Improved effective mass theory for silicon nanostructures

TLDR: In this paper, the authors show that effective mass theory is known to fail for nanostructures of indirect band gap materials such as silicon, and they show that this situation can be remedied by going beyond the conventional second order expansion in the wave vector k. This approach opens the way for accurate simulations of realistic quantum devices avoiding heavy calculations.

Abstract: Effective mass theory is known to fail for nanostructures of indirect band gap materials such as silicon. We show that this situation can be remedied by going beyond the conventional second order expansion in the wave vector k. The method including fourth order terms is developed for the conduction band of silicon and applied to the ⟨100⟩-oriented wells, wires, and dots. The energy minima, their shift in k-space, as well as the variation in the effective mass with size are fully predicted from analytical equations containing only bulk parameters. This approach opens the way for accurate simulations of realistic quantum devices avoiding heavy calculations.