Compliant Micron-Sized Patterned InGaN Pseudo-Substrates Utilizing Porous GaN

The compliant behavior of densely packed 10 × 10 µm2 square patterned InGaN layers on top of porous GaN is demonstrated. The elastic relaxation of the InGaN layers is enabled by the low stiffness of the porous GaN under layer. High resolution X-ray diffraction measurements show that upon InGaN re-growths on these InGaN-on-porous GaN pseudo-substrates, not only was the regrown layer partially relaxed, but the degree of relaxation of the InGaN pseudo-substrate layer on top of the porous GaN also showed an increase in the a-lattice constant. Furthermore, methods to improve the surface morphology of the InGaN layers grown by metal-organic chemical vapor deposition (MOCVD) were explored in order to fabricate InGaN pseudo-substrates for future optoelectronic and electronic devices. The largest a-lattice constant demonstrated in this study using this improved method was 3.209 Å, corresponding to a fully relaxed InGaN film with an indium composition of 0.056.


Introduction
The (In,Ga)N alloy system is attractive for various optoelectronic and electronic applications, owing to its wide tunable bandgap spanning from 0.7 to 3.4 eV. While high brightness blue and white light emitting diodes (LEDs) are commercially available, the fabrication of highly efficient (Ga, In) N based green, yellow, or red light emitting diodes (LEDs) still remains challenging [1]. Achieving high indium incorporation into InGaN alloys while maintaining high film quality remains difficult in particular due to the large lattice mismatch of 10% between GaN and InN [2,3]. The misfit strain also leads to reduced indium incorporation through the so-called compositional pulling effect [4]. A suppression of the indium incorporation into compressively strained InGaN films compared to relaxed, strain-free InGaN was found in both experimental as well as thermodynamic studies [5][6][7][8][9][10]. Due to the reduced lattice mismatch between a relaxed InGaN buffer and the quantum wells (QWs), a higher indium incorporation efficiency can be achieved. Typically, the indium composition in the quantum wells (QWs) must stay below 20-25% to maintain good film quality [6].

Materials and Methods
All epitaxial layers in this study were grown by metal-organic chemical vapor deposition using the precursors trimethylgallium (TMGa), triethylgallium (TEG, for InGaN growths), trimethylindium (TMI), ammonia, and disilane on c-plane sapphire substrates. The epitaxial layer structure of the samples for porosification consisted of a 2.8 µm-thick unintentionally doped (u.i.d.) GaN layer followed by 800-nm-thick Si-doped GaN with a doping of 5 × 10 18 cm −3 , and a 80 or 200-nm-thick compressively strained In x Ga 1−x N (0.05 ≤ x ≤ 0.125) top layer (Figure 1a).
The samples were first patterned and dry etched using a 100 W BCl 3 /Cl 2 etch chemistry, resulting in 10 µm × 10 µm wide tiles. The spacing between each tile was 2 µm, making the fill factor for tiles 10 µm × 10 µm over 12 µm × 12 µm, or 69%. The total etch depth was 580 or 700 nm, corresponding to In x Ga 1−x N layer thicknesses of 80 or 200 nm, respectively. Afterward a doping selective electrochemical (EC) etch was used for the porosification of the exposed regions of the 800 nm thick GaN: Si layers [10]. The EC etch was performed with a metal contact to the 800-nm-thick n+ GaN: Si layer on the sample as anode and a Pt wire which acted as the cathode. The redox reaction resulting in etching progressed as a result of the current flowing through this GaN: Si layer etching the region exposed to the 0.3 M Oxalic acid electrolyte resulting in the formation of tiles comprised of In x Ga 1−x N on top of porous GaN as shown in Figure 1b [26]. Following this process, the samples were used as pseudo-substrates for subsequent regrowth of 100 or 200 nm thick In y Ga 1−y N with TMI and TEG flows of 11.3 and 6.5 µmol/min at 869 • C. A co-loaded GaN-on-sapphire template served as the reference sample for each experiment.
All epitaxial layers in this study were grown by metal-organic chemical vapor deposition using the precursors trimethylgallium (TMGa), triethylgallium (TEG, for InGaN growths), trimethylindium (TMI), ammonia, and disilane on c-plane sapphire substrates. The epitaxial layer structure of the samples for porosification consisted of a 2.8 µm-thick unintentionally doped (u.i.d.) GaN layer followed by 800-nm-thick Si-doped GaN with a doping of 5 × 10 18 cm −3 , and a 80 or 200-nm-thick compressively strained InxGa1−xN (0.05 ≤ x ≤ 0.125) top layer (Figure 1a).  The surface morphology of the samples was assessed using an Asylum MFP3D atomic force microscope (AFM). The V-defect density on the sample surface was determined by counting the V defects over an area of 5 µm × 5 µm from multiple AFM scans and averaged to obtain the V defect density for each sample. The cross-sectional images were taken using a Field Electron and Ion (FEI) Helios Dualbeam Nanolab 600 Focused Ion Beam (FIB) tool operated at 5 kV. High-resolution X-ray diffraction (XRD) (ω-2θ)-ω reciprocal space maps (RSMs) were recorded around the GaN (1124) reflection to evaluate the InGaN relaxation across the tiles. In addition, ω-2θ scans around the GaN (0002) reflection were measured, all using an X'PertPro Panalytical Pixcel 3D diffractometer. The lattice constants of the In x Ga 1−x N layer before and after regrowth and the In y Ga 1−y N after regrowth, were determined using the X-pert Epitaxy software using 'a' lattice constants of 3.1893 Å and 3.538 Å for GaN and InN, respectively. The lattice constant 'a new ' of an In z Ga 1−z N layer, which was relaxed, R%, was calculated following Vegard's law:

Experiment 1: In x Ga 1−x N Layer Thickness 200 nm (Sample Series A)
In the first experiment, we investigated the relaxation of a 200 nm-thick In x Ga 1−x N layer with x = 0.08, which was initially grown strained to the GaN base layers (sample A, Figure 1a additional 100 -nm-thick-In y Ga 1−y N layer with y = 0.145 (sample A1, Figure 1c). Post EC etch at a bias of~30 V, the In x Ga 1−x N layer with x = 0.08 was~45% relaxed (Figure 1e) or R = 45, resulting in a lattice constant of 3.202 Å. Upon subsequent regrowth of 100 nm In y Ga 1−y N under the conditions described above, an indium mole fraction of y = 0.145 was measured for the In y Ga 1−y N regrown on the tile sample, compared to only y = 0.12 for the co-loaded GaN-on-sapphire reference sample.
The enhanced indium uptake can be explained by the composition pulling effect, as the lower misfit strain on the tiles led to a higher indium incorporation in the regrown layer [9]. Interestingly, regrowth of the In y Ga 1−y N layer with a higher indium content (y = 0.145) than that of the In x Ga 1−x N layer underneath (x = 0.08) led to an increase in the degree of relaxation of the In x Ga 1−x N layer from 45% to~71% as shown in Figure 1f, corresponding to an increase of its 'a' lattice constant from 3.202 to 3.209 Å. This result indicates that the use of porous GaN as a mechanically flexible layer allows the In x Ga 1−x N layer on the top to change its lattice constant, as known for compliant layers.
The reciprocal space map displayed in Figure 1f also shows a slight offset in the 'Qx-axis' direction between the peaks of the In x Ga 1−x N and In y Ga 1−y N layers, indicating that the In y Ga 1−y N layer was about 20% relaxed compared to the In x Ga 1−x N layer, with an 'a' lattice constant of 3.214 Å. This may be attributed to the formation of additional V-defects, as their density increased from 4.1 × 10 8 cm −2 to about 4.8 × 10 8 cm −2 after In y Ga 1−y N layer regrowth, resulting in additional relaxation of the In y Ga 1−y N layer. The V-defects often originate at the GaN/InGaN hetero-interface and their diameter increases with increasing layer thickness [27,28].
The AFM image displayed in Figure 2a shows that the V-defect density was already relatively high, and larger V defects were visible upon the deposition of the 200 nm thick strained In x Ga 1−x N (x = 0.08) layer. Upon regrowth of the 100-nm-thick In y Ga 1−y N (y = 0.145) layer ( Figure 2b) the V-defects started to coalesce, and additional defect features were visible on the surface. Similar defects had been observed for thick InGaN layers previously [29]. In view of the deteriorating surface morphology after 100 nm In y Ga 1−y N deposition, regrowth on 200-nm-thick In x Ga 1−x N layers was not further pursued. The reciprocal space map displayed in Figure 1f also shows a slight offset in the 'Qx-axis' direction between the peaks of the InxGa1−xN and InyGa1−yN layers, indicating that the InyGa1−yN layer was about 20% relaxed compared to the InxGa1−xN layer, with an 'a' lattice constant of 3.214 Å. This may be attributed to the formation of additional V-defects, as their density increased from 4.1 x10 8 cm −2 to about 4.8 x10 8 cm −2 after InyGa1−yN layer regrowth, resulting in additional relaxation of the InyGa1−yN layer. The V-defects often originate at the GaN/InGaN hetero-interface and their diameter increases with increasing layer thickness [27,28].
The AFM image displayed in Figure 2a shows that the V-defect density was already relatively high, and larger V defects were visible upon the deposition of the 200 nm thick strained InxGa1−xN (x = 0.08) layer. Upon regrowth of the 100-nm-thick InyGa1−yN (y = 0.145) layer ( Figure 2b) the V-defects started to coalesce, and additional defect features were visible on the surface. Similar defects had been observed for thick InGaN layers previously [29]. In view of the deteriorating surface morphology after 100 nm InyGa1−yN deposition, regrowth on 200-nm-thick InxGa1−xN layers was not further pursued. In the following experiments, the thickness of the InxGa1−xN layer was reduced to 80 nm to reduce both the size and the density of the V-defects. Three samples with indium mole fractions of 0.05 (referred to as sample B), 0.09 (referred to as sample C), and 0.12 (referred to as sample D) were

Experiment 2: In x Ga 1−x N Layer Thickness 80 nm, with Varying 'x' (Sample Series B, C and D)
In the following experiments, the thickness of the In x Ga 1−x N layer was reduced to 80 nm to reduce both the size and the density of the V-defects. Three samples with indium mole fractions of 0.05 (referred to as sample B), 0.09 (referred to as sample C), and 0.12 (referred to as sample D) were grown. After tile fabrication and porosification (samples B0, C0, and D0), 100 and 200 nm thick In y Ga 1−y N layers were regrown. The samples with 100 nm thick In y Ga 1−y N layers will be referred to as samples B1, C1, and D1, and those with 200 nm thick In y Ga 1−y N, as samples B2, C2, and D2.
The lattice constants obtained from the reciprocal space maps of samples B0, C0, and D0 taken after tile fabrication and porosification are displayed in Figure 3). The extracted lattice constants were 3.193 Å, 3.194 Å, and 3.194 Å for the In 0.05 Ga 0.95 N, In 0.09 Ga 0.91 N, and In 0.12 Ga 0.88 N samples, respectively. This lattice constant corresponds to a fully relaxed InGaN layer with mole-fraction 0.01-0.02. The small differences between the lattice constants reflected limited relaxation of the In x Ga 1−x N layer for the three samples due to the thin In x Ga 1−x N layer thickness.
After regrowth of 100 nm In y Ga 1−y N the samples were examined again (samples B1, C1, and D1). The measured indium compositions of the 100 nm thick regrown In y Ga 1−y N layers were approximately 0.105, 0.11, and 0.12 for samples B1, C1, and D1, respectively. Note that these samples were co-loaded in the reactor to ensure the same growth conditions. The extracted 'a' lattice constants were 3.197 Å, 3.201 Å, and 3.207 Å, respectively (Figure 3e), corresponding to a degree of relaxation of the In y Ga 1−y N layers of 21%, 31% and 43%, respectively (Figure 3e).
After regrowth of the 100-nm-thick In y Ga 1−y N layer, the lattice constants of the In x Ga 1−x N layer increased as well, from 3.193 to 3.197 Å for samples B0/B1 (x = 0.05), from 3.194 to 3.201 Å for samples C0/C1 (x = 0.09), and 3.194 to 3.207 Å for samples D0/D1 (x = 0.12), as illustrated in Figure 3d. Comparing sample C1(lattice constant 3.201 Å) with sample A0 (lattice constant 3.202 Å), with similar mole-fraction and total InGaN layer thickness, we observe that sample C1 has nominally the same lattice constant but without the penalty of degraded morphology as can be observed from their AFM scans in Figure 2a,d, respectively.
For the samples with 200 nm thick In y Ga 1−y N layers (B2, C2, and D2), which were all co-loaded in the reactor again, the following results were obtained (Figure 3d,e): the measured indium compositions of the 200-nm-thick regrown In y Ga 1−y N layers were 0.106, 0.11, and 0.12 for samples B2, C2, and D2, respectively. The extracted 'a' lattice constants were 3.203 Å, 3.209 Å, and 3.214 Å, respectively (Figure 3e), corresponding to a degree of relaxation of the In y Ga 1−y N layers of 39%, 54% and 60% (Figure 3e).
Similar to the previous observations, upon regrowth of the In y Ga 1−y N layer, the lattice constants of the In x Ga 1−x N layer increased again, from 3.193 to 3.203 Å for samples B0/B2 (x = 0.05), from 3.194 to 3.209 Å for samples C0/C2 (x = 0.09), and 3.195 to 3.214 Å for samples D0/D2 (x = 0.12) (Figure 3d). The increase in In y Ga 1−y N thickness resulted in additional stretching of In x Ga 1−x N layer, which behaved as compliant layer due to its position on top of the porous GaN. In addition, the relaxation of the In y Ga 1−y N layer itself increased, from 21% to 39% (samples B1/B2), 31% to 54% (samples C1/C2), and 43% to 60% (samples D1/D2) with higher thickness of the regrown In y Ga 1−y N layer. With increasing In y Ga 1−y N thickness, the nominal strain in the layer rose resulting in a stronger driving force towards relaxation. In elastic continuum theory, the strain energy per unit area, E h , for a pseudomorphic epilayer of thickness 'h' on a (0001) substrate, with misfit strain ' ', shear modulus 'G' and poisson's ratio 'υ' is given by [30]: Considering the In y Ga 1−y N layer as the epilayer and the In x Ga 1−x N layer underneath as the substrate, the strain energy per unit area is directly proportional to the thickness of the In y Ga 1−y N layer. When both layers are positioned on top of porous GaN, 'a' lattice constant of the In x Ga 1−x N bottom layer is allowed to change and the strain energy can be lowered. For y ≥ x the 'a'-lattice constant of the In x Ga 1−x N layer increased leading to a reduction in the lattice mismatch between the In y Ga 1−y N and In x Ga 1−x N layers and a decrease of the misfit strain in Equation (2). This effect was more pronounced with the thicker In y Ga 1−y N layer as the strain energy increased with thickness. To compensate for this strain energy increase, the degree of relaxation of the In y Ga 1−y N layers increased (Figure 3e). C0/C1 (x = 0.09), and 3.194 to 3.207 Å for samples D0/D1 (x = 0.12), as illustrated in Figure 3d. Comparing sample C1(lattice constant 3.201 Å) with sample A0 (lattice constant 3.202 Å), with similar mole-fraction and total InGaN layer thickness, we observe that sample C1 has nominally the same lattice constant but without the penalty of degraded morphology as can be observed from their AFM scans in Figure 2a,d, respectively.
For the samples with 200 nm thick InyGa1−yN layers (B2, C2, and D2), which were all co-loaded in the reactor again, the following results were obtained (Figures 3d,e): the measured indium compositions of the 200-nm-thick regrown InyGa1−yN layers were 0.106, 0.11, and 0.12 for samples B2, C2, and D2, respectively. The extracted 'a' lattice constants were 3.203 Å, 3.209 Å, and 3.214 Å, respectively (Figure 3e), corresponding to a degree of relaxation of the InyGa1−yN layers of 39%, 54% and 60% (Figure 3e). In addition, the decrease in lattice mismatch between the In y Ga 1−y N and In x Ga 1−x N layers with increasing x value resulted in an increase in the mole fraction y of the regrown In y Ga 1−y N layers from 0.105 to 0.12 due to the composition pulling effect. Thereby the compositions measured for samples B1 and B2 with the lowest x value of 0.05 were similar to those obtained for the In y Ga 1−y N layers on the corresponding GaN-on-sapphire reference samples, which amounted to y = 0.1 and y = 0.104 after 100 and 200 nm In y Ga 1−y N regrowth, respectively.

Morphology Analysis Based on V Defect Density
While a higher indium mole fraction and thickness of the InGaN layers allowed the demonstration of layers with larger a lattice constants, the epitaxial parameter space was limited by the formation of defects. In MOCVD growth of strained In x Ga 1-x N on GaN typically V-defects form in order to release strain energy [27,28,31]. Their density increases with increasing In x Ga 1−x N composition and thickness (Equation (2)). As expected, the V-defect density on the surface of sample A with a 200-nm-thick In 0.08 Ga 0.92 N layer (Figure 2a), 4.1 × 10 8 cm −2 , was higher than that of 3.3 × 10 8 cm −2 observed for sample C with 80-nm-thick In 0.09 GaN 0.91 layer ( Figure 2c). As discussed earlier, when the V-defect density is high and the V-defects penetrate deep into the (In,Ga)N layer, strain relaxation can occur as the sidewalls of the V-defects are free to move to accommodate the strain, often resulting in a measurable enhancement of the In incorporation in the near surface region of InGaN layers (as observed for sample A1) or InGaN/GaN superlattices [32], due to the composition pulling effect. If the strain is too high, additional defects will form leading to a degradation of the InGaN layer properties, as observed for sample A1 (Figure 2b) in this study and as has been widely studied in the past [3,27,28,33,34].
In order to mitigate the degradation in layer properties when starting with 200 nm thick as-grown strained In x Ga 1−x N layers (A series of samples), an alternate approach to achieve thicker InGaN layers was to start out with a thinner, only 80-nm-thick as-grown strained In x Ga 1−x N layer with a lower V-defect density. Following with porosification of the GaN:Si underneath in order to allow partial relaxation of the In x Ga 1−x N layer, and continuing the InGaN deposition process afterwards, utilizing the compliant property of the 80-nm-thick In x Ga 1−x N layer during the deposition, resulted in a much lower V defect density. Sample C0 with 80-nm-thick In 0.09 Ga 0.91 N, for example, exhibited only 3. After depositing a further 100-nm-thick In y Ga 1−y N layer with y = 0.11 on top of sample C0, the V-defect density on the surface increased only slightly to 3.5 × 10 8 cm −2 (sample C1, Figure 2d) and was still lower than that of sample A0 (200 nm In 0.08 Ga 0.92 N, V-defect density 4.1 × 10 8 cm −2 ). When increasing the In y Ga 1−y N (y = 0.11) layer thickness to 200 nm (sample C2, Figure 2e), the V-defect density rose to 3.8 × 10 8 cm −2 , but was still lower than that of sample A0, despite its higher average indium composition of 0.105 and higher thickness of 280 nm, compared to sample A0 with an average indium composition of x = 0.08 and for the only 200 nm thick sample A0.
The average V-defect densities of all samples belonging to series B to D are shown in Figure 4. Note that upon porosification of the as-grown samples no change in the V -defect density was observed. For the as-grown samples with 80-nm-thick In x Ga 1−x N layers, the V-defect density increased from 3.3 × 10 8 cm −2 to 4 × 10 8 cm −2 when increasing x from 0.05 to 0.12. Although the differences in v-defect densities may not seem drastic, it provides us with an overall guidance towards the trends to be observed for samples with different mole-fraction and total InGaN thickness.
Note that upon porosification of the as-grown samples no change in the V -defect density was observed. For the as-grown samples with 80-nm-thick InxGa1−xN layers, the V-defect density increased from 3.3 × 10 8 cm −2 to 4 × 10 8 cm −2 when increasing x from 0.05 to 0.12. Although the differences in v-defect densities may not seem drastic, it provides us with an overall guidance towards the trends to be observed for samples with different mole-fraction and total InGaN thickness.  As the In x Ga 1−x N layers are initially grown coherently strained on top of the GaN:Si layers (samples B,C, and D) the strain energy increases with increasing mole fraction x, leading to a higher number of V-defects for MOCVD grown samples. Similarly, the number of V-defects in the regrown In y Ga 1−y N layers increased with increasing x value, as the average composition of the combined layers, In x Ga 1−x N and the In y Ga 1−y N, rose as well. The more pronounced increase in V-defect density with increasing thickness of the In y Ga 1−y N layer, samples B2, C2, and D2 versus samples B1, C1, and D1, can be attributed to the higher strain energy in the thicker layers. The circumstance, that once a V-defect has formed, it typically does not coalesce or fill under the growth conditions required for InGaN deposition, low temperatures, and the use of nitrogen as carrier gas in order to obtain sufficient indium incorporation in the MOCVD process, may contribute to this trend. For the above reasons, a low strain energy in the initially coherently strained In x Ga 1−x N layers aided in achieving compliant partially relaxed In x Ga 1−x N/In y Ga 1−y N composite layers with low V-defect density. The degree of relaxation and the a-lattice constant of the In x Ga 1−x N/In y Ga 1−y N layer stack can be further increased through continued process optimization. In addition to thickness and composition of the layers on top of porous GaN, the degree of relaxation of the top layers is strongly dependent on the size of the etched patterns. Our previous study on stripe patterns showed that when the stripe width was reduced from 10 to 2 µm, the relaxation perpendicular to the stripes dramatically increased from about 60% to 100%, respectively [10]. The 10 µm × 10 µm tiles in this study were chosen for their compatibility with the micro-LED size regime. As micro-LEDs are pushed towards smaller sizes for applications in advanced micro displays, the pattern size for the InGaN pseudo-substrate fabrication process described here can be reduced as well, taking advantage of the larger lattice constants which can be obtained using smaller patterns. A detailed study towards the V-defect behavior and the relaxation mechanism of the InGaN layers on porous GaN is currently underway and will be presented elsewhere.

Conclusions
In conclusion, a method to fabricate compliant InGaN pseudo-substrates was demonstrated, allowing the fabrication of partially relaxed In x Ga 1−x N/In y Ga 1−y N (x = 0.09, y = 0.11) composite pseudo-substrates with an a-lattice constant of 3.209 Å, corresponding to fully relaxed InGaN with an indium mole fraction of 0.056. The presence of the porous GaN under-layer enabled the compliant behavior of the InGaN top layers. The fabricated InGaN pseudo-substrates are attractive for the fabrication of future electronic and optoelectronic devices.