Thermal stress modelling of diamond on GaN/III-Nitride membranes
Jerome A. Cuenca, Matthew D. Smith, Daniel E. Field, Fabien C-P. Massabuau, Soumen Mandal, James Pomeroy, David J. Wallis, Rachel A. Oliver, Iain Thayne, Martin Kuball, Oliver A. Williams
TThermal stress modelling of diamond on GaN/III-Nitridemembranes
Jerome A. Cuenca a, ∗ , Matthew D. Smith b , Daniel E. Field c , Fabien C-P. Massabuau d,e , SoumenMandal a , James Pomeroy c , David J. Wallis d,f , Rachel A. Oliver d , Iain Thayne b , Martin Kuball c ,Oliver A. Williams a a School of Physics and Astronomy, Cardiff University Cardiff, Wales, CF24 3AA, UK b School of Engineering, University of Glasgow, G12 8LT, UK c Centre for Device Thermography and Reliability, University of Bristol, BS8 1TL, UK d Cambridge Centre for Gallium Nitride, Department of Materials Science and Metallurgy, Cambridge, CB3 0FS, UK e Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, UK f School of Engineering, Cardiff University Cardiff, Wales, CF24 3AA, UK
Abstract
Diamond heat-spreaders for gallium nitride (GaN) devices currently depend upon a robust waferbonding process. Bonding-free membrane methods demonstrate potential, however, chemicalvapour deposition (CVD) of diamond directly onto a III-nitride (III-N) heterostructure membraneinduces significant thermal stresses. In this work, these thermal stresses are investigated usingan analytical approach, a numerical model and experimental validation. The thermal stresses arecaused by the mismatch in the coefficient of thermal expansion (CTE) between the GaN/III-Nstack, silicon (Si) and the diamond from room temperature to CVD growth temperatures. Simpli-fied analytical wafer bow models underestimate the membrane bow for small sizes while numericalmodels replicate the stresses and bows with increased accuracy using temperature gradients. Thelargest tensile stress measured using Raman spectroscopy at room temperature was approximately1.0 ± . GPa while surface profilometry shows membrane bows as large as µ m . This largebow is caused by additional stresses from the Si frame in the initial heating phase which are heldin place by the diamond and highlights challenges for any device fabrication using contact lithog-raphy. However, the bow can be reduced if the membrane is pre-stressed to become flat at CVDtemperatures. In this way, a sufficient platform to grow diamond on GaN/III-N structures withoutwafer bonding can be realised. ∗ Corresponding author
Email address: [email protected] (Jerome A. Cuenca)
Preprint submitted to Journal of L A TEX Templates February 22, 2021 a r X i v : . [ phy s i c s . a pp - ph ] F e b eywords: cvd diamond, gallium nitride, membranes, thermal stress, finite element modelling
1. Introduction
Increasing demand for high power microwave devices has driven research into gallium nitride(GaN), in particular, high electron mobility transistors (HEMTs)[1]. Current device technologieseither have impressive high power handling (e.g. Si) or high frequency capability (e.g. GaAs andInP), though not both. GaN is a possible candidate although, despite significant progress, its powerhandling capability is still limited by self-heating[1]. This is due to the limited thermal conductivityof GaN with values between 160 and 210 W/mK[2]. Additionally, some substrates for GaN alsohave a low thermal conductivity such as sapphire (Al O ) and silicon (Si) at around 30 and 150W/mK, respectively[2, 3, 4]. This can be overcome with sufficient heat extraction by integrationwith substrates of much higher thermal conductivity such as silicon carbide (SiC) at 400 W/mK,which is commonly used for electronic applications. Diamond is another candidate which in itssingle crystal form is capable of achieving thermal conductivities in excess of 2,000 W/mK[5, 6].Several studies have shown reduced operating temperatures of GaN devices when using integrateddiamond heat spreading technology[7, 8, 9].GaN-on-diamond is not trivial to fabricate, but can be realised either by surface activated waferbonding[10, 11, 12, 13, 14] or heteroepitaxial growth. Growth of GaN onto diamond[15] or dia-mond onto GaN can be achieved using interlayers such as silicon nitride (SiN) or group-III-Nitride(III-N) structures. Examples of III-N structures include aluminium nitride (AlN) and aluminiumgallium nitride (AlGaN)[16, 17, 6, 18, 19]. In the wafer bonding approach, it is imperative toachieve a sub-nanometre surface roughness in order for Van der Waals bonding to occur. How-ever, it has been calculated that a large thermal barrier resistance of Van der Waals bonded dia-mond on GaN is expected, reducing the efficacy of diamond heat spreading technology[20]. Forheteroepitaxial growth of diamond onto III-N structures, this can only be achieved at present withpolycrystalline diamond (PCD) using chemical vapour deposition (CVD) at lower than atmosphericpressure and at high temperatures (0.1 to 0.2 atm at temperatures from 600 to 800 ◦ C[8]). Addition-ally in contrast to single crystal diamond (SCD), PCD can be grown over large areas, making thisapproach more commercially viable. A number of CVD methods exist for depositing PCD. Mi-crowave plasma assisted chemical vapour deposition (MPCVD) offers diamond growth over small2 afer Bonding MethodMembrane Method
GaNAlN/AlGaNSi Si TempOxide/NitrideGaNAlN/AlGaNSi AlN/AlGaNGaNOxide/NitrideSi Temp DiamondAlN/AlGaNGaNOxide/NitrideSi Temp DiamondAlN/AlGaNGaN (cid:9) (cid:9)
AlN/AlGaNSiGaN GaN SiSiAlN AlGaN GaN SiSi DiamondAlN AlGaN
Figure 1: Approaches to diamond on GaN/III-N integration using wafer bonding steps prior to CVD diamond growth(top) and membrane fabrication (bottom). ‘Si Temp’ is defined as a temporary Si carrier wafer. areas (<100 mm diameter wafers) and can be optimised for very fast growth rates (50 to µ m h − )[21]. Larger area coverage (>100 mm diameter wafers) can be achieved with hot filament(HFCVD), although repeatability is challenging and growth rates are generally much lower (1 to µ m h − ) [22, 23, 24].Direct diamond growth on GaN is challenging owing to a number of factors. The first is that astable carbide bond is difficult to achieve on either side of the GaN faces which can be overcomeusing interlayers that form carbides. The second issue is that GaN is widely deposited using metalorganic chemical vapour deposition (MOCVD) where the Ga-polar HEMT layer is typically at thetop of the stack. While growing diamond on the Ga-polar side has been demonstrated for thinfilms at less than µ m [7], this creates additional challenges to embed the diamond layer duringdevice fabrication. Also, it has been shown that the thermal conductivity of diamond can be verylow at these thicknesses[8]. Therefore, the diamond must ideally be grown on the underside or theN-polar side of the GaN/III-N stack. The N-polar side is chemically very different to the Ga-polarsurface and thick film growth requires significant investigation[19]. This requires wafer bondingto a temporary carrier, flipping, etching and then growing the diamond on the exposed III-N stackas is shown in Fig. 1. Finally, a prominent issue is the thermal stress and strain (bow) from themismatch in the coefficient of thermal expansion (CTE) between the layers in the stack[25]. Hightemperature CVD diamond growth generates large stresses upon cooling which bows the wafer3nd may mechanically fracture the GaN. Additionally, these high temperatures may also result incomplete destruction of the GaN/III-N stack and so ensuring the growth temperature is as low aspossible mitigates the risk of damage or fracturing upon cooling.A potential method which enables fast access to the correct polarity face of the GaN/III-N stackfor diamond growth, without the need for costly and time consuming wafer bonding, is to use aGaN/III-N membrane, as is shown in Fig. 1. This can be achieved using an inductively coupledplasma (ICP)[17]. This membrane technique has been realised for other GaN applications includinglight emitting diodes, planar photonic devices[26, 27, 28] and impedance based sensors[29, 30, 31].The details of the integration of diamond with GaN membranes are seldom reported, specificallyowing to the fragile nature of the membrane and the high temperatures required to grow diamond.Previous reports have shown diamond on GaN/III-N membranes from 0.5 to 5 mm in diameterunder stresses of around 0.7 GPa due to the thermal cycling [17]. The stress is lower than theexperimentally reported mechanical strength of GaN (compressive strength of 10 to 15 GPa andtensile strength of 4 to 7.5 GPa)[32, 33, 34] and far less than density functional theory (DFT)estimates of the tensile strength (30 to 40 GPa)[35, 36]. The stresses are also equivalent to thosemeasured in a typical diamond on GaN/III-N sample produced through the wafer bonding method(0.67 to 1 GPa)[37], demonstrating a potentially viable approach for circumventing wafer bonding.However, the membrane deformations and bow are not reported which may significantly impactdevice fabrication using contact lithography. Since the membrane structure is far more complexwhen compared to a cylindrical wafer stack, an understanding of the parameters which cause thesedeformations and induced thermal stresses is required before considering this approach for anydevice fabrication.In this work, the thermal stress and strains (membrane bow) associated with the growth of CVDdiamond on GaN/III-N membranes have been investigated using analytical modelling, numericalmodelling and experimental work. First, a simplified Stoney analytical model is briefly describedfor stress in a two layer cylindrical stack. Following this a finite element model (FEM) is presentedwhich calculates the anticipated thermal stresses in circular membranes and investigates the effectof varying the geometry, materials and temperature. Next, experimental data is presented on thegrowth and characterisation of diamond on GaN/III-N membranes to validate the model. Finally,comparisons and discussions are drawn, particularly on the limitations of the CVD diamond on4aN/III-N membrane approach.
2. Analytical Model
Thin film deposition at elevated temperatures requires careful consideration of stress. At roomtemperature, the net stresses are due to a combination of intrinsic stresses and extrinsic stresses.Intrinsic stresses arise mainly due to the imperfections in the microstructure of the deposited filmsuch as crystal grain boundaries, voids, impurities and defects caused by the lattice mismatch be-tween the film and the substrate. For example, the lattice mismatch between GaN and Si results inresidual intrinsic stresses after MOCVD[38]. Additionally, it is well-known that intrinsic stressesare also present in CVD diamond depending on the experimental conditions[39, 40]. Extrinsicstresses are due to externally applied forces such as mechanical loading or thermal stress, the latterof which is a well-known challenge for thin film deposition and is the subject of this study.
Figure 2: Temperature dependent CTE of diamond, Si, AlN and GaN[25, 41, 42].
Thermal stresses arise due to the thermomechanical properties of the layers in the stack. Inisolation, each material preferentially expands/contracts to different volumes at different tempera-tures. However, for a three dimensional (3D) sample with all layers bound axially in the z direction,the deformations in the xy plane are constrained. The CTE of diamond and the layers in a typicalGaN-on-Si wafer are shown in Fig. 2. AlN and GaN have very similar values at typical CVDgrowth temperatures of 600 to 1000 ◦ C and a small difference at room temperature of around 1.55 − K − . Diamond and Si have lower values than the GaN/III-N layers across the temperaturerange. At room temperature Si intersects with AlN while diamond is much lower than all of thematerials. It is therefore expected that after cooling to room temperature, the CVD diamond on themembrane will be held in compression, whilst the GaN and III-N layers in tension. Thus, carefulconsideration of the tensile strength of the GaN/III-N stack must be made to ensure that the mem-brane does not fracture through upon cooling. The resultant deformations caused by thermal stresscan be determined for a simplified cylindrical wafer stack using the following analytical model. In a cylindrical coordinate system ( ρ, θ, z ), consider an axially symmetric wafer stack consistingof two unbound layers of differing thicknesses ( t film and t sub ) with differing CTE ( α film and α sub ).The layer thicknesses in the z direction are much smaller than the radius of the cylindrical stack.When the temperature is lowered, depending on the CTE, the volumes of the layers shrink with anegligible change in thickness compared to a much larger radial change. Using the linear thermalexpansion model, the resultant radial 1D strains are: ε film = r film ( T ) r = 1 + α film ( T ) [ T − T ] (1) ε sub = r sub ( T ) r = 1 + α sub ( T ) [ T − T ] (2)where T is the temperature in K, r ( T ) is the temperature dependent radius of the layer in m, r denotes the initial radius in m at a reference temperature of T and α ( T ) is the temperaturedependent CTE of the layer in K − . If the layers are bound, the radial strain at the interface mustbe equal, with one layer being held in tension while the other is held in compression. Therefore,an additional strain is required to keep the materials bound at the interface, equal to the differencebetween the two unbound strains: ∆ ε = ε sub − ε film = [ T − T ] [ α sub ( T ) − α film ( T )] = ∆ T ∆ α (3)6he calculated stress associated with this strain is related through the Young’s modulus: σ = E · ∆ T ∆ α (4)where σ is the induced thermal stress in Pa and E is the Young’s modulus of the layer in Pa.Considering 2D axial symmetry however, this generated 1D radial stress is not the equilibrium stateas the two layer system is not restricted along the z axis. The induced internal stress thus results in afinite strain in the z direction. For an axially symmetric sample, this results in a radius of curvature R through a relation with the biaxial modulus, otherwise known as the Stoney formula[39, 43, 44]: R = E sub (1 − ν sub ) t sub t film
16 1 σ (5)where R is the radius of curvature of the substrate, E sub / (1 − ν sub ) is the biaxial modulus of thesubstrate and ν sub is the Poisson’s ratio. With the radius of curvature known, the wafer bow can becalculated for a given wafer diameter. This is simply related through arclength[25]: w = R (cid:16) − cos (cid:104) r sub R (cid:105)(cid:17) (6)where w is the displacement of the central point in the z direction of the wafer in m or bow.Knowing the diameter of the wafer ( r sub ), one can predict the radius of curvature of a cylindricalstack for a given thermal stress.The stresses in a cylindrical stack that are associated with the CVD diamond growth processat various deposition temperatures can be approximated using typical thicknesses, diameters andvalues of E , ν and α ( T ) for GaN and diamond as given in Fig. 2 and Table 1. Fig. 3 showsmodels of GaN-on-Si wafers heated to CVD growth temperatures and diamond on GaN waferscooled to room temperature. Here, the GaN/AlGaN and AlN nucleation layers are grouped andmodelled as one thin GaN layer ( t film = µ m ) while the substrate is modelled as Si upon heating( t sub = µ m ) or diamond on cooling ( t sub = µ m ). With a constant radius of curvature, it is clearthat the bow increases with diameter. At temperatures between 600 and 800 ◦ C, the initial heatingbow is associated with a stress of around 0.3 to 0.41 GPa while the cooling bow is associated witha stress around of 0.43 to 0.53 GPa. An important note is that the analytical model implies thatmembranes of 0.5 mm in diameter have a bow of less than µ m . Low temperature growths (<8007 aN on Si Heat Diamondon GaN Cool (a) (b) Figure 3: Analytical model of bow using Eq. (5) for two scenarios: (a) the heating of a cylindrical GaN on Si stackto CVD growth temperatures, resulting in an upward bow and (b) the cooling of a cylindrical diamond on GaN stackfrom CVD growth temperatures to room temperature, also resulting in an upward bow.Table 1: Material properties used in analytical and numerical models.
Material Young’s Modulus Poisson’s Density Thermal Specific Ref. E (GPa) Ratio ρ (g/m ) Conductivity Heat ν κ (W/mK) C p (J/kg · K) Diamond 1000 0.2 3.51 2270 0.52 [45, 46]GaN 295 0.25 6.16 253 0.42 [33]AlN . − . T e − T . − . T ◦ C) are chosen in this study since most sucessful growths on GaN occur at lower temepratures tominimise thermal stress. This analytical model predicts a net stress in the GaN as high as 0.94 GPa.This value is lower than the reported tensile strength of GaN (4 to 7.5 GPa at room temperature)and similar to those reported in previous studies[17, 34].A prominent limitation of this model is its simplicity; the membrane structure in reality is nota millimetre sized GaN-on-Si wafer but a millimetre sized GaN membrane that is suspended by amuch larger Si border. The stresses induced by the Si cannot be taken into account since it is boundto both the edges of the membrane and the rest of the GaN film. It is also assumed that the diamondthickness is constant on the top of the membrane, which is not true since lateral growth will occuron the edges of the Si. Such model complexities can be readily implemented using a numericalmodel. 8 . Numerical Model
Diamond - 1 to µ m Si - 75 to µ m III-N - 1 to µ m GaN - µ m
15 mm 15 mm z xy SS .. f f . f Boundary Conditions f → u (0 , , w ) f → u (0 , v, f → u ( u, , S → Symmetry T = 25 ◦ C SS .. f f . f T = 720 ◦ CFigure 4: Cross-sectional diagram of the base numrical membrane model, not to scale. Boundary conditions showsymmetry planes to reduce the model size and fixed constraints which restrict the velocity field ( u ) at specific points( f ) . The wafer stack has been modelled in the COMSOL Multiphysics® FEM package using theThermal Stress module which incorporates both Solid Mechanics and Heat Transfer. A cross sec-tion schematic of the model stack is shown in Fig. 4 and consists of a GaN device layer on thebottom, a lumped III-N layer, a Si frame which defines the membrane pattern and a CVD diamondlayer. The lumped III-N layers represent a combination of the AlN nucleation layer and AlGaNstrain relief layers, conservatively approximated as AlN. The base model thicknesses are given as t GaN = 2 µ m , t III-N = 3 µ m , t Si = 75 µ m and t Dia = 50 µ m . The dimensions have been chosen torepresent a typical MOCVD sample which has been thinned from the Si side and cleaved to dimen-sions of 15 mm by 15 mm for MPCVD. This sample size has been chosen since successful diamonddepositions have been achieved on AlN on Si in previous work at this size in a high power densityplasma[17, 48]. Also, smaller samples minimise any diamond thickness variation over the sampleowing to the small plasma size at these conditions. The boundary conditions of the structure arealso shown in Fig. 4 whereby the centre point of the GaN is fixed in xy space and free to displace inthe z direction. Two symmetry planes are also defined to reduce the size of the model. The growthtemperature of the base structure is homogenous with no gradients and chosen to match the exper-imental pyrometer data in the centre of the sample during diamond growth for a low temperature9ecipe (720 ◦ C)[17]. The material parameters are the same as those used in the analytical modelwith additional thermomechanical properties, shown in Table 1.[32, 41, 42, 46, 47, 49, 50]
0. Initial 1. Membrane 2. Diamond 3. Diamond 4. Combined cooledGaN-on-Si heated to CVD deformed to fit stress-relieved diamond andmembrane temperatures onto structure and cooled initial membraneFigure 5: Steps taken in the FEM with colour plot showing the von Mises stress in GPa and the resultant deformationfield, × z scale for visibility. The model is run in an automated stepped process as is shown in Fig. 5. Step 0 shows theinitial geometry of the model. Step 1 is the heating model, where the structure is heated to growthtemperatures to obtain the initial thermal stresses in the absence of any diamond. Convergenceof this step is crucial as it defines the initial shape of the deposited diamond. This step typicallyconverged to two solutions, whereby the GaN-on-Si membrane either had a positive bow (GaNdisplaces upwards into the Si) or a negative bow (GaN displaces away from the Si), although withthe same magnitude. The presented results show the positive bow solutions since this was whatwas found in later experiments. Step 2 uses this displacement field to deform the diamond layerto fit on top of the stressed membrane geometry. Step 3 isolates the diamond layers and relievesthe previously computed stress in this deformed configuration as it is assumed that the diamond isdeposited stress-free. The diamond layer is then cooled in isolation to obtain the deformation atroom temperature. The reason why the diamond is separately cooled is for stability during modelconvergence. This can only be assumed if there is no hysteresis in the thermal cycling. Step 4integrates the cooled diamond by stretching the initial room temperature membrane structure overthe cooled diamond to give the final deformation and stresses associated with this state. To validatethis stepped process, the absence of diamond in the final step shows no deformation.10a) (b)
Figure 6: Simulated results for varying the CVD growth temperature are given in (a) and (b) for the membrane bowand the average residual stress in the GaN membrane, relative to step 0, respectively. Base model layer thicknesseshave been used: t GaN = 2 µ m , t III-N = 3 µ m , t Si = 75 µ m and t Dia = 50 µ m . The modelled membrane results are shown in Fig. 6, 7 and 8 where the dotted lines show theheated sample and the solid lines show the final state where the cooled diamond is integrated withthe structure. A positive z displacement refers to a membrane bow into the Si while a negative z displacement refers to away from the Si, as per the defined coordinate system in Fig. 4. The vonMises stress denote the residual stress associated with the displacement fields.Fig. 6 shows the base model displacement as a function of membrane diameter and at varyinggrowth temperatures. It is clear from Fig. 6.a that the bow increases with membrane diameter. Itis also shown that, as expected, the bow increases with deposition temperature, although to a lesserdegree, resulting in an increase in stress. The heated stresses in Fig. 6.b are approximately 0.2 GPafor larger membranes and increase to 0.4 GPa for smaller membranes. These values are in the samerange as the heated stresses for the analytical model. However, the heated bow is much larger thanthe analytical model; for example in Fig. 6 upon changing the temperature from 600 to 800 ◦ C,the 5 mm membrane bows, respectively, from 80 to µ m in the numerical model while in Fig.3, the calculated bow for the same membrane is 22 to µ m in the analytical model. This largedifference is attributed to the additional thermal stress contribution from the Si border which is nottaken into account in the analytical approach, demonstrating a significant limitation in using Eq.(4) with (5) to predict the bow in membrane structures. After cooling with the diamond introduced,the overall bow is relatively unchanged, implying that when the diamond is deposited, it attempts11a) (b)(c) (d) Figure 7: Simulated results for varying t Dia are given in (a) and (b) for the membrane bow and the average residualstress in the GaN membrane relative to step 0, respectively. Results for varying E Dia are given in (c) and (d) for themembrane bow and stress, respectively. The traces marked ‘All’ refer to the heating phase of all the model cases sincethe diamond is introduced afterwards. The base model layer thicknesses have been used for other layers: t GaN = 2 µ m , t III-N = 3 µ m and t Si = 75 µ m . A deposition temperature of T g = 720 ◦ C was used as to simulate low temperaturegrowth recipes for GaN/III-N membranes[17]. The base value of E Dia = 1
TPa. to hold the deformed membrane into place upon cooling owing to its extreme hardness and lowCTE across the temperature range. This results in a large increase in the residual stresses, as theinitial membrane model in Step 0 should be flat at room temperature but is held in the bowed state.These residual stresses also decrease as the growth temperature is reduced. As shown in Fig. 6.b,GaN/III-N membranes with diameters between 1 and 5 mm will be under a stress between 1.0 to1.7 GPa which is still less than the tensile strength (4 to 7.5 GPa at room temperature)[34].Fig. 7 shows the models for varying the diamond thickness, where the traces marked ‘All’stipulate the result for all cases for the heating models; the initial geometry is not varying only thediamond and its properties. A lower limit of µ m has been chosen since it has been shown that12a) (b)(c) (d) Figure 8: Simulated results for varying t III-N are given in (a) and (b) for the membrane bow and the average residualstress in the GaN membrane, relative to step 0, respectively. Results for varying t Si are given in (c) and (d) for themembrane bow and stress, respectively. The base model layer thicknesses have been used for the other layers: t GaN =2 µ m , t III-N = 3 µ m , t Dia = 50 µ m and t Si = 75 µ m . A deposition temperature of T g = 720 ◦ C was used as to simulatelow temperature growth recipes for GaN/III-N membranes[17] thinner diamond films result in incredibly low thermal conductivities[8]. The diamond thicknessappears to have minimal effect on the observed bow but a significant effect on the residual stressin the membrane. This result also demonstrates that even a µ m thin diamond layer is enoughto hold the membranes into the heated bowed state by several tens of micrometres owing to theextreme stiffness of diamond. To further demonstrate this, Fig. 7.c and 7.d show the results forvarying the diamond Young’s Modulus ( E Dia ) for a µ m thick diamond layer. Decreasing thestiffness decreases the final membrane bow and stress. At very low values of around 200 GPa,the diamond is no longer rigid enough to fully sustain the deformation thereby reducing the finalbow and stress. However, such low values of E Dia are not expected for CVD diamond, even forultra-nano-crystalline (UNCD) films[46, 51]. 13ig. 8.a and 8.b show the effect of varying the III-N stack thickness, revealing minimal differ-ences in both bow and cooled stress. The heated bow and stress, however, increases with thicknesswhich is not favourable at high temperatures since GaN weakens towards 1000 ◦ C[52]. A similarcase is found for increasing the Si thickness, although a much larger bow is seen in Fig.8 across allmembrane sizes. The average stress in the membrane is also marginally relieved upon cooling asthe Si is thickened, shown in Fig. 8.d. Since the Si thickness can be varied by a much larger rangeat tens of microns compared to the III-N layers at a few microns, changes to the Si are expected tohave a more profound effect on the bow and stress than the III-N layers. This implies a potentialroute to minimising the bow through Si thickness, however it would need to be much less than µ m .In the presented models, it is apparent that after CVD diamond deposition, the final stress inthe membranes is within the mechanical limits of GaN, however, the anticipated bow of largemembranes is significant, imposing challenges for device manufacturing through contact photo-lithography. The models imply that only small membranes are a potentially viable route. To verifythese findings, circular GaN/III-N membrane samples of varying diameter were fabricated withsimilar dimensions to the models. The effect of CVD diamond deposition on the mechanical prop-erties was investigated through measurement.
4. Experiment
There were 3 samples in total, fabricated using commercially obtained wafers, diced to squaredimensions of 15 mm by 15 mm. The fabrication of the membranes and details can be found inprevious work[17]. In brief, the as received GaN/III-N on Si wafer was etched from the Si sideusing a high power ICP at 900 W, followed by membrane patterning using photolithography and fi-nally a lower power ICP etch at 600 W to completely remove the Si and expose an AlN layer on theGaN/III-N membranes. The thickness of the remaining Si handle border was was measured usinga micrometer. Following this, CVD diamond growth was achieved using a Carat systems CTS6UMPCVD reactor. The temperature of the sample was measured using a Williamson pyrometer(Model DWF-24-36C) which uses dual wavelengths at around µ m to minimise emissivity errors.Prior to growth, a non-ultrasonic seeding method was used owing to the fragility of the mem-branes. Briefly, the exposed GaN/III-N membranes were first pre-treated in a N /H microwave14 eforeAfter Initial Heating
Figure 9: Photos of the 3 GaN/III-N membrane samples before (top row), after MPCVD diamond growth (middle row)and at the beginning of MPCVD growth (bottom row) with numerical model of the displacement field in micrometres( z scale ×
10 for visibility). All samples are grown one by one, positioned centrally on the sample holder as shown inthe bottom photo. plasma with a forward power of 1.5 kW at 20 Torr. This step allows some control over the seedingdensity by decreasing the streaming potential of the AlN. This brief plasma pre-treatment stagehas been shown to increase the oxygen surface content on AlN by partially etching and subsequentadsorption of oxygen onto the surface once the sample is brought to atmosphere[48]. Followingthis, a nano-diamond colloid solution was pipetted onto the exposed GaN/III-N membrane side,covering both the membrane and the Si handle border. The samples were rinsed carefully in de-ionised water and dried on a hotplate for 10 minutes set to 115 ◦ C. Diamond growth was achievedin a CH /H microwave plasma with a forward power of 5.5 kW at 110 to 120 Torr and a CH concentration of 3% at a total flow rate of 500 sccm. At these conditions, the pyrometer measureda temperature of around 720 to 750 ◦ C. With a typical growth rate at these conditions of approxi-mately to µ m /hour, growth runs were conducted for 19 hours to achieve a diamond thickness ofaround 38 to µ m . 15
20 40 60 80 100 0 5 101520
Figure 10: Cross-sectional HAADF-STEM microgaph and EDX data of CVD diamond grown on a 0.5 mm GaN/III-Nmembrane.
Following growth, surface profilometry was used to determine the membrane bow with a pro-filer tip of diameter of µ m , a force of 1 mg and a maximum travel time of 60 seconds across themembrane. Raman spectroscopy was used to determine the structural signatures of the GaN/III-Nand CVD diamond and infer the stress in the membranes, achieved using a Renishaw inVia Ramanspectrometer with a 514 nm laser. To ensure that there is an adhered interface between the CVDdiamond and the N-polar side of the III-N stack, cross-sectional observation of the samples wasconducted by high angle annular dark field scanning transmission electron microscopy (HAADF-STEM) and energy dispersive X-ray spectroscopy (EDX) in an FEI Tecnai Osiris microscope op-erated at 200 kV. The TEM foil was prepared by focused ion beam (FIB) from the GaN/III-N sideof the membrane.The fabricated membranes are shown in Fig. 9, before, after and at the start of CVD diamondgrowth. After deposition, the 0.5 and 2 mm diameter membranes have high optical transparency,implicit of a successful growth, however, the 5 mm diameter membrane shows a much darker filmimplying that the GaN membrane is significantly damaged. This is likely due to the membranebowing upwards towards the CH /H microwave plasma and melting. Referring to the image ofthe sample inside the MPCVD chamber during the first hour of growth in Fig. 9, it is clear that thecentre of the membrane is at elevated temperatures. Also, the sample corners are at much highertemperatures than the rest of the sample. This is corroborated by the displacement fields of thenumerical model that shows that these regions are significantly elevated during growth.16 .1. Scanning Transmission Electron Microscopy A Cross sectional STEM micrograph of the CVD diamond grown on the GaN/III-N membranestack (0.5 mm diameter) is shown in Fig. 10. The EDX analysis shows the carbon rich layer boundto an aluminium and nitrogen rich layer, where the former is the deposited CVD diamond layer andthe latter corresponds to an AlN nucleation layer ( ∼
130 nm ). Underneath the AlN nucleation layer,the AlGaN strain relief layers can be clearly seen ( ∼ . µ m ) which is then followed by the GaNdevice layer ( ∼ . µ m ) and AlGaN barrier layers which forms the device 2DEG. In between thediamond and the AlN nucleation layer shows a very thin layer of silicon and oxygen, most likelySiO based on the atomic ratios. This is a curious finding owing to the absence of any oxygen inthe gas precursors. There are two possible origins for this SiO layer. The first is from leftoverSi after the ICP etch which then forms an oxide when brought to atmosphere the MPCVD stages.The second is that the Si border is etched in the MPCVD plasma pre-treating stage before seeding,resulting in redeposition of the Si on the membrane and subsequent oxide formation when thesample is brought to atmosphere; more discussion on this is given later. The Raman spectra of the 0.5 mm membrane sample is shown in Fig. 11 at different stagesof the fabrication process. Fig. 11.a shows a free-standing diamond sample produced at similargrowth conditions with the Si removed. This sample shows a sharp peak at 1333 cm − associatedwith diamond and minimal signs of non-diamond carbon impurities. Fig. 11.b shows the as-received GaN-on-Si wafer with the Si substrate contribution at 520 cm − and the GaN/III-N layersat around 569 cm − and 734 cm − , corresponding to the E (high) and the A longitudinal opticalmodes of GaN, respectively[53]. After photolithography and ICP etching to create the membrane,Fig. 11.c shows the spectra on the membrane and demonstrates that no Si mode could be detected,implicit of a successful etch, while Fig. 11.d shows that on the Si border the GaN/III-N featuresare relatively unchanged. Fig. 11.e to Fig. 11.h show the spectra after diamond growth. Fig. 11.eshows that after growth the GaN/III-N on the Si border is minimally changed, however, on themembrane in Fig. 11.f, there is also a sharp diamond peak at around 1333 cm − . This is due to the ∼ µ m thick diamond layer on the underside of the GaN/III-N membrane. There also exists verysmall and broad D and G bands at 1350 cm − and 1580 cm − , attributed to a very low concentration17 igure 11: Raman spectra of the 0.5 mm GaN membrane sample at stages during the fabrication process. Spectra weretaken at different spot locations for (a) free-standing diamond reference, (b) as received GaN-On-Si wafer, (c) and (d)GaN side after membrane fabrication, (e) and (f) GaN side after CVD diamond growth and (g) and (h) diamond sideafter CVD diamond growth. Background subtraction has been achieved using a linear fit. of non-diamond (graphitic like) carbon that is introduced during MPCVD growth. Fig. 11.g showsthe diamond grown on the Si. Finally, Fig. 11.h shows the Raman spectra on the GaN membranefrom the diamond side which has a similar spectra to the membrane side in Fig 11.f.Since the diamond layer is much thicker than the GaN/III-N layers, the high intensity diamondpeak dominates the spectra on the membrane, masking the GaN/III-N features. Magnified views ofthe GaN and diamond regions are given in Fig. 12. For both the 0.5 mm and 2 mm samples, the GaN E (high) peaks are clearly shown, however, for the 5 mm sample this peak was not consistentlyfound at multiple regions on the membrane. This is likely caused by damage owing to the elevatedregions as is shown in Fig. 9. For the 0.5 mm and 2 mm samples, the GaN E (high) peaks areshifted to lower frequencies of − . ± . cm − and − . ± . cm − , respectively. This impliesthat the GaN/III-N layers are held in tension when the diamond is deposited which is anticipated18a) (b)(c) (d) Figure 12: Magnified view of the Raman spectra of the GaN/III-N membranes. (a) and (b) show the spectra at theSi peak and GaN E (high) peak while (c) and (d) show the spectra at the diamond peak for membrane diameters of0.5 mm and 2 mm, respectively. Color schemes are the same as Fig. 11. Numerical values are the peak average withstandard deviation of 3 different measurements of a similar region. Spectra obtained with a laser wavelength of 514 nmand background subtraction using a linear fit while Lorentzian peak fits are obtained using least squares curve fitting. from the stress models. The estimated magnitude of the residual biaxial stress can be calculatedusing a linear frequency shift relation of 2.9 cm − GPa − [53]. Using the E (high) peak from the as-received GaN/III-N on Si wafer as the reference peak, an average tensile stress over various regionsof the 0.5 and 2 mm membranes gave approximately 1.0 ± . GPa and 1.0 ± . GPa, respectively.The magnified diamond peak region in Fig. 12.b shows minimal shift between the free-standingdiamond film reference and at various regions on the grown sample. The free-standing film showsa marginal compressive shift to the value of 1332.8 ± . cm − from the typically observed valueof 1332.5 cm − [45, 54]. In contrast to the GaN/III-N spectra which all show tensile shifts from thereference GaN-on-Si wafer, the diamond peaks in both samples show varying global shifts from thereference film; compressive shifts for the 0.5 mm sample and tensile shifts for the 2 mm sample.These global shifts here show very small differences (around 0.2 GPa using a linear shift relation19 efore After BeforeAfter (a) (b)
BeforeAfter (c) (d)
Figure 13: Surface profilometry of GaN/III-N membranes before and after CVD diamond growth. (a) to (c) showtwo traces taken orthogonally across the membrane. The bow ( ∆ z ) is the average of the displacement over the twoorthogonal directions, with the largest standard deviation of µ m . The stress is estimated from Eq. (5) using thecurvature for the initial bow to obtain the initial stress ( σ ) of a pre-stressed GaN film on Si and the curvature forthe final bow to obtain the final stress ( σ ) for a GaN film on diamond. The stress is estimated using thicknesses: t GaN/III-N = 5 . µ m , t Dia = 50 µ m , t Si = 75 µ m . (d) shows ∆ z and σ as a function of membrane diameter. of 2.87 cm − GPa − [55]) in the intrinsic stresses in the deposited diamond. The surface profilometry of the GaN side of the membranes before and after CVD growthis shown in Fig. 13. In addition to the prediction of thermal stresses, the analytical model canalso be used to infer the stresses using Eq. (5) and the defined radii of curvature. An indicationas to whether a simplified analytical model can be used accurately or not can be determined by20orroborating these values with the Raman spectroscopy measurements. A clear trend of increasingbow with diameter is found, however, large discrepancies are noted for the implied stress data.Starting with the smallest 0.5 mm diameter membrane, the initial bow was minimal at less than µ m . After diamond growth, the bow was around µ m . The calculated stress using Eq. (5)suggests an initial value of around 0.8 GPa and increases to a very large value of around 23.6 GPaafter growth , a value much higher than the experimentally measured tensile strength[34]. The 2mm membrane showed a larger initial bow of µ m and increased by µ m after CVD diamondgrowth. The initial stress is similar at 0.8 GPa with a stress after growth of 5.4 GPa, much lowerthan the 0.5 mm membrane. Finally, the 5 mm membrane shows a much larger initial strain in theopposite direction. While the initial strain is different, the stresses can be compared with the othersamples based on the net stress. Also, after diamond growth, a considerable difference is foundbetween the orthogonal traces, with a large region warped in the centre of the membrane. This isdue to the fact that the large membrane has bowed significantly away from the heat sunk sampleholder and pushed further into the plasma resulting in thermal runaway and damage to the GaN/III-N film. Using the initial curvature from the edges of the membrane, the maximum estimated netbow is considerably larger at around µ m .
5. Discussion
There are several key findings of this thermal stress study that should be considered before de-signing and fabricating diamond on GaN/III-N membranes: (1) analytical and numerical modellingaccuracy, (2) damage to larger membranes, (3) etching and redeposition of the Si border and finally(4) approaches to reducing membrane bow.
The presented analytical model does not give an accurate reproduction of the experimentalresults; larger bow for large membranes, overall smaller stresses than those found in experiment andmost pertinent is the almost a non-existent bow for much smaller membranes. This is indeed dueto the additional stresses caused by the Si border that are not analytically modelled. The numericalmodel produces a better representation of the experimental data by exhibiting a measurable bow atsmaller sizes, however, there still exists a discrepancy in larger sizes as with the analytical model.21 igure 14: Comparison of membrane bow from experimental measurements, analytical model and numerical modelwith additional temperature gradients introduced. The numerical model parameters used were: t GaN = 1 . µ m , t III-N =3 . µ m , t Dia = 50 µ m , t Si = 75 µ m and a deposition temperature of T g = 720 ◦ C and variation induced using Eq. 7.The analytical model uses the same constant deposition temperature and thicknesses with a combined GaN/III-N layerand the result showing the combined heating and cooling stresses.
Fig. 7, show bows of almost twice the experimental values, implying that the induced thermalstress is much higher in the model.One important factor that has not been considered in either of the models is the temperaturegradient across the sample. In Fig. 9, it is clear that the corners of the sample are at much highertemperatures, owing to the bowing upwards of the edges into the plasma. The base thermal stressmodel assumes a uniform temperature across the whole sample. A simple linear spatial temperaturegradient can be imposed to replicate this phenomenon that is scaled to the sample size through thefollowing: T ( x, y ) = T g (cid:32) β (cid:112) x + y ) W sub (cid:33) (7)where T is the spatially dependent temperature in ◦ C, T g is the growth temperature in the centre ofthe membrane, β is a temperature variation parameter, x and y are the initial positions in Cartesiancoordinates and W sub is the width of whole sample. Fig. 14 demonstrates the use of a temperaturegradient, which drastically reduces the bow in the centre to align with experimental values whileincreasing the stress by a small amount. For example, at a β value of 0.5, the temperature linearlyincreases from 720 ◦ C at the centre to 1,080 ◦ C at the corner tip of the sample which in turn createsadditional stresses which counteract the central bow. This demonstrates the importance of usingnumerical models for examining thermal stresses in GaN/III-N membrane structures.22 .2. Heat sinking during MPCVD
The damage to the largest membrane marks an interesting issue in the CVD diamond onGaN/III-N membrane approach. This comes down to a matter of bow and thermal runaway. Notethat while the net bow of the 5 mm diameter membrane is µ m its vertical displacement above thezero point ( ∼ µ m ) is not that much larger than the 2 mm diameter membrane ( ∼ µ m ) whichwas not damaged. A plausible reason as to why the larger membrane sustained damage is that theheat sinking capability is less effective over larger areas owing to the poor thermal conductivityof GaN and AlGaN. The temperature at the membrane surface was likely much higher than forthe other samples. This ultimately limits any large area CVD diamond growth over GaN/III-Nmembranes unless appropriate heat sinking is employed. The thin layer of SiO at the interface between the CVD diamond and the N-polar side of theAlN is a potentially serendipitous finding. This SiO layer facilitates a stable carbide bond for thediamond to the III-N stack; a SiN bond with the N-polar side of the AlN and a SiC bond with thediamond. There are two cases where this layer may be deposited. The first is at the ICP membraneetch stage where the SiO layer is simply due to an incomplete etch through the Si and the remainingfew nanometres oxidise from exposure to air after the sample is brought up to atmosphere. A secondorigin is during the MPCVD N /H plasma pre-treating stage before the seeding process where theSi border is etched and redeposited on the membrane. There are numerous studies on Si in H microwave plasmas which demonstrate the production of the volatile silane (SiH ) gas that diffusesto and reacts with a target substrate to redeposit Si[56, 57]. Pure SiH as a source gas can alsobe used to co-deposit diamond onto substrates[58]. Once the sample is brought up to atmosphereafter the N /H plasma pre-treatment, the deposited silicon oxidises to form a SiO layer and thediamond seeds are introduced. It’s also shown that the N-Polar face of AlN has been shown to havea high concentration of surface oxide groups[59] which may contribute to the formation of SiO .From a stress perspective, the adhesion strength needs investigation as high stresses in this layerwill result in delamination. This layer may be incredibly important for creating an interface withN-polar faces and CVD diamond, subject of another study[60].23 .4. Reducing membrane bow Finally, the micron large membrane bows found for the CVD diamond on GaN/III-N mem-branes presents the biggest challenge for device manufacturing using contact lithography. Suchlarge membrane bows cannot be dealt with as is, however, it is important to note that the resultsin this study demonstrate the net membrane bows. This means that if the membrane is sufficientlypre-stressed before growth in the opposite direction, the bow upon heating will be counteracted andthe CVD diamond would be deposited on a flat
GaN/III-N membrane. As per the model findings,the extreme stiffness of the diamond should then hold the membrane flat upon cooling, resulting infar less bow. This would also solve the heat sinking issues for larger membranes in point (2) as themembrane would not bow towards the plasma and become damaged. As a final processing step, themembranes can then be laser cut to reveal a free-standing GaN/III-N/diamond stack, ready for de-vice processing. This idea of course requires significant GaN-on-Si wafer development to producepre-stressed wafers, out of scope of this study.
6. Conclusion
The thermal stresses of the membrane approach for the integration of chemical vapour deposited(CVD) diamond with gallium nitride (GaN) on group-III-N (III-N) layers have been investigatedusing analytical and numerical modelling and experimental results. In utilising the Stoney analyti-cal model in the presented way, the anticipated thermal stresses in GaN/III-N membrane structuresare not accurately reproduced to the values found in experiment. While this is covered using numer-ical modelling, the result still requires careful consideration of the spatial temperature distributionover the sample whereby simple linear gradients appear to suffice. The dependence of various pa-rameters including layer thicknesses, temperature and diamond stiffness on the membrane stressand bow has been modelled with the overall conclusion that the membrane deformation when it isheated defines the expected structure after cooling to room temperature. A CVD diamond layer asthin as µ m is enough to lock this deformation in place, meaning that this initial deformation isthe key to reducing bow. Experimental measurements using Raman spectroscopy corroborate thenumerical models and additionally, simply using the radius of curvature from surface profilometrydata to infer the stress is invalid at sizes lower than several millimetres. The use of a Si border in thismembrane method also introduces SiO at the interface between the diamond and the GaN/III-N24tack. The membrane bow is the biggest issue that must be addressed as large membranes bow to-wards the microwave plasma and become damaged, however, if the membranes can be pre-stressedbefore growth, the final bow is expected to reduce.
7. Acknowledgements
This project has been supported by Engineering and Physical Sciences Research Council (EP-SRC) under program Grant GaN-DaME (EP/P00945X/1). J. A. Cuenca is an EPSRC Postdoctoralresearcher. DJ Wallis acknowledges support of EPSRC fellowship (EP/N01202X/2).
References [1] F. Ejeckam et al. , “GaN-on-diamond: A brief history,” in . IEEE, aug 2014, pp. 1–5.[2] Q. Zheng, C. Li, A. Rai, J. H. Leach, D. A. Broido, and D. G. Cahill, “Thermal conductivityof GaN, 71GaN, and SiC from 150 K to 850 K,”
Physical Review Materials , vol. 3, no. 1, p.014601, jan 2019.[3] V. Pishchik, L. A. Lytvynov, and E. R. Dobrovinskaya,
Sapphire . Boston, MA: Springer US,2009.[4] J. W. Pomeroy, M. Bernardoni, D. C. Dumka, D. M. Fanning, and M. Kuball, “Low thermalresistance GaN-on-diamond transistors characterized by three-dimensional Raman thermog-raphy mapping,”
Applied Physics Letters , vol. 104, no. 8, p. 083513, feb 2014.[5] L. Wei, P. K. Kuo, R. L. Thomas, T. R. Anthony, and W. F. Banholzer, “Thermal conductivityof isotopically modified single crystal diamond,”
Physical Review Letters , vol. 70, no. 24, pp.3764–3767, jun 1993.[6] K. Hirama, Y. Taniyasu, and M. Kasu, “AlGaN/GaN high-electron mobility transistors withlow thermal resistance grown on single-crystal diamond (111) substrates by metalorganicvapor-phase epitaxy,”
Applied Physics Letters , vol. 98, no. 16, p. 162112, apr 2011.257] M. J. Tadjer et al. , “Reduced Self-Heating in AlGaN/GaN HEMTs Using NanocrystallineDiamond Heat-Spreading Films,”
IEEE Electron Device Letters , vol. 33, no. 1, pp. 23–25, jan2012.[8] Y. Zhou et al. , “Thermal characterization of polycrystalline diamond thin film heat spreadersgrown on GaN HEMTs,”
Applied Physics Letters , vol. 111, no. 4, p. 041901, jul 2017.[9] Y. Han, B. L. Lau, G. Tang, and X. Zhang, “Thermal Management of Hotspots Using Di-amond Heat Spreader on Si Microcooler for GaN Devices,”
IEEE Transactions on Compo-nents, Packaging and Manufacturing Technology , vol. 5, no. 12, pp. 1740–1746, dec 2015.[10] T. Gerrer et al. , “Transfer of AlGaN/GaN RF-devices onto diamond substrates via van derWaals bonding,”
International Journal of Microwave and Wireless Technologies , vol. 10, no.5-6, pp. 666–673, jun 2018.[11] D. Francis, F. Faili, D. Babi´c, F. Ejeckam, A. Nurmikko, and H. Maris, “Formation and char-acterization of 4-inch GaN-on-diamond substrates,”
Diamond and Related Materials , vol. 19,no. 2-3, pp. 229–233, feb 2010.[12] F. Mu, R. He, and T. Suga, “Room temperature GaN-diamond bonding for high-power GaN-on-diamond devices,”
Scripta Materialia , vol. 150, pp. 148–151, jun 2018.[13] K. Wang, K. Ruan, W. Hu, S. Wu, and H. Wang, “Room temperature bonding of GaN ondiamond wafers by using Mo/Au nano-layer for high-power semiconductor devices,”
ScriptaMaterialia , vol. 174, pp. 87–90, jan 2020.[14] J. C. Kim et al. , “Challenging endeavor to integrate gallium and carbon via direct bonding toevolve GaN on diamond architecture,”
Scripta Materialia , vol. 142, pp. 138–142, jan 2018.[15] Z. Dong et al. , “Preparation and Characteristics of GaN Films on Freestanding CVD ThickDiamond Films,”
Chinese Physics Letters , vol. 27, no. 1, p. 018102, jan 2010.[16] H. Sun et al. , “Reducing GaN-on-diamond interfacial thermal resistance for high power tran-sistor applications,”
Applied Physics Letters , vol. 106, no. 11, p. 111906, mar 2015.2617] M. D. Smith et al. , “GaN-on-diamond technology platform: Bonding-free membrane manu-facturing process,”
AIP Advances , vol. 10, no. 3, p. 035306, mar 2020.[18] M. Hetzl et al. , “GaN Nanowire Arrays for Efficient Optical Read-Out and OptoelectronicControl of NV Centers in Diamond,”
Nano Letters , vol. 18, no. 6, pp. 3651–3660, jun 2018.[19] S. Mandal et al. , “Surface Zeta Potential and Diamond Seeding on Gallium Nitride Films,”
ACS Omega , vol. 2, no. 10, pp. 7275–7280, 2017.[20] W. M. Waller, J. W. Pomeroy, D. Field, E. J. Smith, P. W. May, and M. Kuball, “Thermalboundary resistance of direct van der Waals bonded GaN-on-diamond,”
Semiconductor Sci-ence and Technology , 2020.[21] C.-s. Yan, Y. K. Vohra, H.-k. Mao, and R. J. Hemley, “Very high growth rate chemical va-por deposition of single-crystal diamond,”
Proceedings of the National Academy of Sciences ,vol. 99, no. 20, pp. 12 523–12 525, oct 2002.[22] M. Ali and M. Ürgen, “Surface morphology, growth rate and quality of diamond films syn-thesized in hot filament CVD system under various methane concentrations,”
Applied SurfaceScience , vol. 257, no. 20, pp. 8420–8426, 2011.[23] G. D. Barber and W. A. Yarbrough, “Growth Rate of Diamond on Polycrystalline <110>Diamond Substrates from Carbon Disulfide in Hydrogen by Hot-Filament-Assisted ChemicalVapor Deposition,”
Journal of the American Ceramic Society , vol. 80, no. 6, pp. 1560–1566,jan 1997.[24] M. Amaral, A. Fernandes, M. Vila, F. Oliveira, and R. Silva, “Growth rate improvements inthe hot-filament CVD deposition of nanocrystalline diamond,”
Diamond and Related Materi-als , vol. 15, no. 11-12, pp. 1822–1827, nov 2006.[25] M. J. Edwards, C. R. Bowen, D. W. E. Allsopp, and A. C. E. Dent, “Modelling wafer bow insilicon-polycrystalline CVD diamond substrates for GaN-based devices,”
Journal of PhysicsD: Applied Physics , vol. 43, no. 38, 2010.[26] X. Li et al. , “Suspended p–n Junction InGaN/GaN Multiple-Quantum-Well Device With Se-lectable Functionality,”
IEEE Photonics Journal , vol. 7, no. 6, pp. 1–7, dec 2015.2727] Yongjin Wang et al. , “Circular GaN Membrane Gratings,”
IEEE Photonics Technology Let-ters , vol. 26, no. 9, pp. 915–918, may 2014.[28] Q. Liu, C. Wang, W. Yang, H. Wang, and R. Xu, “GaN Membrane With Nano-Grooves forSingle-Band Coupling in the Entire Visible Wavelength Range,”
IEEE Photonics Journal ,vol. 10, no. 2, pp. 1–12, apr 2018.[29] B. S. Kang et al. , “Capacitance pressure sensor based on GaN high-electron-mobilitytransistor-on-Si membrane,”
Applied Physics Letters , vol. 86, no. 25, p. 253502, jun 2005.[30] T. Lalinský et al. , “Micromachined membrane structures for pressure sensors based on Al-GaN/GaN circular HEMT sensing device,”
Microelectronic Engineering , vol. 98, pp. 578–581, oct 2012.[31] Y. Alifragis, G. Roussos, A. K. Pantazis, G. Konstantinidis, and N. Chaniotakis, “Free-standing gallium nitride membrane-based sensor for the impedimetric detection of alcohols,”
Journal of Applied Physics , vol. 119, no. 7, p. 074502, feb 2016.[32] T. H. Sung, J. C. Huang, J. H. Hsu, and S. R. Jian, “Mechanical response of GaN film andmicropillar under nanoindentation and microcompression,”
Applied Physics Letters , vol. 97,no. 17, pp. 1–4, 2010.[33] R. Nowak et al. , “Elastic and plastic properties of GaN determined by nano-indentation ofbulk crystal,”
Applied Physics Letters , vol. 75, no. 14, pp. 2070–2072, 1999.[34] J. Brown, A. Baca, K. Bertness, D. Dikin, R. Ruoff, and V. Bright, “Tensile measurementof single crystal gallium nitride nanowires on MEMS test stages,”
Sensors and Actuators A:Physical , vol. 166, no. 2, pp. 177–186, apr 2011.[35] Y. N. Ahn, S. H. Lee, S. K. Lim, K. J. Woo, and H. Kim, “The role of inversion domainboundaries in fabricating crack-free GaN films on sapphire substrates by hydride vapor phaseepitaxy,”
Materials Science and Engineering: B , vol. 193, no. C, pp. 105–111, mar 2015.[36] Y. Umeno, A. Kubo, and S. Nagao, “Density functional theory calculation of ideal strengthof SiC and GaN: Effect of multi-axial stress,”
Computational Materials Science , vol. 109, pp.105–110, nov 2015. 2837] B. L. Hancock et al. , “Ultraviolet micro-Raman spectroscopy stress mapping of a 75-mmGaN-on-diamond wafer,”
Applied Physics Letters , vol. 108, no. 21, p. 211901, may 2016.[38] X. Pan, M. Wei, C. Yang, H. Xiao, C. Wang, and X. Wang, “Growth of GaN film on Si (111)substrate using AlN sandwich structure as buffer,”
Journal of Crystal Growth , vol. 318, no. 1,pp. 464–467, mar 2011.[39] H. Windischmann, G. F. Epps, Y. Cong, and R. W. Collins, “Intrinsic stress in diamond filmsprepared by microwave plasma CVD,”
Journal of Applied Physics , vol. 69, no. 4, pp. 2231–2237, feb 1991.[40] A. Rajamani et al. , “Chemistry-induced intrinsic stress variations during the chemical vapordeposition of polycrystalline diamond,”
Journal of Applied Physics , vol. 96, no. 6, pp. 3531–3539, 2004.[41] G. A. Slack and S. F. Bartram, “Thermal expansion of some diamondlike crystals,”
Journalof Applied Physics , vol. 46, no. 1, pp. 89–98, jan 1975.[42] C. Roder, S. Einfeldt, S. Figge, and D. Hommel, “Temperature dependence of the thermalexpansion of GaN,”
Physical Review B , vol. 72, no. 8, p. 085218, aug 2005.[43] K. Seshan,
Handbook of Thin Film Deposition , ser. Materials Science and Process Technol-ogy. Elsevier Science, 2001.[44] S. Franssila,
Introduction to Microfabrication . Wiley, 2010.[45] V. G. Ralchenko, E. Pleiler, D. N. Sovyk, and V. I. Konov, “Strength of optical quality poly-crystalline CVD diamond,”
Inorganic Materials: Applied Research , vol. 2, no. 5, pp. 439–444, oct 2011.[46] M. Mohr et al. , “Young’s modulus, fracture strength, and Poisson’s ratio of nanocrystallinediamond films,”
Journal of Applied Physics , vol. 116, no. 12, p. 124308, sep 2014.[47] R. Bruls, H. Hintzen, G. de With, and R. Metselaar, “The temperature dependence of theYoung’s modulus of MgSiN2, AlN and Si3N4,”
Journal of the European Ceramic Society ,vol. 21, no. 3, pp. 263–268, mar 2001. 2948] S. Mandal et al. , “Thick, Adherent Diamond Films on AlN with Low Thermal Barrier Resis-tance,”
ACS Applied Materials & Interfaces , vol. 11, no. 43, pp. 40 826–40 834, oct 2019.[49] H. Shibata et al. , “High thermal conductivity of gallium nitride (GaN) crystals grown byHVPE process,”
Materials Transactions , vol. 48, no. 10, pp. 2782–2786, 2007.[50] R. Rounds et al. , “Thermal conductivity of single-crystalline AlN,”
Applied Physics Express ,vol. 11, no. 7, p. 071001, jul 2018.[51] O. Williams, A. Kriele, J. Hees, M. Wolfer, W. Müller-Sebert, and C. Nebel, “High Young’smodulus in ultra thin nanocrystalline diamond,”
Chemical Physics Letters , vol. 495, no. 1-3,pp. 84–89, jul 2010.[52] I. Yonenaga and K. Motoki, “Yield strength and dislocation mobility in plastically deformedbulk single-crystal GaN,”
Journal of Applied Physics , vol. 90, no. 12, pp. 6539–6541, dec2001.[53] M. Kuball, “Raman spectroscopy of GaN, AlGaN and AlN for process and growth monitor-ing/control,”
Surface and Interface Analysis , vol. 31, no. 10, pp. 987–999, oct 2001.[54] A. Dychalska, K. Fabisiak, K. Paprocki, A. Dudkowiak, and M. Szybowicz, “Temperaturedependence of stress in CVD diamond films studied by Raman spectroscopy,”
MaterialsScience- Poland , vol. 33, no. 3, pp. 620–626, 2015.[55] H. Boppart, J. van Straaten, and I. F. Silvera, “Raman spectra of diamond at high pressures,”
Physical Review B , vol. 32, no. 2, pp. 1423–1425, jul 1985.[56] T. Yamada, H. Ohmi, K. Okamoto, H. Kakiuchi, and K. Yasutake, “Effects of Surface Tem-perature on High-Rate Etching of Silicon by Narrow-Gap Microwave Hydrogen Plasma,”
Japanese Journal of Applied Physics , vol. 51, no. 10 PART 2, p. 10NA09, oct 2012.[57] H. Ohmi, A. Goto, D. Kamada, Y. Hamaoka, H. Kakiuchi, and K. Yasutake, “Purified Sifilm formation from metallurgical-grade Si by hydrogen plasma induced chemical transport,”
Applied Physics Letters , vol. 95, no. 18, 2009.3058] V. S. Sedov et al. , “Co-deposition of diamond and β -SiC by microwave plasma CVD in H2-CH4-SiH4 gas mixtures,” Diamond and Related Materials , vol. 98, no. July, p. 107520, 2019.[59] T. Yoshikawa et al. , “Electrostatic Self-Assembly of Diamond Nanoparticles onto Al- andN-Polar Sputtered Aluminum Nitride Surfaces,”
Nanomaterials , vol. 6, no. 11, p. 217, nov2016.[60] D. E. Field et al. , “Crystalline interlayers for reducing the effective thermal boundary resis-tance of GaN-on-diamond,”