Critical Thickness for the Si_1-xGe_x/Si Heterostructure

Abstract

An energy balance theory for predicting the critical thickness of the Si1-x Ge x /Si heterostructure is derived based on an experimentally identified dislocation generation mechanism. The theory is in close agreement with experimental results. The critical thickness predicted by this theory is about four times that by the mechanical balance theory of Matthews and Blakeslee.

Defect structure of InAlAs/InP layers

“…It was found that contribution of 60 • and 90 • dislocations is 65 and 35%, respectively. One can notice that existence of the 90 • dislocations confirm validity of relaxation model [4,5].…”

“…In this model, originally applied to relaxation of the layer subjected to tensile strain, the half loop dissociates into 30 • and 90 • Shockley partial dislocations. Based on transmission electron microscopy studies, Fukuda et al [4,5] proposed a critical layer thickness model for films under tensile and compressive strains in which the nucleation of dissociated V-shaped misfit dislocations is preferred at the semicircular perfect loops. This model assumes dissociation of 60 • misfit dislocation into 90 • partial dislocation placed in the strained interface and 30 • partial dislocation in the substrate.…”

Formation of compressively strained Si/Si1−xCx/Si(100) heterostructures using gas-source molecular beam epitaxy

“…For a typically attainable concentration of the substitutional carbon (i.e., around 1%), the maximum stress is around 0.5 GPa. Calculated critical thickness for this condition differs according to models proposed in literatures: 30 nm (after [41]) to 140 nm (after [36,42]), which were deduced assuming that strain relaxation is achieved by generation of perfect dislocation. Cross-sectional TEM images in Fig.…”

Structural characterization of Si1−xGex alloy layers grown by molecular beam epitaxy on Si(001) substrates

“…Our present results seem to suport the smaller critical thickness given by van de Leur et al 20 or Fukuda, Kohama, and Ohmachi. 21 On the surface of sample B3 with xϭ0.17 ͓Fig. 3͑c͔͒, the undulations running parallel to ͓110͔ and ͓110͔ directions are observed all over the surface.…”

“…It has been pointed out from energy considerations that V-shaped dislocations are more favorably nucleated in the SiGe systems than semicircular ones. 21 Dislocations are also observed in the substrate. In sample B9 ͓xϭ0.30, Fig.…”