Transport, Growth Mechanisms, and Material Quality in GaN Epitaxial Lateral Overgrowth
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photolithography techniques. Sub-sets of dot and line patterns, varied systematically with respect to both nucleation and mask dimensions were included in a single pattern. The dimensions in each sub-set are denoted as w:m, where w is nucleation width (varied from I jim to 8jtm) and m is the masked width (varied from Iltm to 32jtm). A fill factor 0 is defined as w/(w+m). Line and dot patterns were oriented both in the preferential ELO direction and in the < 1210> direction, which yields a smaller lateral to vertical growth ratio [5]. The ELO growth was performed at substrate temperatures of I000°C, 1050'C, or 1090'C using H2 as a carrier gas. The total pressure was 140 Torr with a TMG flow rate of 18 sccm and 44% NH 3. An in-situ optical growth monitor was used to measure the growth rate of a center control section with a 1 cm diameter that contained no patterning. Samples were characterized by scanning electron microscopy (SEM) and cathodoluminescence (CL). MODEL OF ELO TRANSPORT LIMITATIONS In ELO, growth does not occur on the dielectric masking material. Thus, the Ga precursor is not consumed (depleted) above the mask, creating an extra supply of reactants that can be transported via gas-phase diffusion to unmasked areas. This additional source of Ga species leads to growth rate enhancement on the unmasked regions, which will drop-off with distance from the mask. We have constructed a steady-state (time-independent) 2-D finite-difference model of the gas-phase diffusive transport and growth-rate enhancement of GaN during ELO. The model solves the diffusion equation (Laplace's equation) for the Ga concentration, n, in 2-D, 02 n 0'2n (1) ax2 a 20 using a simple iteration scheme. The top boundary condition specifies that the concentration is a constant across the domain. Zero-flux boundary conditions are used at the left and right boundaries. At the surface, there is a zero-flux boundary condition on masked regions. For exposed regions, the boundary condition states that the diffusive flux of Ga species to the surface equals the rate of destruction due to deposition chemistry, i.e., D-
an = kn,
ay
(2)
where D is the diffusion constant (with units of cm 2/s), and k is the surface reaction rate constant (with units of cm/s). The model calculates the growth rate enhancement, i.e., the growth rate in the unmasked region divided by the normal growth rate when masking (ELO) is not used. The only parameter needed in the model is the ratio D/k. The diffusion constant is estimated from previous work modeling GaAs growth [ 12] to be 28.1 cm 2 /s at 1050 TC and 140 Torr. A surface reaction probability of one for the Ga species corresponds to a rate constant k of 24,700 cm/s [13], which yields a value of Dik of 11.4 jtm. Using a unit reaction probability might seem unreasonable. However, since the system is transport limited, results of the model are insensitive to the value of the rate constant used. Figure 1 shows the calculated growth rate (normalized by the growth rate go for the case of no masking) for patterns in the
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