Quantum capture area in layered quantum well structures

Abstract

Carrier capture in quantum well structures defines high-speed properties of the lasers and amplifiers based on them. We introduce general definition of the capture area in low-dimensional heterostructures based on intersubband coupling coefficient. Spatial dependencies of intersubband coupling coefficient, which governs in fact capture rate, suggest on insufficiency of classical definition of capture area and necessity of quantum-mechanical computation of this value. Special case of layered quantum-well structures is considered. Computational results show necessity to take into account dependence of capture area on the temperature and device operating point.

Introduction

Designing and engineering of new photonic elements of active components of the optical systems are one of the bases for the progress of the up-to-date optical technologies. Low-dimensional heterostructures are most used building blocks for creation of wide band semiconductor optical amplifiers (SOA) and high-speed semiconductor lasers. At present, they are SOA and lasers based on layered quantum well (QW) structures. The predictions of differential gain enhancement and of threshold current reduction, due to the quantization of the density of states and to band structure engineering, have been widely verified in QW lasers. These effects are key factors for enhancement of modulation bandwidth in single quantum well lasers. However, the carrier transport effects become important in the multiple-quantum well lasers. These effects dictate nonuniform distribution of carriers along the active region [1], [2]. Following the classical conception of carrier transport in quantum well structures, the motion of carriers can be presented as a sequence of the following processes. Diffusion/drift through the optical confinement layer, then—capture to the QW and relaxation. Further carriers can tunnel into the adjacent QWs or move up to continuum states due to thermal escape, after that diffuse/drift through the next optical confinement layer. Conceptually these processes are depicted in Fig. 1. In known works, for example [3], under analyzing transport process in QWs the main consideration to drift-diffusion transfer was given due to the fact that diffusion is a longer process as compared to the capture. However, in work [4] it was shown, that despite smallness of capture time, capture processes can significantly affect the modulation properties of QW lasers.

It seems to be verisimilar that capture processes become more intensive when a carrier appears in an immediate vicinity to the QW, being in quasi-continuum state. Therefore, it is often supposed under simulation of QW structures that carriers in bulk-like quasi-continuum states interact with QW only in the case if they are within so called interaction area or capture area. Note, that this conception occurs only in the case when laser (amplifier) is treated as a distributed system instead of lumped. The capture area is introduced in the literature in various manners from author to author. In [5], [6] capture area is equated to three widths of a QW. In [7] this area equals to QW width. Therefore, in first case it is assumed that only those carriers interact with QW, which are located within the QW in the quasi-continuum states and within the QW width from the QW boundaries. While in the second case [7] only carriers located in quantum layer may be captured into QW. In both cases, the capture area was introduced to describe the local quantum capture processes and include them into drift-diffusion simulation of dynamics of QW lasers. However, to our knowledge, there is no substantiation of either one or another definition of capture area.

The aim of this work is to define properly the capture area, compute its value, and discover its dependence on the number of quantum states, carrier energy in the continuum state, temperature, and device operating point. If answers for these questions are found, we will be able to analyze many dynamical models for QW lasers, and we can to give practically important recommendations concerning design of QW lasers.