A general derivation of the density of states function for quantum wells and superlattices

We suggest a method for calculating electronic spectra in ordered and disordered semiconductor structures (superlattices) forming double quantum wells (QW). In our method, we represent the solution of Schr\"odinger equation for QW potential with the help of the solution of the corresponding diffusion equation. This is because the diffusion is the mechanism, which is primarily responsible for amorphization (disordering) of the QW structure, leading to so-called interface mixing. We show that the electron spectrum in such a structure depends on the shape of the quantum well, which, in turn, corresponds to an ordered or disordered structure. Namely, in a disordered substance, QW typically has smooth edges, while in ordered one it has an abrupt, rectangular shape. The present results are relevant for the heterostructures like GaAs/AlGaAs, GaN/AlGaN, HgCdTe/CdTe, ZnSe/ZnMnSe, Si/SiGe, etc., which may be used in high-end electronics, flexible electronics, spintronics, optoelectronics, and energy harvesting applications.

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“…For bulk semiconductors, the corresponding 3D DOS g 3 (E) is given by the formula (see, e.g. [26,27])…”

Section: Discussion Of the Experimental Manifestationsmentioning

confidence: 99%

Electron spectra in double quantum wells of different shapes

2022

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“…Abbildung 2.9 (b). Für die dazugehörige zweidimensionale Zustandsdichte des ersten Subbands (N = 1) gilt [62,63]:…”

Section: Zustandsdichte In üBergitternunclassified

Electronic band structures and effective-mass parameters of wurtzite GaN and InN

Yeo¹,

Chong²,

Li³

1998

Journal of Applied Physics

286

102

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The electronic band structures of wurtzite GaN and InN are calculated by the empirical pseudopotential method (EPM) with the form factors adjusted to reproduce band features which agree with recent experimental data and accurate first-principles calculations. The electron and hole effective masses at the Γ point are obtained using a parabolic line fit. Further, using the effective-mass Hamiltonian and the cubic approximation for wurtzite semiconductors, band edge dispersion at the Γ point obtained using the k.p method is fitted to that calculated using the EPM by adjusting the effective-mass parameters. Thus, we derived important band structure parameters such as the Luttinger-like parameters for GaN and InN which will be useful for material design in wide-gap nitride-based semiconductor lasers employing InGaN. The results also showed that the cubic approximation is fairly successful in the analysis of valence band structures for wurtzite nitrides.

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“…In this estimation, we have assumed a quantum well with a finite offset. The density of states in the single QW layer (2-dimensional), g 2D (E) and the barrier layer (3-dimensional), g 3D (E) can respectively be written as [4] …”

Section: Carrier Confinement Ratiomentioning

confidence: 99%