Critical Layer Thickness in Exponentially Graded Heteroepitaxial Layers

Abstract

Exponentially graded semiconductor layers are of interest for use as buffers in heteroepitaxial devices because of their tapered dislocation density and strain profiles. Here we have calculated the critical layer thickness for the onset of lattice relaxation in exponentially graded In x Ga 1Àx As/GaAs (001) heteroepitaxial layers. Upwardly convex grading with x ¼ x 1 1 À e Àc=y À Á was considered, where y is the distance from the GaAs interface, c is a grading length constant, and x 1 is the limiting mole fraction of In. For these structures the critical layer thickness was determined by an energy-minimization approach and also by consideration of force balance on grown-in dislocations. The force balance calculations underestimate the critical layer thickness unless one accounts for the fact that the first misfit dislocations are introduced at a finite distance above the interface. The critical layer thickness determined by energy minimization, or by a detailed force balance model, is approximately h c % 0:243 lm c=1 lm ð Þ 0:5 x 1 =0:1 ð Þ À0:54 : Although these results were developed for exponentially graded In x Ga 1Àx As/GaAs (001), they may be generalized to other material systems for application to the design of exponentially graded buffer layers in metamorphic device structures such as modulation-doped field-effect transistors and light-emitting diodes.

Computational Analysis of Low-Energy Dislocation Configurations in Graded Layers

“…Furthermore, we considered a two-dimensional (2D) system with MDs modeled as infinite straight defects with dislocation line lying along a direction orthogonal to the simulation cell. This greatly simplifies the analysis and allow us a direct comparison with previously reported models [34,36,40]. However, this assumption neglects the presence of the orthogonal dislocation array relaxing strain in the other direction and thus attention should be taken before comparing our results with experimental works, as will be discussed later in the paper.…”

Low-Temperature and Metamorphic Buffer Layers

“…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].…”

“…Sidoti et al [142] considered force balance on a grown-in dislocation to determine the critical layer thickness in a sublinearly graded buffer with an exponential lattice mismatch profile given by f ¼ f N (1 À e Àg/y ), where f N is the limiting mismatch, y is the distance from the interface, and g is the grading length constant. Sidoti et al [142] considered force balance on a grown-in dislocation to determine the critical layer thickness in a sublinearly graded buffer with an exponential lattice mismatch profile given by f ¼ f N (1 À e Àg/y ), where f N is the limiting mismatch, y is the distance from the interface, and g is the grading length constant.…”

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].…”