Computing with DFT Band Offsets at Semiconductor Interfaces: A Comparison of Two Methods

Two DFT-based methods using hybrid functionals and plane-averaged profiles of the Hartree potential (individual slabs versus vacuum and alternating slabs of both materials), which are frequently used to predict or estimate the offset between bands at interfaces between two semiconductors, are analyzed in the present work. These methods are compared using several very different semiconductor pairs, and the conclusions about the advantages of each method are discussed. Overall, the alternating slabs method is recommended in those cases where epitaxial mismatch does not represent a significant problem.

A tight nonlinear approximation theory for time dependent closed quantum systems

The approximation of fixed points by numerical fixed points was presented in the elegant monograph of Krasnosel’skii et al. (1972). The theory, both in its formulation and implementation, requires a differential operator calculus, so that its actual application has been selective. The writer and Kerkhoven demonstrated this for the semiconductor drift-diffusion model in 1991. In this article, we show that the theory can be applied to time dependent quantum systems on bounded domains, via evolution operators. In addition to the kinetic operator term, the Hamiltonian includes both an external time dependent potential and the classical nonlinear Hartree potential. Our result can be paraphrased as follows: For a sequence of Galerkin subspaces, and the Hamiltonian just described, a uniquely defined sequence of Faedo–Galerkin solutions exists; it converges in Sobolev space, uniformly in time, at the maximal rate given by the projection operators.

Magnetic field induced trions in a Telluride-based II–VI material

Effects of geometrical confinement and magnetic field strength on the binding energies of trions (positive trion and negative trion) in a CdTe/ZnTe parabolic dot are investigated. Coulomb interaction energy is obtained by employing Hartree potential and the results are found numerically. The modified Chandrasekhar wavefunctions are employed to obtain the respective energies. The confined energies and the respective binding energies of charged trions are investigated by the self-consistent method. The Poisson equation is used to find the electron and hole potentials. The dielectric mismatch is included throughout the calculations. Magneto-optical transition energies for charged trions in the presence of magnetic field are observed. The effective Landé factor is brought out. Raman shift and the Raman intensity of positive and negative trions for various magnetic field strengths in the CdTe/ZnTe nanostructures are investigated. The dependence of Raman resonance on the magnetic field and the geometrical confinement effect is brought out.

Electron Mobility in an Unintentionally Doped GaN/AlGaN Surface Quantum Well

We present a theoretical study the two-dimensional electron gas 2DEG at low temperature in an unintentionally doped GaN/AlGaN surface quantum well, taking adequate account of the roughness-induced scattering mechansms and effect due to sheet polarization charges. Within model of surface quantum wells 2DEG be described by an extended Fang-Howard wave function, we are able to derive an analytic expression for the self-consistent Hartree potential. Thus, we obtained simple expresion describing the enhancement of the 2DEG screening and unscreened\break potentials for different scattering sources. We studied the electron mobility due to different scattering sources and the total electron mobility in an unintentionally doped GaN/AlGaN surface quantum well.

Formation of a Bound State in the Presence of Repulsive Interaction

We have examined the effective interaction of two fermions in terms of the T-matrix and shown that there are two different series of ladder diagrams in describing the effective interaction: (1) the exchange ladder diagrams giving rise to the T-matrix for the triplet state with poles for attractive interaction and (2) the Hartree ladder diagrams describing the multiple scattering on the Hartree potential and producing the T-matrix for the singlet state with poles for repulsive interaction. It is verified that a bound state of two fermions in the singlet state exists only in the presence of repulsive interaction between them. We further argue that the potential in the Schrodinger equation should be spin-dependent to describe both the singlet and triplet states.