Selective area growth (SAG) of gallium nitride (GaN) on silicon (Si) wafers efficiently relaxes the tensile stress that is generated in the GaN layer, when the structure is cooled down to room temperature after the growth. Hence, SAG enables the growth of thicker layers that are capable of operating at higher voltages than those grown in 2D layers. In this study, two GaN layers are grown by SAG on 200 mm-diameter Si(111) wafers by metal organic vapor phase epitaxy for the fabrication of pseudo-vertical p–n diodes. During the growth, the SiH4 precursor flow for the first sample was double than that for the second one. The uniformity of the doping concentration of the layers is investigated by scanning spreading resistance microscopy and the p- and n-type doped regions are examined by scanning capacitance microscopy. A low net doping concentration of 1.4 × 1016 cm−3 is extracted from capacitance–voltage measurements and a destructive breakdown occurs at 700 V for a 90 μm-diameter pseudo-vertical p–n diode. These results show the high potential of the SAG of GaN on Si wafers for vertical power devices.

Wide-bandgap semiconductors, such as gallium nitride (GaN) and silicon carbide (SiC), are excellent candidates for replacing silicon (Si) in high-power applications. For devices operating at high voltage, it is important to choose materials that have a large energy gap and high critical electric field. The energy bandgap of GaN is three times larger than that of Si (GaN: 3.4 eV, Si: 1.12 eV), which means that GaN-based devices can operate at very high temperatures, with temperatures reported being above 400 up to 900 °C.1–3 Si-based metal–oxide-semiconductor field-effect transistors (MOSFETs) usually have a maximum operating temperature of 150 °C. Moreover, the theoretical value of the critical electric field of GaN is 11 times higher than that of Si (GaN: 3.3 MV cm−1, Si: 0.3 MV cm−1). Although the actual value of epitaxial GaN layers is expected to be lower due to defects and dislocations, GaN-based devices are capable of operating at significantly higher voltages than their Si-based counterparts for a given layer thickness.4 

Native GaN wafers would be the ideal choice for the growth of GaN. However, due to their high cost and limited size, alternative substrates are attractive. Large-diameter Si wafers are an excellent choice due to their low cost and the challenges in processing them are minimized. Nonetheless, the lattice and coefficient of thermal expansion (CTE) mismatch between GaN and Si is a major concern, since they lead to a high dislocation density, and unless the strain is correctly engineered, the GaN layers tend to be cracked.5 

The epitaxy of GaN on Si wafers requires an AlN nucleation layer, since GaN cannot be directly grown on Si wafers due to meltback etching.6 In addition, AlGaN buffer layers are used to introduce compressive stress in the grown GaN layer to compensate the large tensile stress generated during cool-down from growth temperature, because of the CTE mismatch between GaN and Si. For thicker GaN layers, it is also challenging to introduce sufficient compressive strain without making the wafers more fragile.7 Therefore, the thickness of full-wafer GaN layers that can be grown without cracking is limited to less than 8 μm.8 Selective area growth (SAG) is an efficient technique to relax the tensile stress in the GaN layer elastically, and consequently, grow thicker layers.

During SAG, Ga atoms diffuse toward the mask openings, where the mesas are grown. The surplus of the Ga atoms in the openings results in a lateral overgrowth, covering a small part of the mask and resulting in the formation of superelevations in the areas adjacent to the mask openings. This means that the thickness in these areas can be greater than that at the center of the mesas; hence, the thickness profile is not uniform. The extent of the lateral and vertical overgrowth depends on the growth conditions and the mask area surrounding the openings. In addition, during this diffusion, the Ga atoms may slightly etch the mask, incorporating atoms that are good n-type dopants of GaN, for example, silicon or oxygen. The use of conventional dielectrics as mask materials, such as SiO2 or SiN, leads to a grown GaN layer with a high unintentional doping concentration.9–11 We have shown that by using Al2O3 as the mask material, a very low unintentional doping concentration is achieved, around 1016 cm−3.11 

After growth, thick GaN structures from SAG can be used for the fabrication of vertical power devices. The vertical configuration enhances the reliability of the devices by moving the peak electric field away from the surface and into the bulk of the layer. As a result, vertical devices can operate at high electric fields, closer to the critical electric field of the material,12 while failure by avalanche avoids destructive failure modes found in high electron mobility transistor (HEMT) devices. Furthermore, the more uniform electric field leads to a more uniform current distribution, which can make the thermal management of such devices easier.13 Finally, carbon doping is typically used to reduce leakage current in HEMT devices, which can lead to trapping and increased dynamic resistance.14 As carbon is avoided in the growth of vertical structures, reduced trapping is expected for these devices.

In other studies, the selective area growth of GaN has been carried out on sapphire substrates with doping concentrations of 5 × 1016 and slightly higher than 1016 cm−3 by using Al2O3 as the mask material. On these layers, pseudo-vertical Schottky diodes were fabricated, on which destructive breakdown occurred at 500 V and soft breakdown at 450 V, respectively.10,15

In this study, two samples are grown for the fabrication of pseudo-vertical p–n diodes with different doping concentrations. The purpose of this study is to demonstrate that a low intentional doping concentration close to 1016 cm−3 and 9 μm-thick crack-free structures are achievable by SAG. Therefore, this work is a crucial step toward the successful growth of GaN drift layers for high voltage vertical power devices. Scanning spreading resistance microscopy (SSRM) and scanning capacitance microscopy (SCM) are employed to provide spatial information on the doping concentration of the drift layer by electrically characterizing the cross sections of the layers. The thickness profiles of the structures are measured by stylus profilometry, and finally, the net donor concentrations ND–NA of the drift layers are extracted by capacitance–voltage (C–V) measurements16 and the breakdown voltages measured by reverse bias I–V measurements.

The growth of the samples took place in a single-wafer AIXTRON Crius-R200 metal organic vapor phase epitaxy (MOVPE) tool on 200 mm-diameter Si(111) wafers. The template structures consisted of the 400 nm-thick AlN and 1.5 μm-thick AlGaN buffer layers, a 300 nm-thick undoped GaN layer, and three silicon doped GaN layers, each 350 nm-thick each, with doping concentrations of 5 × 1016, 5 × 1017, and 5 × 1018 cm−3 from the bottom to the top. The purpose of these layers was to serve as a reference for the investigation of the doping concentration of the drift layer through the SSRM and SCM measurements on the cross section of the sample and to serve as a lateral connection between the anode and the cathode for the pseudo-vertical diodes. Next, a 50 nm-thick Al2O3 mask was deposited by atomic layer deposition (ALD) at 300 °C, patterned with photolithography and etched. Finally, the selective area growth of GaN was performed in the openings of the mask.

The n-doped GaN drift layers on both samples, sample 1 and sample 2, were grown at 1040 °C, the pressure of the chamber was 400 mbar, and the NH3 flow was set to 10 slm. The nominal growth rate was 1.5 μm/h (for full-wafer growth) and the growth time was 3.5 h. The n-GaN dopant was Si, and the flow of its precursor, silane (SiH4), was double for sample 1 than that for sample 2. On top of the n-type drift layer, a 400 nm-thick p-type Mg-doped GaN layer was grown, with a doping concentration of 4 × 1018 cm−3, and a 50 nm-thick p-type Mg-doped capping layer with a doping concentration of 1 × 1019 cm−3. The precursors for GaN and Mg were tri-methyl gallium (TMGa) and cyclopentadienyl-magnesium (Cp2Mg), respectively. The precursor flows were set to those for a planar wafer growth. After the growth, the Al2O3 mask was not removed.

The cross sections were prepared by cleaving the samples and finalized by ion polishing in a Leica TIC-3X tool. Scanning spreading resistance microscopy (SSRM) and scanning capacitance microscopy (SCM) were carried out on the cross sections, in order to extract information on the electrical characteristics of the drift layer.

SSRM is a good technique for providing spatial mapping of the doping concentration in a semiconducting layer. It is based on contact-mode atomic force microscopy (AFM) and doped-diamond coated tips are used to penetrate the oxide layer that may form on the surface of the layer. An electrical current flows through the biased semiconducting layer and the conductive tip, and hence, the local resistivity of the sample is extracted. A current logarithmic amplifier with a range from 10 pA to 100 μA is included in the measurement setup, which means that the resistance of both low- and high-doped semiconducting layers can be measured.17,18 In this work, silver paint was applied to the bottom n-doped GaN layers of the template structure to give an electrical contact. The SSRM measurements were performed in air on a Bruker Dimension ICON AFM tool at atmospheric pressure.

SCM is also a contact-mode AFM based technique. This method is normally performed on an oxidized surface so that a metal-oxide-semiconductor (MOS) junction is formed among the tip, the oxide, and the layer. However, SCM can be efficient even in the absence of the oxide layer, as long as a Schottky barrier is formed between the semiconducting layer and the tip. During the measurement, an AC bias is applied to the tip, which induces capacitance changes in the doped layer because of the accumulation or depletion of the layers. Small changes of the bias result in local capacitance changes, which are dependent on the local carrier density. Measurement of the magnitude of these capacitance changes allows information on the dopant concentration to be extracted. Furthermore, by measuring the difference in phase between the capacitance changes and the AC bias, precise information on the sign of the charges can be extracted.19,20 The SCM measurements were carried out on the same tool as the SSRM measurements in air and at atmospheric pressure.

In order to complete the fabrication of the pseudo-vertical p–n diodes, anode and cathode contacts were deposited on top of the p-doped layer and around the regrown n-doped layer, respectively. The p-doped layer was activated by rapid thermal annealing in an O2/N2 atmosphere prior to device processing. First, the Al2O3 mask was etched by Cl2 and the metal stack Ti/Al/Ni/Au (95/200/20/265 nm) was deposited to form the cathode. This contact was then annealed at 750 °C. Next, the anode contact Ni/Au (50/150 nm) was deposited and annealed at 600 °C. Pseudo-vertical devices on 90 and 140 μm-diameter circular structures were fabricated in this study, with a mask distance of 10 μm around them. Figure 1 shows a schematic of these pseudo-vertical p–n diodes.

FIG. 1.

Schematic of the fabricated pseudo-vertical p–n diodes.

FIG. 1.

Schematic of the fabricated pseudo-vertical p–n diodes.

Close modal

For the growth of the samples, an existing mask pattern was used. Figure 2(a) shows the mask layout for the growth of the 90 μm-diameter circular structures, and Fig. 2(b) shows the scanning electron microscopy (SEM) image of this area after SAG. After the growth, the mesas have developed a hexagonal shape due to the wurtzite structure of GaN grown in the c-plane (0001) direction.21 In addition, superelevations are visible on mesas G and H, which are the two mesas that have the highest mask distance [the distance between the central area and the outside area where growth occurs, shown by the black arrow on Fig. 2(a)] around them. Hence, more material arrives at the edges of these regrown structures due to the diffusion of the Ga atoms from the mask during the growth. The diffusion rates on the mask and on the surface of the regrown layer are not the same, and the material is not able to diffuse across the entire radius of the opening during growth, resulting in the thickness at the edges of these mesas being slightly higher than that at the center.

FIG. 2.

(a) Mask layout for the 90 μm-diameter circular structures with different mask distances around them. The blue color shows the area where the growth occurs, and the white color shows the area covered by the mask. The black double arrow shows the mask distance and (b) SEM image of the structures on sample 1. The Al2O3 mask appears with dark gray color, the names of the grown mesas are shown with black color, and the mask distance around each mesa in μm is shown in yellow.

FIG. 2.

(a) Mask layout for the 90 μm-diameter circular structures with different mask distances around them. The blue color shows the area where the growth occurs, and the white color shows the area covered by the mask. The black double arrow shows the mask distance and (b) SEM image of the structures on sample 1. The Al2O3 mask appears with dark gray color, the names of the grown mesas are shown with black color, and the mask distance around each mesa in μm is shown in yellow.

Close modal

The thickness profiles of mesas B, D, F, and G were measured by stylus profilometry, SSRM measurements were performed on the cross sections of mesas B and F, and SCM measurements were carried out on the cross sections of mesas B and G. These specific structures were chosen in order to investigate the effect resulting from the increasing mask distance on their doping concentration.

Figure 3 shows the extracted thickness profiles of mesas B, D, F, and G of sample 1 and sample 2. On both samples, mesas B and D have very similar uniform thickness profiles and they are about 8.4 and 6.8 μm thick on sample 1 and sample 2, respectively. Mesa F also has a uniform profile on both samples, but this is not the case for mesa G on sample 1. The superelevations, observed in Fig. 2(b), are about 20 μm wide and the thickness at the center of the structure decreases from 11 to 9.4 μm. Mesa G on sample 2 has a uniform thickness profile, and it is 8.7 μm thick. As the mask distance around the opening has increased from 10 to 30 μm, more materials have diffused toward the opening, increasing the growth rate of the mesa at the edge, creating a less uniform thickness profile.

FIG. 3.

Stylus profilometry measurements of mesas B, D, F, and G on sample 1 and sample 2.

FIG. 3.

Stylus profilometry measurements of mesas B, D, F, and G on sample 1 and sample 2.

Close modal

Figure 4(a) shows the SSRM measurement on the cross section at the edge of mesa B on sample 1, and Fig. 4(b) shows the measurement at the edge of mesa F. Both measurements were carried out under a DC bias of −6 V. Below the regrown GaN layer, the three differently doped n-type GaN layers can be distinguished, with darker color for the more doped layers. On the top of the mesa, the p-doped GaN layer can be distinguished by its light pink color. The regrown GaN layer appears to have the same color in the SSRM images throughout its thickness, indicating that it has a uniform doping concentration. A change in the color observed toward the middle of the image, and, hence, in the resistance, is most probably due to an artifact of the measurement, rather than a change in the resistance of the layer. Similarly, at the edge of the mesa, the color becomes brighter over small areas, suggesting that the resistance of the regrown layer increases. However, as these are aligned vertically, in the same direction as the scanning tip, this is likely to be due to the damaged surface, because SSRM is carried out in the contact mode and the diamond tip scratches the surface of the sample. The comparison of the resistances between the bottom GaN layers and the regrown GaN layer shows that the doping concentration of the latter is significantly lower than 5 × 1018 cm−3. However, it is difficult to determine if its doping concentration is in the order of 1017 or 1016 cm−3. Finally, at the edge of mesa F, a thin layer of lower resistance is observed, and, thus, of higher doping concentration, the width of which decreases toward the top of the layer. The color indicates that the doping is probably of the order of 1017 cm−3. This layer could originate from the diffusion of the Ga atoms, having incorporated donor impurities from the mask, most probably oxygen, resulting in higher unintentional doping concentration, or due to different incorporations of donor impurities such as oxygen on the semi-polar plane.

FIG. 4.

SSRM measurements on the edge of the cross sections of (a) mesa B and (b) mesa F on sample 1 under a DC bias of −6 V. The doping concentrations of the bottom n-doped GaN layers are shown in yellow.

FIG. 4.

SSRM measurements on the edge of the cross sections of (a) mesa B and (b) mesa F on sample 1 under a DC bias of −6 V. The doping concentrations of the bottom n-doped GaN layers are shown in yellow.

Close modal

Figures 5(a) and 5(b) show the SCM measurements on the edge of the cross sections of mesas B and G, respectively. This method illustrates the p- and n-doped regions, with both measurements performed under a DC bias of 0 V. On top of the regrown layer, the p-doped GaN layer is shown in orange, while the n-doped drift layer is blue. For both of these images, we note that no p-GaN layer is seen at the edge of these islands, only on the top surface. This could be due to reduced magnesium incorporation on semi-polar planes,22 due to depletion in the layers, or due to very thin layers which cannot be seen with the resolution of the SCM. Regarding mesa B, the local change in the intensity of the signal in the drift layer along a vertical line is probably an artifact from the measurement, as these are in the same direction as the scanning of the tip, as for the SSRM measurements. The drift layer of mesa G shows a uniform SCM signal. At the edge of the mesa, there appears to be a thin layer, which has a more intense signal, and its shape is very similar to that of Fig. 4(b). However, since the SCM data are a combination of both SCM amplitude and phase signal, it is not possible to extract the doping concentration of the layer.

FIG. 5.

SCM measurements on the edge of the cross sections of (a) mesa B and (b) mesa G on sample 1 under a DC bias of 0 V. The p-doped regions are shown in orange and the n-doped regions in blue.

FIG. 5.

SCM measurements on the edge of the cross sections of (a) mesa B and (b) mesa G on sample 1 under a DC bias of 0 V. The p-doped regions are shown in orange and the n-doped regions in blue.

Close modal

Figure 6(a) shows the optical microscopy image of a 140 μm-diameter diode fabricated on sample 2. As seen for the structures of Fig. 2, the mesa has developed a hexagonal shape and is free from cracks. A circular ring, which has cracks, surrounds the structure; however, the area of interest, where the anode contact is deposited, is crack free. The cathode contact is visible on the image with a bright yellow color surrounding the ring.

FIG. 6.

(a) Optical microscopy image of the 140 μm-diameter circular structure on sample 2 surrounded by a circular disk. The regrown mesa on which the anode is deposited is crack free. The anode and cathode contacts are noted in the image, (b) stylus profilometry measurements on the 90 and 140 μm-diameter structures on sample 1 (red color) and sample 2 (blue color).

FIG. 6.

(a) Optical microscopy image of the 140 μm-diameter circular structure on sample 2 surrounded by a circular disk. The regrown mesa on which the anode is deposited is crack free. The anode and cathode contacts are noted in the image, (b) stylus profilometry measurements on the 90 and 140 μm-diameter structures on sample 1 (red color) and sample 2 (blue color).

Close modal

Figure 6(b) shows the extracted thickness profiles of the two structures to be made into devices on sample 1 and sample 2. After the growth, all the structures have uniform thickness profiles on both samples. On sample 1, the 90 μm-diameter structure has a thickness of 7.4 μm and the 140 μm-diameter structure is 7.7 μm thick. On sample 2, both structures are about 6.4 μm thick.

Figure 7 shows the AFM images at the center of these structures for both samples. The white spots that are shown on the AFM images of sample 1 are likely to be residues from the cleaving of the sample for the preparation of the cross section. Smooth crack-free surfaces have been obtained after the growth, and the atomic steps are clearly visible.

FIG. 7.

2 × 2 μm2 AFM images at the center of the (a) 90 and (b) 140 μm-diameter structures on (i) sample 1 and (ii) sample 2.

FIG. 7.

2 × 2 μm2 AFM images at the center of the (a) 90 and (b) 140 μm-diameter structures on (i) sample 1 and (ii) sample 2.

Close modal

The root mean square surface roughness of the 90 μm-diameter structures is 0.21 and 0.20 nm for sample 1 and sample 2, respectively. For the 140 μm-diameter structures, the roughness is 0.24 and 0.22 nm for sample 1 and sample 2, respectively.

On the 140 μm-diameter structures for both samples, the C–V measurements were performed in order to extract the net doping concentration of the drift layers. Figure 8(a) shows the 1/C2 graph vs the voltage applied on the anode contact. From the linear fitting on these curves, the extracted net doping concentration of the drift layer was 3.0 × 1016 and 1.4 × 1016 cm−3 for samples 1 and 2, respectively. The decrease of the SiH4 flow by half during the growth of the layer of sample 2 has resulted in half the doping concentration, implying that compensation by carbon is not a significant effect. Figure 8(b) shows the net doping concentration ND–NA as a function of the depletion width in the drift layer. The concentration appears to be uniform in the layer, and this profile is not expected to change in the drift layer, as the SSRM measurements show uniform resistivity through the thickness of the layers.

FIG. 8.

(a) 1/C2 vs voltage and extracted net doping concentrations from the linear fitting and (b) ND–NA vs depletion width for the 140 μm-diameter structures on sample 1 (red color) and sample 2 (blue color).

FIG. 8.

(a) 1/C2 vs voltage and extracted net doping concentrations from the linear fitting and (b) ND–NA vs depletion width for the 140 μm-diameter structures on sample 1 (red color) and sample 2 (blue color).

Close modal

Finally, forward and reverse bias I–V measurements were performed on several of these structures to evaluate the electrical behavior of the fabricated p–n diodes. The normalization of current to extract the current density is with regard to the area of the contact. Figures 9(a) and 9(b) show the forward and reverse bias I–V measurements, in the log scale and in log and linear scales, respectively, for several devices on the 90 and 140 μm-diameter structures of sample 1 and sample 2. Regarding the forward bias I–V characteristics of the devices of sample 1, the output current density of the 140 μm-diameter devices is a few mA/cm2 at 10 V. For the 90 μm-diameter devices, the output current density at the same voltage is about 15 mA/cm2. The devices fabricated on the structures of sample 2 exhibit a similar, slightly higher current density between 10 and 100 mA/cm2. These low current values are likely to be due to the large distance between the anode and the cathode contact, which is about 350 μm for both the 90 and 140 μm-diameter structures, and also due to a worse than expected quality of the anode contact. The first is a consequence of the mask design, which was not originally intended for these devices, and so is a long way from being optimized. Simulations of these devices show the access resistance [Fig. 9(c)]. Figure 9 is likely to account for 80% of the total resistance. Improvements to the quality of the anode contact are currently being studied.

FIG. 9.

(a) Forward bias I–V measurements in log and linear scales, (b) reverse bias I–V measurements in the log scale of the 90- and 140 μm-diameter structures of sample 1 and sample 2, and (c) 2D schematic showing a cross section of the samples and the access resistance of the template layer.

FIG. 9.

(a) Forward bias I–V measurements in log and linear scales, (b) reverse bias I–V measurements in the log scale of the 90- and 140 μm-diameter structures of sample 1 and sample 2, and (c) 2D schematic showing a cross section of the samples and the access resistance of the template layer.

Close modal

Figure 9(b) shows the reverse bias I–V measurements on devices fabricated on the same structures on both samples. The compliance current for the measurements was set to 10 mA, in order to ensure that destructive breakdown would occur. The normalization of the current was with regard to the contact area. On sample 1, destructive BV values of 440 and 448 V were measured for the 140 and 90 μm-diameter structures, respectively. On the other hand, on sample 2, several devices had a BV greater than 600 V. In particular, the highest BV values were 700 and 681 V for devices fabricated on the 90 and 140 μm-diameter structures, respectively. 700 V BV is the highest value reported for a p–n diode without any periphery protection, fabricated on a GaN drift layer grown on a Si wafer by selective area growth.

By using the equations reported in Maeda et al.23 and Cooper and Morisette,24 it is estimated that a 7.5 μm-thick GaN drift layer with a doping concentration of 3 × 1016 cm−3 and a 6.5 μm-thick GaN drift layer with a doping concentration of 1.4 × 1016 cm−3 can theoretically yield BVs as high as 650 V and 1.1 kV, respectively. The BV values found for sample 1 and sample 2 were around 250 and 400 V lower than the theoretical values, respectively, but considering that the fabricated pseudo-vertical devices have no periphery protection, this is a very promising result.

In this work, two GaN drift layers were grown on 200 mm-diameter Si wafers by selective area growth and pseudo-vertical p–n diodes were fabricated on them. SSRM measurements showed that the regrown layer has a uniform doping concentration and SCM measurements validated the successful growth of the n- and p-doped layers. The thickness profiles of the structures extracted from stylus profilometry are uniform, and up to 9 μm-thick crack-free structures that are 90 μm in width have been grown. Moreover, by decreasing the SiH4 precursor flow, a low net doping concentration of 1.4 × 1016 cm−3 has been achieved. The pseudo-vertical p–n diode fabricated on a 6.5 μm-thick layer exhibited a breakdown voltage of 700 V, with no periphery protection. This value is the highest reported up to now, for a p–n diode grown by the selective area growth of GaN on Si wafers. The next step would be the optimization of the device fabrication process by including edge termination techniques, and reducing the lateral distance between the anode and the cathode to reduce the access resistance. The results obtained in this study are very promising for the selective area growth of GaN on Si, and the fabrication of high-power, high voltage, vertical devices.

A part of this work, carried out on the Platform for Nanocharacterization (PFNC), was supported by the “Recherches Technologiques de Base” program. This work is part of the ELEGANT project (No. ANR-22-CE05-0010). This work was supported by the VERTIGAN GANEXT project (No. ANR-11-LABX-0014).

The authors have no conflicts to disclose.

Thomas Kaltsounis: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Visualization (equal); Writing – original draft (equal). Mohammed El Amrani: Formal analysis (equal); Investigation (supporting). David Plaza Arguello: Resources (lead); Visualization (supporting). Hala El Rammouz: Conceptualization (equal); Resources (equal). Matthieu Lafossas: Resources (equal). Simona Torrengo: Resources (equal). Laurent Mendizabal: Resources (equal). Alain Gueugnot: Resources (lead). Denis Mariolle: Formal analysis (equal); Investigation (equal); Visualization (equal). Thomas Jalabert: Formal analysis (supporting); Investigation (equal); Visualization (equal). Julien Buckley: Conceptualization (equal); Writing – review & editing (equal). Yvon Cordier: Conceptualization (lead); Formal analysis (equal); Supervision (lead); Visualization (supporting); Writing – review & editing (lead). Matthew Charles: Conceptualization (equal); Formal analysis (equal); Project administration (equal); Resources (equal); Supervision (equal); Visualization (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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