Distributions of kinetic pathways in strain relaxation of heteroepitaxial films
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The kinetic relaxation pathways for strained heteroepitaxial films are mapped using a process simulator that integrates experimental and model descriptions of the energetic and kinetic parameters that define the nucleation, propagation, and interaction of strain relieving dislocations. This paper focuses on GexSi1x/Si(100), but the methodologies described should be extendible to other systems. The kinetic pathways for strain evolution are plotted for film growth as functions of the primary kinetic parameters: growth temperature, growth rate, and initial lattice mismatch, generating relaxation surfaces for parameter pairs. Sensitivity analyses are presented of how deviations from mean parameters disperse the resultant relaxation surfaces. Finally, multiparameter “fingerprinting” of the dislocation array is shown to illustrate how fundamental kinetic mechanisms—particularly dislocation nucleation mechanisms—define the final dislocation array. The overarching goal is to establish a robust framework for predicting, interrogating, and optimizing strain relaxation pathways and underlying mechanisms, for misfit dislocations in strained heteroepitaxial films.
I. INTRODUCTION
We describe how a previously implemented simulator for the relaxation of epitaxial layer strain by misfit dislocations1 can be used to predict relaxation pathways, to examine sensitivities to parameter variations, and to “fingerprint” dislocation nucleation mechanisms. The simulator integrates extensive experimental measurements of kinetic parameters that describe the nucleation and propagation of misfit dislocations with models for the critical thickness for dislocation introduction, the excess stress driving dislocation motion and nucleation, and dislocation interactions. In this paper, we focus on the GexSi1x/Si(100) system due to the large body of experimental and theoretical work in this system, and its extensive application in high speed semiconductor devices and circuits, but we have also extended the simulator to the GexSi1x/Si(110) and III-nitride systems.2 The simulator combines descriptions of the kinetic processes of dislocation nucleation, motion, and interaction to simulate the system state at each stage of an epilayer growth or thermal annealing process. II. OVERVIEW OF THE PROCESS SIMULATOR
Figure 1(a) shows the architecture of the process simulator. It iteratively calculates the stress, strain, and Contributing Editor: Artur Braun a) Address all correspondence to this author. e-mail: [email protected] This paper has been selected as an Invited Feature Paper. DOI: 10.1557/jmr.2017.374
dislocation populations during fixed intervals (typically one second, but adjustable by the user) of a growth or annealing cycle. The outputs are the excess stress (rex), the strain state of the film (e), the average distance between misfit dislocations (p), the number of misfit dislocations (N), and the average misfit dislocation length (lave) for each step in the simulation. A. Dislocation energetics
The simulator must first calculate the operative dislocation type a
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