Molecular Beam Epitaxial Growth Mode Transitions on Vicinal Surfaces
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ABSTRACT Kinetic model of MBE growth on vicinal surface is investigated. The model includes step propagation, nucleation and growth of islands on the terraces and Schwoebel barrier at descending step edges as well. By numerical solution of kinetic rate equations for growth on stepped surface, adatom and island density profiles across a terrace are obtained. With using simple criterion for growth mode transition the "phase diagram" of growth modes in parametric space y-P is constructed, y-J/D and P-tan- 24), where J is the atomic flux, D is the surface diffusion coefficient and 4 is the substrate miscut angle. The transition curve in the y-3 plane separating step flow mode region from the mixed (step-flow+nucleation) growth mode region is well describded by a simple equation y=A/P 3 where constant A=10 and 100 with and without Schwoebel effect. The relations for critical terrace width (miscut angle) and transition temperature are derived and it is shown that these relations are in fairly well agreement with available experimental data on the MBE growth of GaAs. INTRODUCTION The development of advanced optoelectronic devices requires the ability to grow the heteroepitaxial structures with atomically smooth (sharp) interfaces. Therefore a detailed understanding of the mechanism of MBE growth, especially the locations of the different growth modes as a function of the controlling physical parameters is not only of fundamental interest but also has technological importance. As a consequence the theoretical and experimental efforts devoted to elucidating these aspects of MBE growth on singular and vicinal surfaces have significantly intensified in recent years (e.g., [1-10]). In this work, partially published in [11] we analyse the MBE growth modes on vicinal surfaces. (The growth on singular surfaces is considered in another paper which will be published elsewhere [12]). To that end the recently proposed generalized BCF model for MBE growth on vicinal surface [1,2] is further extended to include island growth on the terraces and Schwoebel barrier at descending step edges. By numerical solution of kinetic rate equations it is shown that the growth mode on stepped surface is determined by two dimensionless parameters: 3-tan-24 and y-J/D where J is the atomic flux, D the surface diffusion coefficient and 4 the substrate miscut angle. With using simple criterion for growth mode transition the "phase diagram" of growth modes in parametric space y-3 is constructed. The transition curve in the y-P plane separating step flow mode region from the mixed (step-flow+nucleation) growth mode region is described by a simple equation y=A/0 3 where constant A=10 and 100 with and without Schwoebel effect. The relation for critical terrace width for step flow above which nucleation of islands starts and relation for transition temperature are derived. It is shown that these relations are in fairly well agreement with available experimental data on the MBE growth of GaAs. 47 Mat. Res. Soc. Symp. Proc. Vol. 399 ©1996 Materials Research Soci
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