Intersubband Transitions in Quantum Wells

Abstract

The potential energy profile in semiconductor heterostructures can now be controlled in a fascinating way that could barely be dreamed of twenty years ago ¹. When dealing with interband optical transitions, additional features related to electron-hole interactions (see for instance exciton descriptions in this book) are coming into play and the one-electron wavefunctions and energy levels may fail to describe or predict experimental results. Moreover, the quantization energy is usually small compared to the forbidden band gap, so that typical interband transitions always occur in the same energy range for a given materials pair. On the contrary, intersubband transitions (ISBT) are very sensitive to the exact potential profile and transitions have been observed at wavelengths between lμm and 100μm. In addition, they can be quantitatively described by a simple formalism based on one-electron approaches and many-body effects usually appear as small corrections only. Since 1985², many devices have been designed according to this quantum engineering and have shown unsurpassed properties³. Various materials have been successfully used for these quantum well (QW) heterostructures: GaAs/AlGaAs, InP/InGaAs/InAlAs, Si/SiGe, D/VI compounds…We will focus here on the GaAs/AlGaAs system which has been the most widely studied. First, the calculation of the ISBT matrix element will evidence two major characteristic properties: the optical transitions take advantage of giant dipoles but must verify in the same time a rather drastic selection rule. Then, examples will be given in different fields of application: detection, modulation and emission. Some interesting aspects of coupling and propagation in these structures involve a photon mode density alteration. Finally, a detailed study of second order non linearities will exemplify the beauty of quantum engineering for improving optical properties.