Quantum confined stark effect in wide parabolic quantum wells: real density matrix approach

Sylwia Zielińska-Raczyńska,David Ziemkiewicz,Gerard Czajkowski

doi:10.1140/epjb/e2015-60623-2

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.

Highlights

The effects on optical spectra when an external electric field is applied, known in atomic physics as the Stark effect, evolved very rapidly with the invention and development of semiconductor nanostructures
We consider a wide parabolic quantum wells (WPQWs) with GaAs as the optically active layer and Ga1−xAlxAs as the barriers, where the active layer is of the extension of a few excitonic Bohr radii, and the constant electric field is applied in the growth direction, which we identify with the z axis
We have developed a simple mathematical procedure to calculate the electrooptical functions of wide parabolic quantum wells

Summary

Introduction

The effects on optical spectra when an external electric field is applied, known in atomic physics as the Stark effect, evolved very rapidly with the invention and development of semiconductor nanostructures. We consider a WPQW with GaAs as the optically active layer and Ga1−xAlxAs as the barriers, where the active layer is of the extension of a few excitonic Bohr radii, and the constant electric field is applied in the growth direction, which we identify with the z axis.

Results

Conclusion