Scaling of the surface migration length in nanoscale patterned growth

Scaling of the surface migration length in nanoscale patterned growth (NPG) is 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 is avoided through the evaporation and surface out-diffusion of adatoms. The upper limit of LM for NPG LM,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 Fc in the form (D/Fc)1/α with α decreasing from 4 to 2 as evaporation becomes dominant. NPG of GaAs for LM,c∼200 nm(α∼3.8) is demonstrated at ∼600 °C with molecular beam epitaxy.