Optical characterization of semiconductor interfaces and envelope-function matching

Abstract

Excitons in narrow quantum wells can be used to probe the two interfaces and supply information about their structure. Typical experimental quantities analysed in such studies are the widths of the absorption or of the photoluminescence lines, the Stokes shifts between them and the so-called 'monolayer splittings' attributed to the fluctuations of the well width. On the theoretical side, practically all calculations are based on the effective-mass approximation (EMA), and the discrepancies between theory and experiment are usually attributed to the departure of the potential from the ideal square-well shape. Various rapidly varying modifications of the potential have been used, even though they are outside the range of validity in the EMA. In the present paper it is shown that the consistent way of representing the interfaces (both perfect and imperfect) is to modify the boundary conditions (BC) for the envelope functions. The BC at the interfaces have been obtained by several authors from first-principles calculations, but different methods have led to different results. The imperfect ('rough') interfaces have not been treated in such calculations. Here it is argued that it is better to obtain the BC from the fit to the experiment. One microscopic parameter is introduced for each particle (electron, heavy hole and light hole) and its value can be obtained from the fit to the monolayer splittings of the optical spectra. This is demonstrated with the example of GaAs/AlGaAs and InGaAs/InP narrow quantum wells.