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The modified local density approximation (MLDA) was developed to describe quantum corrections due to size quantization near a semiconductor-oxide interface for parabolic ellipsoidal bands. In this paper, we propose an extended MLDA model in order to consider arbitrary band structures. The results are compared with the original MLDA model and to self-consistent Poisson-Schrödinger solutions using both constant effective mass and confined six-band Hamiltonians. The extended MLDA model is verified for three major surface orientations and high stress conditions.