The role of the carrier mass in semiconductor quantum dots

In the present work we undertake a re-examination of effective mass theory (EMT) for a semiconductor quantum dot. We take into account the fact that t he effective mass (m(i)) of the carrier inside the dot of radius R is disti nct from the mass (m(0)) in the dielectric coating surrounding the dot. The electronic structure of the quantum dot is determined in crucial ways by t he mass discontinuity factor beta = m(i)/m(0). In this connection we propos e a novel quantum scale, sigma, which is a dimensionless parameter proporti onal to beta(2)V(0)R(2), where V-0 represents the barrier due to dielectric coating. The scale sigma represents a mass modified "strength" of the pote ntial. We show both by numerical calculations and asymptotic analysis that the charge density near the nanocrystallite surface, rho(r = R), can be lar ge and scales as 1/sigma. This fact suggests a significant role for the sur face in an EMT based model. We also show that the upshift in the ground sta te energy is weaker than quadratic, unlike traditional EMT based calculatio ns, and chart its dependence on the proposed scale sigma. Finally, we demon strate that calculations based on our model compare favorably with valence band photoemission data and with more elaborate theoretical calculations.