DISORDER AND SIZE EFFECTS IN THE ENVELOPE-FUNCTION APPROXIMATION

We investigate the validity and limitations of the envelope-function a pproximation (EFA), widely accepted for the description of the electro nic states of semiconductor heterostructures. We consider narrow quant um wells of GaAs confined by AlxGa1-xAs barriers. Calculations perform ed within the tight-binding approxima tion using ensembles of supercel ls are compared to the EFA results. Results for miniband widths in sup erlattices obtained in different approximations are also discussed. Th e main source of discrepancy for narrow wells is the treatment of allo y disorder within the virtual crystal approximation. We also test the two key assumptions of the EFA: (a) that the electronic wave functions have Bloch symmetry with well-defined (k) over right arrow in the all oy region; (b) that the periodic parts of the Bloch functions are the same throughout the heterostructure. We show that inaccuracies are mai nly due to the former assumption.