Quantum Confined Stark Effect in Wide Parabolic Quantum Wells

TL;DR

This paper presents an analytical approach to compute the electrooptical properties of Wide Parabolic Quantum Wells under an electric field, revealing Stark shifts, symmetry forbidden transitions, and dependence on quantum well parameters.

Contribution

It introduces a method using the Real Density Matrix Approach to derive analytical expressions for the electrooptical functions of WPQWs, including effects of electric field and valence band structure.

Findings

Red shift of absorption maxima due to Stark effect

Asymmetric response when reversing electric field direction

Emergence of new peaks related to parity states

Abstract

We show how to compute the optical functions of Wide Parabolic Quantum Wells (WPQWs) exposed to uniform electric F applied in the growth direction, in the excitonic energy region. The effect of the coherence between the electron-hole pair and the electromagnetic field of the propagating wave including the electron-hole screened Coulomb potential is adopted, and the valence band structure is taken into account in the cylindrical approximation. The role of the interaction potential and of the applied electric field, which mix the energy states according to different quantum numbers and create symmetry forbidden transitions, is stressed. We use the Real Density Matrix Approach (RDMA) and an effective e-h potential, which enable to derive analytical expressions for the WPQWs electrooptical functions. Choosing the susceptibility, we performed numerical calculations appropriate to a GaAs/GaAlAs WPQWs. We have obtained a red shift of the absorption maxima (Quantum Confined Stark Effect), asymmetric upon the change of the direction of the applied field (F -> -F), parabolic for the ground state and strongly dependent on the confinement parameters (the QWs sizes), changes in the oscillator strengths, and new peaks related to the states with different parity for electron and hole.