Growth mode in heteroepitaxial system from nano- and macro-theoretical viewpoints

Abstract

Growth mode in semiconductor heteroepitaxial system such as InAs/GaAs is systematically investigated from nano- and macro-theoretical viewpoints, where ab initio, empirical interatomic potential, and phenomenological macroscopic theory are used. The nanoscopic theories clarify that the misfit dislocation (MD) formation energy depends on orientation such as 1.14 eV/Å for (0 0 1), 0.96 eV/Å for (1 1 0), and 0.68 eV/Å for (1 1 1)A. On the basis of these calculated results, growth mode boundary between two-dimensional with MD formation (2D-MD) and three-dimensional Stranski-Krastanov island (3D-SK) growth modes is successfully determined as functions of surface energy and degree of strain relaxation. The region of 3D-SK growth mode is the largest for (0 0 1) while (1 1 1)A has the largest 2D-MD region and that for (1 1 0) is in between. Using surface energy obtained by ab initio calculations and the degree of strain relaxation estimated by continuum elasticity theory, it is found that (0 0 1) favors 3D-SK growth mode while 2D-MD growth mode appears for (1 1 0) and (1 1 1)A. It should be noted that the (1 1 0) data stay near the growth mode boundary between 3D-SK and 2D-MD growth modes. Reflecting this, growth mode transition from 2D-MD to 3D-SK occurs for (1 1 0) due to In0.25Ga0.75As layer insertion at the interface that decreases surface energy from 50.9 meV/Å2 to 49.1 meV/Å2. Versatility of this approach is discussed by comparing with experimental findings.