. In addition to the FWHM, the full-width-at-quarter-maximum (FWQM) and full-width-at-eighth-maximum (FWEM) are also indicated schematically. However, with large-area, commercial GaN crystals and wafers there is the possibility that the x-ray beam will illuminate two grains, with a low-angle boundary,Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01or tilt boundary, between them. FIG. 5B shows an idealized case where two grains having a tilt angle A® between them that is equal in value to twice the FWHM of each sub-peak, with each grain contributing an equal intensity to the x-ray reflection. In this case, we see that each of the FWHM, FWQM, and FWEM, each expressed with the respect to the doublet peak, are significantly broadened relative to the corresponding values shown in FIG. 5A and the presence of the doublet peak is easily discerned. FIG.5C shows an idealized case where, again, two grains are illuminated by the x-ray beam, but the tilt angle A® between them is now only 0.9 times the FWHM of each of the subpeaks. In this case, each of the FWHM, FWQM, and FWEM, each expressed with the respect to the doublet peak, are significantly broadened relative to the corresponding values shown in FIG. 5A, but now the presence of the doublet peak is barely discernable (a double peak is no longer apparent if the tilt angle is only approximately 0.8 times the FWHM). FIG. 5D shows another idealized case where three grains are present, with two sub-grains whose ra values are shifted from that of the main grain by ±1.5 times the FWHM of each isolated sub-grain and whose x-ray intensities are only 20% of that of the main grain. This case may illustrate some situations that may arise in real commercial GaN crystals and wafers, where two or more sub-grains are present, in addition to a main grain, within an area of the crystal being examined by XRC. In this case, again comparing to FIG. 5A, we see that there is little or no difference in the FWHM, a small difference in the FWQM, and a large difference in the FWEM.Therefore, we argue that use of all of these metrics, rather than just the FWHM, provides a better gauge for crystalline quality of real, commercial bulk GaN crystals, particularly large-area crystals that had an origin, somewhere in their growth history, in a heteroepitaxially-grown layer on a non-GaN substrate such as sapphire or GaAs, were tiled together from smaller crystals, or were formed by coalescence of point seeds or other smaller entities. In preferred embodiments, the XRC measurements are made with wide-open diffractometer slits, for example, incident slits 1 millimeter high by 2 millimeters, 5 millimeters, or 10 millimeters wide and receiving slits 1 millimeter high by 1 millimeter wide.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01

[0042] In addition to the FWQM and FWEM providing more sensitivity to mosaicity than the FWHM, strain gradients within real, commercial GaN crystals may give rise to an asymmetric rocking curve peak. This asymmetry will be better captured by focusing on the tail of the rocking curve (i.e., FWQM and FWEM), in addition to the traditional focus on the upper half of the rocking curve.

[0043] FIGs. 2A, 2B, and 2C and FIGs. 3A, 3B, 3C, 3D, 3E, and 3F are schematic cross-sectional views of a LEO method for growing a bulk GaN layer 219 on a substrate 101, predominantly in a single crystallographic orientation, by means of a pattern. In certain embodiments, substrate 101 consists of or includes a substrate material that is a single-crystalline group-ill metal nitride, gallium-containing nitride, or gallium nitride. The substrate 101 may be grown by HVPE, ammonothermally, or by a flux method. One or both large area surfaces of substrate 101 may be polished and / or chemical-mechanically polished. A large-area surface 102 of substrate 101 may have a crystallographic orientation within 10 degrees, within 5 degrees, within 2 degrees, within 1 degree, or within 0.5 degree of (0001 ) +c-plane, (000-1 ) -c-plane, {10-10} m-plane, {11-2+2}, {60-6+1}, {50-5±1}. {40-4+1}, {30-3+1}, {50-5±2}, {70-7+3}, {20-2+1}, {30-3±2}, {40-4+3}, {50-5+4}, {10-1±1 }, {1 0 -1 ±2}, {1 0 -1 ±3}, or {2 1 -3 ±1}. Large-area surface 102 may have an (h k i I) semipolar orientation, where / = -( / ? + k) and / and at least one of h and k are nonzero. Large-area surface 102 may have a maximum lateral dimension between about 5 millimeters and about 600 millimeters and a minimum lateral dimension between about 1 millimeter and about 600 millimeters and substrate 101 may have a thickness between about 10 micrometers and about 10 millimeters, or between about 100 micrometers and about 2 millimeters.

[0044] Substrate 101 may have a surface threading dislocation density iess than about 107cm-2, less than about 106cm2, less than about 105cm’2, less than about 104cm-2, less than about 103cm-2, or less than about 102cm-2. Substrate 101 may have a stacking-fault concentration below about 104cm-1, below about 103cm-1, below about 102cm-1, below about 10 cm-1or below about 1 cm-1. Substrate 101 may have a symmetric x-ray rocking curve full width at half maximum (FWHM) less than about 500 arcsec, less than about 300 arcsec, less than about 200 arcsec, less than about 100Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01arcsec, less than about 50 arcsec, less than about 35 arcsec, less than about 25 arcsec, or less than about 15 arcsec. Substrate 101 may have a crystallographic radius of curvature greater than 0.1 meter, greater than 1 meter, greater than 10 meters, greater than 100 meters, or greater than 1000 meters, in at least one, at least two, or in three independent or orthogonal directions.

[0045] Substrate 101 may comprise regions having a relatively high concentration of threading dislocations separated by regions having a relatively low concentration of threading dislocations. The concentration of threading dislocations in the relatively high concentration regions may be greater than about 105cm-2, greater than about 106cm-2, greater than about 107cm-2, or greater than about 108cm-2. The concentration of threading dislocations in the relatively low concentration regions may be less than about 106cm-2, less than about 105cm-2, or less than about 104cm-2. Substrate 101 may comprise regions having a relatively high electrical conductivity separated by regions having a relatively low electrical conductivity. Substrate 101 may have a thickness between about 10 microns and about 100 millimeters, or between about 0.1 millimeter and about 10 millimeters. Substrate 101 may have a maximum dimension, including a diameter, of at least about 5 millimeters, at least about 10 millimeters, at least about 25 millimeters, at least about 50 millimeters, at least about 75 millimeters, at least about 100 millimeters, at least about 150 millimeters, at least about 200 millimeters, at least about 300 millimeters, at least about 400 millimeters, or at least about 600 millimeters.

[0046] Large-area surface 102 of substrate 101 (cf. FIGs. 2A and 3A) may have a crystallographic orientation within about 5 degrees of the (000-1 ) N-face, c-plane orientation, may have an x-ray diffraction to-scan rocking curve full-width-at-half-maximum (FWHM) less than about 200 arcsec less than about 100 arcsec, less than about 50 arcsec, or less than about 30 arcsec for the (002) and / or the (102) reflections and may have a dislocation density less than about 107cm-2less than about 106cm-2, or less than about 105cm-2. In some embodiments, the threading dislocations in large-area surface 102 are approximately uniformly distributed. In other embodiments, the threading dislocations in large-area surface 102 are arranged in homogeneously as a one-dimensional array of rows of relatively high- and relatively low-concentrationAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01regions or as a two-dimensional array of high-dislocation-density regions within a matrix of low-dislocation-density regions. The crystallographic orientation of large-area surface 102 may be approximately constant, that is, may vary by less than about 5 degrees, less than about 2 degrees, less than about 1 degree, less than about 0.5 degrees, less than about 0.2 degrees, less than about 0.1 degrees, or less than about 0.05 degrees.

[0047] In certain embodiments, large-area surface 102 is etched, for example, to remove surface damage or to improve adhesion of a mask layer. In certain embodiments, large-area surface 102 is etched by one or more of chemical etching, electrochemical etching, photoelectrochemical etching, reactive ion etching, chemically-assisted ion beam etching, or by another form of wet or dry etching.

[0048] In certain embodiments, a patterned mask layer is provided on large-area surface 102 before growing bulk GaN layer 219 on substrate 101. Referring again to FIGs. 2A and 3A, patterned mask layer 111 may be deposited on surface 102 of substrate 101 by methods that are known in the art. In certain embodiments, patterned mask layer 111 includes one or more of adhesion layer 105, diffusion-barrier layer 107, and inert layer 109. The adhesion layer 105 may comprise one or more of Ti, TiN, TiNy, TiSi2, Ta, TaNy, Al, Ge, AlxGey, Cu, Si, Cr, V, Ni, W, TiWx, TiWxNy, or the like and may have a thickness between about 1 nanometer and about 1 micrometer. The diffusion-barrier layer 107 may comprise one or more of TiN, TiNy, TiSi2, W, TiWx, TiNy, WNy, TaNy, TiWxNy, TiWxSizNy, TiC, TICN, Pd, Rh, Cr, or the like, and have a thickness between about 1 nanometer and about 10 micrometers. The inert layer 109 may comprise one or more of Au, Ag, Pt, Pd, Rh, Ru, Ir, Ni, Cr, V, Ti, or Ta and may have a thickness between about 10 nanometers and about 100 micrometers. The one or more patterned mask layers 111 may be deposited by sputter deposition, thermal evaporation, electron-beam evaporation, electroplating, electroless plating, a combination or sequence of these techniques, or the like. Exposed regions, or openings 112 may be formed by one or more of negative photoresist lift-off, shadow masking, positive photoresist reactive ion etching, wet chemical etching, ion milling, and nanoimprint lithography, laser cutting, or the like. In certain embodiments, trenches areAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01prepared underlying exposed growth centers 120; for example, by one or more of wet etching and laser cutting, according to methods that are known in the art.

[0049] FIGs. 1A, 1B, 1C, 1D, 1E, 1F, 1G, 1H, 1I, 1J, 1K, 1L, and 1M are top views of arrangements of exposed regions or growth centers 120 in patterned mask layers 111 on substrate 101. The exposed regions 120 (or also referred to herein as growth centers or primary growth centers), which are illustrated, for example, in FIGs. 1A-1M, may be defined by and / or include the openings 112 formed in patterned mask layer(s) 111 shown in FIG. 2A. In certain embodiments, the exposed regions 120 are arranged in a one-dimensional (1 D) array in the Y-direction, such as a single column of exposed regions 120 as shown in FIG. 1D. In certain embodiments, the exposed regions 120 are arranged in a two-dimensional (2D) array in X-direction and Y-directions, such as illustrated in FIGs. 1A-1D and 1H-1M. The openings 112, and thus exposed regions 120, may be round, square, rectangular, triangular, hexagonal, or the like, and may have an opening dimension W (or diameter W or width w1) between about 1 micrometer and about 5 millimeters, between about 3 micrometers and about 5 millimeters or between about 10 micrometers and about 500 micrometers such as illustrated in FIGs.1 A-1 M. The exposed regions 120 may be arranged in a 2D hexagonal or square array with a pitch dimension L between about 5 micrometers and about 20 millimeters, between about 200 micrometers and about 15 millimeters, or between about 500 micrometers and about 10 millimeters, or between about 0.8 millimeter and about 5 millimeters, such as illustrated in FIGs. 1A and 1B. The exposed regions 120 may be arranged in a 2D array, in which the pitch dimension Li in the Y-direction and pitch dimension L2 in the X-direction may be different from one another, as illustrated in FIGs.1C and 1E-1G. The exposed regions 120 may be arranged in a rectangular, parallelogram, hexagonal, or trapezoidal array (not shown), in which the pitch dimensions L in the Y-direction and L2 in the X-direction may be different from one another, as illustrated in FIGs. 1C and 1E-1G. The array of exposed regions 120 may also be linear or irregular shaped. The exposed regions 120 in patterned mask layer(s) 111 may be placed in registry with the structure of substrate 101. For example, in certain embodiments, large-area surface 102 has a hexagonal crystallographicAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01orientation, e.g., a (0001) or (000-1) crystallographic orientation, and the openings in patterned mask layer(s) 111 comprise a 2D hexagonal array such that the separations between nearest-neighbor openings are parallel, to within ±5°, ±3°, ±2°, or ±1°, to <11-20> or <10-10> directions in large-area surface 102. In certain embodiments, large-area surface 102 of the substrate is nonpolar or semipolar and the exposed regions 120 comprise a 2D square or rectangular array such that the separations between nearest-neighbor openings are parallel to the projections of two of the c-axis, an m-axis, and an a-axis on large-area surface 102 of substrate 101. In certain embodiments, the pattern of exposed regions 120 is obliquely oriented with respect to the structure of substrate 101, for example, wherein the exposed regions 120 are rotated by between about 1 degree and about 44 degrees with respect to a high-symmetry axis of the substrate, such as a projection of the c-axis, an m-axis, or an a-axis on large-area surface 102 of substrate 101 that has a hexagonal crystal structure, such as a Wurtzite crystal structure. In certain embodiments, the exposed regions 120 are substantially linear rather than substantially round. In certain embodiments, the exposed regions 120 are slits having a width W and period L that run across the entire length of substrate 101, as illustrated in FIG. 11. In certain embodiments, the exposed regions 120 are slits that have a width Wr in the Y-direction and a predetermined length W2 in the X-direction that is less than the length of substrate 101 and may be arranged in a 2D linear array with period Li in the Y-direction and period L2 in the X-direction, as illustrated in FIGs. 1E-1G. In certain embodiments, the slits are oriented to within ±5°, ±3°, ±2°, or ±1° toward <11-20> or <10-10> directions in large-area surface 102. In some embodiments, adjacent rows of exposed regions 120 (e.g., slits) may be offset in the X-direction from one another rather than arranged directly adjacent, as shown in FIG. 1 F and 1G. In a specific embodiment, exposed regions 120 include or consist of slits oriented to within ±3°, ±2°, or ±1° toward a <10-10> (X) direction and the separation between adjacent rows of slits in the y, or <11-20>, direction, L1-W1, is less than or equal to (W2-½L2) / √3 and greater than or equal to (W2-½L2) / (3√3) Put differently, the overlap s between exposed regions 120 in adjacent rows is greater than or equal to √3 (L1-W1) and may be less than or equal to 3√3 (L1-W1). In this way, wings growing laterally from adjacentAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01growth centers can coalesce after growth in a <11-20> direction only, with no <10-10> growth being required. In a specific embodiment, the axial separation between slits (L2-W2) is between about 5 micrometers and about 200 micrometers, or between about 10 micrometers and about 150 micrometers, or between about 25 micrometers and about 125 micrometers. In FIG. 1E the actual period of the array of exposed regions 120 in the X-direction is equal to the period L2between adjacent rows of exposed regions. The period in the X-direction is also equal to L2in FIG. 1F but the unit cell is a parallelogram rather than a rectangle as in FIG. 1 E. In other embodiments, the actual period in the X-direction may be a multiple of L2, for example, 2L2, 3L2, 4L2, 5L2, or 6L2. In certain embodiments, the adjacent rows of exposed regions 120 (e.g., slits) may be offset in the longitudinal Y-direction from one another, as shown in FIG. 1F. In certain embodiments, the exposed regions 120 include slits that extend in two or more different directions, for example, the X-direction and the Y-direction, as shown in FIG. 1G. In certain embodiments, the exposed regions 120 (e.g., slits) may be arranged in a way that reflects the hexagonal symmetry of the substrate. In certain embodiments, the exposed regions 120 (e.g., slits) may extend to the edge of the substrate 101. In certain embodiments, surface 102 is masked by a rim adjacent to its edge, so that none of the exposed regions may extend to the edge of substrate 101. In certain embodiments, the masked rim has a width between about 25 micrometers and about 1 millimeter.

[0050] In certain embodiments, surface 102 has an orientation within about 10 degrees, within about 5 degrees, within about 2 degrees, within about 1 degree, or within about 0.5 degree of a (0001 ) or (000-1 ) c-plane. in certain embodiments, as shown schematically in FIG. 1H, growth centers (i.e., exposed regions 120), which as shown can include slits formed in a mask layer, are provided along each of three directions, rotated by 120 degrees from one another and having a common period L2 along each of the three directions, in certain embodiments, approximately a third of each of the growth centers are arranged within ±3°, ±2°, or ±1° toward [10-10], [01-10] and [-1100] directions. In certain embodiments, approximately a third of each of the growth centers are arranged within ±3°, ±2°, or ±1° toward [11-20], [1-210], and [-2110] directions. In certain embodiments, the lengths of the growth centers are long inAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01comparison to l_2, so that intersections 701 between three lines of growth centers are included within the growth centers. Intersections are also referred to herein as vertices and an intersection point is also referred to herein as a vertex. In certain embodiments, a primitive unit cell 709 for the pattern includes one and only one intersection 701, around which six growth centers are arranged with 60° angles between them. In certain embodiments, the growth centers extend to the edge of surface 102. In certain embodiments, the growth centers extend to a rim that is parallel to the edge of surface 102 and terminate there, where the rim has a width between about 25 micrometers and about 2 millimeters.

[0051] A possible disadvantage of having growth centers having a length that is comparable to a lateral dimension or diameter of substrate 102, as in FIGs. 1D or 1H is that relaxation may occur only in laterally-grown material but not in the direction parallel to the growth centers. Interruptions in the growth centers, for example, as shown schematically in FIGs. 1E, 1F, and 1G, may enable relaxation in each of two orthogonal directions. Interruptions may similarly be introduced into the pattern shown schematically in FIG. 1H. In the pattern shown schematically in FIG. 11, rather than intersections 701 being open, they are masked. The presence of masked intersections 701, with slit-shaped growth centers radiating from it, can cause slow coalescence above the intersections, as <10-10> direction growth may be required to cover them. In certain embodiments, a primitive unit cell 709 for the pattern includes one and only one intersection 701, around which six growth centers are arranged with 60° angles between them.

[0052] The pattern shown in Figure 11 includes a plurality of linear arrays of growth centers that are formed in regular repeating patterns. In the example shown in Figure 11, the plurality of linear arrays of growth centers include a first linear array of growth centers 751, a second linear array of growth centers 752 and a third linear array of growth centers 753. The first linear array of growth centers 751 includes a plurality of growth centers 761 that are aligned in a first direction, such as the X-direction. The second linear array of growth centers 752 includes a plurality of growth centers 762 that are aligned in a second direction, which is aligned at an angle of 60 degrees from theAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01first direction. The third linear array of growth centers 753 includes a plurality of growth centers 763 that are aligned in a third direction, which is aligned at an angle of 120 degrees from the first direction. The pattern shown in Figure 11 also includes a plurality of intersections 701 (also referred to a vertices) that are formed at each of the points where the first linear array of growth centers, the second linear array of growth centers and the third linear array of growth centers cross in the formed repeating patterns. For clarity, intersections 701 refer to locations where lines, having a width equal to five times the width of the growth centers, passing through the centers of the first linear array of growth centers, the second linear array of growth centers, and the third linear array of growth centers, and oriented along the directions of the directions of the first linear array of growth centers, the second linear array of growth centers, and the third linear array of growth centers, respectively, intersect.

[0053] In certain embodiments, as shown schematically in FIG. 1 J, each vertex or intersection has a growth center of a single, specific orientation running through it. In a specific embodiment, adjacent intersections 703, 705, and 707 have siit-shaped growth centers oriented within ±3°, ±2°, or ±1° toward [10-10], [01-10] and [-1100] directions, respectively. In another specific embodiment, adjacent intersections 703, 705, and 707 have slit-shaped growth centers oriented within ±3°, ±2°, or ±1° toward [11-20], [1-210], and [-2110] directions, respectively. In the specific embodiment shown in FIG. 1 J, the period in the X-direction l_3 is 3l_2, where l_2 is the separation between adjacent intersections in the X-direction, without regard to the type of intersection point. In certain embodiments, the period in the X-direction, and in each of two directions rotated by 120 degrees with respect to the X-direction, is equal to at least one of L2, 2L2, 3 L2, 4 l_2, 5 L2, 6 L2, or a larger multiple of L2. In certain embodiments, the period in the Y-direction, and in each of two directions rotated by 120 degrees with respect to the Y-direction, is equal to at least one of Li, 2Li, 3Li, 4 Li, 5Li, 6U, or a larger multiple of Li. The growth centers may have a width W1. Short growth centers, which do not extend through the vertices, may have a length W2. Long growth centers, which may extend through one and only one intersection, may have a length W3. In certain embodiments, a primitive unit cell 709 for the pattern includes nine and only nine vertices, includingAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01three each of types of adjacent intersections 703, 705 and 707, around which six growth centers are arranged with 60° angles between them.

[0054] The pattern shown in Figure 1 J includes a plurality of linear arrays of growth centers that are formed in an alternate regular repeating pattern of growth centers. In the example shown in Figure 1 J, the plurality of linear arrays of growth centers include a first linear array of growth centers 751a, a second linear array of growth centers 752a and a third linear array of growth centers 753a. In the example shown in Figure 1 J, the first, second and third linear arrays of growth centers include two different types of growth centers, such as a long growth center 761a, 762a, 763a and a short growth center 761b, 762b, 763b, respectively, that are each aligned in their respective linear array direction. Each of the linear arrays of growth centers include at least one growth center (e.g., long growth center 761a, 762a, 763a) that extends through every third intersection 701 taken in the direction that the linear array of growth centers extend. For example, the first linear array of growth centers 751a includes a plurality of growth centers 761a and 761b, and the growth centers 761a extend through a first intersection 703 and a fourth intersection 719 as the first linear array of growth centers extend in the first direction (e.g., X-direction). The long growth centers 761a, 762a, 763a positioned in a linear sequence of the intersections 701, such as intersections 703, 705, and 707 in Figure 7C, include intersections where the long growth centers 761a, 762a, 763a sequentially extend through the center of the intersection and are oriented in the first direction, the second direction, and the third direction, respectively.

[0055] In certain embodiments, rows of growth centers from a configuration like that shown schematically in FIG. 11 are displaced to avoid intersections 701 to which multiple neighboring growth centers point. An example of these embodiments is shown schematically in FIG. 1 K. In certain embodiments, approximately a third of each of the growth centers are oriented within ±3°, ±2°, or ±1° toward [10-10], [01-10] and [-1100] directions. In certain embodiments, approximately a third of each of the growth centers are oriented within ±3°, ±2°, or ±1° toward [11-20], [1-210], and [-2110] directions. In certain embodiments, one end of each of the growth centers points toward a centralAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01portion of a neighboring growth center or slit and the other end points toward an end portion of a neighboring growth center or slit. In certain embodiments, the period Li is the same in each of three orientations, for example, in the Y-direction and in directions rotated by ±120° with respect to the Y-direction. In certain embodiments, at least six growth centers are included within primitive unit cell 709. In certain embodiments, precisely six growth centers are included within primitive unit cell 709.

[0056] The pattern shown in Figure 1 K includes a plurality of linear arrays of growth centers that are formed in an alternate regular repeating pattern of growth centers. In this example, the plurality of linear arrays of growth centers are formed in a two-dimensional array of growth centers, wherein the growth centers 781 within the two-dimensional array have a rectangular shape with a short dimension and a long dimension, and a first end 781a of each of the growth centers 781 is positioned a first distance 785 from a central point 786, and each growth center is oriented so that a line 787 (only one shown) that extends through a center of each growth center 781 and is parallel to the long dimension of the growth center is not coincident with the central point 786.

[0057] The pattern shown in Figure 1 L includes a plurality of linear arrays of growth centers that are formed in a regular repeating pattern of growth centers that also include a plurality of secondary openings. In one example, the pattern shown in Figure 1 L includes a plurality of linear arrays of primary growth centers that are configured similarly to the configuration shown in Figure 1 J, and also includes a plurality of second openings 711. In some cases, it has been found that, depending on the pitch of the pattern (e.g., Li and L?) and the growth conditions, coalescence may be slower than desired. In some embodiments, as shown in Figure 1L, secondary openings 711 (or secondary growth centers), or additional growth centers, may be included within a larger pattern that consists or includes primary growth centers, for example, within triangular-shaped features, as shown schematically in FIG. 1L. In certain embodiments, the secondary openings 711 are round, square, rectangular, triangular, hexagonal, or the like. In certain embodiments, the secondary openings 711 include or consist of slitshaped features. In certain embodiments, slits within the secondary openings 711 areAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01oriented within ±3°, ±2°, or ±1° toward [10-10], [01-10] and / or [-1100] directions, in certain embodiments, slits within the secondary openings 609 are oriented within ±3°, ±2°, or ±1° toward [11-20], [1-210], and [-2110] directions. In certain embodiments, as shown schematically in FIG. 1L, secondary openings 711 have a chevron shape and are positioned within triangular-shaped regions of the pattern. In certain embodiments, secondary openings 711 include two intersecting slit-shaped features that are oriented at an angle to each other. In certain embodiments, secondary openings 711 include two slit-shaped features that meet at one end with an angle of approximately 60 degrees, for example, between about 55 degrees and about 65 degrees. The width W4 of the secondary openings 711 may be similar to, or less than, the width Wi of the primary openings. In certain embodiments, the ratio of the length W5 of the secondary openings to the length W2 of the short primary openings is between about 0.9 and about 0.01, or between about 0.5 and about 0.05, or between about 0.3 and about 0.1. In certain embodiments, at least 3, at least 9, at least 18, at least 27, or at least 50 secondary openings 711 are included within primitive cell 709 that is defined by the primary openings.

[0058] In certain embodiments, as shown schematically in FIG. 1M, sets of long, slitshaped growth centers in at least one direction (e.g., the X-direction, as shown in FIG.1 M) are displaced laterally from one another, by dimension t, and overlap, by dimension s, somewhat similarly to the pattern shown schematically in FIG. 1F, rather than being colinear as in FIG. 1 J. Other features of this pattern may be similar to that shown schematically in FIG. 1J, with the openings or growth centers having width wi, shorter slit-shaped openings or growth centers having length W2, longer openings or growth centers having length W3, and parallel openings or growth centers being separated by distance Li, for example, in the Y-direction.

[0059] The minimum parallel separation, defined as the minimum distance between parallel lines through adjacent sets of openings or growth centers, plays an important role in achieving superior crystalline quality relative to earlier methods. For the pattern shown schematically in FIG. 1A the minimum parallel separation is √3 / 2 L; in FIG. 1B itAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01is L; in FIG. C it is the lesser of Li and L2; in FIGs. 1E, 1F, 1G, 1H, 11, 1J, and 1L it is Lt; and in FIG. 1M it is the quantity Li-t.

[0060] Additional details on the preparation of a substrate with patterned exposed regions may be found in U. S. Pat. Nos. 9,589,792 and 11,705,322 and in U. S. Pat. Appl. No. 2023 / 0295839.

[0061] Additional details about substrate 101 and its preparation are described further below.

[0062] Substrate 101, which may be unmasked, may have a patterned mask (FIG.2A), or may have a patterned mask with patterned trenches 115 (FIG. 3A), is then used as a substrate for bulk crystal growth, for example, comprising ammonothermal growth, HVPE growth, or flux growth. In the discussion below the grown GaN layer will be referred to as an ammonothermal layer, even though other bulk growth methods, such as HVPE or flux growth, may be used instead. In certain embodiments, comprising ammonothermal bulk growth, the substrate 101, which may be patterned, may then be suspended on a seed rack and placed as a seed 811 within interior volume 803 of a sealable container 801, such as a capsule, an autoclave, or a liner within an autoclave, as shown schematically in FIG. 8A. In certain embodiments, one or more pairs of patterned substrates are suspended back to back, with the patterned large area surfaces facing outward. A group III metal source, such as polycrystalline group III metal nitride 813, at least one mineralizer composition, and ammonia (or other nitrogen containing solvent) are then added to the sealable container (e.g., capsule or autoclave) and the sealable container is sealed. In some embodiments, the mineralizer composition may comprise an alkali metal such as Li, Na, K, Rb, or Cs, an alkaline earth metal, such as Mg, Ca, Sr, or Ba, or an alkali or alkaline earth hydride, amide, imide, amido-imide, nitride, or azide. In some embodiments, the mineralizer may comprise an ammonium halide, such as NH4F, NH4CI, NH4Br, or NH4I, a gallium halide, such as GaF3, GaCl3, GaBr3, GaI3, or any compound that may be formed by reaction of one, two, or more of F, Cl, Br, I, HF, HCI, HBr, HI, Ga, GaN, and NH3. In some embodiments, the mineralizer may comprise other alkali, alkaline earth, or ammoniumAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01salts, other halides, urea, sulfur or a sulfide salt, or phosphorus or a phosphorus-containing salt. The sealable container (e.g., capsule) may then be placed in a high pressure apparatus, such as an internally heated high pressure apparatus or an autoclave, and the high pressure apparatus sealed. The sealable container, containing the substrates 101, which may be patterned, is then heated to a temperature above about 400 degrees Celsius and pressurized above about 50 megapascals to perform ammonothermal crystal growth. In certain embodiments, the substrate is exposed to an etch-back process, for example, by applying a reverse or reduced temperature gradient, that is, a temperature gradient opposite in sign and / or reduced in magnitude from that used for crystal growth. For example, a reverse temperature gradient may have a value between approximately 1 degree Celsius and approximately 50 degrees Celsius and may be held for a time between approximately 1 minute and approximately 24 hours. A reduced temperature gradient may have a magnitude between zero and 5 degrees Celsius and may be held for a time between approximately 1 minute and approximately 24 hours. In certain embodiments, the etch-back process removes a thickness between about 1 micrometer and about 50 micrometers from one or more surfaces of substrate 101 before the onset of growth.

[0063] FIGs. 2A-2C illustrate bulk crystal growth by a lateral epitaxial overgrowth (LEO) process with no trenches below mask openings. During a bulk crystal growth process, group III metal nitride layer 213 grows through the openings 112 of patterned mask layer 111, grows outward through the openings, as shown in FIG. 2B, grows laterally over patterned mask layer 111, and coalesces, as shown in FIG. 2C. After coalescence, group III metal nitride layer 213 comprises window regions 215, which have grown vertically with respect to the openings in patterned mask layer 111, wing regions 217, which have grown laterally over patterned mask layer 111, and coalescence fronts 219, which form at the boundaries between wings growing from adjacent openings in patterned mask layer 111. Threading dislocations 214 may be present in window regions 215, originating from threading dislocations that were present at the surface of the substrate 101.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01

[0064] FIGs. 3A-3C illustrate a bulk group III nitride sidewall LEO process. Figure 3A illustrates a substrate that includes a patterned, masked trench 115, for example, formed by wet etching and / or by laser patterning. In a sidewall LEO process, a group ill metal nitride material 221 grows on the sides and bottoms of the patterned, masked trenches 115 as shown in FIG. 3B. As group III metal nitride material 221 on the sidewalls of trenches 115 grow inward, it becomes progressively more difficult for group III nitride nutrient material to reach the bottom of the trenches, whether the nutrient material comprises an ammonothermal complex of a group III metal (in the case of ammonothermal growth), a group III metal halide (in the case of HVPE), or a group III metal alloy or inorganic complex (in the case of flux growth). Eventually group III metal nitride material 221 pinches off the lower regions of the trenches, forming voids 225 as shown in FIG. 3C. It has been found that the concentration of threading dislocations in group III metal nitride material 221, which has grown laterally, is lower than that in substrate 101. Many threading dislocations 223, originating from substrate 101, terminate on the surfaces of voids 225. Concomitantly, the group III metal nitride layer 213 grows upward through openings 112 (or windows) in patterned mask layer 111. However, since laterally-grown group HI metal nitride material 221 has a lower concentration of threading dislocations than substrate 101 and many dislocations from substrate 101 have terminated at surfaces of voids 225, the dislocation density in the vertically grown group III metal nitride layer 213 is considerably reduced, relative to a conventional LEO process, as described above in conjunction with Figure 2A-2C.

[0065] FIGS. 3D-3E illustrate the continuation of the sidewall LEO growth process. As in the conventional LEO process (FIGs. 2A-2C), group III metal nitride layer 213 grows within the openings 112 of patterned mask layer 111, grows outward through the openings as shown in FIG. 3D, grows laterally over patterned mask layer 111, and coalesces, as shown in FIG. 3E. After coalescence, group III metal nitride layer 213 comprises window regions 215 (FIG. 3E), which have grown vertically with respect to the openings 112 in patterned mask layer 111, wing regions 217, which have grown laterally over patterned mask layer 111, and coalescence fronts 219, which form at the boundaries between wings growing from adjacent openings in patterned mask layerAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01111, as shown in FIG. 3E. Since laterally-grown group III metal nitride material 221 has a lower concentration of threading dislocations than substrate 101 and many threading dislocations from substrate 101 have terminated in voids 225, the concentration of threading dislocations in window regions 215 is significantly lower than in the case of conventional LEO.

[0066] Ammonothermal group III metal nitride layer 213 may have a thickness between about 10 micrometers and about 100 millimeters, or between about 100 micrometers and about 20 millimeters as measured in the Z-direction shown in FIG. 3E.

[0067] In certain embodiments, ammonothermal group III metal nitride layer 213 is subjected to one or more processes, such as at least one of sawing, lapping, grinding, polishing, chemical-mechanical polishing, or etching.

[0068] In certain embodiments, the concentration of extended defects, such as threading dislocations and stacking faults, in the ammonothermal group III metal nitride layer 213 may be quantified by defect selective etching. Defect-selective etching may be performed, for example, using a solution comprising one or more of H3PO4, H3PO4 that has been conditioned by prolonged heat treatment to form polyphosphoric acid, and H2SO4, or a molten flux comprising one or more of NaOH and KOH. Defect-selective etching may be performed at a temperature between about 100 degrees Celsius and about 500 degrees Celsius for a time between about 5 minutes and about 5 hours, wherein the processing temperature and time are selected so as to cause formation of etch pits with diameters between about 1 micrometer and about 25 micrometers, then removing the ammonothermal group III metal nitride layer, crystal, or wafer from the etchant solution.

[0069] The concentration of threading dislocations in the surface of the window regions 215 may be less than that in the underlying substrate 101 by a factor between about 10 and about 104. The concentration of threading dislocations in the surface of the window regions 215 may be less than about 108cm’2, less than about 107cm-2, less than about 106cm-2, less than about 105cm-2, or less than about 104cm-2. The concentration of threading dislocations in the surface of wing regions 217 may be lower,Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01by about one to about three orders of magnitude, than the concentration of threading dislocations in the surface of the window regions 215, and may be below about 105cm-2, below about 104cm-2, below about 103cm-2, below about 102cm-2, or below about 10 cm-2. Some stacking faults, for example, at a concentration between about 1 cm-1and about 104cm-1, may be present at the surface of the window regions 215. The concentration of stacking faults in the surface of wing regions 217 may be lower, by about one to about three orders of magnitude, than the concentration of stacking faults in the surface of the window regions 215, and may be below about 102cm-1, below about 10 cm-1, below about 1 cm-1, or below about 0.1 cm-1, or may be undetectable. Threading dislocations, for example, edge dislocations, may be present at coalescence fronts 219, for example, with a line density that is less than about 1×105cm-1, less than about 3×104cm-1, less than about 1×104cm-1, less than about 3×103cm-1, less than about 1×103cm-1, less than about 3×102cm-1, or less than 1×102cm-1. The density of dislocations along the coalescence fronts may be greater than 5 cm-1, greater than 10 cm1, greater than 20 cm1, greater than 50 cm-1, greater than 100 cm-1, greater than 200 cm, or greater than 500 cm-1.

[0070] In certain embodiments, the process of masking and bulk group III nitride crystal growth is repeated one, two, three, or more times. In some embodiments, these operations are performed while the first bulk group III metal nitride layer remains coupled to substrate 101. In other embodiments, substrate 101 is removed prior to a subsequent masking and bulk crystal growth operation, for example, by sawing, lapping, grinding, and / or etching.

[0071] FIGs. 4A and 4B are simplified diagrams illustrating a method of forming a free-standing group III metal nitride boule and free-standing group III metal nitride wafers. In certain embodiments, substrate 101 is removed from ammonothermal group III metal nitride layer 213 (FIG. 3E), or the last such layer deposited, to form freestanding ammonothermal group III metal nitride boule 413. Removal of substrate 101 may be accomplished by one or more of sawing, grinding, lapping, polishing, laser liftoff, self-separation, and etching to form a processed free-standing laterally-grown group III metal nitride boule 413. The processed free-standing laterally-grown group III metalAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01nitride boule 413 may include a similar or essentially identical composition as the ammonothermal group III metal nitride layer and etching may be performed under conditions where the etch rate of the back side of substrate 101 is much faster than the etch rate of the front surface of the ammonothermal group III metal nitride layer. In certain embodiments, a portion of ammonothermal group III metal nitride layer 213, or the last such layer deposited, may be protected from attack by the etchant by deposition of a mask layer, wrapping the portion of the layer with Teflon, clamping the portion of the layer against Teflon, painting with Teflon paint, or the like. In a specific embodiment, substrate 101 comprises single crystal gallium nitride, large-area surface 102 of substrate 101 has a crystallographic orientation within about 5 degrees of a (0001) crystallographic orientation, and substrate 101 is preferentially etched by heating in a solution comprising one or more of H3PO4, H3PO4 that has been conditioned by prolonged heat treatment to form polyphosphoric acid, and H2SO4 at a temperature between about 150 degrees Celsius and about 500 degrees Celsius for a time between about 30 minutes and about 5 hours, or by heating in a molten flux comprising one or more of NaOH and KOH. Surprisingly, patterned mask layer(s) 111 may facilitate preferential removal of substrate 101 by acting as an etch stop. The processed free-standing ammonothermal group III metal nitride boule 413 may include one or more window regions 415 that were formed above exposed growth centers 120, such as openings 112 in patterned mask layer(s) 111, on a substrate 101. The processed freestanding laterally-grown group III metal nitride boule 413 may also include one or more wing regions 417 that were formed above non-open regions in patterned mask layer(s) 111, and a pattern of iocally-approximately-linear arrays 419 of threading dislocations, as shown in FIG. 4A. One or more of front surface 421 and back surface 423 of freestanding ammonothermal group III metai nitride boule 413 may be lapped, polished, etched, and chemical-mechanically polished. As similarly discussed above, the pattern of iocally-approximately-linear arrays 419 may include a coalescence front region that includes a “sharp boundary” that has a width iess than about 25 micrometers or less than about 10 micrometers that is disposed between the adjacent wing regions 417, or an “extended boundary” that has a width between about 25 micrometers and aboutAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO011000 micrometers or between about 30 micrometers and about 250 micrometers that is disposed between the adjacent wing regions 417, depending on the growth conditions.

[0072] In certain embodiments, the edge of free-standing ammonothermal group ill metal nitride boule 413 is ground to form a cylindrically-shaped ammonothermal group ill metal nitride boule. In certain embodiments, one or more flats is ground into the side of free-standing ammonothermal group ill metal nitride boule 413. In certain embodiments, free-standing ammonothermal group III metal nitride boule 413 is sliced into one or more free-standing ammonothermal group III metal nitride wafers 431, as shown in Figure 4B. The slicing may be performed by multi-wire sawing, multi-wire slurry sawing, slicing, inner-diameter sawing, outer-diameter sawing, cleaving, ion implantation followed by exfoliation, spalling, laser cutting, or the like. One or more large-area surface of free-standing ammonothermal group III metal nitride wafers 431 may be lapped, polished, etched, electrochemically polished, photoeiectrochemically polished, reactive-ion-etched, and / or chemical-mechanically polished according to methods that are known in the art. In certain embodiments, a chamfer, bevel, or rounded edge is ground into the edges of free-standing ammonothermal group III metal nitride wafers 431. The free-standing ammonothermal group III metal nitride wafers may have a diameter of at least about 5 millimeters, at least about 10 millimeters, at least about 25 millimeters, at least about 50 millimeters, at least about 75 millimeters, at least about 100 millimeters, at least about 150 millimeters, at least about 200 millimeters, at least about 300 millimeters, at least about 400 millimeters, or at least about 600 millimeters and may have a thickness between about 50 micrometers and about 10 millimeters or between about 150 micrometers and about 1 millimeter. One or more large-area surface of free-standing ammonothermal group III metal nitride wafers 431 may be used as a substrate for group III metal nitride growth by chemical vapor deposition, metalorganic chemical vapor deposition, hydride vapor phase epitaxy, molecular beam epitaxy, flux growth, solution growth, ammonothermal growth, among others, or the like.

[0073] The process of preparing one or more seed crystals, performing a bulk crystal growth process on the seed crystals, and slicing the resultant boules to form two orAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01more resultant wafers (which may or may not have a rounded edge), is referred to as a growth cycle.

[0074] While x-ray diffraction provides an extremely useful tool for quantifying crystal quality, narrow or exciusive use of the FWHM metric may miss important details, particularly when applied to only one or a few areas on a large-area substrate. Two non-standard procedures are found to be helpful for better differentiating crystalline quality. First, referring to FIGs. 6A and 6B (with one or more optional wafer flats or side facets not shown), the crystalline quality of a crystal or wafer may be assessed by performing XRC measurements at each of five points, at each of six points, at each of seven points, at each of eight points, at each of nine points, or at each of a larger number of points distributed approximately uniformly within the central 40 to 80% of its area. Second, we define an XRC quality metric Q asQ = Σ4-2-“i=1FWQM(i) FWEM(i)where 100 / FWHM( / ), 100 / FWQM( / ), and 100 / FWEM( / ) are the average values of the quantities 100 / FWHM, 100 / FWQM, and 100 / FWEM, respectively, of the / th reflection at each of five points, at each of six points, at each of seven points, at each of eight points, at each of 9 points, or at each of a larger number of points, distributed approximately evenly within the central 40 to 80% of the area of the crystal or wafer, and / =1 corresponds to the rocking curve for a symmetric reflection rocking about a first axis, i=2 corresponds to the rocking curve for the same symmetric reflection rocking about a second axis, orthogonal to the first axis, i=3 corresponds to the rocking curve for an asymmetric reflection, and the FWHM, FWQM, and FWEM values are in units of arc-seconds. In a specific embodiment, growth of the crystal is performed in the

[0001] and / or [000-1] directions, the / '=1 rocking curve corresponds to a symmetric (002) reflection rocking about an a-axis, the / =2 rocking curve corresponds to a symmetric (002) reflection rocking about an orthogonal m-axis, and the / =3 rocking curve corresponds to an asymmetric (201 ) reflection. Alternatively, (004) or (006) symmetric reflections can be used instead of the (002) reflection. Typically, a high-resolution monochromator is not used with the diffractometer, so that the instrumental line width isAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01approximately 12-15 arcsec, which sets an upper bound of approximately 60-75 for the value of Q for a perfect crystal. We find that values of Q generally lie between 10 and 25 when the crystals are grown using prior-art methods, including LEO methods.

[0075] Other functional forms for an XRC quality metric that make use of the rarely-used FWQM and FWEM, in addition to the commonly-used FWHM, are certainly possible. Understanding that the factor of 100 is purely a matter of convenience, this particular functional form has the following advantages. First, the use of the sum of reciprocals of the FWHM, FWQM, and FWEM means that all three of these quantities must be relatively narrow in order for a crystal to obtain a high score and that regions of extremely high crystalline quality are favored. As described above, the FWQM and FWEM may be more sensitive to certain types of defects than the FWHM, particularly when the crystalline quality is high. In addition, even modest reductions in these quantities in high quality crystals will significantly increase the overall score, whereas if the FWHM, FWQM, and FWEM scores were instead added (rather than adding their reciprocals), such effects might easily be missed. Second, the use of rocking-curves for symmetric reflections around orthogonal axes means that the tilt mosaicity must be low in both directions in order for a crystal to obtain a high score. Third, the use of an asymmetric reflection means that the twist mosaicity must also be low in order for a crystal to obtain a high score. Fourth, performing these measurements at many points over the central 40 to 80% of the crystal ensures that the crystalline quality is high across the entire crystal, rather than just within one or two areas that are sampled by the x-ray beam.

[0076] in some embodiments, the x-ray rocking curves of individual crystallographic reflections, and the FWHM, FWQM, and FWEM values derived from them, are measured using relatively large slits in a commercial x-ray diffractometer. In certain embodiments, an incident source slit width may be between about 2 millimeters and about 12 millimeters, between about 5 millimeters and about 10 millimeters, or between about 6 millimeters and about 8 millimeters. A source length-limiting slit width may be between about 2 millimeters and about 25 millimeters, between about 3 millimeters andAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01about 20 millimeters, or between about 5 millimeters and about 15 millimeters. An illuminated area on a crystal being analyzed may have a surface area of at least about 9 square millimeters (e.g., 3 mm x 3 mm), at least about 30 square millimeters (e.g., 3 mm x 10 mm), or at least about 45 square millimeters (e.g., 3 mm x 15 mm).

[0077] To further illustrate the usefulness of the parameter Q for quantification of crystalline quality, XRC parameters for a number of crystals are listed in Table 1, many of which are described further in the Examples and Comparative Examples below.

[0078] In some embodiments, a first set of improved growth methods that enable growth of crystals with values of Q between about 25 and about 40, and a second set of improved growth methods that enable growth of crystals with values of Q greater than about 40, for example, between about 40 and about 60. These improved methods are described in more detail below and are illustrated in the Examples and Comparative Examples.

[0079] First, particularly when beginning with a large area substrate whose growth history includes heteroepitaxial growth on a non-GaN substrate such as sapphire or GaAs, it is important to control the level of oxygen and the value of the oxygen gradient in the crystals. As described in more detail in U. S. Patent Application Publ. No.2023 / 0170213, the presence of oxygen during early-stage crystal growth can increase the ratio of the growth rates in lateral versus vertical directions, increasing the fraction of a grown surface that maintains a smooth morphology, and may enable stress relaxation by virtue of modifying the lattice constant. However, oxygen also increases optical absorption and can create strain that can lead to cracking. Referring to FIG. 7, the concentration of oxygen as a function of position within a crystal or wafer 431 with respect to a reference surface 859, assuming that the oxygen gradient is predominantly one-dimensional, can be mapped out by preparing a wedge-shaped sample by means of a first cross cut 845 at an angle α with respect to first surface 841 and measuring the oxygen concentration as a function of position across first surface 841, second surface 843, and cross-cut surface 855 by calibrated secondary ion mass spectrometry (SIMS). The oxygen concentration can alternatively be extracted from the optical absorptionAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01coefficient, as iong as the quantitative relationship between the two has been measured for a given set of growth conditions. Optionally, a second cross-cut 847 may be performed, for example to measure the optical absorption coefficient. The concentration profile of oxygen within crystals can be controlled by one or more of introducing controlled quantities of oxygen (e.g., as water or Ga2Ch) into the sealable container before growth, introducing an oxygen dopant and / or doping profile into the polycrystalline nutrient, use of an etchable barrier, or addition of oxygen to silver furniture or capsule, which can then be released during the crystal growth process.

[0080] Referring again to FIG. 7, a similar approach can be used to quantify the efficacy of coalescence of laterally-grown wings (cf. FIGs. 2C and 3E) by preparing a double-normal section, that is, by making first cross cut 845 and second cross cut 847 with angle a = 90°. In preferred embodiments, first cross cut 845 and second cross cut 847 are made in a plane that is perpendicular to the lateral growth directions, for example, in the plane of the page for FIGs. 2A-2C and FIGs. 3A-3E. Cross-cut surface 855 may be polished and the sliced sample may be examined by optical microscopy with transmitted light. Different crystallographic sectors may be readily distinguished by color differences resulting from differential impurity uptake.

[0081] An example of lateral growth and coalescence is shown in FIG. 9, which is a schematic representation of an optical micrograph of a double-normal section of a GaN crystal with angle a = 90° (cf. FIG. 7). In the specific embodiment shown in FIG. 9, vertical growth occurred in the [000 -1] direction and lateral growth occurred in the [1 1 -2 0] and [-1 -1 20] directions, with the [1 -1 00] direction extending out of the plane of the page. During the growth process, -c-sector material 965 (item 213 in FIG. 2B) grew from substrate 101 in the [000 -1] direction through openings 112 in patterned mask layer 111. After emerging from openings 112, material began growing in the [1 1 -20] and [-1 -1 20] directions, forming a-sector material 967 (item 217 in FIG. 2C). Sector boundary 961 between -c-sector material 965 and a-sector material 967 is readily observable by transmission microscopy or by fluorescence microscopy, as a-sector material 967 is lighter in color under normal visible illumination than -c-sector material 965 and has different fluorescence characteristics. As opposing laterally-growing wingAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01regions begin to approach one another during the crystal growth process, nutrient materia! from the supercritical ammonia solvent begins to have difficulty reaching the lateral growth fronts, leading to formation of solvent-filled gaps 963 between opposing laterally-growing wing regions which may then become overgrown by a-sector material 967. Shortly after coalescence of the laterally-grown wings occurs, -c-sector material 965 may overgrow a-sector material 967. Coalescence fronts 219 are typically not visible in the double-normal section but can be observed as threading dislocations on the (000 -1) growth facet. The rate at which the laterally-growing wings coalesce and are overgrown by -c-sector material 965 may be quantified as the coalescence distance 969, defined as the separation between surface 102 and a coalescence plane 959 that is parallel to surface 102 of substrate 101 and intersects the uppermost portion of one or more a-sector regions 967.

[0082] In ideal cases, as shown schematically in FIGS. 1A, 2C, and 3E, growth on an un-paterned or patterned seed crystal produces an as-grown boule with a smooth, flat surface, for example, a (000 -1) facet. In some cases, however, growth produces some regions that are smooth and other regions that are rough, as shown schematically in FIG. 12. FIG. 12 is a schematic illustration of an as-grown boule 1200 with an (000 -1) upper surface and {1 0 -1 -1} side facets. Smooth region 1271 of the (000 -1) upper surface has a smooth morphology, while depression region 1273 has a rougher morphology characterized by one or more depressions, with the depression region bounded by boundary 1275, and trench / cellular region 1277, bounded by boundary 1279. In some cases, boundary 1275 is relatively sharply defined between smooth region 1271 and depression region 1273. Typically, boundary 1279 is not so sharply defined, due to irregularity in the morphology of trench / cellular region 1277. In some cases, trench / cellular region 1277 is adjacent to, and may surround depression region 1273. In other words, some or all of boundary 1275 may be between depression region 1273 and trench / cellular region 1277, rather than only between depression region 1273 and smooth region 1271, the case shown schematically in FIG. 12. The root-mean-square (rms) surface roughness within smooth region 1271 may be between about 0.1 nanometer and about 50 micrometers, or between about 10 nanometers and about 10Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01micrometers, and may include areas dominated by step growth, including both single steps and multiple steps. The smooth morphology indicates that growth has proceeded predominantly in the [000 -1] direction, that impurity concentrations should be relatively uniform, and that minimal yield loss may occur during watering operations. The root- mean-square surface roughness within depression portion 1273 may be between about 10 micrometers and about 1 millimeter, between about 20 micrometers and about 500 micrometers, or between about 30 micrometers and about 200 micrometers. The average height within depression region 1273 may be less, by between about 100 micrometers and about 5 millimeters, or between about 200 micrometers and about 2 millimeters, than the height of smooth portion 1271. Trench / cellular region 1277 typically includes one or more trench-iike features, each of which may be characterized by a local width between about 250 micrometers and about 5 millimeters, or between about 500 micrometers and about 3 millimeters, a local depth between about 500 micrometers and about 10 millimeters, or between about 1 millimeter and about 5 millimeters, and a length between about 1 millimeter and about 10 millimeters, or between about 2 millimeters and about 5 millimeters. The trench-like features are typically irregular in shape, with tilted sidewails and branched structures.Morphological features within depression region 1273 may include one or more of macroscopic step-bunching growth and hillocks. Morphological features within trench / cellular region 1277 may include one or more of incompletely-coalesced trenches, cellular growth, and dendritic growth. The rough morphology in depression regions 1273 and trench / cellular regions 1277, particularly the latter, indicates that growth may not have occurred predominantly in the [000 -1] direction in these regions, that impurity concentrations may have significant lateral and axial variations, that significant stresses may be present, and that significant yield loss may occur during watering operations such as sawing, grinding, and polishing.

[0083] In a specific embodiment, a Phase 1 seed wafer is prepared by the following process. In some embodiments of the process, the substrate 101 includes an intermediate-quality substrate, which may be a c-plane HVPE substrate, for example, having a front side crystallographic orientation that is miscut from (0001 ) by between 0.1Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01degree and 1 degree, or by between 0.2 and 0.8 degree toward an m-direction and by less than 0.2 degrees toward an orthogonal a-direction and an average dislocation density between about 5*105cm-2and about 3*107cm-2. The intermediate-quality substrate is patterned on the N (back) surface, as described above, and masked or covered on the Ga (front) surface. An ammonothermai layer, with a thickness between about 1 millimeters and about 15 millimeters, or between about 2 millimeters and about 10 millimeters, is grown in the [000-1] direction, with an initial oxygen concentration between about 1 *10!9cm-3and about 6*10f9cm’3. Since the influence of oxygen relaxes not only the macroscopic strain of the HVPE substrate but also the local strain center and the mismatch caused by the lattice mismatch, the crystal can be thickened without generating a rough growth surface, such as that shown schematically in FIG. 12. One or more slices may be prepared by multi-wire sawing, with a pitch between about 0.5 millimeters and about 2 millimeters, or between about 0.6 millimeters and about 1.5 millimeters, from the ammonothermal layer. In certain embodiments, after additional optional preparation steps, such as one or more of grinding, polishing, chemical-mechanical polishing, or final cleaning, a slice may be used for device fabrication if specifications permit. In certain embodiments, one or more of a grinding process, a polishing process, or a chemical mechanical polishing process may be performed in addition to or instead of a multiwire sawing process, in certain embodiments, the crystal quality can be further improved by repeating a similar procedure using these slices as Phase 1 seed wafers, that is, performing additional growth cycles. Phase 1 seed wafers may then be prepared from the slices by etching in phosphoric acid at a temperature between about 100 degrees Celsius and about 300 degrees Celsius for a time between about 30 seconds and about three hours or, alternatively, by etching in aqueous potassium hydroxide at a temperature between about 60 degrees Celsius and about 120 degrees Celsius for a time between about 30 minutes and about five hours. In some embodiments, a slice containing the original intermediate-quality substrate is recovered and, after preparing the N-face surface by etching, reused as an intermediate-quality substrate for growth of additional Phase 1 seed wafers. Finally, when an as-grown (000-1) surface of an ammonothermal layer isAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01found to be substantially flat and smooth after growth, that is, with an area of any trench / cellular region (region 1277 in FIG. 12) being less than 1% of the area of the as-grown (000-1) surface, an area of a depression region (region 1273 in FIG. 12) being iess than 10% of the area of the as-grown (000-1) surface, and where a root-mean-square surface roughness in the smooth region (region 1271 in Figure 12) is between about 0.1 nanometers and about 20 micrometers, or between about 0.1 micrometers and about 5 micrometers, the crystal may be considered to be a Phase 2 crystal. A depression region, if present on the (000-1) face of the as-grown Phase 2 crystal, may be characterized by a root-mean-square surface roughness between about 10 micrometers and about 1 millimeter, between about 20 micrometers and about 500 micrometers, or between about 30 micrometers and about 200 micrometers, and by an average height that is less, by between about 100 micrometers and about 5 millimeters, or between about 200 micrometers and about 2 millimeters, than the height of the smooth portion 1271 of the (000-1 ) face of the as-grown Phase 2 crystal. In certain embodiments, some cracks may be present in the Phase 2 crystal.

[0084] Phase 2 seed crystals can be obtained from the ammonothermal layer portion of the Phase 2 crystal and may be regrown with the same procedure without a patterned mask. However, crystals grown using Phase 2 seeds are found to have a greatly improved growth yield even if the initial oxygen concentration is not increased to the same level. For example, in certain embodiments, the initial oxygen concentration is set to a level between about 3*1018cm3and about 1 x o19cm3rather than to an initial concentration between about 1 *1018cm-3and about 6*1019cm-3. In addition, since it is not necessary to avoid a region having such a large initial oxygen content, the production efficiency also increases. When the as-grown (000-1) surface of an ammonothermal layer is found to be substantially flat and smooth after growth, that is, with 100% of the area of the (000-1) surface having a root-mean-square surface roughness in a first region (e.g., portion 1271 in Figure 12) between about 0.1 nanometers and about 20 micrometers and 100% of the area of the (000-1) surface being free of cracks, free of trench / celiular regions, and free of depression regions characterized by a depth greater than about 5 micrometers and less than about 100Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01micrometers, or greater than about 20 micrometers and less than about 100 micrometers, with respect to the balance of the (000-1) surface (e.g., portion 1271 in Figure 12), the crystal may be considered to be a Phase 3 crystal.

[0085] Phase 3 seed crystals can be obtained from the ammonothermal layer portion of the Phase 3 crystal and may be regrown with the same procedure without a patterned mask. Crystals grown using Phase 3 seeds are found to have a further improved growth yield even if the initial oxygen concentration is not increased to the same level. For example, in certain embodiments, the initial oxygen concentration is set to a level between about 3*10!8cnr3and about 1*10!9cnr3rather than to an initial concentration between about 1 *1019cm-3and about 6*1019cm-3. In addition, since it is not necessary to avoid a region having such a large initial oxygen content, the production yield, that is, the fraction of the crystal that can be fabricated into salable wafers, may also increase.

[0086] The procedures described above are able to routinely produce free-standing ammonothermal group ill metal nitride boules and wafers with dislocation densities in the 104cnr2range. However, as noted above, without additional improvements or process steps the Q values of these crystals generally lie in the 10-25 range. Some examples of this behavior are illustrated in several Comparative Examples below.

[0087] Free-standing ammonothermal group Ell metal nitride boules and wafers with dislocation densities in the 103cm-2range, for example, between about 3*102cm2and about 104cm-2, and Q values in the 25-40 range may be grown using the following procedures.

[0088] (1) Beginning, optionally, with large-area, commercial group III metal nitride wafers, form Phase 2 or Phase 3 crystals, using at least three growth cycles, as described above. Optionally, form Phase 1 and Phase 2 crystals as intermediate steps.

[0089] (2) Using a seed crystal with at least Phase 2 quality, apply a pattern to the (000-1 ) face with a minimum parallel separation of at least 1.25 millimeters. In preferred embodiments, the minimum parallel separation of the pattern is at least about 1.5 millimeters, at least about 2 millimeters, at least about 3 millimeters, or at least about 4Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01millimeters. In certain embodiments, a pitch of the pattern is at least about 2.5 millimeters, at least about 3 millimeters, at least about 4 millimeters, or at least about 6 millimeters.

[0090] (3) Place the large-pitch-patterned (000-1 ) seed in an “outer” position within the sealable container and perform extended lateral growth on the large-pitch-patterned (000-1 ) seed to a thickness of at least about 4 millimeters, at least about 5 millimeters, or at least about 6 millimeters, forming a large-pitch-patterned boule. If further crystal growth or device fabrication is to be performed, form at least one large-pitch-patterned wafer from the large-pitch-patterned boule a distance of at least about one millimeter above the coalescence plane in the boule, completing another growth cycle.

[0091] (4) Optionally, use the at least one wafer prepared from the boule grown on the large-pitch-patterned (000-1) seed to a thickness of at least 4 millimeters as a seed crystal. Place the seed crystal in an “outer” position within the sealable container and grow to a thickness of at least about 4 millimeters, forming a next-generation large-pitch-patterned boule, by an ammonothermal method. Form at least one nextgeneration large-pitch-pattemed wafer from the boule a distance of at least one millimeter above the seed interface.

[0092] Regarding steps (2) and (3) above, while large-pitch patterns have been used in the past, it was found not to be possible to form crystals with Q values above 25 without the two additional new process discoveries, and without at least a total of five growth cycles (repeated growth-wafer- forming cycles).

[0093] Referring again to FIG. 8A, a side view of a sealable container, multiple seed crystals 811 may be placed within interior 803 of sealable container 801 along with polycrystalline nutrient 813. Growth zone 807 may be separated from nutrient zone 805 by a baffle 809, which may consist of or include at least one disk or shape with one or more of holes, apertures, and annular clearance from an inner diameter of sealable container 801 having a percent open area between about 1% and about 20%, between about 2% and about 15%, or between about 3% and about 10%. Seed crystals 811 may be arranged in two or more tiers 815 positioned axially above one another.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01Referring now to FIG. 8B, a cross-sectional view of growth zone 807 of sealable container 801, a cylindrical boundary 820 separates outer interior zone 803A from inner interior zone 803B. Seed crystals 811 A are positioned completely or predominantly within outer interior zone 803A, while seed crystals 811B are positioned completely or predominantly within Inner interior zone 803B. In preferred embodiments, (000-1 ) surfaces of seed crystals 811 A are outward facing, that is, face toward an inner diameter of sealable container 801. Cylindrical boundary 820 may have a diameter between 70% and 95% or between 75% and 90% of an inner diameter of sealable container 801. In certain embodiments, a radial gap between cylindrical boundary 820 and an inner diameter of sealable container 801 may be between 5 about millimeters and about 100 millimeters, between 10 millimeters and about 70 millimeters, or between about 20 millimeters and about 50 millimeters.

[0094] Surprisingly, the crystalline quality of boules grown within outer interior zone 803A is found to be superior to that of boules grown within inner interior zone 803B, at least as quantified by the newly-discovered Q-value metric. As wiil be appreciated, depending on the dimensions of sealable container 801, cylindrical boundary 820, and of seed crystals 801, only a modest minority of seed crystals 811 may be able to be placed within outer interior volume 803A, increasing the cost of the seed fabrication process. The superior crystalline quality of crystals grown within outer interior volume 803A is surprising because nuclei typically form on an inner diameter of sealable container 801, grow, and coalesce, forming a rough and continuously-growing boundary for the crystals growing within. Without wishing to be bound by theory, the improved crystalline quality within this zone may be induced by an increased shear velocity of fluid flowing proximate to the wall, relative to fluid flow within the body of the array of seed crystals 811 B. The formation of adventitious, polycrystalline deposits 825 on the inner diameter of sealable container 801 may increase this behavior further, as fluid flow over the deposits may become more turbulent due to their rough geometry, as shown schematically in FIG. 8C.

[0095] Regarding step (3), above, again, the coalescence plane 959 above the pattern after a growth process is shown schematically in FIG. 9. In preferredAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01embodiments, the boule grown by coalescence over the pattern is sliced, the sliced crystals are prepared for use as seeds, and then regrown. A-sector material 967 extends beyond the height of solvent-filled gaps 963, and it is believed that slight differences in the lattice constants with respect to -c-sector material 965 generate stress that can impact the crystallographic quality of material regrown on a seed if the seed has been sliced at a position less than about 1 millimeter above coalescence plane 959. In preferred embodiments, therefore, seeds prepared from -c-sector material 965 are prepared by slicing at a position at least one millimeter, at least 1.5 millimeters, or at least 2 millimeters above coalescence plane 959.

[0096] The procedure described above enables fabrication of group III metal nitride boules, crystals, and wafers having very high crystalline quality, as quantified by Q values between about 25 and about 40, and with approximately the same diameter as seed crystals having a significantly lower crystalline quality, for exampies, commercial HVPE-grown wafers, although multiple crystal growth cycles are required.

[0097] Referring again to FIGs. 4A and 48, the large-area surfaces of the freestanding ammonothermal group III metal nitride boule 413 or wafers 431 may be characterized by a pattern of iocaily-approximately-linear arrays 419 of threading dislocations that propagated from coalescence fronts 219 formed during the epitaxial lateral overgrowth process, as discussed above in conjunction with FIGs. 3A-3F. The pattern of Iocaily-approximately-linear arrays of threading dislocations may be 2D hexagonal, square, rectangular, trapezoidal, triangular, 1 D linear, or an irregular pattern that is formed at least partially due to the pattern of the exposed regions 120 (FIGs. 1A-1M) used during the process to form free-standing laterally-grown group III metal nitride boule 413. One or more window regions 415 are formed above the exposed regions 120 (FIGs. 1F-1L, 3A-3E,7), and one or more wing regions 417 are formed on portions that are not above the exposed regions 120, that is, were formed by lateral growth. As discussed above, the formed coalescence fronts 219 or pattern of Iocaily-approximately-linear arrays 419 may Include coalescence front regions that have a lateral width (i.e., perpendicular to the Iocaily-approximately-linear arrays 419) that can vary depending on the growth conditions. In certain embodiments, the lateral width of coalescence fronts isAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01between about 5 micrometers and about 500 micrometers, between about 10 micrometers and about 250 micrometers, or between about 20 micrometers and about 100 micrometers.

[0098] The pattern 502 of locally-approximately-linear arrays of threading dislocations may be characterized, in certain embodiments, by a linear array of threading dislocations that have a pitch dimension L between about 5 micrometers and about 20 millimeters or between about 200 micrometers and about 5 millimeters. The pattern 502 of locally-approximately-linear arrays of threading dislocations may be characterized, in certain embodiments, by a pitch dimension L (cf. FIGs. 1A, 1B, 1D), or by pitch dimensions Li and L? in two orthogonal directions (cf. FIGs. 1C, 1E-1M), between about 5 micrometers and about 20 millimeters or between about 200 micrometers and about 5 millimeters, or between about 500 micrometers and about 2 millimeters. In certain embodiments, the pattern 502 of locally-approximately-linear arrays of threading dislocations is approximately aligned with the underlying crystal structure of the group III metal nitride, for example, with the locally-approximately-linear arrays lying within about 5 degrees, within about 2 degrees, or within about 1 degree of one or more of <1 0 -1 0>, <1 1 -20>, or [000 ±1] or their projections in the plane of the surface of the free-standing ammonothermal group III metal nitride boule 413 or group III metal nitride wafer 431. The linear concentration of threading dislocations in the pattern may be less than about 1 *105cm ’, less than about 3><104cm1, less than about 1 *104cm1, less than about 3*103cm-1, less than about 1×103cm-1, less than about 3*102cm1, or less than about 1 102cm1. The linear concentration of threading dislocations in the pattern 502 may be greater than 5 cm1, greater than 10 cm1, greater than 20 cm1, greater than 50 cm1, greater than 100 cm1, greater than 200 cm’1, or greater than 500 cm.

[0099] The patterns of threading dislocations described above may become smeared out after three growth cycles, five growth cycles, ten growth cycles, or an even larger number of growth cycles, but a residue of the locally-approximately-linear arrays of threading dislocation may persist. Specifically, referring to a first large-area surface onAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01a large-pitch-paterned boule or a large-pitch-patterned boule wafer prepared from such a boule may be characterized by an average concentration of threading dislocations between 101cm-2and 104cm-2, wherein the average concentration of threading dislocations on the first surface varies periodically by at least a factor of 1.2, at least a factor of 1.5, or at least a factor of two in a first direction, the period of the variation in the first direction being between 1.5 millimeters and about 20 millimeters and the first surface having a maximum dimension in the first direction greater than about 45 millimeters, greater than about 95 millimeters, greater than about 145 millimeters, or greater than about 195 millimeters. In certain embodiments, the average concentration of threading dislocations on the first surface also varies periodically by at least a factor of 1.2, at least a factor of 1.5, or at least a factor of two in a second direction orthogonal to the first direction and to the thickness of the large-pitch-patterned boule or a large- pitch-patterned boule wafer, the period of the variation in the second direction being between about 1.5 millimeters and about 20 millimeters.[001001 A method for evaluating a position-dependent average concentration of threading dislocations is shown schematically in FIG. 11A. First, a series of cells across the first large-area surface of a crystal or wafer in the first direction 1101 may be defined, where the Nth ceil is characterized by a width 3N and by a length bw. In the example shown in FIG. 11 A the lengths bu are all the same but different lengths may be chosen. In general, the widths aw should be chosen to be small enough, for example, 0.25 millimeter, 0.5 millimeter, 1 millimeter, or 2 millimeters, so that any periodicity in the dislocation density can be resolved, but large enough so that a sufficient number of dislocations can be counted for a reasonably-accurate measurement. Similarly, the lengths bn should be large enough so that a sufficient number of dislocations can be counted for a reasonably-accurate measurement. The number of threading dislocations in each cell may be counted by a convenient method. In certain embodiments, for example, where the final growth of the crystal is performed by HVPE, the local cathodoluminescence dark-spot density may be taken as the local dislocation density. In other embodiments where cathodoluminescence does not provide a reliable indication of threading dislocations, a defect-selective etching process may be appliedAttorney Ref. No.: Kll-SLT 0031 Attorney Docket No. 135423-0001 WO01to the crystal, for example, heating in one or more of aqueous H3PO4, aqueous H2SO4, molten NaOH / KOH or molten Na2O2 / NaOH, as is known in the art. The resulting local etch pit density may then be taken as the local threading dislocation density. The nu ber of islocations (e.g., ark spots or etch pits) in each cell may then be ivided by the cell area to calculate the local threading dislocation density and plotted as a function of distance X in the first direction 1101, as shown schematically in FIG. 11 B. The presence of a periodicity, and the pitch, can be readily determined, even if the average dislocation density is 103cm-2or lower. If necessary, a Fast Fourier Transform may be applied to the local dislocation density as a function of distance to determine the pitch. In the specific example shown in FIG. 11B, the crystal was modeled as a 50 mm diameter wafer, the average dislocation density was 1 103cm’2, and additional dislocations were added every 5 millimeters. The actual number of dislocations within a specific cell was assumed to follow a Lorentzian distribution (i.e., were random), with the standard deviation equal to the square root of the number of dislocations in each cell. The level of noise could be reduced by increasing the length bw of the cells, for example. Nonetheless, it is apparent from FIG. 11B that the dislocation density varies periodically in first direction 1101 with a period of about 5 millimeters and that the “high” values of the dislocation density are 20-30% higher than the “low” values of the dislocation density.

[0101] Referring to Table 1, in addition having Q values between about 25 and about 40, the group III metal nitride boules, crystals, and wafers having very high crystalline quality fabricated by the procedures described above may be characterized by a sum of the three average FWHM values at the three specified reflections, the three average FWQM values at the three specified reflections, and the three average FWEM values at the three specified reflections that is between about 240 and about 350 arc-seconds. The group III metal nitride boules, crystals, and wafers having very high crystalline quality fabricated by the procedures described above may be characterized by a sum of the three average FWEM values at the three specified reflections that Is between about 100 and about 175 arc-seconds. The group III metal nitride boules, crystals, and wafers having very high crystalline quality fabricated by the procedures described above mayAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01be characterized by a crystallographic radius of curvature having a magnitude of at least about 40 meters or at least about 50 meters.

[0102] Even higher crystalline quality may be achieved by performing extended lateral growth from suitably-prepared seed crystals under suitable growth conditions. A process for extended lateral growth was described in US patent 9,175,418, but the processes for suitable seed preparation and suitable growth conditions are newly discovered. In addition, whereas the previous methods, using a “proto-seed”, typically led to “upper” and “lower” a-wings, with a gap in between, whereas the new improved seed crystals and growth methods typically lead to formation of a homogenous a-wing, with no gap between a Ga-sector and an N-sector. Furthermore, it has been found that application of the methods described in the aforementioned patent often gave rise to crystals having a saw-tooth edge with poor crystalline quality, rather than a well-formed a-edge and well-formed a-corner in crystals grown using the new, improved methods.

[0103] Free-standing ammonothermal group III metal nitride boules and wafers with dislocation densities in the 1 to 100 cm2range and Q values in the 40-70 range may be grown using the following procedures.

[0104] (1) Beginning, optionally, with large-area, commercial group III metal nitride wafers, form Phase 2 or Phase 3 crystals, using at least three growth cycles, as described above. Optionally, form Phase 1 and Phase 2 crystals as intermediate steps.

[0105] (2) Using a seed crystal with at least Phase 2 quality, apply a pattern to the (000-1) face with a minimum planar separation of at least 1.25 millimeters.

[0106] (3) Place the large-pitch-patterned (000-1) seed in an “outer” position within the sealable container and perform extended lateral growth on the large-pitch-patterned (000-1 ) seed to a thickness of at least 3 millimeters. Form at least one wafer from the boule a distance of at least one millimeter above the highest coalescence region in the boule, completing another growth cycle.

[0107] (4) Use the at least one wafer prepared from the boule grown on the large-pitch-patterned (000-1) seed to a thickness of at least 3 millimeters as a seed crystal. Place the seed crystal in an “outer" position within the sealable container and grow to aAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01thickness of at least 3 millimeters. Optionally, form at least one wafer from the boule a distance of at least one millimeter above the seed interface.

[0108] (5) Using a boule 1030 grown using a large-pitch pattern at an “outer’’ position, or a wafer 1032 prepared from such a boule, slice off an a-corner 1040 or 1042, as shown schematically in FIG. 10A. In certain embodiments, a-corner 1040 or 1042 includes a portion of seed crystal 1020 or was grown vertically therefrom. Boule 1030 or wafer 1032 may have a substantially hexagonal habit or shape, with edges that are parallel to m-planes (e.g., (1-100), (10-10), (01-10), (-1100), (-1010), and (0-110)) or to corresponding semipolar facets (e.g., (1-10-1), (10-1-1), (01-1-1), (-110-1), (-101-1), and (0-11-1)). The slicing may be performed using a single-wire saw, dicing saw, laser cutting, cleaving, or the like. The fresh edge 1050 that is produced may have an orientation within 10 degrees, within 5 degrees, within 2 degrees, or within 1 degree of an a-plane (e.g., (11-20)). Residual damage on fresh edge 1050 may be removed by wet etching, by dry etching, by photoelectrochemical etching, by reactive ion etching, by chemical-mechanical polishing, or by other methods as known in the art. Although FIG.10A describes further processing of fresh edge 1050 prepared on boule 1030 or wafer 1032, similar processing may be performed also on the mating surface of a-corner 1040 or 1042, and one or more additional a-corners may be sliced from boule 1030 or wafer 1032.

[0109] (6) Perform extended lateral growth on fresh edge 1050 of boule 1030 or wafer 1032, as shown schematically in FIG. 10B, forming 100%-laterally-grown a-wing 1060. In preferred embodiments, grown a-edge 1062 is substantially flat and planar, with a crystallographic orientation within about 1 degree of a-plane (e.g., (11-20)) and a root-mean-square roughness below about 50 microns, below about 25 microns, or below about 10 microns. 100%-laterally-grown a-wing 1060 may have a width between about 1 millimeter and about 50 millimeters, between about 2 millimeters and about 25 millimeters, or between about 3 millimeters and about 15 millimeters. In preferred embodiments, lateral faces 1064 of 100%-laterally-grown a-wing 1060 include or consist of one or more of m-plane facets and semipolar {10-1-1} facets, with a local crystallographic orientation within about 1 degree of the nominal orientation and a root-Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01mean-square surface roughness below about 50 microns, below about 25 microns, or below about 10 microns.

[0110] (7) Remove 100%-laterally-grown a-wing 1060 from boule 1030 or wafer 1032, forming free-standing-100%-laterally-grown a-wing 1070, as shown schematically in FIG. 10B. The slicing may be performed using a single-wire saw, dicing saw, laser cutting, cleaving, or the like. The fresh edge 1075 that is produced may have an orientation within 10 degrees, within 5 degrees, within 2 degrees, or within 1 degree of an a-plane (e.g., (11-20)). Residual damage on fresh edge 1075 may be removed by wet etching, by dry etching, by chemical-mechanical polishing, or by other methods as known in the art.

[0111] (8) Perform further lateral growth on free-standing-100%-laterally-grown a-wing 1070, forming ultrahigh-quality boule 1080, as shown schematically in FIG. 10C. Lateral growth occurs both on fresh edge 1075 and on a-edge 1062, forming new 100%-laterally-grown a-wing 1082 and extended 100%-laterally-grown a-wing 1084. Each of new 100%-laterally-grown a-wing 1082 and extended 100%-laterally-grown a-wing 1084 may have a width between about 1 millimeter and about 50 millimeters, between about 2 millimeters and about 25 millimeters, or between about 3 millimeters and about 15 millimeters. In addition, vertical growth in the c-direction occurs concurrently, along with lateral growth in the <10-10> and <10-1-1 > directions. In certain embodiments, newly-grown a-edges 1086 and 1088, if present, are substantially flat and planar, with a crystallographic orientation within about 1 degree of a-plane e.g., (11-20)) and a root-mean-square roughness below about 50 microns, below about 25 microns, or below about 10 microns. In preferred embodiments, lateral faces 1092 and 1094 of 100%-laterally-grown a-wings 1082 and 1084 1060 include or consist of one or more of m-plane facets and semipolar {10-1-1} facets, with a local crystallographic orientation within about 1 degree of the nominal orientation and a root-mean-square surface roughness below about 50 microns, below about 25 microns, or below about 10 microns. In certain embodiments, one or both of newly-grown a-edges 1086 and 1088 will have grown themselves out of existence, so that lateral faces 1092 and 1094 extendAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01to an apex. In the limit that both newly-grown a-edges have grown themselves out of existence, ultrahigh-quality boule 1080 may have the shape of a rhombus.

[0112] Ultrahigh-quality boule 1080 is characterized by extremely high crystalline quality, as quantified by a Q value, measured on either the (000-1) N-face or (0001) Ga-face, between about 35 and about 72, or between about 40 and about 60, and by an average dislocation density, measured on either the (000-1 ) N-face or (0001 ) Ga-face, between about 1 cm-2and about 50 cm-2, or between about 3 cm-2and about 20 cm-2.

[0113] Ultrahigh-quality boule 1080 may be used as a seed crystal for further bulk crystal growth, for example, to continue expanding the crystal in both the c-directions and in the m-directions. In one specific embodiment, the further bulk crystal growth comprises ammonothermal bulk crystal growth. In another specific embodiment, the further bulk crystal growth comprises high temperature solution crystal growth, also known as flux crystal growth. In yet another specific embodiment, the further bulk crystal growth comprises HVPE. Ultrahigh-quality boule 1080, and / or the further-grown crystal, may be sliced, lapped, ground, polished, etched, and / or chemically-mechanically polished by methods that are known in the art to form one or more ultra-high-quality wafers. After removal of residual damage from wafer processes such as multi-wire sawing and grinding, for example, by etching and / or by chemical-mechanical polishing, the crystalline quality of the wafers will be similar to that of the ultrahigh-quality boule, that is, being characterized by a Q value, measured on either the (000-1) N-face or (0001 ) Ga-face, between about 40 and about 72, or between about 45 and about 60, and by an average dislocation density, measured on either the (000-1) N-face or (0001) Ga-face, between about 1 cm-2and about 50 cm-2, or between about 3 cm-2and about 20 cm-2. The surface of the wafers may be characterized by a root-mean-square surface roughness measured over a 10-micrometer by 10-micrometer area that is less than about 1 nanometer or less than about 0.2 nanometers.

[0114] Ultrahigh-quality boule 1080 may have a longest lateral dimension between about 25 millimeters and about 300 millimeters and may have a thickness between about 0.2 millimeter and about 25 millimeters. Ultrahigh-quality boule 1080 and / or aAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01wafer prepared from ultrahigh-quality boule 1080 may have a crystallographic radius of curvature greater than about 50 meters, greater than about 100 meters, greater than about 300 meters, or greater than about 1000 meters. In a specific embodiment, the top and bottom surfaces of the ultrahigh-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 may have impurity concentrations of O, H, C, Na, and K between about 1×1017cm-3and 1×1019cm-3, between about 1×1017cm-3and 2×1019cm-3, below 1×1017cm-3, below 1×1016cm-3, and below 1×1016cm-3, respectively, as quantified by calibrated secondary ion mass spectrometry (SIMS). In another embodiment, the top and bottom surfaces of the ultrahigh-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 may have impurity concentrations of O, H, C, and at least one of Na and K between about 1×1017cm-3and 1×1019cm-3between about 1×1017cm-3and 2×1019cm-3, below 1×1017cm-3, and between about 3×1015cm-3and 1×1018cm-3, respectively, as quantified by calibrated secondary ion mass spectrometry (SIMS). In still another embodiment, the top and bottom surfaces of the ultrahigh-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 may have impurity concentrations of O, H, C, and at ieast one of F and Cl between about 1×1017cm-3and 1×1019cm-3, between about 1×1017cm-3and 2×1019cm-3, below 1×1017cm-3, and between about 1×1015cm-3and 1×1017cm-3, respectively, as quantified by calibrated secondary ion mass spectrometry (SIMS). In some embodiments, the top and bottom surfaces of the ultrahigh-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 may have impurity concentrations of H between about 5×1017cm-3and 1×1019cm-3, as quantified by calibrated secondary ion mass spectrometry (SIMS). In a specific embodiment, the ultrahigh-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 has an infrared absorption peak at about 3175 cm-1, with an absorbance per unit thickness of greater than about 0.01 cm-1.

[0115] A wafer prepared from ultrahigh-quality boule 1080 may have a large-area crystallographic orientation within 5 degrees, within 2 degrees, within 1 degree, within 0.5 degree, within 0.2 degree, within 0.1 degree, within 0.05 degree, within 0.02 degree, or within 0.01 degree of (0001) +c-plane, (000-1 ) -c-plane, {10-10} m-plane, {1 1 -20}Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01a-plane, {11-2+2}, {60-6+1}, {50-5+1}, {40-4+1}, {30-3+1}, {50-5+2}, {70-7±3}, {20-2+1}, {30-3+2}, {40-4+3}, {50-5+4}, or {10-1+1}.

[0116] The ultrahigh-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 may be characterized by a wurtzite structure substantially free from any cubic entities or other crystal structures, the other structures being less than about 0.1% in volume in reference to the substantially wurtzite structure.

[0117] The ultra high-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 may be characterized by a variation in miscut angle across a large-area surface that is less than about 0.1 degree, less than about 0.05 degree, or less than about 0.025 degree in each of two orthogonal crystallographic directions. The ultrahigh-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 may be characterized by n-type electrical conductivity, with a carrier concentration between about 1x1017cm-3and about 3x1019cm-3and a carrier mobility greater than about 100 cm-2 / V-s. In alternative embodiments, the ultrahigh-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 is characterized by p-type electrical conductivity, with a carrier concentration between about 1×1015cm-3and about 1×1019cm-3. In still other embodiments, the ultrahigh-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 is characterized by semi-insulating electrical behavior, with a room-temperature resistivity greater than about 107ohm-centimeter, greater than about 108ohm-centimeter, greater than about 109ohm-centimeter, greater than about 1010ohm-centimeter, or greater than about 1011ohm-centimeter. In certain embodiments, the ultrahigh-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 is highly transparent, with an optical absorption coefficient at a wavelength of 400 nanometers that is less than about 10 cm-1, less than about 5 cm-1, less than about 2 cm-1, less than about 1 cm-1, less than about 0.5 cm-1, less than about 0.2 cm-1, or less than about 0.1 cm-1.

[0118] Referring again to Table 1, in addition having Q values between about 40 and about 72, ultrahigh-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 may be characterized by a sum of the three average FWHM values at theAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01three specified reflections, the three average FWQM values at the three specified reflections, and the three average FWEM values at the three specified reflections that is between about 100 and about 250 arc-seconds. Ultrahigh-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 may be characterized by a sum of the three average FWEM values at the three specified reflections that is between about 50 and about 100 arc-seconds. Ultrah igh-quality boule 1080 and / or a wafer prepared from ultrahigh-quality boule 1080 may be characterized by a crystallographic radius of curvature having a magnitude of at least about 50 meters or at least about 60 meters.

[0119] In certain embodiments, the disclosure describes a free-standing crystal, comprising a group III metal and nitrogen, wherein the free-standing crystal comprises: a wurtzite crystal structure; a first surface having a maximum edge-to-edge dimension in a first direction; and a second surface on the opposite side of the crystal from the first surface that is separated from the first surface in a second direction that is orthogonal to the first direction and to the first surface, wherein the first surface is characterized by a root-mean-square surface roughness less than about 50 micrometers and an average concentration of threading dislocations below about 104cm-2; the first surface is further characterized by an x-ray rocking curve quality metric Q having a value greater than about 25, where Q is defined asQ = ∑FWHM(i) + FWQM(i) + FWEM(i)

[0120] where 100 / FWHM( / ), 100 / FWQM( / ), and 100 / FWEM( / ) are the average values of the quantities 100 divided by the full-width-at-half-maximum (FWHM), 100 divided by the fuli-width-at-quarter-maximum (FWQM), and 100 divided by the full-width-at-eighth-maximum (FWEM), respectively, of the th reflection at each of at least five points that are distributed approximately uniformly over the central 40 to 80% of the area of the first surface, and =1 corresponds to the rocking curve for a symmetric reflection rocking about a first axis that is parallel to the first direction, =2 corresponds to the rocking curve for the same symmetric reflection rocking about a second axis, orthogonal to the first axis and to the second direction, / =3 corresponds to the rocking curve for an asymmetric reflection, and the FWHM, FWQM, and FWEM values are inAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01units of arc-seconds, and the x-ray rocking curves are measured using incident slit dimensions of at least 1 millimeter high by 2 millimeters wide and receiving slit dimensions of at least 1 millimeter high by 1 millimeter wide.

[0121] In some embodiments, the x-ray rocking curve quality metric Q of the free standing crystal has a value ranging from about 25 to about 40, about 25 to about 35, about 25 to about 30, or about 35 to about 40. In some embodiments, the x-ray rocking curve quality metric Q of the free standing crystal has a value ranging from about 40 to about 60. In some embodiments, the x-ray rocking curve quality metric Q of the free standing crystal has a value greater than 40.

[0122] In some embodiments, the first surface of the free-standing crystal has a crystallographic orientation within about 5 degrees of (0001 ) or (000-1), the =1 rocking curve corresponds to a symmetric reflection chosen from one of (002), (004) or (006) rocking about an a-axis, the i=2 rocking curve corresponds to the same symmetric reflection rocking about an orthogonal m-axis, and the i=3 rocking curve corresponds to an asymmetric (201) reflection.

[0123] In some embodiments, the first dimension of the free standing crystal is at least 45 millimeters, at least 50 millimeters, at least 55 millimeters, at least 60 millimeters, at least 65 millimeters, at least 70 millimeters, at least 75 millimeters, at least 80 millimeters, at least 85 millimeters, at least 90 millimeters, at least 95 millimeters, or at least 100 millimeters.

[0124] in some embodiments, the root-mean-square roughness of the first surface of the free standing crystal is less than about 5 nanometers, less than about 4 nanometers, less than about 3 nanometers, less than about 2 nanometers, less than about 1 nanometer, or less than about 0.5 nanometers.

[0125] in some embodiments, the first surface of the free standing crystal is characterized by an average concentration of threading dislocations that varies periodically by at least a factor of 1.2 in a third direction, the period of the variation in the third direction being between about 1.5 millimeters to about 20 millimeters. In some embodiments, the first surface of the free standing crystal is characterized by anAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01average concentration of threading dislocations that varies periodically in a third direction by at ieast a factor of 1.2, at least a factor of 1.4, at least a factor of 1.5, at least a factor of 1.7, at ieast a factor of 2, or at least a factor of 2.5. In some embodiments, the period of the variation in the third direction is about 1.5 millimeters to about 20 millimeters, about 1 millimeter to about 25 millimeters, about 1.5 millimeters to about 15 millimeters, or about 0.5 millimeters to about 30 millimeters.

[0126] In some embodiments, the first surface is further characterized by an average concentration of threading dislocations that varies periodically by at least a factor of 1.2 in a fourth direction, the fourth direction being orthogonal to the third direction and the period of the variation in the fourth direction being between about 1.5 millimeters to about 20 millimeters. In some embodiments, the first surface of the free standing crystal is characterized by an average concentration of threading dislocations that varies periodically in a fourth direction by at least a factor of 1.2, at least a factor of 1.4, at least a factor of 1.5, at ieast a factor of 1.7, at least a factor of 2, or at least a factor of 2.5. In some embodiments, the period of the variation in the fourth direction is about 1.5 millimeters to about 20 millimeters, about 1 millimeter to about 25 millimeters, about 1.5 millimeters to about 15 millimeters, or about 0.5 millimeters to about 30 millimeters.

[0127] In some embodiments, the first surface is characterized by average impurity concentrations of: oxygen (O) between 1×1016cm-3and 5×1019cm-3; hydrogen (H) between 1×1016cm-3and 8×1019cm-3; and at least one of fluorine (F) and chlorine (Cl) between 1×1015cm-3and 1×1019cm-3.

[0128] In some embodiments, ratio of the impurity concentration of H to an impurity concentration of O for the free standing crystal is between about 0.3 to about 10.

[0129] In some embodiments, the disclosure describes a method of fabricating a free standing crystal, the method comprising providing a first seed crystal obtained by slicing a crystal that had been formed by at least three previous growth / wafering cycles and had an as-grown (000-1 ) surface on which less than 1% of Its area had trenchesAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01having a local width between about 250 micrometers to about 5 millimeters and a local depth between about 500 micrometers to about 10 millimeters, less than 10% of its area comprised depressions having a depth greater than about 5 micrometers to less than about 100 micrometers, and the balance of its area having a root-mean-square surface roughness between about 0.1 nanometers to about 20 micrometers; applying a pattern to the (000-1) face of the first seed crystal, the pattern having a minimum parallel separation of at least 1.25 millimeters; placing the patterned, first seed crystal within an outer position of a sealable container, such that most or all of the first seed crystal is positioned in an outer position with respect to a cylindrical boundary having a diameter between about 70% to about 95% of an inner diameter of the sealable container; growing the first seed crystal to form a first boule having a thickness of at least 3 millimeters by an ammonothermal method; and forming at least a second crystal from the first boule by slicing at a distance at least one millimeter above a highest coalescence region within the first boule.

[0130] In some embodiments, the crystal that had been formed by at least three previous growth / wafering cycles and had an as-grown (000-1) surface on which less than 1 % of its area had trenches has a local width between about 200 micrometers to about 500 micrometers, about 500 micrometers to about 1 millimeter, about 1 millimeter to about 2 millimeters, about 2 millimeters to about 3 millimeters, about 3 millimeters to about 5 millimeters, about 250 micrometers to about 5 millimeters, about 200 micrometers to about 5 millimeters, or about 200 micrometers to about 7 millimeters.

[0131] In some embodiments, the crystal that had been formed by at least three previous growth / wafering cycles and had an as-grown (000-1 ) surface on which less than 1 % of its area had trenches has a local depth between about 250 micrometers to about 500 micrometers, about 500 micrometers to about 1 millimeter, about 1 millimeter to about 2 millimeters, about 2 millimeters to about 3 millimeters, about 3 millimeters to about 4 millimeters, about 4 millimeters to about 5 millimeters, about 5 millimeters to about 6 millimeters, about 6 millimeters to about 7 millimeters, about 7 millimeters to about 8 millimeters, about 8 millimeters to about 9 millimeters, about 9 millimeters to about 10 millimeters, or about 500 micrometers to about 10 millimeters.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01

[0132] In some embodiments, the crystal that had been formed by at least three previous growth / wafering cycles and had an as-grown (000-1 ) surface on which less than 1% of its area had trenches has less than 10% of its area comprised depressions having a depth about 5 micrometers to about 10 micrometers, about 10 micrometers to about 25 micrometers, about 25 micrometers to about 50 micrometers, about 50 micrometers to about 75 micrometers, about 75 micrometers to about 100 micrometers, or about 5 micrometers to about 100 micrometers.

[0133] In some embodiments, the crystal that had been formed by at least three previous growth / wafering cycles and had an as-grown (000-1 ) surface on which less than 1% of its area had trenches has the balance of its area having a root-mean-square surface roughness between about 0.1 nanometers to about 0.5 nanometers, about 0.5 nanometers to about 1.0 nanometer, about 1.0 nanometer to about 5.0 nanometers, about 5.0 nanometer to about 50 nanometers, about 50 nanometer to about 100 nanometers, about 100 nanometers to about 1.0 micrometer, about 1.0 micrometer to about 5.0 micrometers, about 5.0 micrometers to about 10 micrometers, about 10 micrometers to about 20 micrometers, or about 0.1 nanometers to about 20 micrometers.

[0134] In some embodiments, the pattern on the face of the first seed crystal has a minimum parallel separation of at least 0.5 millimeters, at least 0.75 millimeters, at least 1.0 millimeters, at least 1.25 millimeters; at least 1.5 millimeters, or at least 2.0 millimeters.

[0135] In some embodiments, most or all of the first seed crystal is positioned in an outer position with respect to a cylindrical boundary having a diameter between about 60% to about 70%, about 70% to about 80%, about 80% to about 95%, or about 70% to about 95% of an inner diameter of the sealable container. In some embodiments, the first seed crystal is grown to form a second boule having a thickness of at least 1 millimeter, at least 2 millimeters, at least 3 millimeters, at least 4 millimeters, or at least 5 millimeters by an ammonothermal method.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01

[0136] In some embodiments, the method of fabricating a free standing crystal further comprises placing a second seed crystal, the second seed crystal comprising at least a portion of the second crystal, within an outer position of a sealable container, such that most or all of the second seed crystal is positioned in an outer position with respect to a cylindrical boundary having a diameter between about 70% to about 95% of an inner diameter of the sealable container; growing the second seed crystal to form a second boule having a thickness of at least 3 millimeters by an ammonothermal method; and forming at least a third crystal from the first boule by slicing at a distance at least one millimeter above a highest coalescence region within the first boule. In some embodiments, most or all of the second seed crystal is positioned in an outer position with respect to a cylindrical boundary having a diameter between about 60% to about 70%, about 70% to about 80%, about 80% to about 95%, or about 70% to about 95% of an inner diameter of the sealable container. In some embodiments, the second seed crystal is grown to form a second boule having a thickness of at least 1 millimeter, at least 2 millimeters, at least 3 millimeters, at least 4 millimeters, or at least 5 millimeters by an ammonothermal method.

[0137] In some embodiments, the method of fabricating a free standing crystal further comprises slicing off an a-corner from the second crystal or the third crystal, forming an a-edge on the second or third crystal having an orientation within about 10 degrees of a {11-20} a-plane; performing ammonothermal growth on the seed crystal with the a-edge, forming a 100%-laterally-grown a-wing having a width between about 1 millimeter to about 50 millimeters and lateral facets comprising one or more of m-plane facets and semipolar {10-1-1} facets; removing the 100%-laterally-grown a-wing, forming a free-standing- 100%-iaterally-grown a-wing; and performing ammonothermal growth on the free-standing-100%-laterally-grown a-wing.

[0138] In some embodiments, the pattern applied to the (000-1) face of the first seed crystal has a minimum parallel separation of at least 2 millimeters.EMBODIMENTSAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01Embodiment 1 A free-standing crystal, comprising a group III metal and nitrogen, wherein the free-standing crystal comprises:a wurtzite crystal structure;a first surface having a maximum edge-to-edge dimension in a first direction; and a second surface on the opposite side of the crystal from the first surface that is separated from the first surface in a second direction that is orthogonal to the first direction and to the first surface, wherein:the first surface is characterized by a root-mean-square surface roughness less than about 50 micrometers and an average concentration of threading dislocations below about 104cm2;the first surface is further characterized by an x-ray rocking curve quality metric Q having a value greater than about 25, where Q is defined asQ = ∑3i=1100 / FWHM(i) + 100 / FWQM(i) + 100 / FWEM(i)2-“i=1FWQM© FWEM©where 100 / FWHM( / ), 100 / FWQM(), and 100 / FWEM( / ) are the average values of the quantities 100 divided by the full-width-at-half-maximum (FWHM), 100 divided by the full-width-at-quarter-maximum (FWQM), and 100 divided by the full-width-at-eighth-maximum (FWEM), respectively, of the fth reflection at each of at least five points that are distributed approximately uniformly over the central 40 to 80% of the area of the first surface, and / =1 corresponds to the rocking curve for a symmetric reflection rocking about a first axis that is parallel to the first direction, =2 corresponds to the rocking curve for the same symmetric reflection rocking about a second axis, orthogonal to the first axis and to the second direction, / =3 corresponds to the rocking curve for an asymmetric reflection, and the FWHM, FWQM, and FWEM values are in units of arc- seconds, and the x-ray rocking curves are measured using incident slit dimensions of at least 1 millimeter high by 2 millimeters wide and receiving slit dimensions of at least 1 millimeter high by 1 millimeter wide.Embodiment 2 The free-standing crystal of embodiment 1, wherein the x-ray rocking curve quality metric Q has a value ranging from about 25 to about 40.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01Embodiment 3 The free-standing crystal of any of embodiments 1 or 2, wherein the first surface has a crystallographic orientation within about 5 degrees of (0001 ) or (000- ), the;=1 rocking curve corresponds to a symmetric reflection chosen from one of (002), (004) or (006) rocking about an a-axis, the 1=2 rocking curve corresponds to the same symmetric reflection rocking about an orthogonal m-axis, and the i=3 rocking curve corresponds to an asymmetric (201 ) reflection.Embodiment 4 The free-standing crystal of any of embodiments 1 or 2, wherein the first dimension is at least 45 millimeters.Embodiment 5 The free-standing crystal of any of embodiments 1 or 2, wherein the first dimension is at least 95 millimeters.Embodiment 6 The free-standing crystal of any of embodiments 1 or 2, wherein the root-mean-square roughness of the first surface is less than about 1 nanometer.Embodiment 7 The free-standing crystal of any of embodiments 1 or 2, wherein the first surface is characterized by an average concentration of threading dislocations that varies periodically by at least a factor of 1.2 in a third direction, the period of the variation in the third direction being between about 1.5 millimeters to about 20 millimeters.Embodiment 8 The free-standing crystal of embodiment 7, wherein the first surface is further characterized by an average concentration of threading dislocations that varies periodically by at least a factor of 1.2 in a fourth direction, the fourth direction being orthogonal to the third direction and the period of the variation in the fourth direction being between about 1.5 millimeters to about 20 millimeters.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01Embodiment 9 The free-standing crystal of embodiment 7, wherein the first surface is characterized by an average concentration of threading dislocations that varies periodically by at least a factor of 2 in a third direction, the period of the variation in the third direction being between about 1.5 millimeters to about 20 millimeters and wherein the first surface is further characterized by an average concentration of threading dislocations that varies periodically by at least a factor of 2 in a fourth direction, the fourth direction being orthogonal to the third direction and the period of the variation in the fourth direction being between about 1.5 millimeters to about 20 millimeters.Embodiment 10 The free-standing crystal of any of embodiments 1-2, wherein the first surface is characterized by average impurity concentrations of:oxygen (O) between 1×1016cm-3and 5×1019cm-3;hydrogen (H) between 1×1016cm-3and 8×1019cm-3; andat least one of fluorine (F) and chlorine (Cl) between 1×1015cm-3and 1×1019cm-3.Embodiment 11 The free-standing crystal of embodiment 10, wherein a ratio of the impurity concentration of H to an impurity concentration of O is between about 0.3 to about 10.Embodiment 12 The free-standing crystal of embodiment 1, wherein the x-ray rocking curve quality metric Q has a value greater than about 40.Embodiment 13 A method for fabricating a free-standing crystal, the method comprising:providing a first seed crystal obtained by slicing a crystal that had been formed by at least three previous growth / wafering cycles and had an as-grown (000-1 ) surface on which less than 1 % of its area had trenches having a local width between about 250 micrometers to about 5 millimeters and a local depth between about 500 micrometers to about 10 millimeters, less than 10% of its area comprised depressions having a depth greater than about 5 micrometers to less than about 100 micrometers, and the balanceAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01of its area having a root-mean-square surface roughness between about 0.1 nanometers to about 20 micrometers;applying a pattern to the (000-1 ) face of the first seed crystal, the pattern having a minimum parallel separation of at least 1.25 millimeters;placing the patterned, first seed crystal within an outer position of a sealable container, such that most or all of the first seed crystal is positioned in an outer position with respect to a cylindrical boundary having a diameter between about 70% and about 95% of an inner diameter of the sealable container;growing the first seed crystal to form a first boule having a thickness of at least 3 millimeters by an ammonothermal method; andforming at least a second crystal from the first boule by slicing at a distance at least one millimeter above a highest coalescence region within the first boule.Embodiment 14 The method of embodiment 13, further comprising:placing a second seed crystal, the second seed crystal comprising at least a portion of the second crystal, within an outer position of a sealable container, such that most or all of the second seed crystal is positioned in an outer position with respect to a cylindrical boundary having a diameter between about 70% to about 95% of an inner diameter of the sealable container;growing the second seed crystal to form a second boule having a thickness of at least 3 millimeters by an ammonothermal method; andforming at least a third crystal from the first boule by slicing at a distance at least one millimeter above a highest coalescence region within the first boule.Embodiment 15 The method of any of embodiments 13-1, further comprising:slicing off an a-corner from the second crystal or the third crystal, forming an a-edge on the second or third crystal having an orientation within about 10 degrees of a {11-20} a-plane;performing ammonothermal growth on the seed crystal with the a-edge, forming a 100%-laterally-grown a-wing having a width between about 1 millimeterAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01to about 50 millimeters and lateral facets comprising one or more of m-plane facets and semi polar {10-1-1} facets;removing the 100%-laterally-grown a-wing, forming a free-standing-100%- laterally-grown a-wing; andperforming ammonothermal growth on the free-standing-100%-laterally- grown a-wing.Embodiment 16 The method of any of embodiments 13-14, wherein the pattern applied to the (000-1) face of the first seed crystal has a minimum parallel separation of at least 2 millimeters.EXAMPLES

[0139] Embodiments provided by the present disclosure are further illustrated by reference to the following examples. It will be apparent to those skilled in the art that many modifications, both to materials, and methods, may be practiced without departing from the scope of the disclosure.Comparative Example 1

[0140] A set of c-plane-oriented, bulk GaN seed crystals, some un-patterned, some patterned, and some patterned and trenched, were placed in a silver capsule having an inner diameter of approximately 229 mm along with a 7%-open-area baffle and polycrystalline GaN nutrient. A first seed crystal was unmasked and un-patterned and had already been subjected to three crystal growth cycles, and was placed in an inner position, by reference to FiG. 8C, at a distance greater than 63.5 millimeters from the inner diameter of the capsule, at a diameter less than 45% of the inner diameter of the capsule. In the growth cycle previous to the present run, a seed with two previous growth cycles was masked with a pattern similar to that shown schematically in FIG. 1 G, with values of Li, wi, W2, and s of approximately 1.2 mm, 40 microns, 5.0 mm, and 1.25 mm, respectively, and grown to a thickness of approximately 1.54 mm to form the first seed crystal. It is evident from FIG. 1 G and the dimensions listed above that theAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01minimum parallel separation in this pattern was Li, or 1.2 mm in this case. The ratio of the weight of the weight of the silver to the weight of polycrystalline GaN nutrient was approximately 2.86, and the silver had an average oxygen content of approximately 10 parts per million, based on a measurement of similarly-prepared parts by instrumental gas analysis (IGA). Prior to placement in the capsule, the polycrystalline GaN was deposited as a several-millimeter-thick film on Mo foil by reaction of GaCI, formed by bubbling Ch through Ga at a temperature of approximately 825°C, with NH3, at a temperature of approximately 900°C, and then recovered. The polycrystalline GaN nutrient had a porosity of approximately 0.66%, as measured by mercury intrusion porosimetry and an oxygen content of approximately 7 parts per million, as measured by glow discharge mass spectrometry. Before insertion in the capsule, the polycrystalline GaN nutrient was cleaned with mineral acids, washed in deionized water, and baked at a temperature of approximately 220°C overnight. After insertion of the solid raw materials, the capsule was evacuated, back-filled with argon, evacuated again, heated to a temperature of approximately 210°C, back-filled with argon, reevacuated, held at temperature for approximately 70 hours, and then cooled. The capsule was chilled to dry ice temperature and HF and then NH3 were added by the vapor phase, forming NH4F as mineralizer. The ratios of GaN nutrient and NH4F mineralizer to ammonia were approximately 4.29 and 0.099 respectively, by weight. The capsule was placed in an internally-heated high pressure apparatus and heated to temperatures of approximately 667 degrees Celsius for the upper, nutrient zone and approximately 678 degrees Celsius for the lower, crystal growth zone, maintained at these temperatures for approximately 1500 hours, and then cooled and removed. A wedge-shaped analysis sample was prepared from an ammonothermal GaN layer grown on separate, un-patterned test substrate, as shown in FIG. 7 with wedge angle a = 9°, and SIMS measurements were performed at eight points along surface 855. The maximum oxygen concentration, extrapolated to the regrowth interface, was approximately 9.1×1018cm-3, and the average gradient, measured between depths of 0.05 mm and 2.4 mm from the (000 -1) seed interface, was approximately -4.1×1019Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01cm in the [000 -1] direction. The average H / O ratio was approximately 0.68 and the average F / O ratio was approximately 0.27%.

[0141] The first seed crystal was grown to a thickness of approximately 5.0 mm, forming a first boule (Crystal D in Table 1 ) and the crystalline quality of its as-grown (000-1 ) face was quantified by x-ray diffraction. The diffractometer source incident slit width was 7 mm, the length-limiting slit was 15 mm long, the receiving slits on the analyzer side were 20 mm long, and the illuminated spot on the crystal was approximately 3 mm wide and 15 mm high. X-ray rocking curves were measured for (002) rocking about a and (002) rocking about m at each of 11 points across the central 60% of the area of the crystal, and for (201 ) at each of 9 points across the central 60% of the area of the crystal, as shown schematically in FIG. 6B. The Q parameter was evaluated as 21.1.

[0142] By comparison to the examples described below, it is concluded that the crystalline quality of the first seed crystal, the pitch and the minimum parallel separation of the pattern, and the number of growth cycles were insufficient to achieve a higher crystalline quality, even though the dislocation density was in the mid 104cm-2range. Comparative Example 2

[0143] A set of c-plane-oriented, bulk GaN seed crystals, some un-patterned, some patterned, and some patterned and trenched, were placed in a silver capsule having an inner diameter of approximately 229 mm along with a 7%-open-area baffle and polycrystalline GaN nutrient. A second seed crystal, derived from a Phase 3 grade boule, was unmasked and un-patterned and had already been subjected to five crystal growth cycles, and was placed in an inner position, by reference to FIG. 8C, at a distance greater than 63.5 millimeters from the inner diameter of the capsule. In the growth cycle previous to the present run, a third seed crystal, also Phase 3 grade, with four previous growth cycles was masked with a pattern similar to that shown schematically in FIG. 1 J, with values of L, w, L2, W2, and L3 of approximately 4.80 mm, 40 microns, 5.54 mm, 5.14 mm, and 16.3 mm, respectively, and grown to a thickness of approximately 5.82 mm to form a third boule. It is apparent from FIG. 1 J and theAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01dimensions listed above that the minimum parallel separation, in the Y-direction, is equal to Li, or 4.8 mm in this specific case. The second seed was prepared from the third boule by multi-wire sawing and etching, such that the second seed was approximately 1 millimeter away from the regrowth interface at the (000-1 ) surface of the third seed. Referring to FIG. 9, the second seed was not positioned above coalescence plane 959 and, in fact, some pits originating from solvent-filled gaps 963 in the third boule were present in the (0001 ) surface of the second seed crystal.

[0144] The ratio of the weight of the weight of the silver to the weight of polycrystalline GaN nutrient in the capsule containing the second seed crystal was approximately 2.77, and the silver had an average oxygen content of approximately 10 parts per million, based on a measurement of similarly-prepared parts by instrumental gas analysis (IGA). Prior to placement in the capsule, the polycrystalline GaN was deposited as a several-millimeter-thick film on Mo foil by reaction of GaCI, formed by bubbling CI2 through Ga at a temperature of approximately 825°C, with NH3, at a temperature of approximately 900°C, and then recovered. The polycrystalline GaN nutrient had a porosity of approximately 0.66%, as measured by mercury intrusion porosimetry and an oxygen content of approximately 7 parts per million, as measured by glow discharge mass spectrometry. Before insertion in the capsule, the polycrystalline GaN nutrient was cleaned with mineral acids, washed in deionized water, and baked at a temperature of approximately 220°C overnight. After insertion of the solid raw materials, the capsule was evacuated, back-filled with argon, evacuated again, heated to a temperature of approximately 210°C, back-filled with argon, reevacuated, held at temperature for approximately 70 hours, and then cooled. The capsule was chilled to dry ice temperature and HF and then NH3 were added by the vapor phase, forming NH4F as mineralizer. The ratios of GaN nutrient and NH4F mineralizer to ammonia were approximately 4.50 and 0.101 respectively, by weight. The capsule was placed in an internally-heated high pressure apparatus and heated to temperatures of approximately 667 degrees Celsius for the upper, nutrient zone and approximately 675 degrees Celsius for the lower, crystal growth zone, maintained at these temperatures for approximately 1500 hours, and then cooled and removed. AAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01wedge-shaped analysis sample was prepared from an ammonothermal GaN layer grown on a separate, un-patterned test substrate, as shown in FIG. 7 with wedge angle = 13°, and SIMS measurements were performed at eight points along surface 855. The maximum oxygen concentration, extrapolated to the regrowth interface, was approximately 1.26*1019cm’3, and the average gradient, measured between depths of 0.09 mm and 3.3 mm from the (000 -1) seed interface, was approximately -3.5×1019cm in the [000 -1] direction. The average H / O ratio was approximately 0.68 and the average F / O ratio was approximately 1.1%.

[0145] The second seed crystal was grown to a thickness of approximately 5.9 mm, forming a second boule (Crystal J in Table 1), and the crystalline quality of its as-grown (0001) face was quantified by x-ray diffraction, using the same diffractometer parameters as described in Comparative Example 1. X-ray rocking curves were measured for (002) rocking about a and (002) rocking about m at each of 11 points across the central 60% of the area of the crystal, and for (201 ) at each of 9 points across the central 60% of the area of the crystal, as shown schematically in FIG. 6B. The Q parameter of the as-grown (000-1 ) surface was evaluated as 19.4. The (000-1 ) surface was planarized by grinding with a 6000-grit grinding wheel and the residual surface damage was removed by wet etching. The Q parameter of the ground / etched (000-1 ) surface was evaluated as 22.1, quite similar to that of the as-grown surface.

[0146] By comparison to the examples described below, it is concluded that although the pitch and minimum parallel separation of the pattern were large enough to achieve a higher crystalline quality and the number of growth cycles was likely sufficient; however, the presence of residual stress in the second seed from the pits on the (0001 ) surface and growth of this seed in an inner position rather than an outer position limited the achieved crystalline quality, even though the dislocation density was in the mid 104cm’2range.Example 1

[0147] A set of c-plane-oriented, bulk GaN seed crystals, some un-patterned, some patterned, and some patterned and trenched, were placed in a silver capsule having anAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01inner diameter of approximately 229 mm along with a 7%-open-area baffle and polycrystalline GaN nutrient. A fourth seed crystal, derived from a boule having a surface morphology inferior to Phase 2 grade, was masked with a pattern similar to that shown schematically in FIG. 1 J, with values of L, w, L2, W2, and L3 of approximately 4.80 mm, 40 microns, 5.54 mm, 5.14 mm, and 16.3 mm, respectively, and was placed in an outer position, by reference to FIG. 8C, at a distance of approximately 34.5 millimeters from the inner diameter of the capsule. It is apparent from FIG. 1 J and the dimensions listed above that the minimum parallel separation, in the Y-direction, is equal to Li, or 4.8 mm, and the pitch in the X-direction is equal to L3, or 16.3 mm, in the specific case of the fourth seed crystal. In the growth cycle previous to the present run, a fifth seed, also having a surface morphology inferior to Phase 2 grade and five previous growth cycles, was masked with a pattern similar to that shown schematically in FIG. 1 J, with values of Li, wi, L2, W2, and L3 of approximately 1.80 mm, 40 microns, 2.08 mm, 1.68 mm, and 6.24 mm, respectively, and grown to a thickness of approximately 6.91 mm to form a fifth boule. The fourth seed crystal was prepared from the fifth boule by multi-wire sawing and etching, such that the fourth seed crystal was approximately 2.1 millimeter away from the regrowth interface at the (000-1 ) surface of the fifth seed crystal. Referring to FIG. 9, the fourth seed was positioned above coalescence plane 959 of the fifth seed crystal by approximately 1 millimeter.

[0148] The ratio of the weight of the weight of the silver to the weight of polycrystalline GaN nutrient in the capsule containing the fourth seed crystal was approximately 2.79, and the silver had an average oxygen content of approximately 10 parts per million, based on a measurement of similarly-prepared parts by instrumental gas analysis (IGA). Prior to placement in the capsule, the polycrystalline GaN was deposited as a several-millimeter-thick film on Mo foil by reaction of GaCI, formed by bubbling Cl₂ through Ga at a temperature of approximately 825°C, with NH3, at a temperature of approximately 900°C, and then recovered. The polycrystailine GaN nutrient had a porosity of approximately 0.66%, as measured by mercury intrusion porosimetry and an oxygen content of approximately 7 parts per million, as measured by glow discharge mass spectrometry. Before insertion in the capsule, theAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01polycrystalline GaN nutrient was cleaned with mineral acids, washed in deionized water, and baked at a temperature of approximately 230°C overnight. After insertion of the solid raw materials, the capsule was evacuated, back-filled with argon, evacuated again, heated to a temperature of approximately 220°C, back-filled with argon, reevacuated, held at temperature for approximately 70 hours, and then cooled. The capsule was chilled to dry ice temperature and HF and then NH3 were added by the vapor phase, forming NH4F as mineralizer. The ratios of GaN nutrient and NH4F mineralizer to ammonia were approximately 4.38 and 0.098 respectively, by weight. The capsule was placed in an internally-heated high pressure apparatus and heated to temperatures of approximately 668 degrees Celsius for the upper, nutrient zone and approximately 677 degrees Celsius for the lower, crystal growth zone, maintained at these temperatures for approximately 1566 hours, and then cooled and removed. A wedge-shaped analysis sample was prepared from an ammonothermal GaN layer grown on a separate, un-patterned test substrate, as shown in FIG. 7 with wedge angle = 18°, and SIMS measurements were performed at six points along surface 855. The maximum oxygen concentration, extrapolated to the regrowth interface, was approximately 5.26* 1018cm-3, and the average gradient, measured between depths of 0.10 mm and 3.8 mm from the (000 -1) seed interface, was approximately -1.1×1019cm-4in the [000 -1] direction. The average H / O ratio was approximately 0.77 and the average F / O ratio was approximately 0.46%.

[0149] The fourth seed crystal was grown to form a fourth boule having a thickness of approximately 5.8 mm and a surface morphology consistent with a Phase 3 crystal. A sixth seed crystal was prepared from the fourth boule by multi-wire sawing and etching, such that the sixth seed crystal was approximately 2 millimeters away from the regrowth interface at the (000-1 ) surface of the fourth seed crystal. Referring to FIG. 9, the sixth seed was positioned above coalescence plane 959 of the fourth seed crystal by approximately 1 millimeter.

[0150] The sixth seed crystal, with its (000-1) surface unmasked and un-patterned, was placed into the same capsule as that described in Comparative Example 1 and grown at the same time as the first seed crystal. The sixth seed crystal was grown toAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01form a sixth boule (Crystal H in Table 1 ) having a thickness of approximately 5.6 mm and a Phase 3 surface morphology. The crystalline quality of the as-grown (0001 ) face of the sixth boule was quantified by x-ray diffraction, using the same diffractometer parameters as described in Comparative Example 1. X-ray rocking curves were measured for (002) rocking about a and (002) rocking about m at each of 11 points across the central 60% of the area of the crystal, and for (201) at each of 9 points across the central 60% of the area of the crystal, as shown schematically in FIG. 6B. The Q parameter of the as-grown (000-1) surface was evaluated as 30.6, considerably higher than that of the crystals described in Comparative Examples 1 and 2. Although the Q parameter of the fourth boule was not measured, it is believed to have been similar to that of the sixth boule, and its very high crystalline quality was preserved during the last growth cycle.Example 2

[0151] A seventh seed crystal was prepared from the sixth boule, described in Example 1, by multi-wire sawing and etching, such that the sixth seed crystal was approximately 2.1 millimeters away from the regrowth interface at the (000-1) surface of the sixth seed crystal. Referring to FIG. 9, the seventh seed crystal was positioned above coalescence plane 959 of the sixth seed crystal by approximately 1 millimeter. Although it may not have been necessary, the (000-1) surface of the seventh seed crystal was masked with a pattern similar to that shown schematically in FIG. 1 J, with values of Li, wi, f_2, W2, and l_3 of approximately 4.80 mm, 40 microns, 5.54 mm, 5.14 mm, and 16.3 mm, respectively. It is apparent from FIG. 1 J and the dimensions listed above that the minimum parallel separation, in the Y-direction, is equal to Li, or 4.8 mm in the specific case of the seventh seed crystal. The seventh seed crystal was placed into the same capsule as that described in Comparative Example 2 in an inner position, close to the center of the capsule, and grown to form a seventh boule (Crystal I in Table 1 ), with a thickness of approximately 6.28 mm at the same time as the growth of the second boule.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01

[0152] The crystalline quality of the as-grown (0001 ) face of the seventh boule was quantified by x-ray diffraction, using the same diffractometer parameters as described in Comparative Example 1. X-ray rocking curves were measured for (002) rocking about a and (002) rocking about m at each of 11 points across the central 60% of the area of the crystal, and for (201 ) at each of 9 points across the central 60% of the area of the crystal, as shown schematically in FIG. 6B. The Q parameter was evaluated as 31.5. The Q parameter of the as-grown (000-1 ) surface of the seventh boule was evaluated as 31.5. The (000-1 ) surface was planarized by grinding with a 6000-grit grinding wheel and the residual surface damage was removed by wet etching. The Q parameter of the ground / etched (000-1) surface was evaluated as 31.3.

[0153] It is seen that a Q value between 25 and 35 was achieved with the seventh boule, despite the seventh seed being placed in an inner position in the capsule. The high quality of the seventh boule is attributed to high quality already having been achieved in the sixth boule where, as described in Example 1, a seed with 5 previous growth seeds was patterned with a minimum parallel separation greater than 4 millimeters and grown in an outer position within the capsule.Example 3

[0154] An eighth seed crystal was prepared by slicing and etching a Phase 3 crystal that was approximately 5.51 mm thick that had been previously grown by four growth cycles, at a distance of approximately 0.4 mm from the regrowth interface with its predecessor seed. The eighth seed crystal was masked with a pattern similar to that shown schematically in FIG. 1 J, with values of Li, wi, l_2, ws, and l_3 of approximately 4.80 mm, 40 microns, 5.54 mm, 5.14 mm, and 16.3 mm, respectively, and was placed in an outer position, by reference to FIG. 8C, at a distance of approximately 54 millimeters from the inner diameter of the same capsule as was described in Comparative Example 1 and Example 1. It is apparent from FIG. 1 J and the dimensions listed above that the minimum parallel separation, in the Y-direction, is equal to Li, or 4.8 mm in the specific case of the eighth seed crystal. The eighth seed crystal was grown, at the same time as the first seed crystal and the sixth seed crystal,Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01to a form an eighth boule (Crystal H in Table 1) having a thickness of approximately 6.38 mm.

[0155] The crystalline quality of the as-grown (0001 ) face of the eighth boule was quantified by x-ray diffraction, using the same diffractometer parameters as described in Comparative Example 1. X-ray rocking curves were measured for (002) rocking about a and (002) rocking about m at each of 11 points across the central 60% of the area of the crystal, and for (201 ) at each of 9 points across the central 60% of the area of the crystal, as shown schematically in FIG. 6B. The Q parameter was evaluated as 31.5. The Q parameter of the as-grown (000-1 ) surface of the seventh boule was evaluated as 30.5.

[0156] It is seen that the use of a relatively high-quality seed crystal, for example, being prepared from a Phase 2 or Phase 3 boule, together with the use of a large-minimum-parallel-separation pattern, ammonothermal growth in an “outer” position to a thickness of at least 4 millimeters, and formation of next-generation seed crystals at a distance at least about 1 millimeter away from the coalescence plane above a patterned seed, is able to reproducibly prepare crystals with an as-grown surface being characterized by a Q value in the range of 25-35.Example 4

[0157] A ninth seed crystal was prepared by slicing and etching a Phase 3 crystal that was approximately 6.52 mm thick that had been previously grown by four growth cycles, at a distance of approximately 2.8 mm from the regrowth interface with its predecessor seed. The ninth seed crystal was masked with a pattern similar to that shown schematically in FIG. 1M, with values of Li, wi, W2, ws, s, and t of approximately 1.60 mm, 40 microns, 1.50 mm, 3.86 mm, 0.40 mm, and 0.20 mm, respectively, and was placed in an outer position, by reference to FIG. 8C, at a distance of approximately 54 millimeters from the inner diameter of a similar capsule as was described in the previous Examples. It is apparent from FIG. 1M and the dimensions listed above that the minimum parallel separation, in the Y-direction, is equal to Li-t, or 1.4 mm in the specific case of the ninth seed crystal. The ninth seed crystal was grown, under similarAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01process conditions as those described in the previous Exampies, to form a ninth boule, with a thickness of approximately 3.94 mm and a Phase 3 surface morphology. A tenth seed crystal was prepared by slicing and etching the ninth boule at a distance of approximately 0.36 mm from the regrowth interface with its predecessor seed (the ninth seed crystal). The tenth seed crystal, with its (0001) face masked and its (000-1) face unmasked and un-patterned, was placed in an outer position, by reference to FIG. 8C, at a distance of approximately 54 millimeters from the inner diameter of a similar capsule as was described in the previous Examples. The tenth seed crystal was then grown, under similar process conditions as those described in the previous Examples, to a form a tenth boule, with a thickness of approximately 4.65 mm and a Phase 3 surface morphology. Two of the edges of the tenth boule bounded an a-corner and were quite straight, consisting essentially of {10-1-1} facets. An a-corner of the tenth boule was sliced off, similar to the schematic illustration of FIG. 10A, forming a fresh a-edge approximately 70 mm long. An eleventh seed crystal was prepared from the remainder of the boule by slicing at a distance of approximately 0.7 mm from the regrowth interface with the tenth seed crystal, as also shown schematically in FIG. 10A. Residual damage on the eleventh seed crystal was removed by wet etching. The eleventh seed crystal, unmasked and un-patterned, was placed in an outer position of an outer position, by reference to FIG. 8C, at a distance of approximately 34.5 millimeters from the inner diameter of a similar capsule as was described in the previous Examples. The eleventh seed crystal was then grown, under similar process conditions as those described in the previous Examples, to a form an eleventh boule, with a thickness of approximately 5.53 mm. As shown schematically in FIG. 10B, a 100%-laterally-grown a-wing grew from the fresh a-edge to a width of approximately 7 mm. The freshly-grown a-edge was quite straight, planar, and homogenous, comprising a facet with a {11-20} orientation. The 100%-lateraily-grown a-wing was then sliced off and the eleventh boule was multi-wire-sawed, as shown schematically in FIG. 10B, and residual damage removed by wet etching, forming several free-standing-100%-laterally-grown a-wing crystals. One of the latter crystals, positioned adjacent to the (0001) face of the eleventh boule, was then prepared as a twelfth seed crystal, unmasked and un-Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01patterned, and placed in an outer position, by reference to FIG. 8C, at a distance of approximately 34.5 millimeters from the inner diameter of a similar capsule as was described in the previous Examples. The twelfth seed crystal was then grown, under similar process conditions as those described in the previous Examples, to form a twelfth boule, with a thickness of approximately 4.09 mm, as shown schematically in FIG. 10C. The first 100%-laterally-grown a-wing grew laterally by an additional 6 millimeters, and a second 100%-laterally-grown a-wing grew laterally, also by approximately 6 millimeters. The twelfth boule was then multi-wire-sawed, forming several 100%-laterally-grown a-wing crystals, as shown schematically in FIG. 10C, and residual damage was removed by wet etching. One of these crystals, which was adjacent to the (0001 ) face of the twelfth boule, was then selected as a thirteenth seed crystal, and placed, unmasked and un-patterned, at an outer position, by reference to FIG. 8C, at a distance of approximately 34.5 millimeters from the inner diameter of the same capsule as the first seed crystal, the sixth seed crystal, and the eighth seed crystal. The thirteenth seed crystal was then grown at the same time as the first seed crystal, the sixth seed crystal, and the eighth seed crystal to a form a thirteenth boule (Crystal K in Table 1 ) having a thickness of approximately 6.38 mm and a width, between straight a-plane edges, of approximately 28 millimeters.

[0158] The crystalline quality of the as-grown (0001 ) face of the thirteenth boule was quantified by x-ray diffraction, using the same diffractometer parameters as described in Comparative Example 1. X-ray rocking curves were measured for (002) rocking about a, (002) rocking about m, and (201) at each of 5 points across the central 50% of the area of the crystal, as shown schematically in FIG. 6A. The Q parameter of the as-grown (000-1 ) surface of the thirteenth boule was evaluated as 46.1.Example 5

[0159] A fourteenth seed crystal was prepared by slicing and etching a Phase 3 crystal that was approximately 6.16 mm thick that had been previously grown by six growth cycles. The fourteenth seed crystal was masked with a patern similar to that shown schematically in FIG. 1 J, with values of Li, wi, L2, W2, and L3 of approximatelyAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO014.80 mm, 40 microns, 5.54 mm, 5.14 mm, and 16.3 mm, respectively, and was placed in an outer position, by reference to FIG. 8C, at a distance of approximately 34.5 millimeters from the inner diameter of a similar capsule as was described in Comparative Example 1 and Example 1. It is apparent from FIG. 1J and the dimensions listed above that the minimum parallel separation, in the Y-direction, is equal to Li, or 4.8 mm in the specific case of the fourteenth seed crystal. The fourteenth seed crystal was grown, at the same time as the first seed crystal, the sixth seed crystal, the eighth seed crystal, and the thirteenth seed crystal, to a form a fourteenth boule having a thickness of approximately 6.89 mm. A fifteenth seed crystal was prepared by slicing and etching the fourteenth boule at a distance of approximately 3.0 mm from the regrowth interface with the fourteenth seed crystal. The fifteenth seed crystal was masked with a pattern similar to that shown schematically in FIG. 1 J, with values of Li, wi, f_2, W2, and l_3 of approximately 14.40 mm, 40 microns, 8.31 mm, 7.91 mm, and 24.94 mm, respectively, and was placed in an outer position, by reference to FIG. 8C, at a distance of approximately 34.5 millimeters from the inner diameter of a similar capsule as was described in Comparative Example 1 and Example 1. It is apparent from FIG. 1 J and the dimensions listed above that the minimum parallel separation, in the Y-direction, is equal to Li, or 7.2 mm in the specific case of the fifteenth seed crystal. The fifteenth seed crystal was grown, under similar process conditions as those described in the previous Examples, to form a fifteenth boule having a thickness of approximately 6.27 mm. A first wafer (Crystal L in Table 1 ) was formed from the fifteenth boule from within the outermost 1 mm of the (000-1) face of the as-grown fifteenth boule.

[0160] The crystalline quality of the (0001 ) face of the first wafer was quantified by x-ray diffraction, using the same diffractometer parameters as described in Comparative Example 1. X-ray rocking curves were measured for (002) rocking about a and (002) rocking about m at each of 7 points across the central 40% of the area of the crystal, and for (201 ) at each of 6 points across the central 40% of the area of the crystal, as shown schematically in FIG. 6B. The Q parameter was evaluated as 32.0.Example 6Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01

[0161] A sixteenth seed crystal was prepared by slicing and etching a crystal that was grown from another seed prepared from a Phase 3 crystal that was approximately 6.15 mm thick that had been previously grown by six growth cycles. The sixteenth seed crystal was masked with a pattern similar to that shown schematically in FIG. 1J, with values of Li, wi, l_2, W2, and l_3 of approximately 4.80 mm, 40 microns, 5.54 mm, 5.14 mm, and 16.63 mm, respectively. It is apparent from FIG. 1 J and the dimensions listed above that the minimum parallel separation, in the Y-direction, is equal to U, or 4.8 mm in the specific case of the sixteenth seed crystal. The sixteenth seed crystal was grown upon in two successive runs, under similar process conditions as in the previous Examples. During the latter growth run, the seed was placed in an outer position, by reference to FIG. 8C, at a distance of approximately 34.5 millimeters from the inner diameter of a similar capsule as was described in Comparative Example 1 and Example 1. The sixteenth seed crystal was grown to form a sixteenth boule having a thickness of approximately 8.02 mm and a Phase 3 surface morphology. A second wafer (Crystal M in Table 1) was formed from the fifteenth boule from within the outermost 1 mm of the (000-1 ) face of the as-grown fifteenth boule.

[0162] The crystalline quality of the as-grown (0001 ) face of the second wafer was quantified by x-ray diffraction, using the same diffractometer parameters as described in Comparative Example 1. X-ray rocking curves were measured for (002) rocking about a and (002) rocking about m at each of 7 points across the central 40% of the area of the crystal, and for (201 ) at each of 6 points across the central 40% of the area of the crystal, as shown schematically in FIG. 6B. The Q parameter was evaluated as 38.2.

[0163] Although the Q parameter was not measured on the as-grown (000-1 ) face of the crystals from which the first and second wafers were prepared, it is believed to have been in the range of 25 to 40, by virtue of the similarities in preparation processes. It is seen that the Q parameters in wafers prepared from the extremely high quality crystals have similarly high values.Example 7Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01

[0164] Three crystals are prepared using procedures similar to those described in Examples 1, 2, and 3. The Q value of the as-grown (000-1 ) face of each crystal is between 28 and 40, where the x-ray rocking curve is measured at each of 11 points across the centrai 60% of the crystal, using similar parameters as in Examples 1, 2, and 3. Each of the crystals is multi-wire sawed, forming 1 to 3 wafers from each. The Ga face of each wafer, having an intentional miscut of 0.5±0.02 degree from (0001 ) and a miscut variation across the central 60% of the wafer less than 0.05 degree, is prepared by chemical-mechanical polishing such that the root-mean-square surface roughness is less than 0.1 nanometer. The Q value of the Ga faces of the wafers are evaluated using the same parameters that had previously been applied to the as-grown N faces. In the case of each wafer, the Q value of the Ga face of each wafer is within 3 points of that of the as-grown crystal from which the wafer was derived, that is, between 25 and 40.Example 8

[0165] Three crystals are prepared using procedures similar to those described in Example 4. The Q value of the as-grown (000-1 ) face of each crystal is between 42 and 48, where the x-ray rocking curve is measured at each of 5 points across the centra! 50% of the crystal, using similar parameters as in Example 4. Each of the crystals is multi-wire sawed, forming 1 to 3 wafers from each. The Ga face of each wafer, having an intentional miscut of 0.5±0.02 degree from (0001) and a miscut variation across the central 80% of the wafer less than 0.03 degree, is prepared by chemical-mechanical polishing such that the root-mean-square surface roughness is less than 0.1 nanometer. The Q value of the Ga faces of the wafers are evaluated using the same parameters that had previously been applied to the as-grown N faces. In the case of each wafer, the Q value of the Ga face of each wafer is within 3 points of that of the as-grown crystal from which the wafer was derived, that is, between 39 and 51.While the foregoing is directed to embodiments of the present disclosure, other and further embodiments of the disclosure may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01TABLE 1. Summary of crystal characteristics. Each of the listed values of XRC fuli-width-at-half maximum (FWHM), full-width-at-quarter-maximum (FWQM), full-width-at-eighth-maximum (FWEM), 100 / FWHM, 100 / FWQM, and 100 / FWEM are the averages of the values of each of these quantities over the central 50-80% of the crystal. The crystallographic radius of curvature (RoC) at the center of the crystal (in meters) was measured about an a-axis and an orthogonal m-axis, respectively. The XRC measurements were performed on the as-grown (000-1 ) surface of each crystals except the ones listed with an asterisk (*}, where they were measured after planarization using a 6000-grit grinding wheel and removal of damage by wet etching or by a dagger (t), where they were measured on the (0001 ) face of an epi-ready wafer prepared from the crystal. Crystals A-F have a surface threading dislocation density in the low-to-mid 104cm-2range, crystals G-l have a surface threading dislocation density in the low 103cm-2range, and crystal K has a surface threading dislocation density in the low 101cm-2range, based on measurements on similarly-prepared crystals.min 002a# growthCrystal parallelcycles FWH FWQ FWE 100 / FWH 100 / FWQ 100 / FWE sep'n (mm) M M M M M MA 1 0.8 34.0 51.1 68.7 3.02 2.00 1.47 B 1 1.2 31.4 46.5 64.5 3.26 2.20 1.59 C 1 1.2 38.6 60.2 81.5 2.66 1.72 1.27 D 3 1.2 32.4 48.8 61.9 3.27 2.11 1.65 E 5 1.4 61.9 92.6 121.7 1.79 1.13 0.86 F 5 1.2 29.3 46.8 63.8 3.97 2.41 1.76 G 5 4.8 18.7 26.5 35.7 5.54 3.81 2.86 H 7 4.8 19.3 28.8 37.3 5.33 3.57 2.73 I* 8 4.8 19.0 30.4 41.2 5.37 3.35 2.45 J* 6 4.8 28.8 49.4 72.7 4.16 2.62 1.81 K 9 1.5 15.4 23.1 27.8 6.55 4.35 3.61 Lt 8 7.2 23.7 39.6 50.4 4.96 2.77 2.12 Mt 9 4.8 20.1 31.4 40.6 5.53 3.50 2.67min 002m# growthCrystal parallelcycles FWH FWQ FWE 100 / FWH 100 / FWQ 100 / FWE sep'n (mm) M M M M M MA 1 0.8 33.7 51.1 68.1 3.07 2.07 1.52Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001 WO01B 1 1.2 31.4 49.1 67.4 3.52 2.22 1.60 C 1 1.2 41.6 62.2 83.5 2.64 1.70 1.26 D 3 1.2 26.5 41.6 54.7 3.93 2.55 1.93 E 5 1.4 62.2 92.0 110.3 1.82 1.20 0.99 F 5 1.2 29.1 46.1 61.2 3.79 2.53 1.86 G 5 4.8 17.3 26.2 35.3 5.93 3.91 2.89 H 7 4.8 20.9 29.8 39.6 4.89 3.40 2.55 I* 8 4.8 18.7 28.5 40.3 5.47 3.54 2.53 J* 6 4.8 35.7 56.3 76.3 4.15 2.59 1.88 K 9 1.5 14.9 22.1 28.3 6.75 4.54 3.54 L+ 8 7.2 22.6 35.5 46.8 4.48 2.85 2.16 M+ 9 4.8 19.5 30.9 40.6 5.22 3.40 2.57min 201# growthCrystal parallelcycles FWH FWQ FWE 100 / FWH 100 / FWQ 100 / FWE sep’n (mm) M M M M M MA 1 0.8 75.0 125.9 164.8 1.38 0.85 0.64 B 1 1.2 59.0 89.4 116.0 1.79 1.20 0.93 C 1 1.2 95.0 149.6 200.2 1.16 0.71 0.53 D 3 1.2 40.9 61.3 78.3 2.60 1.72 1.34 E 5 1.4 110.9 180.4 224.1 0.96 0.62 0.49 F 5 1.2 49.7 78.1 98.3 2.47 1.52 1.17 G 5 4.8 45.9 68.5 78.7 2.51 1.60 1.36 H 7 4.8 27.9 41.8 55.5 3.78 2.50 1.91 i* 8 4.8 26.3 39.2 61.2 4.06 2.60 1.90 J* 6 4.8 50.5 77.0 102.0 2.29 1.45 1.12 K 9 1.5 14.4 19.0 27.4 7.61 5.13 3.98 L+ 8 7.2 18.6 27.2 33.1 5.60 3.91 3.14Mt 9 4.8 14.2 21.6 29.5 7.07 4.67 3.59002a 002m# growth min parallel S FWHM +Crystal Center RoC Center RoCcycles sep'n (mm) S FWEM FWQM + FWEM Q (m) (m)A 1 0.8 -14.90 -20.27 672.34 301.61 16.00 B 1 1.2 -19.89 -29.23 554.67 247.88 18.31 C 1 1.2 -13.35 -17.33 812.34 365.11 13.65 D 3 1.2 -23.74 -29.84 446.18 194.77 21.10 E 5 1.4 -6.62 -9.66 1056.03 456.17 9.86 F 5 1.2 -20.27 -31.37 502.95 223.30 21.47 G 5 4.8 -40.16 -67.14 352.74 149.71 30.46H 7 4.8 -36.42 -61.39 301.03 132.42 30.64Attorney Ref. No.: Kil-SLT 0031 Attorney Docket No. 135423-0001 WO01I* 8 4.8 -43.90 -55.10 304.76 142.69 31.27 J* 6 4.8 -32.60 -65.10 548.70 250.93 22.08 K 9 1.5 -36.73 -65.11 192.41 83.42 46.05 L+ 8 7.2 -35.81 -34.10 297.53 130.32 32.00 Mt 9 4.8 -238.73 -220.73 248.37 110.78 38.22

Claims

Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001WO01CLAIMS1. A free-standing crystal, comprising a group III metal and nitrogen, wherein the free-standing crystal comprises:a wurtzite crystal structure;a first surface having a maximum edge-to-edge dimension in a first direction; anda second surface on the opposite side of the crystal from the first surface that is separated from the first surface in a second direction that is orthogonal to the first direction and to the first surface, wherein:the first surface is characterized by a root-mean-square surface roughness less than about 50 micrometers and an average concentration of threading dislocations below about 104cm-2;the first surface is further characterized by an x-ray rocking curve quality metric Q having a value greater than about 25, where Q is defined as Q _ ya mo+loo+MOAi=i FWQM(i) FWEM(i)where 100 / FWHM( / ), 100 / FWQM( / ), and 100 / FWEM( / ) are the average values of the quantities 100 divided by the full-width-at-half-maximum (FWHM), 100 divided by the full-width-at-quarter-maximum (FWQM), and 100 divided by the full-width-at-eighth-maximum (FWEM), respectively, of the / th reflection at each of at least five points that are distributed approximately uniformly over the central 40 to 80% of the area of the first surface, and / =1 corresponds to the rocking curve for a symmetric reflection rocking about a first axis that is parallel to the first direction, / =2 corresponds to the rocking curve for the same symmetric reflection rocking about a second axis, orthogonal to the first axis and to the second direction, / =3 corresponds to the rocking curve for an asymmetric reflection, and the FWHM, FWQM, and FWEM values are in units of arc-seconds, and the x-ray rocking curves are measured using incident slit dimensions of at least 1 millimeter high by 2 millimeters wide and receiving siit dimensions of at least 1 millimeter high by 1 millimeters wide.Atorney Ref. No.: Kll-SLT 0031 Atorney Docket No. 135423-0001W0012. The free-standing crystal of claim 1, wherein the x-ray rocking curve quality metric Q has a value ranging from about 25 to about 40.

3. The free-standing crystal of any of claims 1 or 2, wherein the first surface has a crystallographic orientation within about 5 degrees of (0001) or (000-1), the / =1 rocking curve corresponds to a symmetric reflection chosen from one of (002), (004) or (006) rocking about an a-axis, the i=2 rocking curve corresponds to the same symmetric reflection rocking about an orthogonal m-axis, and the f=3 rocking curve corresponds to an asymmetric (201) reflection.

4. The free-standing crystal of any of claims 1 or 2, wherein the first dimension is at least 45 millimeters.

5. The free-standing crystal of any of claims 1 or 2, wherein the first dimension is at least 95 millimeters.

6. The free-standing crystal of any of claims 1 or 2, wherein the root-mean-square roughness of the first surface is less than about 1 nanometer.

7. The free-standing crystal of any of claims 1 or 2, wherein the first surface is characterized by an average concentration of threading dislocations that varies periodically by at least a factor of 1.2 in a third direction, the period of the variation in the third direction being between about 1.5 millimeters to about 20 millimeters.

8. The free-standing crystal of claim 7, wherein the first surface is further characterized by an average concentration of threading dislocations that varies periodically by at least a factor of 1.2 in a fourth direction, the fourth direction being orthogonal to the third direction and the period of the variation in the fourth direction being between about 1.5 millimeters to about 20 millimeters.

9. The free-standing crystal of claim 7, wherein the first surface is characterized by an average concentration of threading dislocations that varies periodically by atAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001WO01feast a factor of 2 in a third direction, the period of the variation in the third direction being between about 1.5 millimeters to about 20 millimeters and wherein the first surface is further characterized by an average concentration of threading dislocations that varies periodically by at least a factor of 2 in a fourth direction, the fourth direction being orthogonal to the third direction and the period of the variation in the fourth direction being between about 1.5 millimeters to about 20 millimeters.

10. The free-standing crystal of any of claims 1-2, wherein the first surface is characterized by average impurity concentrations of:oxygen (O) between 1×1016cm-3and 5×1019cm-3;hydrogen (H) between 1×1016cm-3and 8×1019cm-3; andat least one of fluorine (F) and chlorine (Cl) between 1×1015cm-3and 1×1019cm-3.

11. The free-standing crystal of claim 10, wherein a ratio of the impurity concentration of H to an impurity concentration of O is between about 0.3 to about 10.

12. The free-standing crystal of claim 1, wherein the x-ray rocking curve quality metric Q has a value greater than about 40.

13. A method for fabricating a free-standing crystal, the method comprising: providing a first seed crystal obtained by slicing a crystal that had been formed by at least three previous growth / wafering cycles and had an as-grown (000-1) surface on which less than 1% of its area had trenches having a local width between about 250 micrometers to about 5 millimeters and a local depth between about 500 micrometers to about 10 millimeters, less than 10% of its area comprised depressions having a depth greater than about 5 micrometers to less than about 100 micrometers, and the balance of its area having a root-mean-square surface roughness between about 0.1 nanometers to about 20 micrometers;applying a pattern to the (000-1) face of the first seed crystal, the pattern having a minimum parallel separation of at least 1.25 millimeters;placing the patterned, first seed crystal within an outer position of a sealable container, such that most or all of the first seed crystal is positioned in an outerAttorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001WO01position with respect to a cylindrical boundary having a diameter between about 70% to about 95% of an inner diameter of the sealable container;growing the first seed crystal to form a first boule having a thickness of at least 3 millimeters by an ammonothermai method; andforming at least a second crystal from the first boule by slicing at a distance at least one millimeter above a highest coalescence region within the first boule.

14. The method of claim 13, further comprising:placing a second seed crystal, the second seed crystal comprising at least a portion of the second crystal, within an outer position of a sealable container, such that most or ail of the second seed crystal is positioned in an outer position with respect to a cylindrical boundary having a diameter between about 70% to about 95% of an inner diameter of the sealable container;growing the second seed crystal to form a second boule having a thickness of at least 3 millimeters by an ammonothermai method; andforming at least a third crystal from the first boule by slicing at a distance at least one millimeter above a highest coalescence region within the first boule.

15. The method of any of claims 13-14, further comprising:slicing off an a-corner from the second crystal or the third crystal, forming an a-edge on the second or third crystal having an orientation within about 10 degrees of a {11-20} a-plane;performing ammonothermal growth on the seed crystal with the a- edge, forming a 100%-iaterally-grown a-wing having a width between about 1 millimeter and about 50 miilimeters and iateral facets comprising one or more of m-plane facets and semipolar {10-1-1} facets;removing the 100%-laterally-grown a-wing, forming a free-standing- 100%-laterally-grown a-wing; andperforming ammonothermal growth on the free-standing-100%- laterally-grown a-wing.Attorney Ref. No.: KII-SLT 0031 Attorney Docket No. 135423-0001WO0116. The method of any of claims 13-14, wherein the pattern applied to the (000-1) face of the first seed crystal has a minimum parallel separation of at least 2 millimeters.

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