Equilibrium strain and dislocation density in exponentially graded Si1−xGex/Si (001)

Abstract

We have calculated the equilibrium strain and misfit dislocation density profiles for heteroepitaxial Si1−xGex/Si (001) with convex exponential grading of composition. A graded layer of this type exhibits two regions free from misfit dislocations, one near the interface of thickness y1 and another near the free surface of thickness h−yd, where h is the layer thickness. The intermediate region contains an exponentially tapered density of misfit dislocations. We report approximate analytical models for the strain and dislocation density profile in exponentially graded Si1−xGex/Si (001) which may be used to calculate the effective stress and rate of lattice relaxation. The results of this work are readily extended to other semiconductor material systems and may be applied to the design of exponentially graded buffer layers for metamorphic device structures including transistors and light emitting diodes.

Low-Temperature and Metamorphic Buffer Layers

“…It is desirable to maintain a thick MDFZ with large residual strain for maximum effectiveness. Another approach is to alter the grading profile to make it less susceptible to loading, and this can be achieved using sublinear grading adjacent to the device layer [141]. In some cases, this MDFZ may disappear entirely due to loading.…”

“…There have been experimental and modeling studies of sublinear continuous grading in the material systems In x Ga 1Àx As/GaAs [109,142,143], Si 1Àx Ge/Si [102,141], and sublinear step grading has been investigated in the material system InAs y P 1Ày / InP [86].…”

Dislocation reduction in heteroepitaxial In x Ga1-xN using step-graded interlayer for future solar cells

“…Ee et al [21,22] reported the nano-patterned AGOG (Deposition of Aluminum, Growth of Oxide, and Grain growth) sapphire for the growth of GaN template with reduced TD density in LEDs to enhance the output power. Compositional grading is one of the most effective techniques which can be very effective to reduce both MDs and TDs [23][24][25][26][27][28]. In a properly designed graded layer, misfit strain as well as dislocation is greatly reduced due to spreading the strain profile throughout the entire layer of thickness instead being concentrated to a single interface.…”

Strain Relaxation via Misfit Dislocation in Step-Graded In GaN Heteroepitaxial Layers Grown on Semipolar (1122) and (1101) GaN

“…The MD density may be decreased significantly by grading the epitaxial layer with different approach of compositionally grading such as linear grading, nonlinear grading and step grading. Most of the experimental work with graded heteroepitaxial layer has been carried out on linear and nonlinear grading [4]- [5]. Some authors developed reaction model for dislocation reduction in (0001) wurtzite epitaxial GaN thin films [6].…”