Scaling of the surface migration length in nanoscale patterned growth was investigated as a function of the lateral dimension LM of a mask film fabricated on a substrate for selective epitaxy. By reducing LM below the surface migration length, any nucleation on the mask was avoided through the evaporation and surface out-diffusion of adatoms. The upper limit of LM for nanoscale patterned growth LM,c corresponds to the surface migration length on the mask. An equation, identical to that for two-dimensional step-flow growth, was derived for nanoscale patterned growth. However, the boundary conditions at the substrate-mask interface were affected by the surface potential difference and were different from those at the terrace edges of a homogeneous stepped surface. This results in a scaling law for surface migration length, which was proportional to the diffusion constant D and the critical incident flux Fc in the form (D/Fc)1/α with α decreasing from 4 to 2 as evaporation became dominant. nanoscale patterned growth of GaAs for LM,c~200nm (α~3.8) was demonstrated at ~600C with molecular beam epitaxy.

Scaling of the Surface Migration Length in Nanoscale Patterned Growth. S.C.Lee, S.R.J.Brueck: Applied Physics Letters, 2009, 94[15], 153110