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 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.