A Kinetic Model for the Strain Relaxation in Heteroepitaxial Thin Film Systems
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A Kinetic Model for the Strain Relaxation in Heteroepitaxial Thin Film Systems Y.W. Zhang, T.C. Wang1 and S.J. Chua Institute of Materials Research and Engineering National University of Singapore, Singapore, 117602. 1 LNM, Institute of Mechanics, CAS, P.R. China, 10080. ABSTRACT A kinetic model is presented to simulate the strain relaxation in the GexSi1-x/Si(100) systems. In the model, the nucleation, propagation and annihilation of threading dislocations, the interaction between threading dislocations and misfit dislocations, and surface roughness are taken into account. The model reproduces a wide range of experimental results. The implications of its predictions on the threading dislocation reduction during the growth processes of the heteoepitaxial thin film systems are discussed. INTRODUCTION The accumulation of experimental data on the heteroepitaxial growth of the GexSi1-x/Si system [1-5] has inspired many researchers to establish models to interpret these data. Initially, energetic models were proposed [6,7], however, further studies indicated that the strain relaxation process was much more complicated than anticipated and these energetic models only revealed the relaxation process correctly at high temperatures. At lower and intermediate temperature ranges, dislocation kinetics must be taken into account [8,9]. Most of previous kinetic models [2,3,5,10] assumed that the strain relaxation was dependent on the velocity of threading dislocations, the dislocations existing in the film and the excess stress for threading dislocation propagation. Our model is basically along the similar line. However, we argue that the excess stress for threading dislocation nucleation is different from that of threading dislocation propagation. Based on this point, an excess stress for threading dislocation nucleation is derived. Moreover, Fitzgerald et al [11] have shown that threading dislocation density is very sensitive to the surface roughness of the film. So in our model, the effect of surface roughness on threading dislocation nucleation is also taken into account. The present paper is organized in the following manner. First we present our kinetic model for the propagation, nucleation and annihilation of threading dislocations, the hardening effect of misfit dislocations, and the roughness of a film surface. Next we compare our modeling results with a wide range of experimental results. And next the implications of the present model in the reduction of threading dislocation density are discussed. Finally we summarize our main results.
KINETIC MODEL Consider a GexSi1-x thin film with thickness h , shear elastic modulus µ , and Poisson ratio ν , grown on a semi-infinite large Si substrate. Their mismatch strain is ε 0 . For simplicity, we assume that the film and the substrate have same elastic modulus and Poisson ratio. Now we formulate the dislocation kinetic equations.
P5.11.1
a. Threading dislocation propagation. The total stress for threading dislocation propagation is, σ tp = σ exv − σ r , (1)
where, σ exv is
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