Group iii oxide temperature management

Abstract

Methods and devices that help mitigate the effects of the low thermal conductivity of Group III oxide layers are presented. A structure provides effective heat transfer and includes a Group III oxide layer. The Group III oxide layer has one or more cylindrical cavity holes, wherein each of the one or more cylindrical cavity holes has a thermally conducting material coating on the sidewalls.

Description

Docket No.: Cornell 11228-03 GROUP III OXIDE TEMPERATURE MANAGEMENT CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application Serial No. 63 / 668,060, filed July 5, 2024, entitled GROUP III OXIDE TEMPERATURE MANAGEMENT, which is incorporated herein by reference in its entirety and for all purposes. BACKGROUND

[0002] These teachings relate generally to heat removal, spreading, or dissipation for a Group III oxide layer.

[0003] For particularity, although these teachings relate to Group III oxide layers, we consider one illustrative Group III oxide layer, namely, Gallium oxide layers. Gallium oxide (Ga2O3) is a promising ultra-wide bandgap semiconductor for power electronics. Ga2O3, however, has a low thermal conductivity (15W / m K). Under real-world operating conditions, the device will heat up and cause premature device failure. Therefore, to achieve the promised performance of Ga2O3 the heat must be efficiently removed, spread, or dissipated.

[0004] Although a general solution to this problem has not been proposed, multiple approaches are being investigated.

[0005] The general strategy for cooling is to minimize the thickness of the Ga2O3substrate and then deposit a highly-conductive material on the top and / or back of the Ga2O3to spread the heat. Thinning the Ga2O3reduces the distance between the source of the heat and the high thermal conductivity heat spreader. The thinned Ga2O3also requires structural support to prevent the device from breaking during device fabrication and back-end-of-line processing. Providing structural support requires that a relatively thick, structural material be added.

[0006] SmartCut™ technology uses wafer thinning layer depositions, implantation of light ions and wafer bonding to define and transfer a thin single-crystal layer from one substrate to another (See US Patent Nos. RE 93484 and 5882987). SMARTCut™ is one common approach for realizing thinned substrates and creating a heat sink. After the heat sink is formed, additional processing may be performed to increase the surface area, i.e., etching of trenches.

[0007] Wafer bonding Ga2O3 substrates to SiC substrates, a material, which has a higher thermal conductivity than Ga2O3, has also been tried. In some instances, an interlayer is inserted between the Ga2O3 and the SiC to promote bonding. In other instances, liquid cooling has been proposed.Docket No.: Cornell 11228-03

[0008] In yet another instance, a diamond substrate and a top diamond heat spreader have been considered.

[0009] Furthermore, traditional etching of gallium oxide, such as ICP / RIE etching, can damage gallium oxide, creating surface and subsurface defects. (See Wenshen Li, Kazuki Nomoto, Zongyang Hu, Debdeep Jena, and Huili Grace Xing, Fin-channel orientation dependence of forward conduction in kV-class Ga2O3 trench Schottky barrier diodes, Applied Physics Express 12, 061007 (2019).) Recently, a low-damage Ga atomic flux-based etching process has been demonstrated, and a 1.2 µm vertical etch was obtained. (See Sushovan Dhara, Nidhin Kurian Kalarickal, Ashok Dheenan, Sheikh Ifatur Rahman, Chandan Joishi, Siddharth Rajan, β-Ga2O3 Trench Schottky Diodes by Low-Damage Ga-Flux Etching, Appl. Phys. Lett.123, 023503 (2023), which is incorporated by reference herein in its entirety and for all purposes.) Further results are not yet available.

[0010] There is a need for approaches that help mitigate the effects of the low thermal conductivity of Group III oxide layers. BRIEF SUMMARY

[0011] Methods and devices that help mitigate the effects of the low thermal conductivity of Group III oxide layers are presented hereinbelow.

[0012] In one or more instantiations, the structure of these teachings for providing effective heat transfer includes a Group III oxide layer, the Group III oxide layer having one or more substantially cylindrical cavity holes, each one of the substantially cylindrical cavity holes extending substantially through a thickness of the Group III oxide layer, each one of the substantially cylindrical cavity holes having one of a thermally conducting material coating on sidewalls of said each one of the substantially cylindrical cavity holes, or the thermally conducting material substantially filling said each one of the substantially cylindrical cavity holes or the thermally conducting material deposited throughout a length of said each one of the substantially cylindrical cavity holes and a cross sectional area of deposited thermally conducting material being smaller than a cross sectional area of said one of the substantially cylindrical cavity holes, wherein a thermal conductivity of the thermally conductive material is greater than 70 Wm−1K−1at room temperature.

[0013] In one instance, a thin film is deposited on the Group III oxide layer. The thin film can differ from the Group III oxide layer in composition or doping.

[0014] In one or more instantiations, the method of these teachings for providing efficient heat transfer for a Group III oxide layer includes forming one or more substantially cylindrical cavity holes (CCHs) in the Group III oxide layer, each one of the substantially cylindrical cavity holesDocket No.: Cornell 11228-03 extending substantially through a thickness of the Group III oxide layer, and depositing a thermally conducting material by one of (a) coating sidewalls of each one of the substantially cylindrical cavity holes with the thermally conducting material, or (b) substantially filling, by deposition, each one of the substantially cylindrical cavity holes with the thermally conducting material, or (c) depositing the thermally conducting material throughout a length of each one of the substantially cylindrical cavity holes, a cross-sectional area of deposited thermally conducting material being smaller than a cross-sectional area of one of the substantially cylindrical cavity holes, wherein a thermal conductivity of the thermally conductive material is greater than 70 Wm−1K−1at room temperature.

[0015] In one instance, a thin film is deposited on the Group III oxide layer.

[0016] A number of other instantiations are also disclosed.

[0017] For a better understanding of the present teachings, together with other and further objects thereof, reference is made to the accompanying drawings and detailed description, and its scope will be pointed out in the appended claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1A shows an initial state in an instantiation of the method of these teachings;

[0019] Figure 1B shows a first step in an instantiation of the method of these teachings;

[0020] Figure 1B1 shows a result after the first step in another instantiation of the method of these teachings;

[0021] Figure 1B2 shows a view from below of the result after the first step in the other instantiation of the method of these teachings;

[0022] Figure 1B3 shows a view from below of the result after the first step in a further instantiation of the method of these teachings;

[0023] Figure 1B4 shows a view from above for the result after the first step in the other instantiation of the method of these teachings;

[0024] Figure 1C shows another step in an instantiation of the method of these teachings and also shows an instantiation of the device of these teachings;

[0025] Figures 1D, 1D1, and 1E show structures used to elucidate an instantiation of the device and method of these teachings;

[0026] Figure 2 shows an acceptable or ideal depth of one substantially cylindrical cavity hole in an instantiation of these teachings;Docket No.: Cornell 11228-03

[0027] Figures 3A, 3B and 3C show three options available in the first step in the instantiation of the method of these teachings;

[0028] Figures 4A, 4B and 4C show illustrative variations of the diameter of and the density of the substantially cylindrical cavity holes in an instantiation of the method of these teachings;

[0029] Figures 5A, 5B, and 5C show three options available in the second step in an instantiation of the method of these teachings and also instantiations of the device of these teachings;

[0030] Figures 5D1, 5D2, and 5D3 show other configurations of the options shown in Figures 5B and 5C in instantiations of the method of these teachings and also instantiations of the device of these teachings;

[0031] Figures 6A and 6B show two possible groups of materials instantiations of the thermally conductive material used in instantiations of the method of these teachings and instantiations of the device of these teachings; and

[0032] Figure 7 shows another instantiation of the device of these teachings as a result of another instantiation of the method of these teachings. DETAILED DESCRIPTION

[0033] The following description is made for the purpose of illustrating the general principles of the present teachings and is not meant to limit the inventive concepts claimed herein. Further, particular features described herein can be used in combination with other described features in each of the various possible combinations and permutations.

[0034] As additionally used herein, the term “about,” when combined with a value, refers to ±10% of the value.

[0035] "Group III," as used herein, refers to a group of elements in the periodic table including what are now called Group 13 elements: boron (B), aluminum (Al), gallium (Ga), indium (In), thallium (Tl).

[0036] "Group III oxide," as used herein, refers include one of gallium oxide, indium oxide, combination thereof and (AlxGa1-x)2O3 or (AlxInl-x)2O3.

[0037] “Etching,” as used herein, refers to dry etching, Ga flux etching, or wet etching.

[0038] Dry etching, as used herein, refers to a form of processing used to fabricate integrated circuits, which involves a high-speed stream of glow discharge of an appropriate gas mixture being shot (in pulses) at a sample. (See, for example, www.wevolver.com / article / plasma-etching-a- comprehensive-guide-to-the-process-and-applicationsDocket No.: Cornell 11228-03

[0039] Ga flux etching is described in N.K. Kalarickal, A. Fiedler, S. Dhara, H.-L. Huang, A.F.M.A.U. Bhuiyan, M.W. Rahman, T. Kim, Z. Xia, Z.J. Eddine, A. Dheenan, M. Brenner, H. Zhao, J. Hwang, and S. Rajan, Planar and 3-dimensional damage free etching of 1 / 4-Ga2O3 using atomic gallium flux, Appl. Phys. Lett.119, 123503 (2021), which is incorporated by reference herein in its entirety and for all purposes.

[0040] “Focused ion beam”, which uses a focused beam of ions, as used herein, is a technique used particularly in the semiconductor industry for site-specific deposition and ablation of materials.

[0041] “Thickness of the Group III oxide layer,” as used herein, refers to the distance between a first surface of the Group III oxide layer, on which thin films can be deposited, and a second surface of the Group III oxide layer, the second surface located away from the first surface.

[0042] In one or more instantiations, the method of these teachings for providing efficient heat transfer for a Group III oxide layer includes forming a one or more substantially cylindrical cavity holes (CCHs) in the Group III oxide layer, each one of the substantially cylindrical cavity holes extending substantially through a thickness of the Group III oxide layer. The method of these teachings also includes depositing, into each of the substantially cylindrical cavity holes, a thermally conducting material by one of : (a) coating sidewalls of each one of the substantially cylindrical cavity holes with the thermally conducting material, or (b) filling, by deposition, said each one of the substantially cylindrical cavity holes with the thermally conducting material, or (c) depositing the thermally conducting material throughout a length of said each one of the substantially cylindrical cavity holes, a cross sectional area of deposited thermally conducting material being smaller than a cross sectional area of said one of the substantially cylindrical cavity holes, wherein a thermal conductivity of the thermally conductive material is greater than 70 Wm−1K−1at room temperature.

[0043] A “cylinder,” as used herein, refers to a cylinder with an arbitrary cross-section. The mathematical definition of a cylinder with an arbitrary cross-section is a three-dimensional shape formed by translating a two-dimensional shape (the cross-section) along a line perpendicular to the two-dimensional shape. (Cylinders with an arbitrary cross-section have been used in applications such as electromagnetics. See, for example, JACK H. RICHMOND, Scattering by a Dielectric Cylinder of Arbitrary Cross Section Shape, IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, May 1965, pp.334-341.)

[0044] “Cylindrical cavity hole,” as used herein, refers to the space interior to a cylinder.Docket No.: Cornell 11228-03

[0045] “Substantially cylindrical cavity holes,” as used herein, refers to the variation in the characteristic dimensions of any cylindrical cavity hole, due to variations in any processing method, of + / - 25% of the characteristic dimensions of the cylindrical cavity hole. For example, in laser ablation, the cross-sectional area can decrease with depth of the ablated area.

[0046] “Extending substantially through a thickness of the Group III oxide layer,” refers to the variation in length of the deposited thermally conductive material, due to variations in the processing method, ranging from 100% to 80% of the thickness of the bare Group III oxide layer when the substantially cylindrical cavity holes are formed in a bare Group III oxide layer.

[0047] “Extending substantially through a thickness of the Group III oxide layer,” refers to the variation in length of the deposited thermally conductive material, due to variations in the processing method, ranging from 100% of the thickness of the Group III oxide layer plus 10% of the thickness of the thin film deposited on the Group III oxide layer to 80% of the thickness of the Group III oxide layer when the substantially cylindrical cavity holes are formed in a Group III oxide layer having a thin film deposited on the Group III oxide layer.

[0048] In another instantiation, the length of the deposited thermally conductive material is greater than 50% of the thickness of the Group III oxide layer and less than 100% of the thickness of the Group III oxide layer plus 25% of the thickness of the thin film deposited on the Group III oxide layer.

[0049] “Substantially filling, by deposition”, as used herein, refers to the variation in the difference between the cross sectional area of the deposited thermally conductive material and the cross sectional area of the substantially cylindrical cavity hole, due to variations in the processing method, from 0 to -5% of the characteristic dimension (such as a radius in a right circular cylinder) of the substantially cylindrical cavity hole at that specific length of the deposited thermally conductive material.

[0050] Figure 1A shows an initial state in an instantiation of the method of these teachings. Referring to Figure 1A, in the instantiation shown there in, a structure is shown having a Group III oxide layer 10 having a thin film 20 deposited on the Group III oxide layer 10. In Figure 1A, the thin film 20 is patterned as it would be when the thin film 20 comprises a fabricated device.

[0051] Figure 1B shows a first step in an instantiation of the method of these teachings. Referring to Figure 1B, in the embodiment shown therein, a number of substantially cylindrical cavity holes are formed in the group III oxide layer 10 using a source 5 of laser energy, Ga flux, ions, or dry etch (or wet etch). (The identifying numerals are the same for the same materials throughout the drawings.)Docket No.: Cornell 11228-03

[0052] Figure 1B1 shows another instantiation in which one substantially cylindrical cavity hole has been formed in the Group III oxide layer 10. (In the instantiation shown therein, the Group III oxide layer is Ga2O3, and the thin film 20 is not patterned. )

[0053] Figure 1B2 shows a planar view of the surface of the group III oxide layer 10 on which one substantially cylindrical cavity hole 15 is formed.

[0054] Figure 1B3 shows a planar view of the surface of the group III oxide layer 10 of which the substrate facing the front cavity holes 15 are formed. This figure shows a structure with a number of substantially cylindrical cavity holes 15.

[0055] Figure 1B4 shows a planar view of the other surface of the structure from above the structure. The view shown therein is the upper surface of the thin film 20.

[0056] Figure 1C shows another step in an instantiation of the method of these teachings and also shows an instantiation of the device of these teachings. Referring to Figure 1C, in the instantiation shown there in, a thermally conducting material that is deposited in the substantially cylindrical cavity holes that had been formed in the group III oxide layer 10.

[0057] In some of the figures, for concreteness, a specific instantiation of a Group III oxide, Ga2O3, is referred to. It should be noted that these teachings are not limited to only that instantiation.

[0058] Figure 1A shows the instantiation in which a thin film, fabricated to form an arbitrary device, is deposited on the Ga2O3layer. Figure 1B shows a step in that instantiation of the method of these teachings in which substantially cylindrical cavity holes are formed by at least one of etching flux, one or more laser beams or focused ion milling. Formation by one or more lasers includes one- photon absorption and at least two-photon absorption. (See, for example, Mariacristina Rumi and Joseph W. Perry, Two-photon absorption: an overview of measurements and principles, Advances in Optics and Photonics 2, 451–518 (2010), which is incorporated by reference herein in its entirety and for all purposes, Fig.1 in Steffen Bornemann et al., Femtosecond Laser Lift-Off with Sub-Bandgap Excitation for Production of Free-Standing GaN Light-Emitting Diode Chips, Adv. Eng. Mater.2020, 22, 1901192, which is incorporated by reference herein in its entirety and for all purposes, and Maiku Yamaguchi et al., Two-photon absorption induced by electric field gradient of optical near-field and its application to photolithography, Applied Physics Letters 106, 191103 (2015), which is incorporated by reference herein in its entirety and for all purposes.) In some instances of single laser beam ablation, the energy of photons is greater than the bandgap energy, Eg, of Group III oxide material, Ga2O3 in this instance. (Equivalently, the laser has a wavelength less than hc / Eg, where h is Planck’s constant, c is a speed of light in vacuum.) Single laser beam ablation (or one-photon absorption) also includes super bandgap photon illumination (hν>>>Eg, where ν is the photon frequency). (See, for example, H.S. Mavi et al., Spectroscopic investigation of porous GaAs preparedDocket No.: Cornell 11228-03 by laser-induced etching, Journal of Non-Crystalline Solids, 352 (2006), 2236–2242, which is incorporated by reference herein in its entirety and for all purposes.)

[0059] The holes are formed starting from the surface of the Ga2O3 layer that is opposite from the surface on which the thin film 20 is deposited. Figure 1C shows another step in the instantiation of the method of these teachings in which a thermally conducting material 30 is deposited into each of the substantially cylindrical cavity holes. In the instantiation shown, each one of the substantially cylindrical cavity holes is filled with the thermally conducting material. As shown in Figure 2, the substantially cylindrical cavity holes extend substantially through the thickness of the Group III oxide layer 10.

[0060] One practicing the above instantiation of the method of these teachings would want to know how to select the number, location, and cross-sectional area or characteristic dimension of each of the substantially cylindrical cavity holes. The following discussion presents a criterion for doing that and describes available methods for doing so.

[0061] Figures 1D and 1E show structures used to elucidate how to select the number, location and cross-sectional area or characteristic dimensions of each of the substantially cylindrical cavity holes.

[0062] Surface randomness, caused by lattice mismatch or the dislocation of atoms and impurities, is intrinsic to a semiconductor device, and these behaviors result in a temperature rise within the device. The temperature rise at the junction leads to premature device failure, increased leakages, and other adverse effects. The junction temperature is calculated by,

[0063] where Tj and Ta are the junction and ambient temperatures, respectively, PD is the power dissipated by the device, and Θ is the total thermal resistance. The thermal resistance is found by,

[0064] where L is the length, λ is the thermal conductivity, and A is the cross sectional area.Docket No.: Cornell 11228-03

[0065] Fig.1D shows the standard case with no back-side cooling. Here, the junction temperature is,and the Ga2O3 substrate interface.

[0067] If the III-Oxide thin film is also Ga2O3, then Eq.3 becomes,

[0069] Fig.1E shows the case where a hole was drilled and filled with a high-thermal conductivity material. Now the temperature rise becomes,λ1−λ2 thin film and the substrate, and Θint λ1−λ3is the TBR between the III-Oxide thin film and the high thermal conductivity material which is deposited into the hole.

[0071] Since there may be many holes drilled, an effective area, Aeff,sub, is defined as the total remaining area of the Group III oxide layer, once the holes are drilled, and Aeff,HTC, is the effective area of the high thermal conductivity material which is a sum of the the area of the filled holes. Thus, for the case presented in Fig. 1E, Aeff,sub= A2+ A4and , Aeff,HTC= A3. Again, assuming that the III-Oxide layer is also Ga2O3, Eq. 5 becomes:Docket No.: Cornell 11228-03

[0072] In this case, Θint λ1−λ2 is minimized as in the former case since the materials are the same, but Θint λ1−λ3is greater than Θint λ1−λ2due to the layers being different materials.

[0073] This then creates the limiting case,that the additional TBR arising from the interface of the dissimilar materials is offset by the improved thermal conductivity in the bulk.

[0075] In one or more instantiations, the method of these teachings for providing efficient heat transfer for a Group III oxide layer includes forming one or more substantially cylindrical cavity holes (CCHs) in the Group III oxide layer; each one of the substantially cylindrical cavity holes extending substantially through a thickness of the Group III oxide layer. The method of these teachings also includes depositing, into each of the substantially cylindrical cavity holes, a thermally conducting material by one of : (a) coating sidewalls of each one of the substantially cylindrical cavity holes with the thermally conducting material, or (b) filling, by deposition, said each one of the substantially cylindrical cavity holes with the thermally conducting material, or (c) depositing the thermally conducting material throughout a length of said each one of the substantially cylindrical cavity holes, a cross sectional area of deposited thermally conducting material being smaller than a cross sectional area of said one of the substantially cylindrical cavity holes; wherein a thermal conductivity of the thermally conductive material is greater than 70 Wm−1K−1at room temperature. A number, a location, and a cross-sectional area or characteristic dimensions of each one of the substantially cylindrical cavity holes are selected such that an incremental thermal boundary resistance, due to a difference in materials, is offset by an increase in thermal conductivity of the thermally conducting material (Equation (7)).

[0076] In order to determine the number, a location and a cross-sectional area or characteristic dimensions of each one of the substantially cylindrical cavity holes, one has to measure or calculate the needed Thermal boundary resistances (TBRs). J. Chen, et al., “Interfacial thermal resistance: Past, present, and future.” Revs. of Mod. Phys., 94, 025002 (2022), which is incorporated by reference herein in its entirety and for all purposes, presents a review of the experimental methods and of the analytical methods for determining the thermal boundary resistance (TBR). However, performing an experimental measurement for every candidate number, location, and cross-sectionalDocket No.: Cornell 11228-03 area for the substantially cylindrical cavity holes could be a daunting task. Surface randomness, caused by lattice mismatch or the dislocation of atoms, impurities, and inaccuracies in terms, such as interatomic potential, needed in the simulations, or in the boundary conditions, render the simulation also a challenging task. One approach is to apply simulation methods that have shown to at least qualitatively agree with the measured data. Then, one can use those simulation methods that have shown to at least qualitatively agree with the measured data to arrive at a smaller set of candidate number, location and cross-sectional area of the substantially cylindrical cavity holes and perform experimental measurements on those in order to satisfy the criterion of Equation (7). The simulation method in Kongping Wu et al., A comparative study of interfacial thermal conductance between metal and semiconductor, Scientific Reports, (2022) 12:19907, which is incorporated by reference herein in its entirety and for all purposes, presents calculations of TBR (inverse of interfacial thermal conductance “using diffuse mismatch model, acoustic mismatch model and nonequilibrium molecular dynamics methods. Results of theoretical simulation calculations are basically consistent with the current experimental data….The Vienna Ab-initio Simulation software Package (VASP) based on density functional theory is used to calculate the physical properties of these interfaces, and the projection plane wave pseudopotential is used to describe the relationship between the ion core and the valence electron. For the interaction potential, the spatial non-local exchange correlation function (Heyd, Scuseria and Ernzerhof, HSE hybrid functional) method is used to deal with the interaction between electrons…...For NEMD methods, both Cu–C and Cu–Si interfaces were simulated by molecular dynamics simulation package, LAMMPS. And modified embedded-atom method (MEAM) interatomic potentials are employed for the Cu–C and Cu–Si interfaces.

[0077] In this work, the temperature of the heat source and the heat sink were set to 320 K and 280 K, respectively. To ensure that the temperature gradient has a reasonable value. After the system reaches steady state, the temperature gradient is measured, and then the thermal conductance is calculated according to Fourier law.” There is sufficient detail in Kongping Wu et al., A comparative study of interfacial thermal conductance between metal and semiconductor, to guide one in performing the calculation. One can obtain a number of candidate number, location and cross- sectional area of the substantially cylindrical cavity holes and perform experimental measurements on those in order to satisfy the criterion of Equation (7).

[0078] In Syed Ashraf Ali and Sandip Mazumder, Phonon Boltzmann Transport Equation Based Modeling of Time Domain Thermo-Reflectance Experiments, International Journal of Heat and Mass Transfer, Volume 107, April 2017, Pages 607-621, which is incorporated by reference herein in its entirety and for all purposes, “TDTR experiments are simulated using large-scale parallel computations of the phonon Boltzmann Transport Equation (BTE) in a two-dimensionalDocket No.: Cornell 11228-03 computational domain. Silicon is used as the candidate substrate material. Simulations are performed for multiple pulse and modulation cycles of the TDTR pump laser….The metallic transducer layer on top of the substrate is modeled using the Fourier law and coupled to the BTE within the silicon substrate. Studies are conducted for four different laser spot sizes and two different modulation frequencies. The BTE results are fitted to the Fourier law, and effective thermal conductivities are extracted…{T]wo important trends are observed. First, the thermal conductivity does not change significantly with a change in the modulation frequency. These predictions agree with past experimental works, which reported negligible frequency dependence of the thermal conductivity at room temperature

[0030] as well as at low temperature

[0029] . The second point to note from the data shown in Table 2 is that the thermal conductivity is relatively unchanged for large spot sizes and eventually decreases as the spot size is decreased significantly. This behavior of the thermal conductivity with spot size has also been observed experimentally by Minnich et al.

[0029] .” There is in Syed Ashraf Ali and Sandip Mazumder, Phonon Boltzmann Transport Equation Based Modeling of Time Domain Thermo-Reflectance Experiments, sufficient explanation for one two recreate their calculation and obtain a number of candidate number, location and cross-sectional area of the substantially cylindrical cavity holes and perform experimental measurements on those in order to satisfy the criterion of Equation (7).

[0079] Another approach to determining the thermal boundary resistance (TBR) is to start with an extensive collection of published TBR data or to generate an extensive collection of TBR data and use machine learning to generate a model. This has been done in Yen-Ju Wu, Lei Fang, and Yibin Xu, Predicting interfacial thermal resistance by machine learning, npj Computational Materials (2019) 56, which is incorporated by reference herein in its entirety and for all purposes. Yen-Ju Wu, Lei Fang and Yibin Xu, Predicting interfacial thermal resistance by machine learning, “reports ITR predictive models based on experimental data. The physical, chemical, and material properties of ITR are categorized into three sets of descriptors, and three algorithms are used for the models. Those descriptors assist the models in reducing the mismatch between predicted and experimental values and reaching high predictive performance of 96%. Over 80,000 material systems composed of 293 materials were inputs for predictions.” Machine learning is a cost-effective method to address obtaining TBR (also known as interfacial thermal resistance) predictions. In Yen-JuWu et al., Physical and chemical descriptors for predicting interfacial thermal resistance, Scientific Data, (2020), 7:36, which is incorporated by reference herein in its entirety and for all purposes, a “dataset of descriptors for predicting the ITRs is presented. The dataset includes two parts: one part consists of ITRs data collected from 87 experimental papers and the other part consists of the descriptors of 289 materials, which can construct over 80,000 pair-material systems for ITRs prediction. The former partDocket No.: Cornell 11228-03 is composed of over 1300 data points of metal / nonmetal, nonmetal / nonmetal, and metal / metal interfaces. [T]he data [is used in] selection of the ITR prediction as an example.” This data (or the references provided therein) can serve as a stat for generating TBR predictive models based on experimental data by machine learning. Those TBR predictive models can be used to obtain the TBRs for a number of candidate number, location, and cross-sectional area of the substantially cylindrical cavity holes in order to satisfy the criterion of Equation (7).

[0080] Although four approaches have been presented above for obtaining the TBR's for a number of candidate number, location cross-sectional area of the substantially cylindrical cavity holes in order to satisfy the criteria of Equation (7), it should be noted that any approach that provides an estimate of the TBR that qualitatively agrees with experimental measurement can be used in these teachings and these teachings are not limited only to the approaches described above.

[0081] Figures 3A, 3B and 3C show three options available in the first step in the instantiation of the method of these teachings. Figure 3A shows the instantiation where the Group III oxide layer 10 is a bare Group III oxide layer. The hole depth is dictated by the structural integrity of the bare Group III oxide layer. The holes cannot be too deep, or the bare Group III oxide layer will break. The holes can be drilled by one or more lasers, etching, or focused ion milling, and then etching or focused ion milling may be used to finish the drilling after a thin film is deposited on the Group III oxide layer. Figure 3B shows the instantiation where a thin film 20 is deposited on the Group III oxide layer 10. Holes are drilled by one or more lasers, a dry etch, Ga flux etching or focused ion milling, in the Group III oxide layer after thin film growth by a laser, a dry etch or focused ion milling. Figure 3C shows the instantiation where a fabricated device (A patterned thin film 20) is disposed on the Group III oxide layer 10. Holes are drilled in the Group III oxide layer, by one or more lasers, etching or focused ion milling, after thin film growth and after device fabrication.

[0082] Figures 4A, 4B, and 4C show possible variations of diameter of and the density of the substantially cylindrical cavity holes (in the Group III oxide layer 10) in an instantiation of the method of these teachings. Number, location and cross-sectional area of the substantially cylindrical cavity holes can be determined as disclosed hereinabove.

[0083] Figures 5A, 5B and 5C show three options available in the second step in an instantiation of the method of these teachings and also instantiations of the device of these teachings. Figure 5A shows the instantiation where each one of the substantially cylindrical cavity holes (in the Group III oxide layer 10) is substantially filled, by deposition, with the thermally conducting material 30. Figure 5B shows the instantiation where the thermally conducting material 30 is deposited throughout a length of each one of the substantially cylindrical cavity holes, a cross sectional area of deposited thermally conducting material 30 being smaller than a cross sectional area of theDocket No.: Cornell 11228-03 substantially cylindrical cavity hole into which the thermally conducting material 30 is deposited. Figure 5C shows the instantiation where sidewalls of each one of the substantially cylindrical cavity holes are coated with the thermally conducting material.

[0084] Figure 5D1 shows another configuration of the option shown in Figure 5B in an instantiation of the method of these teachings and also an instantiation of the device of these teachings. Referring to Figure 5D1, in the instantiation shown therein, the space in the substantially cylindrical hole between the thermally conducting material 30 and the Group III oxide layer 10 is filled with a second material 40. The second material 40 has different thermal and electrical properties.

[0085] Figure 5D3 shows another configuration of the option shown in Figure 5C in an instantiation of the method of these teachings and also an instantiation of the device of these teachings. Referring to Figure 5D3, in the instantiation shown therein, the sidewalls of each one of the substantially cylindrical cavity holes are coated with high thermal conductivity material and a second material is deposited to fill the rest of each one of the substantially cylindrical cavity holes in the Group III oxide layer 10.

[0086] A number of different options are available for the properties of the high thermal conductivity material 30 and the properties of the second material 40. In one instance, these teachings not being limited to only that instance, sidewalls of each one of the substantially cylindrical cavity holes are coated with high thermal conductivity material 30 that is a poor electrical conductor and a second material 3, which is a good thermal and electrical conductor, deposited to fill the rest of each one of the substantially cylindrical cavity holes.

[0087] Another instantiation is shown in Figure 5D2. Referring to Figure 5D2, in the instantiation shown there in, the second material 40 is deposited on the walls of each one of the substantially cylindrical holes, and the high thermal conductivity material 30 is deposited to fill the rest of each one of the substantially cylindrical holes in the group III oxide layer 10.A number of different options are available for the properties of the high thermal conductivity material 30 and the properties of the second material 40.

[0088] Figures 6A and 6B show two possible groups of materials instantiations of the thermally conductive material used in instantiations of the method of these teachings and instantiations of the device of these teachings. Figure 6A shows the instantiation where the thermally conductive material 30 is an operative electrical and thermal conductor (for example, a metal such as one of copper, silver, gold, Zinc, Nickel, or Platinum). Figure 6B shows the instantiation where the thermally conductive material 30 is a poor electrical conductor, but a good thermal conductor (such as AlN, SiC, boron nitride or diamond).Docket No.: Cornell 11228-03

[0089] Figure 7 shows another instantiation of the device of these teachings as a result of another instantiation of the method of these teachings. In the instantiation shown in Figure 6A, the thermally conductive material is an operative electrical and thermal conductor (for example, a metal such as one of copper, silver, gold, Zinc, Nickel, or Platinum). Under the instantiation shown in Figure 6A, the method of these teachings can also include depositing a layer of electrically conducting material on a surface of the Group III oxide layer opposite another surface of the Group III oxide layer on which thin films are deposited. The electrically conducting material is in electrical contact with the thermally conductive material that also has operative electrical conductivity. The electrically conducting material is at least one of copper, silver, gold, Zinc, Nickel, Platinum, or many others.

[0090] In one or more instantiations, the structure of these teachings for providing effective heat transfer includes a Group III oxide layer 10, the Group III oxide layer 10 having one or more substantially cylindrical cavity holes, each one of the substantially cylindrical cavity holes extending substantially through a thickness of the Group III oxide layer, each one of the substantially cylindrical cavity holes having one of a thermally conducting material coating on sidewalls of said each one of the substantially cylindrical cavity holes, or the thermally conducting material substantially filling said each one of the substantially cylindrical cavity holes or the thermally conducting material deposited throughout a length of said each one of the substantially cylindrical cavity holes and a cross sectional area of deposited thermally conducting material being smaller than a cross sectional area of said one of the substantially cylindrical cavity holes, wherein a thermal conductivity of the thermally conductive material is greater than 70 Wm−1K−1at room temperature. For concreteness, a specific instantiation of a Group III oxide, Ga2O3, is referred to. It should be noted that these teachings are not limited to only that instantiation. Figures 1C, 5A, 5B, 5C, 5D1, 5D2, 5D3, 6A, 6B, and 7 show instantiations of the structure of these teachings.

[0091] In one instance, a number, a location and a cross-sectional area or characteristic dimensions of each one of the substantially cylindrical cavity holes are selected such that an incremental thermal boundary resistance, due to a difference in materials, is offset by an increase in thermal conductivity of the thermally conducting material J. Chen et al., “Interfacial thermal resistance: Past, present, and future,” Revs. of Mod. Phys., 94, 025002 (2022), which is incorporated by reference herein in its entirety and for all purposes, presents a review of the experimental methods and of the analytical methods for determining the thermal boundary resistance (TBR). However, performing an experimental measurement for every candidate number, location, and cross-sectional area for the substantially cylindrical cavity holes could be a daunting task. Surface randomness, caused by lattice mismatch or the dislocation of atoms, impurities, and inaccuracies in terms, such asDocket No.: Cornell 11228-03 interatomic potential, needed in the simulations or in the boundary conditions render simulation also a challenging task. One approach is to apply simulation methods that have shown to at least qualitatively agree with the measured data. Then one can use those simulation methods have shown to at least qualitatively agree with the measured data to arrive at a smaller set of candidate number, location and cross-sectional area of the substantially cylindrical cavity holes and perform experimental measurements on those in order to satisfy the criterion of Equation (7). Four examples of simulation methods have shown to at least qualitatively agree with the measured data are provided hereinabove, Kongping Wu et al., A comparative study of interfacial thermal conductance between metal and semiconductor, Scientific Reports, (2022) 12:19907 and Syed Ashraf Ali and Sandip Mazumder, Phonon Boltzmann Transport Equation Based Modeling of Time Domain Thermo- Reflectance Experiments, International Journal of Heat and Mass Transfer, Volume 107, April 2017, Pages 607-621, and the machine learning approaches described in Yen-Ju Wu, Lei Fang and Yibin Xu, Predicting interfacial thermal resistance by machine learning, npj Computational Materials (2019) 56, and Yen-JuWu et al., Physical and chemical descriptors for predicting interfacial thermal resistance, Scientific Data, (2020), 7:36. Although four approaches have been presented above for obtaining the TBR's for a number of candidate number, location cross-sectional area of the substantially cylindrical cavity holes in order to satisfy the criteria of Equation (7), it should be noted that any approach that provides an estimate of the TBR that qualitatively agrees with experimental measurement can be used in these teachings and these teachings are not limited only to the approaches described above.

[0092] In one instance, shown in Fig.6A, the thermally conductive material is at least one of copper, silver, gold, Zinc, Nickel, or Platinum. In another instance, shown in Fig.6B, the thermally conductive material is the thermally conductive material is at least one of AlN, SiC, boron nitride or diamond.

[0093] In one instance, shown in Fig.3A (at one step in the forming of the structure of these teachings), the Group III oxide layer is a bare Group III oxide layer. In another instance, shown in Fig.3B (at a step in the forming of the structure of these teachings), a thin film is deposited on the Group III oxide layer. In a further instance, shown in Fig.3C (at one step in the forming of the structure of these teachings), a fabricated device including the thin film is disposed on the Group III oxide layer.

[0094] In one instance, shown in Fig.5A, each one of the substantially cylindrical cavity holes has the thermally conducting material 30 filling each one of the substantially cylindrical cavity holes. At another instance, shown in Fig.5B, each one of the substantially cylindrical cavity holes has the thermally conducting material 30 deposited throughout a length of said each one of theDocket No.: Cornell 11228-03 substantially cylindrical cavity holes and a cross-sectional area of the thermally conducting material is smaller than a cross-sectional area of a substantially cylindrical cavity hole into which the thermally conducting material 30 is deposited. At a further instance, shown in Fig.5C, each one of the substantially cylindrical cavity holes has the thermally conducting material 30 coating on the sidewalls of said each one of the substantially cylindrical cavity holes. In still another instance shown in Figure 5D3, each one of the substantially cylindrical cavity holes has the thermally conducting material coating 30 on the sidewalls of said each one of the substantially cylindrical cavity holes, and a second material 40 fills the rest of each of the substantially cylindrical cavity holes. In yet another instance, shown in Figure 5D1, the space in the substantially cylindrical hole between the thermally conducting material 30 and the Group III oxide layer 10 is filled with a second material 40. The second material 40 has different thermal and electrical properties.

[0095] In the instantiation shown in Fig.6A, the thermally conductive material is an electrically conducting metal. In one instance, shown in Fig.7, the instantiation of the structure can have a layer of electrically conducting material deposited on a surface of the Group III oxide layer 10 opposite another surface of the Group III oxide layer on which thin films are deposited; the electrically conducting material being in electrical contact with the thermally conductive material. The electrically conducting material can be at least one of copper, silver, gold, Zinc, Nickel, or Platinum. In the instantiation shown in Fig.7, the electrically conducting material is the same as the thermally conducting material 30.

[0096] For the purposes of describing and defining the present teachings, it is noted that the term“'substantially" is utilized herein to represent the inherent degree of uncertainty that may be attributed to any quantitative comparison, value, measurement, or other representation. The term "substantially" is also utilized herein to represent the degree by which a quantitative representation may vary from a stated reference without resulting in a change in the basic function of the subject matter at issue.

[0097] Although the invention has been described with respect to various embodiments, it should be realized these teachings are also capable of a wide variety of further and other embodiments within the spirit and scope of the appended claims.

Claims

Docket No.: Cornell 11228-03 WHAT IS CLAIMED IS:

1. A structure for providing effective heat transfer, the structure comprising: a Group III oxide layer; a thin film deposited on the Group III oxide layer; the Group III oxide layer comprising one or more substantially cylindrical cavity holes, each one of the substantially cylindrical cavity holes extending substantially through a thickness of the Group III oxide layer; said each one of the substantially cylindrical cavity holes having one of a thermally conducting material coating on sidewalls of said each one of the one or more substantially cylindrical cavity holes, or the thermally conducting material substantially filling said each one of the one or more substantially cylindrical cavity holes or the thermally conducting material deposited throughout a length of said each one of the one or more substantially cylindrical cavity holes and a cross sectional area of deposited thermally conducting material being smaller than a cross sectional area of said one of the one or more substantially cylindrical cavity holes; wherein a thermal conductivity of the thermally conductive material is greater than 70 Wm−1K−1at room temperature.

2. The structure of claim 1, wherein a number, a location and a cross-sectional area or characteristic dimensions of said each one of the one or more substantially cylindrical cavity holes are selected such that an increase in thermal boundary resistance, due to a difference in materials, is offset by an increase in thermal conductivity of the thermally conducting material.

3. The structure of claim 1, wherein the Group III oxide layer comprises a gallium oxide (Ga2O3) layer.

4. The structure of claim 1, wherein the thermally conductive material is at least one of copper, silver, gold, Zinc, Nickel, Platinum, AlN, SiC, boron nitride or diamond.

5. The structure of claim 4, wherein the thermally conductive material is at least one of copper, silver, gold, Zinc, Nickel, or Platinum.

6. The structure of claim 1, wherein the thermally conductive material is at least one of AlN, SiC, boron nitride, or diamond.Docket No.: Cornell 11228-03 7. The structure of claim 1, wherein the thin film layer comprises a fabricated device.

8. The structure of claim 1, wherein said each one of the one or more substantially cylindrical cavity holes has the thermally conducting material coating on sidewalls of said each one of the substantially cylindrical cavity holes.

9. The structure of claim 1, wherein said each one of the one or more substantially cylindrical cavity holes has the thermally conducting material filling said each one of the substantially cylindrical cavity holes.

10. The structure of claim 1, wherein said each one of the one or more substantially cylindrical cavity holes has the thermally conducting material deposited throughout a length of said each one of the substantially cylindrical cavity holes and a cross sectional area of the thermally conducting material being smaller than a cross sectional area of a substantially cylindrical cavity hole into which the thermally conducting material is deposited.

11. The structure of claim 10, wherein another thermally conductive material is deposited in a space of said each one of the one or more substantially cylindrical cavity holes between coated sidewalls of said each one of the one or more substantially cylindrical cavity holes.

12. The structure of claim 5 further comprising a layer of electrically conducting material deposited on a surface of the Group III oxide layer opposite another surface of the Group III oxide layer on which thin films are deposited; the electrically conducting material being in electrical contact with the thermally conductive material.

13. The structure of claim 12, wherein the electrically conducting material is at least one of copper, silver, gold, Zinc, Nickel, or Platinum.Docket No.: Cornell 11228-03 14. A structure for providing effective heat transfer, the structure comprising: a bare Group III oxide layer, the bare Group III oxide layer comprising one or more substantially cylindrical cavity holes, each one of the one or more substantially cylindrical cavity holes extending substantially through a thickness of the bare Group III oxide layer; said each one of the one or more substantially cylindrical cavity holes having one of a thermally conducting material coating on sidewalls of said each one of the substantially cylindrical cavity holes, or the thermally conducting material substantially filling said each one of the substantially cylindrical cavity holes or the thermally conducting material deposited throughout a length of said each one of the one or more substantially cylindrical cavity holes and a cross sectional area of deposited thermally conducting material being smaller than a cross sectional area of said one of the one or more substantially cylindrical cavity holes; wherein a thermal conductivity of the thermally conductive material is greater than 70 Wm−1K−1at room temperature; wherein a number, a location and a cross-sectional area or characteristic dimensions of said each one of the substantially cylindrical cavity holes are selected such that an increase in thermal boundary resistance, due to a difference in materials, is offset by an increase in thermal conductivity of the thermally conducting material.

15. The structure of claim 14, wherein the bare Group III oxide layer comprises a gallium oxide (Ga2O3) layer.

16. The structure of claim 14, wherein a thin film is deposited on the bare Group III oxide layer.

17. The structure of claim 14, wherein a fabricated device is disposed on the bare Group III oxide layer.

18. The structure of claim 14, wherein said each one of the one or more substantially cylindrical cavity holes has the thermally conducting material coating on sidewalls of said each one of the substantially cylindrical cavity holes.

19. The structure of claim 14, wherein said each one of the one or more substantially cylindrical cavity holes has the thermally conducting material filling said each one of the substantially cylindrical cavity holes.Docket No.: Cornell 11228-03 20. The structure of claim 14, wherein said each one of the substantially cylindrical cavity holes has the thermally conducting material deposited throughout a length of said each one of the substantially cylindrical cavity holes and a cross sectional area of the thermally conducting material being smaller than a cross sectional area of a substantially cylindrical cavity hole into which the thermally conducting material is deposited.

21. A method for providing efficient heat transfer for a Group III oxide layer, wherein a thin film is deposited on the Group III oxide layer, the method comprising: forming one or more substantially cylindrical cavity holes (CCHs) in the Group III oxide layer; each one of the one or more substantially cylindrical cavity holes extending substantially through a thickness of the Group III oxide layer; the one or more substantially cylindrical cavity holes starting from a surface opposite a surface of the Group III oxide layer on which the thin film is deposited; and depositing a thermally conducting material by one of : (a) coating sidewalls of each one of the one or more substantially cylindrical cavity holes with the thermally conducting material, or (b) substantially filling, by deposition, said each one of the one or more substantially cylindrical cavity holes with the thermally conducting material, or (c) depositing the thermally conducting material throughout a length of said each one of the one or more substantially cylindrical cavity holes, a cross sectional area of deposited thermally conducting material being smaller than a cross sectional area of said one of the substantially cylindrical cavity holes; wherein a thermal conductivity of the thermally conductive material is greater than 70 Wm−1K−1at room temperature.

22. The method of claim 21, wherein a number, a location and a cross-sectional area or characteristic dimensions of said each one of the substantially cylindrical cavity holes are selected such that an increase in thermal boundary resistance, due to a difference in materials, is offset by an increase in thermal conductivity of the thermally conducting material.

23. The method of claim 21, wherein the one or more substantially cylindrical cavity holes are formed by ablation with one or more lasers.

24. The method of claim 21, wherein forming the plurality of substantially cylindrical cavity holes is initiated by ablation with one or more lasers, and forming the one or more substantially cylindrical cavity holes is completed by at least one of etching or focused ion milling.Docket No.: Cornell 11228-03 25. The method of claim 21, wherein the one or more substantially cylindrical cavity holes are formed by etching.

26. The method of claim 21, wherein the one or more substantially cylindrical cavity holes is formed by focused ion milling.

27. The method of claim 21, wherein deposition or coating is performed by at least one of atomic layer deposition, sputtering, e-beam evaporation, or electroplating.

28. The method of claim 21, wherein the Group III oxide layer comprises a gallium oxide (Ga2O3) layer.

29. The method of claim 21, wherein the thermally conductive material is at least one of copper, silver, gold, Zinc, Nickel, or Platinum.

30. The method of claim 21, wherein the thermally conductive material is at least one of AlN, SiC, boron nitride or diamond.

31. The method of claim 21, wherein the thin film layer comprises a fabricated device.

32. The method of claim 21, wherein the thermally conducting material is deposited by coating sidewalls of each one of the one or more substantially cylindrical cavity holes with the thermally conducting material.

33. The method of claim 21, wherein the thermally conducting material is deposited by substantially filling, by deposition, said each one of the one or more substantially cylindrical cavity holes with the thermally conducting material.

34. The method of claim 21, wherein the thermally conducting material is deposited by depositing the thermally conducting material throughout a length of said each one of the substantially cylindrical cavity holes, a cross sectional area of deposited thermally conducting material being smaller than a cross sectional area of said one of the substantially cylindrical cavity holes.Docket No.: Cornell 11228-03 35. The method of claim 27 further comprising depositing a layer of electrically conducting material on a surface of the Group III oxide layer opposite another surface of the Group III oxide layer on which thin films are deposited; the electrically conducting material being in electrical contact with the thermally conductive material.

36. The method of claim 35, wherein the electrically conducting material is at least one of copper, silver, gold, Zinc, Nickel, or Platinum.

37. The method of claim 32, wherein another thermally conductive material is deposited in a space of said each one of the one or more substantially cylindrical cavity holes between coated sidewalls of said each one of the one or more substantially cylindrical cavity holes.

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