  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 the
effective mass ($m_i$) of the carrier inside the dot of radius R is distinct
from the mass ($m_o$) in the dielectric coating surrounding the dot. The
electronic structure of the quantum dot is determined in crucial ways by the
mass discontinuity factor $\beta \equiv m_i/m_o$. In this connection we propose
a novel quantum scale, $\sigma$, which is a dimensionless parameter
proportional 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 potential. We show both by numerical calculations and asymptotic
analysis that the charge density near the nanocrystallite surface, $\rho (r =
R)$, can be large and scales as $1/\sigma$. This fact suggests a significant
role for the surface in an EMT based model. We also show that the upshift in
the ground state energy is weaker than quadratic, unlike traditional EMT based
calculations, and chart its dependence on the proposed scale $\sigma$. Finally,
we demonstrate that calculations based on our model compare favorably with
valence band photoemission data and with more elaborate theoretical
calculations.
