Anisotropy elimination in monoclinic and triclinic crystal lattice semiconductors and composite substrates thereof

Abstract

A method of identifying an isotropic plane in an anisotropic crystal lattice comprising determining coefficients of thermal expansion for axes of the anisotropic crystal lattice, converting the CTEs into a second rank tensor, diagnalizing, determining maximum, intermediary, and minimum principle axes, determining direction spanned by maximum principle axis and minimum principle axis, such that a CTE of each of the maximum and minimum principle axes is equal to CTE of the intermediate principle axis, and calculating a surface normal between intermediate principle axis and direction, wherein the surface normal is an orientation with isotropic in-plane thermal expansion properties. A method of making a wafer with isotropic in-plane properties from an anisotropic crystal lattice comprising determining an orientation of the anisotropic crystal lattice with isotropic in-plane properties. cutting the anisotropic crystal lattice, and creating a wafer with isotropic in-plane properties. An isotropic β-galhum oxide or β-aluminum gallium oxide crystal lattice.

Description

[0001] Anisotropy Elimination in Monoclinic and Triclinic Crystal Lattice Semiconductors and

[0002] Composite Substrates Thereof

[0003] FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT

[0004] The United States Government has ownership rights in this invention. Licensing inquiries may be directed to Office of Technology Transfer. US Naval Research Laboratory, Code 1004, Washington. D.C. 20375, USA; +1.202.767.7230; techtran@nrl.navy.mil, referencing Navy Case Number 211862-US2.

[0005] REFERENCE TO RELATED APPLICATION

[0006] This application is a non-provisional of, and claims priority to and the benefits of,

[0007] United States Provisional Patent Application Number 63 / 604,242 filed on November 30, 2023.

[0008] TECHNICAL FIELD

[0009] This disclosure concerns a method of identifying an isotropic plane in an anisotropic crystal lattice.

[0010] This disclosure further teaches an approach to integrating anisotropic semiconductors with dissimilar isotropic semiconductors with the purpose of improving the combined properties of the composite wafer, e.g., improved combined thermal conductivity.

[0011] For example, identifying the crystalline orientation of P-gallium oxide that exhibits unique isotropic in-plane properties.

[0012] The method developed is applicable to any crystalline material belonging to any of the seven possible crystal systems. BACKGROUND ART

[0013] Widely recognized as a strong material candidate for next-generation power electronics due to its ultra-wide bandgap (4.6 - 4.9 eV), P-gallium oxide has an appealing high critical electric field (6 - 8 MV / cm) that makes it a competitive material compared to other wide bandgap materials such as gallium nitride and silicon carbide. Rapid strides in developing P-gallium oxide are continuously being reported in the current scientific literature with successful demonstrations towards the realization of this material’s full potential. Successful developments have pushed the gallium oxide frontier along various facets include crystal growth, epitaxy, materials properties and processing, and device engineering.

[0014] However, there are long-standing and critical fundamental challenges that have yet to be fully addressed hindering the full utilization of P-gallium oxide as a high-power electronic material.

[0015] The most pressing hindrance to P-gallium oxide power applications is efficient thermal management. The thermal conductivity of P-gallium oxide is very low ranging from 11 to 27 W / (m-K). which is one to two orders magnitude lower than Si. GaN, 4H-SiC. and diamond.

[0016] It is evident that efficient heat management during P-gallium oxide device performance requires integration with other materials with higher thermal conductivities. Thin film P- gallium oxide growth on various substrates have been demonstrated on sapphire. SiC, and diamond with high thermal boundary conductance values (thermal conductivity across the interface), but all suffer from reduction in thermal conductivity of the P-gallium oxide film due to a high density of defects. Growing on SiC or sapphire results in films with a high density of stacking faults or twin boundaries, respectively. For the case of diamond, the resulting film is polycrystalline, and grain boundaries greatly reduce the film's thermal conductivity.

[0017] Employing wafer bonding techniques, on the other hand, to integrate single crystal - gallium oxide to a high thermal conductivity material would avoid growth-related defects and enable the integration of any P-gallium oxide orientation. Furthermore, utilizing light atom ion implantation, for example, to induce exfoliation and transfer of P-gallium oxide films will achieve high-quality P- gallium oxide thin films of any orientation on a substrate without suffering from defect-induced film thermal conductivity reduction. By engineering the properties of the bonded interface, wafer bonding of P- gallium oxide can be a pathway to fabricate a heterostructure that exhibits a high interfacial thermal boundary conductance and high thermal conductivity of the film simultaneously.

[0018] Another challenge involves the high anisotropy of the coefficients of thermal expansion (CTE) of P-gallium oxide and its alloys. Depending on the direction in three- dimensional space, die expansion of P-gallium oxide in response to temperature can vary significantly.

[0019] The issue of high anisotropy of CTE in P-gallium oxide poses additional issues when P-gallium oxide is integrated with other materials to form heterojunction structures.

[0020] Heterojunctions with p-gallium oxide is a key technology' required for efficient thermal management and dissipation during device operation. Extremely low thermal conductivity of P-gallium oxide is a well-known challenge, which if not properly addressed, can lead to device degradation and even permanent device failure.

[0021] All of the current commercially available p-gallium oxide planes exhibit a high degree of in-planc CTE anisotropy.

[0022] Our previous study has shown that not only does the magnitude of thermal strain greatly fluctuate, but depending on the material P-gallium oxide is integrated with, the strain can vary in sign such that both compressive and tensile strains are present.

[0023] Having variations in both the magnitude and type of strain (compressive / tensile) in a heterojunction structure can pose severe technological limitations in implementing P-gallium oxide technology.

[0024] Herein, we demonstrate a solution to these long-standing problems. A crystallographic orientation with isotropic CTE properties will provide a promising strain management strategy7, which will broaden the application range of P-gallium oxide.

[0025] Here, we disclose the first method of identifying an isotropic plane in an anisotropic crystal lattice.

[0026] Our new method identifies a unique cry stallographic plane in P-gallium oxide that exhibits isotropic CTE properties (i.e.. uniform in-plane lateral thermal expansion) despite its bulk anisotropic properties.

[0027] We also disclose our method for finding this unique plane, which can be employed to find the isotropic plane in any crystalline material from any of the seven possible crystal systems regardless of the degree of anisotropy in its bulk properties.

[0028] Novel products are also described herein concerning an isotropic P-gallium oxide and an isotropic P-aluminum gallium oxide crystal lattice.

[0029] DISCLOSURE OF INVENTION

[0030] Description

[0031] This disclosure teaches the first method of identifying an isotropic plane in an anisotropic cry stal lattice.

[0032] Our new method identifies a unique crystallographic plane in P-gallium oxide that exhibits isotropic CTE properties (i.e., uniform in-plane lateral thermal expansion) despite its bulk anisotropic properties.

[0033] We also disclose our method for finding this unique plane, which can be employ ed to find the isotropic plane in any crystalline material from any of the seven possible crystal systems regardless of the degree of anisotropy in its bulk properties. This disclosure further teaches an approach to integrating anisotropic semiconductors with dissimilar isotropic semiconductors with the purpose of improving the combined properties of the composite wafer, e.g., improved combined thermal conductivity.

[0034] Novel products are also described herein including an isotropic P-gallium oxide and an isotropic P-aluminum gallium oxide crystal lattice.

[0035] BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The following description and drawings set forth certain illustrative implementations of the disclosure in detail, which are indicative of several exemplary ways in which the various principles of the disclosure may be carried out. The illustrated examples, however, are not exhaustive of the many possible embodiments of the disclosure. Other objects, advantages and novel features of the disclosure will be set forth in the following detailed description when considered in conjunction with the drawings.

[0037] FIGURE 1 illustrates an example of isotropic in -plane CTE.

[0038] FIGURE 2 illustrates the elimination of the anisotropic thermal strain profile by utilizing a different P-Ga2O3orientation. The surface normal of this high-index plane is parallel to the [13 31 13] direction.

[0039] FIGURE 3 illustrates a thermal strain profile. Unlike the profile with (010) P-Ga2O3, only one type of strain is present - compressive. From strictly a thermal-strain standpoint, this specific high index plane can be preferable because it can lead to a uniform in-plane strain profile.

[0040] BEST MODE FOR CARRYING OUT THE INVENTION This disclosure teaches the first method of identifying an isotropic plane in an anisotropic crystal lattice.

[0041] Our new method identifies a unique crystallographic plane in P-gallium oxide that exhibits isotropic CTE properties (i.e., uniform in-plane lateral thennal expansion) despite its bulk anisotropic properties.

[0042] We also disclose our method for finding this unique plane, which can be employed to find the isotropic plane in any crystalline material from any of the seven possible crystal systems regardless of the degree of anisotropy in its bulk properties.

[0043] This disclosure further teaches an approach to integrating anisotropic semiconductors with dissimilar isotropic semiconductors to improve the combined properties of the composite wafer, e.g., improved combined thennal conductivity.

[0044] Novel products are also described herein including an isotropic P-gallium oxide and an isotropic P-aluminum gallium oxide crystal lattice.

[0045] We solve the long-standing problems associated with the challenges involving the high anisotropy of the coefficients of thennal expansion (CTE) of P-gallium oxide.

[0046] Currently, the high anisotropy leads to device degradation and even permanent device failure.

[0047] Our invention solves these problems.

[0048] Example 1

[0049] The unique isotropic crystallographic plane in P-gallium oxide is a high index orientation with a uniform in-plane CTE equal to the intermediate CTE value of its three principle axes. This intermediate CTE value is ~6.55 x 1()-6K’1(from room temperature to

[0050] 1000 °C) based on our measurements of CTE along the lattice parameter a-, b-, and c-axes and non-orthogonal lattice parameter angle (3.

[0051] The values of the CTE along the other principle axes are —3.00 x 10’6K1and -7.80 x lO^ K1.

[0052] The directions of the three principle axes are:

[0101] (minimum CTE axis).

[0010] (maximum CTE axis), and surface normal to the (101) plane (intermediate CTE axis).

[0053] The orientation relationship of this isotropic plane is such that it has interplanar angles of: 33° with the (100) plane. 59° with the (010) plane, and 67° with the (001) plane.

[0054] The surface normal of this high -index, CTE-isotropic plane is parallel to the [13 31 13] direction.

[0055] Example 2

[0056] The methodology for finding the isotropic plane in |3-gallium oxide is as follows:

[0057] (1) convert the CTE values along the lattice parameter axes into a second rank tensor

[0058] (2) diagonalize the second rank tensor

[0059] (3) compute the three associated eigenvectors (principle axes) after diagonalization

[0060] (4) determine the direction spanned by the two minimum- and maximum -CTE principle axes such that its CTE is equal to that along the remaining third principle axis associated with the intermediate-CTE value

[0061] (5) calculate the surface normal between the intermediate-CTE principle axis and the direction found in the previous step.

[0062] The result is an orientation with isotropic in-plane thermal expansion properties.

[0063] Example 3

[0064] One of the main uses for this high-index isotropic orientation will be for strain management strategies. The isotropic orientation will be an approach to homogenizing thermal strain for 0- gallium oxide heterojunction structures during processing and device performance.

[0065] The other significant usage of this discovery is the methodology for finding the isotropic plane.

[0066] Despite the degree of bulk anisotropy a material has, we show that any material property that can be described as a second rank tensor will have some orientation with inplane isotropy.

[0067] Other second-rank-tensor properties include: thermal conductivity, stress, strain, magnetic susceptibility, and electrical permittivity.

[0068] Our discovery of the isotropic plane for 0-gallium oxide provides an untapped materials optimization pathway as well as the application of the search methodology for other low-symmetry materials.

[0069] Example 4

[0070] The Navy needs compact and efficient power systems for ship, UAV, USV, UUV, space, and radar. Ultra-wide bandgap semiconductors offer low cost power switching and >1000X performance improvement. The Navy has a primary need for very high voltage power electronic components for high density ship electrical power conversion and distribution.

[0071] Objectives of the invention: This invention teaches (1) a method of identifying an isotropic plane within an anisotropic monoclinic or triclinic crystal lattice and (2) a method and device based on composite wafers comprising wafers of isotropic plane in a monoclinic or triclinic crystal and epitaxial growth on isotropic gallium oxide substrate.

[0072] Composite wafers involve heterogeneous integration of two or more materials for engineering the properties of the interface(s). Emergent properties of the heterointerface(s) improve transport characteristics (e.g., thermal and electrical transport), mitigate material- mismatch-related issues (e.g., thermal strain from CTE). and depending on the combination of materials and crystallographic orientation create emergent properties not present in either material individually that make up the composite wafer structure.

[0073] A pinpose and usefulness of the invention includes to describe the discovery of the crystalline orientation of 0-gallium oxide that exhibits unique isotropic in-plane properties.

[0074] Reduced to practice: (1) initial annealing experiments of bonded (001) Ga C) to 4H-

[0075] SiC and (2) fabrication of high index plane Ga O samples for temperature-dependent XRD measurement of thermal expansion coefficients.

[0076] The present invention describes a method for elimination of in-plane anisotropy in anisotropic crystal lattice materials.

[0077] This approach eliminates challenges associated with thermal strain due to non-uniform coefficient of thermal expansion, which complicates processing and device operation particularly of structures with integrated anisotropic heterojunction structures.

[0078] This method provides a path forward for developing strain mitigation strategies for 0- gallium oxide heterojunctions by producing a uniform in-plane thermal strain profile.

[0079] Example 5

[0080] CTE for any material second rank tensor

[0081] Components a is determined from the CTE values along each lattice parameter axes and angles:

[0082] • CTE = 3.77 / I () l< '

[0083] • CTE = 7.80 x 106K ’

[0084] • CTE = 6.34 x 106K'

[0085] • CTE = 1.26 x 106K ’ Diagonalizing yields CTE values along the principal axes of P-Ga2O3

[0086] Find extrema and their respective directions by calculating their eigenvectors

[0087] Diagonalizing matrix -> principal axes -> min and max CTE values

[0088] Selecting an orientation whose normal is parallel to the intermediate CTE axis corresponds to an orientation with the greatest in-plane CTE variation - (101)

[0089] Some combination of the extrema CTE axes will equal to the intermediate-valued CTE principal axis -

[0171]

[0090] Intermediate-CTE-valued axis must be orthogonal to

[0171] , and consequently, the entire in-plane CTE values spaimed by these two orthogonal directions will be isotropic inplane (6.55 x 106K ’).

[0091] CTE mismatch between materials induces thermal strain at elevated temperatures.

[0092] Typically both tensile and compressive strain is present in prior art devices.

[0093] Anisotropy in thermal strain profiles poses another challenge for |}-Ga2O3heterostructures.

[0094] Our method provides information for modeling of heterointerfaces.

[0095] Thereby, our method develops mitigation strategies for thermal strain management.

[0096] Currently there are no known competitive alternatives to achieve isotropic thermal expansion properties in P-gallium oxide. A commercially available substrate with the least amount of in-plane CTE anisotropy would be the (001) orientation. However, the (001) orientation still has a large -20% variation in in-plane CTE while the isotropic orientation we have discovered has 0% variation. The challenges associated with CTE variation in p-gallium oxide have widely been recognized, but rigorous strategies involving optimizing the cry stallographic orientation had not reported prior to our discovery.

[0097] Our isotropic thermal expansion plane discovery is to-date the first-of-its-kind for P- gallium oxide, thus solving long-standing problems.

[0098] Advantages and New Features

[0099] The main new feature introduced by the present invention and discovery is the complete uniformity in thermal expansion along the in-plane lateral directions of P-gallium oxide.

[0100] The challenges associated with thermal strain due to changes in temperature during processing and device operation of heterojunction structures had not yet been addressed.

[0101] As such, our invention solves these long-standing problems.

[0102] This isotropic crystallographic plane will provide an unexplored path for developing strain management and mitigation strategies for P-gallium oxide heterojunctions by producing a uniform in-plane thermal strain profile.

[0103] For example, an advantage of the current invention is being able to anneal a bonded SiC to a Ga2Ch wafer at temperatures commensurate with those for epitaxial Ga2Os growth (600-1000 °C) and not crack the Ga2Os wafer.

[0104] We demonstrate how the thermal strain can be eliminated by switching from an anisotropic (001) GazOs wafer to an isotropic high-index plane of GazO ,.

[0105] The above examples are merely illustrative of several possible embodiments of various aspects of the present disclosure, wherein equivalent alterations and / or modifications will occur to others skilled in the art upon reading and understanding this specification and the annexed drawings. In addition, although a particular feature of the disclosure may have been illustrated and / or described with respect to only one of several implementations, such feature may be combined with one or more other features of the other implementations as may be desired and advantageous for any given or particular application. Also, to the extent that the terms "including", "includes", "having", "has", "with", or variants thereof are used in the detailed description and / or in the claims, such terms are intended to be inclusive in a manner similar to the term "comprising".

Claims

ClaimsWhat we claim is:

1. A method of identifying an isotropic plane in an anisotropic crystal lattice comprising the steps of: determining coefficients of thermal expansion (CTEs) for axes of the anisotropic crystal lattice; converting the CTEs into a second rank tensor; diagnalizing the second rank tensor; determining a maximum principle axis, a minimum principle axis, and an intermedian ■ principle axis based on the diagonalization; determining a direction spanned by the maximum principle axis and the minimum principle axis, such that a CTE of each of the maximum and minimum principle axes is equal to a CTE of the intermediate principle axis; and calculating a surface normal between the intermediate principle axis and the direction, wherein the surface normal is an orientation with isotropic in-plane thermal expansion properties.

2. The method of identifying an isotropic plane in an anisotropic crystal lattice of claim 1, wherein the crystal lattice comprises a monoclinic or triclinic crystal structure.

3. The method of identifying an isotropic plane in an anisotropic crystal lattice of claim 2. wherein the crystal lattice comprises P-gallium oxide or P-aluminum gallium oxide.

4. The method of identifying an isotropic plane in an anisotropic crystal lattice of claim 2, wherein the cry stal lattice comprises a triclinic perovskite.

5. A method of making a semiconductor wafer with isotropic in-plane second rank tensor properties (e.g., CTE) starting with a semiconductor with an anisotropic cry stal lattice comprising the steps of: determining an orientation of the anisotropic cry stal lattice with isotropic in-plane second rank tensor properties; cutting the anisotropic cry stal lattice based on the orientation of the anisotropic cry stal lattice with isotropic in-plane second rank tensor (e.g., thermal expansion coefficient) properties; and creating a semiconductor wafer with isotropic in-plane second rank tensor properties.

6. The method of making a semiconductor wafer with isotropic in-plane second rank tensor properties (e.g., CTE) starting with a semiconductor with an anisotropic crystal lattice of claim 5, wherein the determining the orientation of the anisotropic crystal lattice with isotropic in-plane thermal expansion properties comprises: determining coefficients of thermal expansion (CTEs) for axes of the anisotropic crystal lattice; converting the CTEs into a second rank tensor; diagnalizing the second rank tensor; determining a maximum principle axis, a minimum principle axis and an intermediary principle axis based on the diagonalization;determining a direction spanned by the maximum principle axis and the minimum principle axis, such that a CTE of each of the maximum and minimum principle axes is equal to a CTE of the intermediate principle axis; and calculating a surface normal between the intermediate principle axis and the direction, wherein the surface normal is the orientation with isotropic in-plane thermal expansion properties.

7. The method of making a semiconductor wafer with isotropic in-plane second rank tensor properties (e.g., CTE) starting with a semiconductor with an anisotropic crystal lattice of claim 6, wherein the crystal lattice comprises a monoclinic or triclinic crystal structure.

8. The method of making a semiconductor wafer with isotropic in-plane second rank tensor properties (e.g., CTE) starting with a semiconductor with an anisotropic crystal lattice of claim 6, wherein the crystal lattice comprises P-gallium oxide or P-aluminum gallium oxide.

9. The method of making a semiconductor wafer with isotropic in-plane second rank tensor properties (e.g., CTE) starting with a semiconductor with an anisotropic crystal lattice of claim 6, wherein the crystal lattice comprises a triclinic perovskite.

10. A semiconductor device comprising: an isotropic plane of P-gallium oxide or an isotropic plane of P-aluminum gallium oxide or an isotropic plane of a monoclinic semiconductor or an isotropic plane of a triclinic semiconductor integrated with a dissimilar isotropic crystalline semiconductor.

11. The semiconductor device of claim 10, wherein the isotropic P-gallium oxide or isotropic P-aluminum gallium oxide cry stal lattice integrated with a dissimilar crystalline material is via wafer bonding at room temperature.

12. An isotropic P-gallium oxide or an isotropic P-aluminum gallium oxide crystal lattice produced by the method of claim 5 and integrated with a semiconductor device as described in claim 10.

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