Substrate fusion techniques

Abstract

Various examples include a substrate and an associated method for bonding a first substrate formed from a cubic material to a second substrate formed from a non-cubic material. Other examples include a method of finding a crystal face of a cubic material that is used as an epitaxial substrate for non-cubic material epitaxy. By selecting low-index crystal planes, a two-dimensional (2D) repeating pattern appears as a parallelogram, which enables epitaxy of non-cubic crystals. For example, a suitable orientation in GaP has been identified as a substrate of a [beta]-Ga2O3 [beta] plane. In other embodiments, the disclosed subject matter describes a method for determining a crystal plane of a cubic material to bond a first substrate formed from a cubic material to a second substrate formed from a non-cubic material. Other methods and techniques are also disclosed.

Description

[0001] Priority declaration

[0002] This patent application claims priority to U.S. Provisional Application Serial No. 63 / 356,842, filed on June 29, 2022, entitled “SUBSTRATE-FUSION TECHNIQUE”; the disclosure of that patent application is incorporated herein by reference in its entirety. Technical Field

[0003] The disclosed subject matter generally relates to the field of epitaxial technology used in semiconductor and related industries (eg, flat panel displays, thin film magnetic heads, etc.) More specifically, in various embodiments, the disclosed subject matter relates to substrate fusion technology associated with various types of crystalline and polycrystalline substrates. Background Art

[0004] Many engineers and researchers in the semiconductor and related industries have believed that it would not be feasible to grow epitaxial layers on substrates of different crystal structures. However, if such epitaxial technology can be established, more and more materials of various types can be grown via epitaxy using commercially available substrate materials. Commercially available substrate materials can even be based on different crystallographic orientations, such as, for example, gallium arsenide (GaAs) and silicon (Si). Being able to grow such different types of materials can increase the device functionality that semiconductor devices will be able to provide.

[0005] The various techniques described herein provide a means to address combining materials having, for example, different crystallographic orientations. Summary of the invention

[0006] This document describes, among other things, a method for finding crystal planes of a cubic material used as an epitaxial substrate for epitaxy of a non-cubic material. By selecting low-index crystal planes, a two-dimensional (2D) repeating pattern appears as a parallelogram, which enables epitaxy of a non-cubic crystal. A suitable orientation in GaP has been identified as a substrate of β-Ga2O3β planes. In other embodiments, the disclosed subject matter describes a method for determining crystal planes of a cubic material to bond a first substrate formed of a cubic material to a second substrate formed of a non-cubic material.

[0007] In various embodiments, the disclosed subject matter is a bonded substrate. The bonded substrate includes a first substrate and a second substrate. The first substrate and the second substrate include at least one set of material pairs for substrates selected from the material pairs including silicon on sapphire, gallium nitride (GaN) on sapphire, aluminum gallium indium phosphide (AlGaInP) on gallium arsenide (GaAs), aluminum gallium indium phosphide (AlGaInP) on diamond, aluminum gallium indium phosphide (AlGaInP) on iridium, and graphene on hexagonal boron nitride (hBN).

[0008] In various embodiments, the disclosed subject matter is a bonded substrate. The bonded substrate includes a first substrate formed of a cubic material and a second substrate formed of a non-cubic material. The lattice mismatch between the cubic material and the non-cubic material is less than about 1%.

[0009] In various embodiments, the disclosed subject matter is a method for determining a crystal plane of a cubic material to be used as an epitaxial substrate for epitaxy of a non-cubic material. The method includes: determining a lattice mismatch between two different materials, the cubic material and the non-cubic material; selecting a low-index crystal plane, which includes selecting a {1 kl} plane, where k is approximately equal to l, and k and l are not limited to integers, the selecting the low-index crystal plane is used to reduce the lattice mismatch; and determining a second lattice mismatch based on the selected low-index crystal plane.

[0010] In various embodiments, the disclosed subject matter is a method for determining a crystal plane of a cubic material to be used as an epitaxial substrate for epitaxy of a non-cubic material. The method includes: determining a lattice mismatch between two different materials, a cubic material and a non-cubic material; selecting a low-index crystal plane, which includes selecting a {1 kl} plane, where k is not equal to l and k is only approximately equal to l, and k and l are not limited to integers, the selecting a low-index crystal plane is used to reduce the lattice mismatch; and determining a second lattice mismatch based on the selected low-index crystal plane.

[0011] In various embodiments, the disclosed subject matter is a method for determining a crystal plane of a cubic material to bond a first substrate formed of a cubic material to a second substrate formed of a non-cubic material. The method includes: determining a lattice mismatch between two different materials, the cubic material and the non-cubic material; selecting a low-index crystal plane, which includes selecting a {1 kl} plane, where k is approximately equal to l, and k and l are not limited to integers, the selecting the low-index crystal plane is used to reduce the lattice mismatch; and determining a second lattice mismatch based on the selected low-index crystal plane.

[0012] In various embodiments, the disclosed subject matter is a method for determining a crystal plane of a cubic material to bond a first substrate formed of a cubic material to a second substrate formed of a non-cubic material. The method includes: determining a lattice mismatch between two different materials, a cubic material and a non-cubic material; selecting a low-index crystal plane, which includes selecting a {1 kl} plane, where k is not equal to l and k is only approximately equal to l, and k and l are not limited to integers, wherein the selected low-index crystal plane is used to reduce the lattice mismatch; and determining a second lattice mismatch based on the selected low-index crystal plane. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The various figures in the accompanying drawings depict only example embodiments of the present disclosure and should not be considered to limit the scope thereof.

[0014] Figure 1 An example of a unit cell of a β-gallium oxide (β-Ga2O3) crystal structure as used in accordance with various embodiments of the disclosed subject matter is shown;

[0015] Figure 2 An exemplary relationship between the surface orientation of a Ga2O3 substrate and the homoepitaxial growth rate for various crystal orientations is shown;

[0016] Figure 3A An example of cutting a unit cube of a Ga2O3 crystal to produce rhombus planes is shown;

[0017] Figure 3B β plane of a Ga2O3 crystal according to various exemplary embodiments of the disclosed subject matter is shown. Figure 3A The resulting rhombus plane;

[0018] Figure 4A An example of cutting a unit cube of a gallium phosphide (GaP) crystal to produce parallelogram planes is shown;

[0019] Figure 4B FIG. 1 shows a (112) plane of a GaP crystal close to various exemplary embodiments of the disclosed subject matter. Figure 4A The resulting parallelogram plane of ; and

[0020] Figure 5 Various embodiments according to the disclosed subject matter are shown. Figure 3B The β plane of Ga2O3 crystal and Figure 4B Comparison of the (112) plane of GaP crystal. DETAILED DESCRIPTION

[0021] The disclosed subject matter is directed to heteroepitaxial techniques associated with various types of crystalline and polycrystalline substrates. The disclosed subject matter described illustrates suitable crystallographic orientations of cubic materials for monoclinic crystal growth and substrate fusion, which can be incorporated into various types of semiconductor integrated circuit devices. Although certain specific examples are provided herein to better describe various embodiments, the disclosed subject matter can be easily extended to general materials not explicitly discussed herein.

[0022] Furthermore, the techniques described herein may be applied to both epitaxial techniques and various types of substrate fusion techniques (eg, wafer fusion or wafer bonding).

[0023] In homoepitaxy, the growth layers are made of the same material as the substrate, whereas in heteroepitaxy, the growth layers are made of a different material than the substrate. Heteroepitaxy is therefore a special case of heterogeneous nucleation, in which there is a clear crystallographic relationship between the orientation of the crystals in the substrate and the orientation of the crystals in the material deposited on this substrate. Heteroepitaxy is therefore a special type of epitaxy performed with materials that are different from each other.

[0024] In heteroepitaxy, crystalline films are grown on a crystalline substrate or film of a different material. This technique is often used to grow crystalline films of materials for which crystals cannot otherwise be obtained, and to make integrated crystalline layers of different materials. Examples include silicon on sapphire, gallium nitride (GaN) on sapphire, gallium arsenide (GaAs) or aluminum gallium indium phosphide (AlGaInP) on diamond or iridium, and graphene on hexagonal boron nitride (hBN).

[0025] Heteroepitaxy occurs when a film with a different composition and / or crystal structure than the substrate is grown. In this case, the amount of strain in the film is determined by the lattice mismatch ε, where

[0026]

[0027] And a f and a s is the lattice constant of the film and the lattice constant of the substrate on which the film is grown. In various embodiments, the film and substrate may have similar lattice spacings. However, as described in more detail below, the film and substrate may have significantly different coefficients of thermal expansion (CTE).

[0028] Cubic semiconductor materials and hexagonal semiconductor materials (e.g., silicon (Si), gallium arsenide (GaAs), gallium nitride (GaN), etc.) have been used in semiconductor and related industries for many years. Various types of materials are expected to be used in the future, but various disadvantages (such as problems with poor thermal conductivity) are currently encountered, as described in more detail below. However, such expected future materials include semiconductor materials with less common crystal structures (e.g., gallium oxide (Ga2O3)). Ga2O3 includes electrical property advantages such as ultra-wide bandgap and high breakdown electric field as semiconductor materials. Traditional epitaxy for making device structures is: homoepitaxial (wherein the epitaxial substrate includes the same material as the growth material (e.g., Si film formed on a Si substrate)); or heteroepitaxial, which uses an epitaxial substrate with the same or similar crystal structure as the material grown on those substrates (e.g., cubic GaAs is used for cubic aluminum indium gallium phosphide (AlInGaP) epitaxial layers, hexagonal sapphire is used for hexagonal GaN, etc.). However, for various semiconductor materials, heteroepitaxial using substrates with different crystal structures has not been considered.

[0029] Gallium phosphide (GaP), the phosphide of gallium, is a compound semiconductor material with an indirect band gap of 2.24 eV at room temperature. Gallium phosphide is used in the manufacture of low-cost red, orange, and green light emitting diodes (LEDs) with low to medium brightness levels.

[0030] Gallium trioxide (Ga2O3); β-Ga2O3 is an emerging ultra-wide bandgap (bandgap of 4.85 eV) transparent semiconductor oxide. β-Ga2O3 crystals exhibit interesting scientific properties. Depending on the growth conditions, they can be insulators or conductors. Therefore, Ga2O3 semiconductors are expected to be an option for the next generation of high-power devices. Research level devices have been demonstrated via homoepitaxial growth using Ga2O3 substrates. However, the main disadvantage of known Ga2O3 crystals is their poor thermal conductivity, which limits device performance. The thermal conductivity and coefficient of thermal expansion (CTE) are shown in Table I below.

[0031] Material Thermal conductivity [W / m·K] CTE[ppm] <![CDATA[β-Ga2O3]]> 12 4-8 GaP 110 4.5 Si 130 2.6 sapphire 46 8 AlN(ceramic) 300 5 <![CDATA[β-Ga2O3 (ceramics)]]> 29 6

[0032] Table I, Material Thermal Properties

[0033] Since Ga2O3 has a low thermal conductivity (12 W / m·K) as compared to many common semiconductor materials (e.g., GaP at 110 W / m·K, Si at 130 W / m·K, or AlN at 300 W / m·K), researchers have considered Ga2O3 to be a poor choice for various integrated circuit devices, especially high power devices, due to its poor thermal conductivity. Although devices have been homoepitaxially grown on the β plane of Ga2O3, there is a general concern that Ga2O3 (especially using Ga2O3 as an epitaxial substrate) is a poor thermal conductor. Therefore, despite the electrical properties of Ga2O3 as a semiconductor material with an ultra-wide bandgap and high breakdown electric field, there is a lack of consideration of integrated circuit devices for Ga2O3.

[0034] As disclosed herein, the use of Ga2O3 can be considered under various conditions. For example, in various embodiments, if the deposition of the grown film is thin, the Ga2O3 material can be used in an integrated circuit device. After reading and understanding the disclosed subject matter, one of ordinary skill in the art will recognize how the term "thin" should be defined for a given integrated circuit device. In various embodiments, Ga2O3 can be used along a specific crystal plane.

[0035] Figure 1 An example of a unit cell 100 of a β-gallium oxide (β-Ga2O3) crystal structure as used in accordance with various embodiments of the disclosed subject matter is shown. Ga2O3 has a monoclinic lattice. The monoclinic system is one of the structural categories into which crystalline solids can be classified. A crystal in this system refers to three axes of unequal lengths - such as a, b, and c - where a is perpendicular to b and c, but b and c are not perpendicular to each other. In crystallography, the monoclinic system is one of seven crystal systems. The crystal system is described by three vectors. In the monoclinic system, the crystals are described by vectors of unequal lengths, just as in the orthorhombic system. They form a rectangular prism with a parallelogram as its base. Therefore, two pairs of vectors are perpendicular (intersecting at right angles), while the third pair of vectors forms an angle other than 90°.

[0036] In the triclinic system, the crystals are described by vectors of unequal length, just as in the orthorhombic system. Furthermore, the angles between these vectors must all be different and cannot include 90°.

[0037] Reference again Figure 1 , and for the unit cell 100 shown, the lattice constants and corresponding angles are shown in Table II below.

[0038]

[0039] Table II, Lattice constants of β-Ga2O3

[0040] Furthermore, among possible epitaxial orientations, the {0 1 0} orientation (β-plane) has been found to have the advantage of a fast epitaxial growth rate.

[0041] For example, now refer to Figure 2 , graph 200 shows an exemplary relationship between the surface orientation of a Ga2O3 substrate and the homoepitaxial growth rate (in nm / hour) for various crystal orientations as a function of the angle between the substrate surface and the (100) plane.

[0042] As described above, growing epitaxial layers on substrates of different crystal structures has been considered unfeasible. Therefore, no attempts have been made to perform epitaxy on substrates of different crystal structures, particularly for the commercialization of devices made from such different materials. However, as disclosed herein, such epitaxy techniques are established, and various additional materials can be epitaxially formed using, for example, commercially available (but in different crystallographic orientations) substrate materials (such as GaAs and Si). Using these techniques can improve the level of device functionality of semiconductor devices.

[0043] In the example of Ga2O3 above, and with continued reference to Table I, the poor thermal conductivity of Ga2O3 is inherent. Therefore, the disclosed subject matter describes the use of heteroepitaxially grown device structures. As described in more detail below, because the prevalent growth plane is the parallelogram β-plane, it is not easy to find a good thermally conductive substrate with a matching lattice.

[0044] As described above, growing epitaxial layers on substrates of different crystal structures has been considered unfeasible. Therefore, no attempts have been made to perform epitaxy on substrates of different crystal structures, particularly for the commercialization of devices made from such different materials. However, as disclosed herein, such epitaxy techniques are established, and various additional materials can be epitaxially formed using, for example, commercially available (but in different crystallographic orientations) substrate materials (such as GaAs and Si). Using these techniques can improve the level of device functionality of semiconductor devices.

[0045] In the example of Ga2O3 above, and with continued reference to Table I, the poor thermal conductivity of Ga2O3 is inherent. Therefore, the disclosed subject matter describes the use of heteroepitaxially grown device structures. As described in more detail below, because the prevalent growth plane is the parallelogram β-plane, it is not easy to find a good thermally conductive substrate with a matching lattice.

[0046] The disclosed subject matter provides a method for finding crystal planes of cubic materials used as epitaxial substrates for epitaxy of non-cubic materials. By selecting low-index crystal planes, two-dimensional (2D) repeating patterns appear as parallelograms, which enables epitaxy of non-cubic crystals. The appropriate orientation in GaP has been identified as a substrate of β-Ga2O3β planes.

[0047] Figure 3A An example of cutting a unit cube 300 of Ga2O3 crystal to produce rhombus-shaped planes is shown. Figure 3A When cut in this manner as shown in FIG. , the cut surface of the crystal has a rhombus shape (see reference below). Figure 3B Such a surface allows rhombus crystals to grow in their low index planes, assuming the lattice constants are approximately matched. Matching the lattice constants depends on the choice of substrate and epitaxial material. Rhombus is the primitive unit cell of the hexagonal pattern, so by approximately matching the lattice constants, such a plane can also allow hexagonal crystals to grow in their low index planes. The lattice mismatch of various heterogeneous systems is shown below with reference to Table V. As indicated, the material combination of β-Ga2O3 and GaP can have a lattice mismatch of 1.0% or less.

[0048] Figure 3B β plane of a Ga2O3 crystal according to various exemplary embodiments of the disclosed subject matter is shown. Figure 3A The resulting diamond-shaped plane 330.

[0049] Figure 4A A unit cube 400 of a gallium phosphide (GaP) crystal is shown cut to produce parallelogram planes 430 (see Figure 4B ) example. Figure 4B FIG. 1 shows a (112) plane of a GaP crystal close to various exemplary embodiments of the disclosed subject matter. Figure 4A The resulting parallelogram plane 430. Assuming the lattice constants are approximately matched, the surface of the parallelogram plane 430 allows triclinic crystals to grow in their low index planes. Triclinic crystals are the lowest symmetry of crystals. The {2 2 1} planes of cubic crystals (such as GaP) are close to parallelogram plane 430.

[0050] Therefore, assuming that the lattice constants are approximately matched, the method of the disclosed subject matter for finding a substrate can be applied to any crystal.As one of ordinary skill in the art will recognize, after reading and understanding the disclosed subject matter, common crystallographic knowledge can be used to find the Miller index of the cutting orientation.

[0051] Figure 5 Various embodiments according to the disclosed subject matter are shown. Figure 3B The β plane (diamond plane 330) of the Ga2O3 crystal and Figure 4B430. Referring to Tables III and IV below, approximate lattice constants and other material information for the two planes 330, 430 are shown. The y0 and z0 items in Table IV are the cubic coordinates of the GaP plane that satisfies the lattice match with the β-Ga2O3 plane.

[0052]

[0053] Table III

[0054]

[0055] Table IV

[0056] For the Ga2O3 example, the disclosed subject matter indicates that the [112.6] orientation of the GaP lattice matches the β plane of β-Ga2O3 with less than 1% mismatch, as shown in the following Table V. Therefore, heteroepitaxy of β-Ga2O3 on thermally conductive GaP becomes feasible.

[0057] Material combination Lattice mismatch [%] GaN on Sapphire 16 AlInGaP(GaAs) and GaP 3.6 GaN and Si 17 <![CDATA[β-Ga2O3 and GaP]]> 1.0 or less

[0058] Table V – Lattice mismatch of various heterogeneous systems

[0059] As disclosed herein, growth of monoclinic crystals in a non-rectangular orientation may be provided as an epitaxial process on a non-cubic material, considering a substrate comprising:

[0060] (1) {1 kl} plane, where k = l (or where both indices are approximately equal to each other), and k and l are not limited to integers. For the sphalerite structure, both "A" and "B" orientations are included when considering this plane.

[0061] (2) The adjacent plane of (1) above, which includes the adjacent plane of {1 k-δ1 l-δ2}, wherein δ1 and δ2 include small values. The small values ​​may include, for example, values ​​of about 0.0 to about 0.1. These small values ​​including adjacent planes are generally referred to as "miscuts" or "offcuts". In various embodiments, the values ​​of δ1 and δ2 are approximately equal to each other.

[0062] (3) The adjacent plane of (1) or (2) above, where k≠l, but k~l (eg, cotangent). In various embodiments, k~l can be characterized as the difference between k and l being within a value of approximately 0.1.

[0063] (4) In various embodiments, a low temperature (LT) nucleation layer for upcoming crystal growth may be utilized to assist each of the growth considerations shown above. In an embodiment, the low temperature growth may be similar to the growth of GaN on sapphire. For example, in an embodiment including GaN on sapphire, low temperature represents a temperature range from about 450°C to about 650°C. Typically, low temperature may be considered to be about 350°C lower than the normal growth temperature used to obtain single crystal semiconductor materials.

[0064] As disclosed herein, growth of crystals in non-rectangular orientation (not necessarily monoclinic) may be provided as an epitaxial process on non-cubic materials, given a substrate comprising:

[0065] (1) {1 kl} plane, where k and l are not limited to integers. For the sphalerite structure, both the "A" and "B" orientations are included when considering this plane.

[0066] (2) In various embodiments, a low temperature (LT) nucleation layer for the upcoming crystal growth may be utilized to assist the growth considerations presented above. In embodiments, the low temperature growth may be similar to the growth of GaN on sapphire.

[0067] The disclosed subject matter described herein can be readily applied to various types of substrate fusion techniques (e.g., wafer fusion or wafer bonding). Substrate fusion of monoclinic device structures in non-rectangular orientations can be provided on cubic material substrates, considering substrates including:

[0068] (1) {1 kl} plane, where k = l (or approximately equal to l), and k and l are not limited to integers. For the sphalerite structure, both the "A" and "B" orientations are included when considering this plane.

[0069] (2) The neighboring planes of (1) above, which include the neighboring planes of {1 k-δ1 l-δ2}, where δ1 and δ2 include small values. These small values ​​of the neighboring planes are often called "mistangents" or "cotangents".

[0070] (3) The adjacent plane of (1) or (2) above, where k≠l, but k~l (e.g., cotangent).

[0071] As described herein, substrate bonding of device structures in non-rectangular orientations can be provided on cubic material substrates, considering substrates comprising:

[0072] (1) {1 kl} plane, where k and l are not limited to integers. For the sphalerite structure, both the "A" and "B" orientations are included when considering this plane.

[0073] As described herein, the disclosed subject matter provides a method for finding crystal planes of cubic materials used as epitaxial substrates for epitaxy of non-cubic materials. By selecting low-index crystal planes, two-dimensional (2D) repeating patterns appear as parallelograms, which enables epitaxy of non-cubic crystals. The appropriate orientation in GaP has been identified as a substrate of β-Ga2O3β planes.

[0074] As used herein, the term "or" may be interpreted as meaning inclusion or exclusion. In addition, based on reading and understanding the disclosure provided, one of ordinary skill in the art will understand other embodiments. In addition, one of ordinary skill in the art will readily understand that various combinations of the techniques and examples provided herein may be applied in various combinations.

[0075] Throughout this specification, multiple instances may implement components, operations or structures described as single instances. Although each operation is shown and described as a separate operation, one or more of each operation may be performed simultaneously, and unless otherwise stated, it is not required that the operation must be performed in the order shown. The structure and function presented as a separate component in the example configuration may be implemented as a combined structure or component. Similarly, the structure and function presented as a single component may be implemented as a separate component. These and other variations, modifications, additions and improvements fall within the scope of the subject matter described herein.

[0076] Furthermore, although not explicitly shown, it will be appreciated by those skilled in the art that each of the various arrangements, quantities, and element numbers may vary (e.g., specific types of elemental and compound materials). Furthermore, each of the examples shown and described herein represents only one possible configuration and should not be considered to limit the scope of the present disclosure.

[0077] Although various embodiments are discussed separately, these separate embodiments are not intended to be considered independent techniques or designs. As described above, each of the various parts can be interrelated, and each can be used alone or in combination with other embodiments discussed herein. For example, although various embodiments of operations, systems, and processes have been described, these methods, operations, systems, and processes can be used alone or in various combinations.

[0078] Therefore, as will be clear to those of ordinary skill in the art, many modifications and variations may be made after reading and understanding the disclosure provided herein. Functionally equivalent methods and devices (except those listed herein) within the scope of the present disclosure will be clear to those skilled in the art from the foregoing description. Portions and features of some embodiments may be included in portions and features of other embodiments, or replace portions and features of other embodiments. Such modifications and variations are intended to fall within the scope of the appended claims. Therefore, the present disclosure will only be limited by the terms of the appended claims and the full scope of equivalents authorized by such claims. It should also be understood that the terms used herein are only for the purpose of describing specific embodiments and are not intended to be restrictive.

[0079] The abstract of the present disclosure is provided to allow the reader to quickly ascertain the nature of the technical disclosure. The abstract is submitted with the understanding that it will not be used to interpret or limit the claims. In addition, in the foregoing detailed description, it can be seen that various features can be combined together in a single embodiment for the purpose of simplifying the present disclosure. This method of disclosure should not be interpreted as limiting the claims. Therefore, the following claims are hereby incorporated into the detailed description, with each claim acting as a separate embodiment by itself.

[0080] The description provided herein includes illustrative examples, devices, and apparatuses embodying various aspects of the matters described in this document. In this description, for the purpose of explanation, many specific details are set forth in order to provide an understanding of the various embodiments of the matters discussed. However, it will be apparent to one of ordinary skill in the art that various embodiments of the disclosed subject matter can be implemented without these specific details. In addition, well-known structures, materials, and techniques are not shown in detail to avoid confusion with the various illustrated embodiments. As used herein, the terms "approximately," "approximately," and "substantially" may refer to values ​​within ±10% of a given value or range of values, for example.

[0081] The following numbered examples are specific embodiments of the disclosed subject matter.

[0082] Example 1: In an exemplary embodiment, the disclosed subject matter is a bonded substrate. The bonded substrate includes a first substrate formed of a cubic material and a second substrate formed of a non-cubic material. The first substrate has a low-index crystal plane, the low-index crystal plane having a {1 kl} plane, where k is approximately equal to l, and k and l are not limited to integers.

[0083] Example 2: The bonded substrate of Example 1, wherein the lattice mismatch between the first substrate and the second substrate is less than about 1%.

[0084] Example 3: A bonding substrate according to any of the preceding examples, wherein the first substrate and the second substrate include at least one set of material pairs selected from the following material pairs: silicon on sapphire, gallium nitride (GaN) on sapphire, aluminum gallium indium phosphide (AlGaInP) on gallium arsenide (GaAs), aluminum gallium indium phosphide (AlGaInP) on diamond, aluminum gallium indium phosphide (AlGaInP) on iridium, and graphene on hexagonal boron nitride (hBN).

[0085] Example 4: The bonded substrate according to any one of the preceding examples, wherein at least the first substrate includes a semiconductor material having a crystal structure formed of gallium oxide (Ga2O3).

[0086] Example 5: The bonded substrate of any of the preceding examples, wherein the lattice mismatch between the two different materials of the cubic material and the non-cubic material is less than about 1%.

[0087] Example 6: A bonded substrate according to any of the preceding examples, wherein at least one of the first substrate and the second substrate is formed by a low-index crystal plane, wherein a two-dimensional (2D) repeating pattern is presented as a parallelogram, thereby achieving additional epitaxy of a non-cubic crystal.

[0088] Example 7: In an exemplary embodiment, the disclosed subject matter is a method for bonding a first substrate formed of a cubic material to a second substrate formed of a non-cubic material. The method includes: determining a crystal plane of the cubic material; determining a lattice mismatch between two different materials of the cubic material and the non-cubic material; selecting a low-index crystal plane, which includes selecting a {1 kl} plane, where k is not equal to l and k is only approximately equal to l, and k and l are not limited to integers, wherein the selected low-index crystal plane is used to reduce the lattice mismatch to less than about 1%; and determining a second lattice mismatch based on the selected low-index crystal plane.

[0089] Example 8: The method of Example 7 further includes determining a neighboring plane similar to the low-index crystal plane, the neighboring plane comprising {1 k-δ1 l-δ2}, wherein δ1 and δ2 comprise small values.

[0090] Example 9: The method of Example 8, wherein the small value is in the range of about 0.0 to about 0.1.

[0091] Example 10: The method of Example 8, wherein the values ​​of δ1 and δ2 are approximately equal to each other.

[0092] Example 11: The method of any one of Examples 7 to 10, wherein both "A" and "B" orientations of the zinc blende structure are included when selecting the low-index crystal plane.

[0093] Example 12: The method according to any one of Examples 7 to 11 further includes forming a low temperature (LT) nucleation layer on at least one of the first substrate and the second substrate before forming the subsequent epitaxial layer.

[0094] Example 13: In an exemplary embodiment, the disclosed subject matter is a bonded substrate. The bonded substrate includes a first substrate and a second substrate. The first substrate and the second substrate include at least one set of material pairs for substrates selected from the material pairs including silicon on sapphire, gallium nitride (GaN) on sapphire, aluminum gallium indium phosphide (AlGaInP) on gallium arsenide (GaAs), aluminum gallium indium phosphide (AlGaInP) on diamond, aluminum gallium indium phosphide (AlGaInP) on iridium, and graphene on hexagonal boron nitride (hBN).

[0095] Example 14: The bonded substrate of Example 13, wherein the lattice mismatch between the first substrate and the second substrate is less than about 1%.

[0096] Example 15: A bonded substrate according to any one of Example 13 or Example 14, wherein the first substrate has a low-index crystal plane having a {1 kl} plane, where k is approximately equal to l, where k and l are not limited to integers.

[0097] Example 16: A bonded substrate according to any one of Examples 13 to 15, wherein at least the first substrate includes a semiconductor material having a crystal structure formed of gallium oxide (Ga2O3).

[0098] Example 17: The bonded substrate of any one of Examples 13 to 16, wherein the lattice mismatch between the two different materials of the cubic material and the non-cubic material is less than about 1%.

[0099] Example 18: A bonded substrate according to any one of Examples 13 to 17, wherein at least one of the first substrate and the second substrate is formed by a low-index crystal plane, wherein a two-dimensional (2D) repeating pattern appears as a parallelogram, thereby achieving additional epitaxy of a non-cubic crystal.

Claims

1. A bonding substrate, comprising: a first substrate formed of a cubic material, the first substrate having low-index crystal planes, the low-index crystal planes having {1kl} planes, where k is approximately equal to l, where k and l are not limited to integers; and A second substrate is formed of a non-cubic material. 2 . The bonded substrate of claim 1 , wherein a lattice mismatch between the first substrate and the second substrate is less than about 1%.

3. The bonding substrate according to claim 1, wherein the first substrate and the second substrate comprise at least one set of material pairs selected from the following material pairs: silicon on sapphire, gallium nitride (GaN) on sapphire, aluminum gallium indium phosphide (AlGaInP) on gallium arsenide (GaAs), aluminum gallium indium phosphide (AlGaInP) on diamond, aluminum gallium indium phosphide (AlGaInP) on iridium, and graphene on hexagonal boron nitride (hBN). 4 . The bonded substrate according to claim 1 , wherein at least the first substrate includes a semiconductor material having a crystal structure formed of gallium oxide (Ga 2 O 3 ). 5 . The bonded substrate of claim 1 , wherein a lattice mismatch between the two different materials of the cubic material and the non-cubic material is less than about 1%. 6 . The bonded substrate according to claim 1 , wherein at least one of the first substrate and the second substrate is formed of a low-index crystal plane in which a two-dimensional (2D) repeating pattern appears as a parallelogram, thereby achieving additional epitaxy of a non-cubic crystal.

7. A method for bonding a first substrate formed of a cubic material to a second substrate formed of a non-cubic material, the method comprising: Identify crystal faces of cubic materials; Determining the lattice mismatch between two different materials, a cubic material and a non-cubic material; Selecting a low-index crystal plane, which includes selecting a {1kl} plane, where k is not equal to l and k is only approximately equal to l, and k and l are not limited to integers, the low-index crystal plane being selected to reduce the lattice mismatch to less than about 1%; and A second lattice mismatch is determined based on the selected low-index crystal plane. 8 . The method of claim 7 , further comprising determining a neighboring plane similar to the low-index crystal plane, the neighboring plane comprising {1k-δ11-δ2}, wherein δ1 and δ2 comprise small values.

9. The method of claim 8, wherein the small value is in the range of about 0.0 to about 0.

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10. The method of claim 8, wherein the values ​​of δ1 and δ2 are substantially equal to each other.

11. The method of claim 7, wherein in selecting the low-index crystal plane, both "A" and "B" orientations of the zinc blende structure are included.

12. The method of claim 7, further comprising forming a low temperature (LT) nucleation layer on at least one of the first substrate and the second substrate before forming the subsequent epitaxial layer.

13. A bonding substrate, comprising: A first substrate and a second substrate, wherein the first substrate and the second substrate include at least one set of material pairs for substrates, which are selected from the following material pairs: silicon on sapphire, gallium nitride (GaN) on sapphire, aluminum gallium indium phosphide (AlGaInP) on gallium arsenide (GaAs), aluminum gallium indium phosphide (AlGaInP) on diamond, aluminum gallium indium phosphide (AlGaInP) on iridium, and graphene on hexagonal boron nitride (hBN).

14. The bonded substrate of claim 13, wherein a lattice mismatch between the first substrate and the second substrate is less than about 1%. 15 . The bonded substrate according to claim 13 , wherein the first substrate has a low-index crystal plane, the low-index crystal plane having a {1kl} plane, wherein k is approximately equal to l, wherein k and l are not limited to integers. 16 . The bonded substrate according to claim 13 , wherein at least the first substrate includes a semiconductor material having a crystal structure formed of gallium oxide (Ga 2 O 3 ).

17. The bonded substrate of claim 13, wherein a lattice mismatch between the two different materials of the cubic material and the non-cubic material is less than about 1%.

18. The bonded substrate of claim 13, wherein at least one of the first substrate and the second substrate is formed of a low-index crystal plane in which a two-dimensional (2D) repeating pattern appears as a parallelogram, thereby achieving additional epitaxy of a non-cubic crystal.

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