Pseudopotential Methods for Superlattices: Applications to Mid-Infrared Semiconductor Lasers
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Abstract Calculations of optoelectronic properties for superlattice materials require accurate subband energies, wavefunctions and radiative matrix elements. We have recently begun using a solution method based on the Empirical Pseudopotential Method, or EPM. This method shows particular strength in analyzing structures with short periods or thin layers, for which the standard method, based on k .,b perturbation theory and the envelope function approximation, may be problematical. We will describe the EPM applied to bulk solids and then demonstrate our direct generalization of the method for applications to superlattice structures. Finally, we will apply the EPM method to several type I1 superlattice samples and compare the predictions to absorbance spectroscopy data.
Introduction Over the last decade, lasers, detectors and other optoelectronic devices using the electronic properties of heterostructures and superlattices have been developed. In many cases, these devices contain extremely thin layers corresponding to just a few monolayers of semiconductor material. The common theoretical method for calculating the electronic and optical properties of these heterostructures and superlattices is based on k- j5
perturbation theory and the envelope function approximation (EFA).[l] Indeed, this approach has been used so extensively that it has been referred to as the Standard Model.[2] Unfortunately, although the Standard Model has considerable intuitive appeal, the theoretical underpinnings are controversial. In particular, the low momentum assumptions of k -P are probably violated in many of the applications, and several options for interface envelope function boundary conditions exist, a situation that can lead to additional uncertainties.[ 1,2] These elements of uncertainty become even more pronounced when the Standard Model is applied to the analysis of structures with Type II band offsets, such as InAs/GaSb superlattices. In the following sections, we will describe an alternative approach for calculating the subbands of superlattices.[3] This method depends on an EPM description of the component materials. We assume that the parameters of the bulk constituent materials do not change when lattice-matched materials are grown together into the superlattice. However, the energy-band lineups or offsets must be specified at each interface. Our method employs a plane-wave expansion ef the superlattice Bloch function, in which
11 Mat. Res. Soc. Symp. Proc. Vol. 607 0 2000 Materials Research Society
each plane-wave corresponds to a point in the superlattice reciprocal lattice space. The method offers several useful features: Rather than being restrictedto all points (planewaves) from the origin out to a cut-off in the reciprocallattice space of the superlattice, we arefree to use a smaller set ofplane-waves representedby a clusterof superlattice reciprocallattice points positioned on each of the bulk constituent material reciprocal lattice vectors. Furthermore,we form our pseudopotentialforthe superlattice usingfit par
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