Abstract
We present an effective mass theory for quantum wells, with an emphasis on calculating the valley splitting. The theory introduces a valley coupling parameter which encapsulates the physics of the quantum well interface. The new effective mass parameter is computed by means of a tight binding theory. The resulting formalism provides rather simple analytical results for several geometries of interest, including a finite square well, a quantum well in an electric field, and a modulation doped two-dimensional electron gas. Of particular importance is the problem of a quantum well in a magnetic field, grown on a miscut substrate. The latter may pose a numerical challenge for atomistic techniques such as tight binding, because of its two-dimensional nature. In the effective mass theory, however, the results are straightforward and analytical. We compare our effective mass results with those of the tight binding theory, obtaining excellent agreement.
- Received 16 November 2006
DOI:https://doi.org/10.1103/PhysRevB.75.115318
©2007 American Physical Society