Ernie Pan

Strain fields in InAs∕GaAs quantum wire structures: Inclusion versus inhomogeneity

This paper studies the elastic fields in InAs∕GaAs quantum wire (QWR) structures arising from the lattice mismatch between InAs and GaAs. The present treatment is different from recent analyses based on the Eshelby inclusion approach where the QWR material, for simplicity, is assumed to be the same as the matrix/substrate. Here, a more complete treatment is developed taking into account the structural inhomogeneity using the boundary integral equation method. We implement our model using discrete boundary elements at the interface between the QWR and its surrounding matrix. The coefficients of the algebraic equations are derived exactly for constant elements using our recent Green’s-function solutions in the Stroh formalism. For both (001) and (111) growth directions, our results show that while the elastic fields far from the QWR are approximated well by the homogeneous inclusion approach, for points within or close to the QWR, the differences between the fields computed with the simplified inclusion and...

Three-dimensional kinetic Monte Carlo simulation of prepatterned quantum-dot island growth

A special prepatterning method is proposed for spatially ordered self-organizing quantum dots on anisotropic semiconductor substrates. Using three-dimensional kinetic Monte Carlo simulations, atoms are deposited with varying intermediate interruption times. We demonstrate the effect of interruption time and long-range anisotropic strain energy on island size uniformity and lateral alignment.

Stress perturbation around a fault by hydraulic fracturing

In this paper we present an exact closed-form solution for the stress perturbation around a fault in a half plane induced by nearby multiple hydraulic cracks. First, we apply the complex potential function method to find the stress field induced by a concentrated displacement discontinuity in a two-dimensional half plane. Then we integrate the fundamental stress field along the crack to find the corresponding field due to a crack with finite length. Method of superposition is simply applied to obtain the corresponding solution due to multiple cracks. Finally, as numerical examples, we apply our exact closed-form solution to a couple of cases to investigate the effect of hydraulic fracturing on the stress field around the fault under different in-situ stress conditions. Particularly, the normal and shear stresses along the fault line are calculated. By applying the Mohr-Coulomb failure criterion to the fault, the critical distances between cracks and fault are estimated with and without the in-situ stress ...

Three-dimensional InAs/GaAs quantum-dot islands size and density study using kinetic Monte Carlo simulation

Three-dimensional (3D) InAs/GaAs quantum dots (QDs) island size and density evolution under different coverage and temperature is studied by using our 3D kinetic Monte Carlo (KMC) model. Our KMC model is based on the solid-on-solid one with bond counting and Ehrlich-Schwoebel barrier being incorporated. It is found that there is a QD island size limit for the growth coverage. Below this limit existing QD islands can adsorb new-coming adatoms; however, beyond the limit new QD islands will form and adopt new coming adatoms. It is also observed that with increasing temperature, the QD islands size will be increased while their density will be reduced.

Strain-induced variations of electronic energy band edges of embedded semiconductor quantum dots in half-space substrates

The strain-induced local electronic band edge states in semiconductor quantum dots (QDs) are studied using a k⋅p description of the electronic eigenstates coupled with the induced lattice strain as calculated using the continuum mechanics (CM) description. In the CM method, the misfit-lattice induced strain can be reduced to an analytical expression that is straightforward to evaluate numerically. Different from most previous analyses for QDs in infinite spaces, we address cubic and pyramidal QDs located in half-space substrates with different lattice orientations, which more realistically describe experimental situations in most instances. The band edges within the cubic and pyramidal InAs QDs embedded in GaAs substrates are predicted within the six-band k⋅p basis via both a published approximation and the presented exact approach. Comparison of the strain-induced local band edge shows that the approximate method adopted previously in literature could result in a substantial error near the interface regi...