A Simple Approach to Growth Mode of InN and InGaN Thin Films on GaN(0001) Substrate
Authors: Nagai Katsuya , Akiyama Toru , Nakamura Kohji , Ito Tomonori 
Published: December 2020

Group-III nitride semiconductors have attracted much attention for application in optoelectronic devices such as light emitting diodes and laser diodes. In particular, highly efficient light emitting devices using self-assembled quantum dots have been pained much attention. For InN and InGaN grown on GaN(0001) substrate, it has been reported that three-dimensional (3D) islands are formed after two-dimensional (2D) wetting layers, resulting in Stranski-Krastanow (SK) growth mode [1,2]. Moreover it has been reported that the growth modes of InN on GaN(0001) substrate during molecular beam epitaxy depend on growth conditions such as V/III ratio and substrate temperature[3]: N-rich condition favors 3D growth, whereas In-rich condition leads to 2D growth. However, it is still unclear what is the crucial factor for determining the growth modes of InN and InGaN depending on the growth condition. In this study, the growth mode of InN and InGaN thin films on GaN(0001) substrate are investigated using the macroscopic theory using free energy formula [4] with the aid of empirical potential calculations [5] as well as ab initio calculations [6]. Effects of pyramids island with {1-103} facets and misfit dislocation (MD) formation are taken into account for the evaluation of free energies of InN and InGaN thin films on GaN(0001) substrate.
The calculations of cohesive energy difference ΔE as a function of InN film thickness for 2D coherent growth (2D-coherent) and 2D growth with MD (2D-MD) using empirical interatomic potentials reveals that 2D-MD is more stable than 2D-coherent for InN films beyond 0.7 monolayers (ML). On the basis of these results, the MD formation energy Ed
and the effective elastic constant M are estimated to be 1.31 eV/Å and 5.60×1011 N/m2. The calculated result of Ed
reasonably agrees with previous calculations for dislocation core energy in bulk InN (1.51 eV/Å) [7]. Moreover, the analysis of free energies using the value of Ed
and M and surface energies obtained by ab initio calculations (~ 0.074 eV/ Å2) demonstrate that the critical thickness between growth 2D-coherent and 2D-MD under In-rich conditions is 0.45 ML. The calculated results are qualitatively consistent with the experimental results [3]. The calculated phase diagram for growth mode as functions of surface energy of (0001) and surface energy difference between (0001) and (1-103) planes suggest that growth mode boundary between 2D-MD and 3D coherent growth with hexagonal pyramid island formation (3D-coherent) strongly depends on the surface energy difference between (0001) and (1-103) planes. 2D-MD is favorable when the surface energy of InN(1-103) is larger than that of InN(0001), whereas 3D-coherent is favorable when the surface energies of InN(1-103) is smaller than InN(0001). These results imply that the relative stability between (0001) and (1-103) planes depending on the growth condition is decisive for the growth modes of InN on GaN(0001) substrate.
[1] S. Ploch et al., Phys. Status. Solidi C 6, 574 (2009). [2] C. Adelmann et al., Appl. Phys. Lett. 76, 1570 (2000). [3] Y. F. Ng et al., Appl. Phys. Lett. 81, 3960 (2002). [4] K. Shiraishi et al., J. Cryst. Growth 237, 206 (2002). [5] K. E. Khor, and S. Das Sarma, Phys. Rev. B 38, 3318 (1988). [6] T. Akiyama et al., Phys. Status Solidi B 255, 1700329 (2018). [7] T. Ito et al., J. Cryst. Growth 298, 186 (2007).
Figure: Phase diagrams of growth modes boundary between 2D-MD and 3D-coherent of InN on GaN(0001) substrate as functions of surface energy of (0001) and surface energy difference between (0001) and (1-103) planes.

Figure 1