Strain-based polarization and charge carrier generation in wurtzite semiconductor devices

Abstract

A device includes a substrate including a template layer, the template layer including a polar material, and a heterostructure supported by the substrate and in contact with the polar material. The heterostructure includes a barrier layer and a channel layer. The barrier layer includes a first wurtzite semiconductor material. The channel layer includes a second wurtzite semiconductor material. The first and second wurtzite semiconductor materials have different in-plane lattice constants such that the channel layer is under lateral strain.

Description

STRAIN-BASED POLARIZATION AND CHARGE CARRIER GENERATION IN WURTZITE SEMICONDUCTOR DEVICESCROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of U.S. provisional application entitled “Strain- Based Polarization and Charge Carrier Generation in Wurtzite Semiconductor Devices,” filed March 25, 2024, and assigned Serial No. 63 / 569,691 , the entire disclosure of which is hereby expressly incorporated by reference.BACKGROUND OF THE DISCLOSUREField of the Disclosure

[0002] The disclosure relates generally to wurtzite semiconductor devices.Brief Description of Related Technology

[0003] Over the past three decades, group Ill-nitrides (GaN, AIN, InN, and their alloys) have been extensively investigated across various fields, including electronics, optoelectronics, piezo-electronics, quantum-photonics, and clean energy. Ill-nitride materials exhibit a stable non-centrosymmetric wurtzite phase. The non-equivalence between the c- axis bond and the c-components of the other three bonds results in a non-zero electric dipole within the structure, leading to strong spontaneous and piezoelectric polarization along the c-direction and plays a useful role in determining the optical and electrical properties of wurtzite nitrides. For example, differences in polarization induce high densities of two-dimensional carrier gases (2DCGs) at the heterostructure interfaces, which have been exploited in modern high-frequency and high-power transistors. The polarization discontinuities also give rise to unwanted built-in electric fields in quantum wells. The resulting quantum-confined Stark effect (QCSE) reduces the electron-hole wave-function overlap and thus the efficiency of light emitters.

[0004] Based on the Modern Theory of Polarization (MTP), the polarization constants have been well-determined in Bernardini etal.’s seminal work by using a zinc-blende structure as reference. The effective application of this theoretical framework in quantitatively interpretingand modeling polarization phenomena in nitride heterostructures has garnered widespread recognition and textbook-level acclaim, serving as a quintessential example of successfully bridging theory with experimental observations.

[0005] Recently, the polarization in wurtzite nitride semiconductors has been unambiguously measured experimentally by different groups. By introducing rare-earth elements into the wurtzite structure, the polarity switching energy barrier is significantly reduced, permitting the first experimental measurement of spontaneous polarization in the wurtzite semiconductors. However, in an unexpected twist, the observed spontaneous polarization values are consistently an order of magnitude larger and oriented in direct opposition to the predictions made by Bernardini etal. that have informed the understanding of wurtzite semiconductors for decades. These fundamental discrepancies profoundly disrupt the foundational comprehension of polarization in these materials and pose significant challenges to both the theoretical framework and device development.SUMMARY OF THE DISCLOSURE

[0006] In accordance with one aspect of the disclosure, a device includes a substrate including a template layer, the template layer including a polar material, and a heterostructure supported by the substrate and in contact with the polar material, the heterostructure including a barrier layer and a channel layer. The barrier layer includes a first wurtzite semiconductor material. The channel layer includes a second wurtzite semiconductor material. The first and second wurtzite semiconductor materials have different in-plane lattice constants such that the channel layer is under lateral strain.

[0007] In accordance with another aspect of the disclosure, a device includes a substrate including a template layer, the template layer including a polar material, and a heterostructure supported by the substrate and in contact with the polar material, the heterostructure including a barrier layer and a channel layer. The barrier layer includes a first wurtzite semiconductor material. The channel layer includes a second wurtzite semiconductor material. The heterostructure further includes a strain layer embedded in the barrier layer. The strain layer includes a material with an in-plane lattice constant differing from the first wurtzite semiconductor material such that lateral strain is established in the barrier layer.

[0008] In accordance with yet another aspect of the disclosure, a device includes a substrate including a template layer, the template layer including a polar material, a structure supported by the substrate and in contact with the polar material, the structure including awurtzite semiconductor material, and a plurality of device terminals supported by the structure. The structure has an in-plane lattice constant or dimensionality different from the polar material of the substrate to establish a lateral strain gradient in the structure such that the wurtzite semiconductor material exhibits a polarization gradient in accordance with the lateral strain gradient.

[0009] In connection with any one of the aforementioned aspects, the devices described herein may alternatively or additionally include or involve any combination of one or more of the following aspects or features. The lateral strain is compressive. The polar material of the substrate is nitrogen-polar. The polar material of the substrate is metal-polar. The substrate includes a bulk substrate. The template layer is supported by the bulk substrate. The polar material is a Ill-nitride semiconductor. The first wurtzite semiconductor material has a smaller in-plane lattice constant than the second wurtzite semiconductor material. The first wurtzite semiconductor material is a rare-earth doped Ill-nitride semiconductor. The second wurtzite semiconductor material is a Ill-nitride semiconductor. The channel layer is supported by the barrier layer. The device further includes a gate electrode and a gate dielectric layer disposed between the gate electrode and the channel layer. The lateral strain is tensile strain. The strain layer is a monolayer. The strain layer has a single digit number of monolayers. The strain layer has a thickness less than about 2 nm. The in-plane lattice constant of the material of the strain layer is less than about 20% greater or lower than an in-plane lattice constant of the first wurtzite semiconductor material. The strain layer includes ScN or InN. The barrier layer is supported by the channel layer. The device further includes a gate electrode and a gate dielectric layer disposed between the gate electrode and the barrier layer. The first wurtzite semiconductor material, the second wurtzite semiconductor material, or both the first and second wurtzite semiconductor materials are not doped. The lateral strain gradient is oriented such that the structure is under decreasing lateral strain as a distance from the polar material of the substrate increases. The dimensionality of the structure varies with distance from the polar material to establish the lateral strain gradient in the structure. The structure is under compressive strain at the polar material. The structure is under tensile strain at the polar material. The plurality of terminals include first and second terminals in contact with the structure, the first and second terminals being spaced apart from one another and configured to form a Schottky diode. The polar material of the substrate is nitrogen-polar. The polar material of the substrate is metal-polar. The thickness of the structure is established by a set of epilayers of the wurtzite semiconductor material. The wurtzite semiconductor material is not doped.BRIEF DESCRIPTION OF THE DRAWING FIGURES

[0010] For a more complete understanding of the disclosure, reference should be made to the following detailed description and accompanying drawing figures, in which like reference numerals identify like elements in the figures.

[0011] Figure 1 schematically depicts a history of works directed to polarization in wurtzite semiconductor materials, which was intuitively understood as a cumulative polarization of the bonds in an exemplary tetrahedron divided by the unit volume. Extensive interest was raised in Ill-nitrides after the demonstration of 2DEGs and HEMT devices by Asif Khan etal., and the first high-efficiency blue light emitting diodes (LEDs) by Akasaki etal. Inspired by the development of the MTP by Resta etal., in 1997, Bernardini etal. first calculated the polarization constants in group-ill nitrides using the Berry phase approach and the zincblende (ZB) structure as reference. The results suggested a spontaneous polarization pointing toward the -c direction yet the zero-polarization assumption for zincblende structure remained questionable. In 2016, Dreyer etal. proposed a layered hexagonal (LH) structure as an alternative reference structure for calculating the polarization constants in wurtzite nitrides. However, due to the lack of experimental proof, the results were merely regarded as magnitude refinements. Figure 1 also schematically depicts a recent work directed to direct experimental measurement of spontaneous polarization using wurtzite ferroelectrics by various groups. Surprisingly, the measured spontaneous polarization is oriented oppositely to, and is one order larger in magnitude than, the conventional understanding, yet correlates well with Dreyer etal.’s calculations. Such work has further been validated by scanning transmission electron microscopy (STEM), piezo-response force microscopy (PFM), wetetching and Density Function Theory (DFT) calculations. These advancements highlight the validity of using the layered hexagonal structure as a standard reference and lead to a rethinking of the polarization in wurtzite semiconductors.

[0012] Figure 2 schematically depicts the spontaneous polarization in wurtzite semiconductor materials and devices via a dipole moment due to a displacement of the nitrogen atoms from a layered hexagonal structure to a wurtzite structure, divided by the volume of the unit cell. ZB is the Born effective charge. Tensile strain leads to an increase in u and a, resulting in reduced polarization, whereas compressive strain results in an increase in polarization. Implementing the new direction of spontaneous polarization and piezoelectric polarization, two-dimensional carrier gases (e.g., 2DEG and 2DHG) may be explained as a result of the larger polarization of GaN compared to AIN, contrary to the physical picture used before.

[0013] Figure 3 schematically depicts a transistor device having strain-based charge carrier generation (2DEG) in accordance with one example.

[0014] Figure 4 schematically depicts a transistor device having strain-based charge carrier generation (2DHG) in accordance with another example.

[0015] Figure 5 depicts a heterostructure having strain-based charge carrier generation (2DEG) via an embedded strain layer in accordance with one example.

[0016] Figure 6 depicts a transistor device having the heterostructure of Figure 5 in accordance with one example.

[0017] Figure 7 depicts a Schottky diode having strain-based charge carrier generation via strain relaxation in a wurtzite semiconductor structure (e.g., under varying compressive strain) in accordance with one example.

[0018] Figure 8 depicts a Schottky diode having strain-based charge carrier generation via strain relaxation in a wurtzite semiconductor structure (e.g., under varying tensile strain) in accordance with another example.

[0019] The embodiments of the disclosed devices may assume various forms. Specific embodiments are illustrated in the drawing and hereafter described with the understanding that the disclosure is intended to be illustrative. The disclosure is not intended to limit the invention to the specific embodiments described and illustrated herein.DETAILED DESCRIPTION OF THE DISCLOSURE

[0020] Transistor, diode, and other devices having one or more wurtzite semiconductor layers or structures exhibiting strain-based polarization (e.g., via lateral strain) are described. The strain-based polarization in either an entire heterostructure stack or one or more respective layers thereof is directed to generating charge carriers for device operation. Such layers and structures of the disclosed devices may be considered strain-doped layers and structures.

[0021] Described herein are devices having one or more structures or layers composed of, or otherwise including a wurtzite semiconductor material. The layer(s) exhibit polarization arising from the non-centrosymmetric wurtzite lattice. As described herein, recent direct experimental measurements unveiled remanent polarization of unexpectedly large magnitudes and opposite orientations to those traditionally anticipated. This significant discrepancy not only poses a formidable challenge to existing theoretical paradigms but also leads to a rethinking and methodological refinement to integrate these novel observationswith established knowledge, mitigating potential misunderstandings and misconceptions in this rapidly evolving field.

[0022] Although described in connection with diode and transistor devices, the polarizationbased effects described herein may be used to form other devices, including, for instance, tunnel junctions, capacitors, non-volatile memory devices, phase change memory devices, etc. A broad range nitride-based electronic, photonic, and piezoelectric devices may thus be realized.

[0023] Although described in connection with examples of epitaxially grown ScAIGaN and ScAIN layers, the disclosed methods and devices may be applied to a wide variety of Ill- nitride alloys and other wurtzite materials. The disclosed methods and devices may thus include or involve the incorporation of scandium into other Ill-nitride wurtzite structures. For instance, the disclosed methods and devices may include or involve one or more epitaxially grown Scxlni.xN structures. Still other wurtzite ferroelectric materials may be used, including, for instance, YAIN, AIBN, YGaN, ZnMgO, etc.

[0024] The configuration, construction, fabrication, and other characteristics of the heterostructures (and ferroelectric structures thereof) may also vary from the examples described. For instance, the heterostructures may include any number of epitaxially grown segments of ferroelectric and non-ferroelectric nature.

[0025] The disclosed methods and devices are not limited to Ill-nitride alloys including scandium. For instance, the Ill-nitride alloys may include additional or alternative group II IB elements, such as yttrium (Y) and lanthanum (La).

[0026] Although described in connection with examples having a base or template layer composed of GaN, the heterostructures of the disclosed devices may include alternative or additional Ill-nitride semiconductor segments as a template, base, intermediate, or other structure or layer. Additional or alternative types of materials may also be used in the heterostructures, including, for instance, other semiconductor materials. For instance, other nitride semiconductors, such as Ill-nitrides without incorporating a II IB element. Still other materials may be used, including, for instance, silicon, silicon carbide, and metals such as aluminum and molybdenum.

[0027] The fabrication of the disclosed devices is not limited to MBE growth procedures. Additional or alternative non-sputtered epitaxial growth procedures may be used. For instance, metal-organic chemical vapor deposition (MOCVD), hydride vapor phase epitaxy (HVPE), atomic layer deposition (ALD), and atomic layer epitaxy (ALE) growth proceduresmay be used. Still other procedures may be used, including, for instance, pulsed laser deposition procedures.

[0028] Further details on the epitaxial growth conditions, procedures, and related parameters that may be used to form the structures and heterostructures described herein are set forth in WO 2023 / 022768 ("Epitaxial Nitride Ferroelectronics"), International Application No. PCT / US23 / 13727 ("Epitaxial Nitride Ferroelectronic Devices" filed February 23, 2023, now published as WO 2023 / 164071), P. Wang, et al., "Fully epitaxial ferroelectric ScAIN grown by molecular beam epitaxy," Applied Physics Letters, vol. 118, p. 223504 (2021), D. Wang et al., "An Epitaxial Ferroelectric ScAIN / GaN Heterostructure Memory," Advanced Electronic Materials, p. 2200005 (2022), D. Wang, et al., "Fully epitaxial ferroelectric ScGaN grown on GaN by molecular beam epitaxy," Appl Phys Lett 119 (11), 111902 (2021), D. Wang et al., "Impact of dislocation density on the ferroelectric properties of ScAIN grown by molecular beam epitaxy," Appl Phys Lett 121 (4), 042108 (2022), P. Wang et al., "Quaternary alloy ScAIGaN: A promising strategy to improve the quality of ScAIN," Appl Phys Lett 120 (1), 012104 (2022), and P. Wang et al. "Ferroelectric Nitride Heterostructures on CMOS Compatible Molybdenum for Synaptic Memristors," ACS Appl. Mater. Interfaces 2023, 15, 14, 18022-18031 (2023), the entire disclosures of which are hereby incorporated by reference.

[0029] The wurtzite structure is characterized by a hexagonal Bravais lattice with four atoms per unit cell and by three parameters: the edge length a of the basal hexagon, the height c of the hexagonal prism, and an internal parameter u expressed as a fraction of c, which determines the relative positions of atoms along the c-axis. The c / a ratio in the wurtzite structure, being less than the ideal tetrahedral value of ^8 / 3 « 1.633, induces a displacement between cation and anion centers, generating a net dipole moment along the c-axis. To attain a mental image of polarization in the wurtzite structure, historically, a tetrahedron has been frequently referenced. When the tetrahedron is ideal (u = 3 / 8), all polarization vectors cancel one another. In the case of a Ill-nitride wurtzite structure (u > 3 / 8), the central atom is not exactly located at the tetrahedral center, leading to a non-zero electric polarization along c-axis, known as the spontaneous polarization. Under homogeneous in-plane strain, the sum of the polarization vectors varies, causing a net polarization along the c-direction, known as the piezoelectric polarization.

[0030] In the 1990s, it became apparent that the more fundamental measure of polarization is the differential polarization, a concept that was further developed by King-Smith, Vanderbilt, and Resta with the advent of the MTP. This approach has been recommendedfor defining the spontaneous polarization of a material, effectively addressing the challenges of multivalued formal polarization. Specifically, for wurtzite semiconductors, the zincblende structure has been utilized as a reference by Bernardini et al. to determine the polarization constants. The effective polarization of the wurtzite structure is conceptualized as a net dipole moment arising from the displacement of the center atom, with the direction of spontaneous polarization oriented opposite to the c-axis. Subsequent calculations of polarization constants for Ill-nitride materials have been applied in interpreting and modeling the 2DCGs and internal fields in quantum wells.

[0031] While this framework has proven effective for conventional nitride materials, applying the same methodology to predict spontaneous polarization in rare-earth-doped Ill- nitride materials presents significant challenges. The discovery of ferroelectricity in wurtzite nitride materials has enabled direct measurements of spontaneous polarization in this material class. However, the breakthrough brought not only excitement but also further challenges.

[0032] First, the direction of spontaneous polarization determined by macroscopic ferroelectric measurements is oriented exactly opposite to the predictions made by Bernardini etal. This discrepancy in lattice polarity orientation relative to measured polarization has been further validated by examining atomic configurations under varying external electric fields.

[0033] Second, the polarization values measured are an order of magnitude greater than those previously predicted using a zincblende reference structure.

[0034] Described herein are a number of devices having heterostructures and other features that generate charge carriers based on the resolution of these two challenges involving discrepancies between conventional theory and recent experimental observations. The disclosed devices are configured in accordance with a new understanding of polarization in wurtzite semiconductor materials, including a recognition that the common practice of using zincblende structure as reference may not be appropriate or suitable as a standard reference for calculating the polarization in wurtzite semiconductor materials.

[0035] In the calculations by Bernardini etal., the interface theorem was consistently applied to circumvent the necessity of identifying a complex adiabatic, gap-preserving deformation pathway. If N- and M-polarities can be defined in the zincblende structure based on the orientation of the vertical bond in the

[0111] direction, similar to that in the wurtzite structure, one would find that the insulating interface constructed between wurtzite and zincblende structures used in their calculations are only based on either N-polar wurtzite toN-polar zincblende, or M-polar wurtzite to M-polar zincblende. Once polarization of one polarity is determined, the polarization for the opposite polarity is simply assumed as inversely equivalent. This, however, causes problems because the reference structures are substantially different while calculating the polarization of opposing polarities. An intuitive physical picture is that, the transition from M-polar zincblende to M-polar wurtzite involves a minimal displacement of the central atom by (u-3 / 8)c. However, the inverted operation of displacing the central atom in M-polar zincblende by -(u-3 / 8)c ends up in a structure that deviates from the expected N-polar wurtzite structure. Instead, a much larger displacement of -(1-u-3 / 8)c is involved. This suggests that utilizing the zincblende structure as a reference can introduce complications in accurately defining the spontaneous polarization even in a single wurtzite material.

[0036] Contrary to prevailing assumptions, the formal polarization of the zincblende structure does not inherently vanish along the

[0111] direction. A closer examination of its ionic contribution reveals that the structure can be visualized as a series of displaced onedimensional ion chains along the

[0111] direction, which exhibit zero polarization only for specific unit cell choices. The value of this conditional non-vanishing polarization is highly dependent on the lattice constant of the chosen reference structure, introducing inaccuracies when calculating the difference of formal polarization across interfaces. In other words, when using a zincblende structure reference, variations in the lattice constant across the interface would lead to varying polarization reference values for the materials constituting the interface, which, however, was not considered in conventional Bernardini etal. ’s theory.

[0037] The layered hexagonal structure is useful as a reference structure for several reasons. First, it establishes that, while deforming the reference structure into the polarization state, the inverted polarization states can be obtained via inverted deforming paths. Second, it exhibits no interface charge when an interface is formed between itself and its mirrored counterpart across the plane of interest, thus assuring vanishing formal polarization. Additionally, to enable accurate calculation of net polarization charges at material interfaces using polarization constants, for materials constructing the interface, it exhibits vanishing polarization, even under strain applied perpendicular to the direction of interest.

[0038] By constructing an interface between N-polar and M-polar wurtzite lattices and in view of the above-outlined considerations, the layered hexagonal structure is unequivocally identified as an ideal reference structure. This approach not only yields calculated magnitudes and orientations of spontaneous polarization that closely match those observed in direct experimental measurements, but also effectively resolves the discrepancieshighlighted above. This framework currently finds its acceptance predominantly within the ferroelectric community, yet with only limited acknowledgment in traditional Ill-nitride work. The disclosed devices highlight the utility of of merging these perspectives on polarization in wurtzite semiconductor materials.

[0039] The disclosed devices take advantage of several revelations based on the abovereferenced direct measurements. First, the magnitude of spontaneous polarization in wurtzite materials exceeds previous estimates by an order of magnitude. Second, contrary to conventional belief, the orientation of spontaneous polarization aligns with +c instead of -c direction. Third, and consequently, piezoelectric polarization due to tensile strain now reduces, rather than enhances, the total polarization. These revelations may be used in a variety of ways in nitride-based devices and systems, including 2DCGs, internal fields, surface band bending, photocurrents, and polarization doping, to name a few.

[0040] The new understanding of polarization in wurtzite materials may be applied via lateral polarity heterostructures and heterostructures that are relaxed, either partially or fully. Such structures are examples of useful application of the revised polarization constants. Non-electrical experimental methods, such as scanning probe microscopy and differential phase contrast imaging, may be used to further illuminate the intrinsic polarization characteristics of the nitride semiconductor materials.

[0041] The new understanding of polarization may be applied in example devices involving 2DCGs in an AIN / GaN system. According to the new understanding, the direction of spontaneous polarization is in the +c direction. The larger spontaneous polarization of AIN over GaN implies that the sign of the interface charge will reverse if spontaneous polarization is considered alone. Therefore, the tensile strain and corresponding piezoelectric polarization of AIN exceeds the difference in spontaneous polarization and ensures a net positive charge at the interface to support the generation of 2DEGs. This suggests that the formation of the 2DEG, and by extension, the two-dimensional hole gas (2DHG) in N-polar systems, as well as polarization doping via composition grading, may predominantly rely on piezoelectric effects.

[0042] While strain is often closely associated with local compositional variance, defects, and relaxation, the 2DEG in nitride systems is remarkably robust. This aspect of nitride systems may be applied in a wide variety of devices that exploit polarization engineering. For instance, in AIN / GaN heterostructures, because the internal parameter u of AIN is greater than that of GaN, the cumulative polarization will always be less than that of GaN when AIN is grown coherently on top of GaN. The same consideration applies to AIGaN barriers.Therefore, regardless of the Al composition, a net positive charge, and thus robust 2DEG, are generated.

[0043] Figure 3 depicts a transistor device 300 having strain-based charge carrier generation in accordance with one example. The device 300 includes a heterostructure 302 supported by a substrate 304 having a template or buffer layer 306 composed of, or otherwise including, a polar material. The template layer 306 may equivalently be considered a component of the heterostructure 302. In this example, the substrate 304 includes a template layer having a nitrogen (N) polar material. The heterostructure 302 includes channel and barrier layers 308, 310 with different in-plane lattice constants such that the channel layer 308 is under compressive strain. The channel and barrier layers 308, 310 may be in contact with one another as shown in Figure 3.

[0044] The channel layer 308 is supported by the barrier layer 310. In the example of Figure 3, the channel layer 308 is grown coherently on top of the barrier layer 310. The channel layer 308 may be composed of, or otherwise include, GaN and / or another wurtzite semiconductor material. The barrier layer 310 may be composed of, or otherwise include, ScAIGaN and / or another wurtzite semiconductor material. When the substrate 304 is bipolar, the spontaneous polarization of the layers points downward. As the barrier (e.g., ScAIGaN) layer 310 has a smaller in-plane lattice constant than the channel (e.g., GaN) layer 308, the channel (e.g., GaN) layer 308 is under compressive strain, resulting in larger total polarization of the GaN layer 308 compared to the ScAIGaN layer 310, resulting in positive net charge at the interface therebetween. Such positive net charge induces a high density of two-dimensional electron gases, which may then be used to realize, for instance, a high-electron-mobility transistor (HEMT) channel.

[0045] The channel layer 308 may be undoped (e.g., not intentionally doped). For instance, the channel layer 308 may be composed of, or otherwise include, an intrinsic GaN layer.

[0046] The compositions of the barrier and channel layers 310, 308 may differ from the example shown. For instance, the barrier layer 310 may be composed of, or otherwise include, ScAIN or ScAIGaN, YAIN or YAIGaN, AIGaN, InAIN or InAIGaN, BAIN or BAIGaN, AIN or AIGaN. The channel layer 308 may be composed of, or otherwise include, AIGaN or GaN.

[0047] The substrate 304 may have a uniform or composite construction. For instance, the substrate 304 may include a template or buffer layer of N-polar AIN or N-polar GaNsupported by a bulk substrate composed of, or otherwise including, silicon, SiC, or sapphire. Alternatively, the substrate 304 may be or include a bulk GaN or AIN substrate.

[0048] The device 300 may include a number of other layers or other structures. For instance, in the example of Figure 3, the device 300 has a gate electrode 312 and a gate dielectric layer 314 disposed between the gate electrode 312 and the channel layer 308.

[0049] Figure 4 depicts a transistor device 400 having strain-based charge carrier generation in accordance with another example. The device 400 may have a number of features in common with the example of Figure 3. For instance, the device 400 includes a heterostructure 402 supported by a substrate 404 having a template layer 406 composed of, or otherwise including, a polar material. The heterostructure 402 includes channel and barrier layers 408, 410 with different in-plane lattice constants such that the channel layer 408 is under compressive strain. In this example, however, the template layer 406 is composed of, or otherwise includes, a metal (M) polar material.

[0050] With the M-polar substrate 404, the spontaneous polarization of the barrier and channel layers 408, 410 points upward. As the barrier layer 410 has a smaller in-plane lattice constant than the channel layer 408, the channel layer 408 is under compressive strain, resulting in larger total polarization of the channel layer 408 compared to the barrier layer 410, resulting in negative net charge at the interface therebetween. Such negative net charge induces a high density of two-dimensional hole gases, which may then be used to form a p-channel of the transistor device 400.

[0051] The composition and other characteristics of the substrate 404, the heterostructure 402, and other layers or structures of the device 400 may vary as described above in connection with the example of Figure 3.

[0052] Figure 5 depicts a heterostructure 500 having strain-based polarization in accordance with one example. The strain-based polarization is realized via a strain layer 502 disposed or embedded in one of the layers of the heterostructure 500. For example, a barrier layer 504 of the heterostructure 500 may have the strain layer 502 disposed or embedded therein. The strain layer 502 has a different lattice constant than the barrier layer 504 to establish lateral strain (e.g., tensile strain) in the barrier layer 504.

[0053] The lattice constant of the strain layer 502 may be significantly larger or smaller than that of the barrier layer 504. For instance, the lattice constants may differ by less than about 20%. The difference may be used to tune the piezoelectric polarization in the barrier layer 504, thereby dramatically tuning the density and mobility of the 2DEG formed thereby. Accordingly, a wide variety of device applications may be accommodated.

[0054] In some cases, one or more monolayers (e.g., less than 2 nm) may be embedded in the barrier layer 504, causing a local tensile strain to the barrier layer 504. Such tensile strain reduces the polarization of the barrier layer 504, and enhances the channel charge carrier concentration, which may be used to improve the power capacity of a transistor device having the heterostructure 500.

[0055] The strain layer 502 may be composed of, or otherwise include, ScN or InN. But the composition of the strain layer 502 may vary in other cases. For instance, the strain layer 502 may be composed of, or otherwise include, ScN, BN, MgsN2, GaN or InN.

[0056] The barrier layer 504 may be composed of, or otherwise include, AIGaN or AIN. But the composition of the barrier layer 504 may vary in other cases. For instance, the barrier layer 504 may be alternatively or additionally composed of, or otherwise include, one or more other wurtzite semiconductor materials, such as ScAIN or ScAIGaN, YAIN or YAIGaN, AIGaN, In AIN or InAIGaN, BAIN or BAIGaN, AIN or AIGaN.

[0057] A channel layer 506 of the heterostructure 500 may be composed of, or otherwise include, one or more wurtzite semiconductor materials, including, for instance, AIGaN or GaN.

[0058] In the example of Figure 5, the heterostructure 500 is supported by a substrate 508 that includes a template layer composed of, or otherwise including, an M-polar material. The substrate 508 may have a composition and / or other characteristics in common with one or more of the examples described herein. For instance, the substrate 508 may include a template layer composed of M-polar AIN or M-polar GaN and a bulk substrate composed of silicon, SiC, or sapphire. Alternatively, the substrate 508 may include a bulk GaN or AIN substrate.

[0059] Figure 6 depicts an example transistor device 600 that includes the heterostructure 500 of Figure 5. In this example, the barrier layer 504 having the embedded strain layer 502 is disposed between a gate electrode 602 and the channel layer 506 as shown.

[0060] Figure 7 depicts a diode device 700 having a wurtzite semiconductor structure 702 supported by a polar substrate 704 in accordance with one example. The wurtzite semiconductor structure 702 has an in-plane lattice constant different from the polar substrate 704 such that the lateral strain level in the wurtzite semiconductor structure 702 changes as distance from the substrate 704 increases. Alternatively or additionally, the wurtzite semiconductor structure may have a dimensionality difference from bottom to top, thereby establishing a relaxation of the strain therein, and thus a strain gradient. As a result of the strain gradient, the wurtzite semiconductor structure 702 exhibits a polarizationgradient. The polarization gradient, in turn, leads to a three-dimensional charge carrier (e.g., electron) gas in the wurtzite semiconductor structure 702. The charge carriers may then be used for low resistance conduction between spaced apart terminals 706, 708 on the wurtzite semiconductor structure 702. A Schottky diode may thus be realized, for example.

[0061] In the example of Figure 7, the wurtzite semiconductor structure 702 may be or include an AIGaN layer grown on a substrate 704 with a smaller in-plane lattice constant than AIGaN and thus compressive strain. Therefore, the AIGaN layer 702 undergoes a slow relaxation during growth. The compressive strain thus tends to reduce from the bottom to the top, leading to a polarization gradient. When the substrate 704 is M-polar as shown, the spontaneous polarization is pointing downward, and positive net polarization charge is generated in the epilayers of the structure 702. Such positive charge helps to create bulk electrons in the structure 702 with or without the help of intentional doping, and can be harnessed to fabricate a low on-resistance Schottky diode device as shown.

[0062] The composition of the wurtzite semiconductor structure 702 may vary. For instance, the structure 702 may be composed of, or otherwise include, GaN or AIN or AIGaN, and either silicon, Ge, either doped or not.

[0063] The substrate 704 may have a composition and / or other characteristics in common with one or more of the examples described herein.

[0064] Figure 8 depicts a diode device 800 having a wurtzite semiconductor structure 802 supported by a polar substrate 804 in accordance with another example. The diode device 800 may have a number of features in common with the example of Figure 7. For instance, the wurtzite semiconductor structure 802 is supported by a substrate 804 having a template layer composed of, or otherwise including, a polar material with a different in-plane lattice constant. In this example, the polar material of the substrate 804 has a larger in-plane lattice constant than the wurtzite semiconductor material 802, leading to tensile strain therein.

[0065] In this example, the wurtzite semiconductor structure 802 is or includes an AIGaN layer grown on a substrate 804 with a larger in-plane lattice constant than the AIGaN layer. Therefore, the AIGaN layer undergoes a slow relaxation during growth. The tensile strain tends to reduce from the bottom to the top, leading to a polarization gradient. When the substrate 804 is M-polar, the spontaneous polarization is pointing downward, and negative net polarization charge is generated in the epilayers of the wurtzite semiconductor structure 802. Such negative charge helps to create bulk holes in the wurtzite semiconductor structure 802 with or without the help of intentional doping, and can be harnessed to form a low on- resistance Schottky diode device as shown.

[0066] The composition of the wurtzite semiconductor structure 802 may vary from the example shown. For instance, the semiconductor structure 802 may be composed of, or otherwise include, GaN or AIN or AIGaN with or without dopants such as Mg and Be.

[0067] In one or more of the examples described above, the lateral strain gradient may be alternatively or additionally established via the dimensionality of the heterostructure layer or other wurtzite structure. For instance, the dimensionality of the layer or structure may vary with the distance from the polar material of the substrate to establish the lateral strain gradient in the layer or structure.

[0068] The term "about" is used herein in a manner to include deviations from a specified value that would be understood by one of ordinary skill in the art to effectively be the same as the specified value due to, for instance, the absence of appreciable, detectable, or otherwise effective difference in operation, outcome, characteristic, or other aspect of the disclosed methods and devices.

[0069] The present disclosure has been described with reference to specific examples that are intended to be illustrative only and not to be limiting of the disclosure. Changes, additions and / or deletions may be made to the examples without departing from the spirit and scope of the disclosure.

[0070] The foregoing description is given for clearness of understanding only, and no unnecessary limitations should be understood therefrom.

Claims

What is Claimed is:

1. A device comprising: a substrate comprising a template layer, the template layer comprising a polar material; and a heterostructure supported by the substrate and in contact with the polar material, the heterostructure comprising a barrier layer and a channel layer; wherein: the barrier layer comprises a first wurtzite semiconductor material; the channel layer comprises a second wurtzite semiconductor material; and the first and second wurtzite semiconductor materials have different in-plane lattice constants such that the channel layer is under lateral strain.

2. The device of claim 1 , wherein the lateral strain is compressive.

3. The device of claim 1 , wherein the polar material of the substrate is nitrogen-polar.

4. The device of claim 1 , wherein the polar material of the substrate is metal-polar.

5. The device of claim 1 , wherein: the substrate comprises a bulk substrate; and the template layer is supported by the bulk substrate.

6. The device of claim 1 , wherein the polar material is a Ill-nitride semiconductor.

7. The device of claim 1 , wherein the first wurtzite semiconductor material has a smaller in-plane lattice constant than the second wurtzite semiconductor material.

8. The device of claim 1 , wherein the first wurtzite semiconductor material is a rare- earth doped Ill-nitride semiconductor.

9. The device of claim 1 , wherein the second wurtzite semiconductor material is a Ill- nitride semiconductor.

10. The device of claim 1 , wherein the channel layer is supported by the barrier layer.

11. The device of claim 1 , further comprising a gate electrode and a gate dielectric layer disposed between the gate electrode and the channel layer.

12. A device comprising: a substrate comprising a template layer, the template layer comprising a polar material; and a heterostructure supported by the substrate and in contact with the polar material, the heterostructure comprising a barrier layer and a channel layer; wherein: the barrier layer comprises a first wurtzite semiconductor material; the channel layer comprises a second wurtzite semiconductor material; the heterostructure further comprises a strain layer embedded in the barrier layer; and the strain layer comprises a material with an in-plane lattice constant differing from the first wurtzite semiconductor material such that lateral strain is established in the barrier layer.

13. The device of claim 12, wherein the lateral strain is tensile strain.

14. The device of claim 12, wherein the strain layer is a monolayer.

15. The device of claim 12, wherein the strain layer has a single digit number of monolayers.

16. The device of claim 12, wherein the strain layer has a thickness less than about 2 nm.

17. The device of claim 12, wherein the in-plane lattice constant of the material of the strain layer is less than about 20% greater or lower than an in-plane lattice constant of the first wurtzite semiconductor material.

18. The device of claim 12, wherein the strain layer comprises ScN or InN.

19. The device of claim 12, wherein the barrier layer is supported by the channel layer.

20. The device of claim 12, further comprising a gate electrode and a gate dielectric layer disposed between the gate electrode and the barrier layer.

21. The device of claim 12, wherein the first wurtzite semiconductor material, the second wurtzite semiconductor material, or both the first and second wurtzite semiconductor materials are not doped.

22. A device comprising: a substrate comprising a template layer, the template layer comprising a polar material; a structure supported by the substrate and in contact with the polar material, the structure comprising a wurtzite semiconductor material; and a plurality of device terminals supported by the structure; wherein the structure has an in-plane lattice constant or dimensionality different from the polar material of the substrate to establish a lateral strain gradient in the structure such that the wurtzite semiconductor material exhibits a polarization gradient in accordance with the lateral strain gradient.

23. The device of claim 22, wherein the lateral strain gradient is oriented such that the structure is under decreasing lateral strain as a distance from the polar material of the substrate increases.

24. The device of claim 22, wherein the dimensionality of the structure varies with distance from the polar material to establish the lateral strain gradient in the structure.

25. The device of claim 22, wherein the structure is under compressive strain at the polar material.

26. The device of claim 22, wherein the structure is under tensile strain at the polar material.

27. The device of claim 22, wherein the plurality of terminals comprise first and second terminals in contact with the structure, the first and second terminals being spaced apart from one another and configured to form a Schottky diode.

28. The device of claim 22, wherein the polar material of the substrate is nitrogen-polar.

29. The device of claim 22, wherein the polar material of the substrate is metal-polar.

30. The device of claim 22, wherein the thickness of the structure is established by a set of epilayers of the wurtzite semiconductor material.

31. The device of claim 22, wherein the wurtzite semiconductor material is not doped.

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