Scaling of the surface migration length in nanoscale patterned growth

摘要

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