Shallow Deep Transitions of Neutral and Charged Donor States in Semiconductor Quantum Dots

TL;DR

This study investigates how impurity states in semiconductor quantum dots transition between shallow and deep levels as the dot size varies, revealing a non-monotonic behavior called SHADES with implications for carrier freeze-out.

Contribution

It introduces the concept of SHADES in impurity states within quantum dots and analyzes their behavior across different confining potentials using EMT, LDA, and HS schemes.

Findings

Donor levels exhibit non-monotonic shallow to deep transitions with decreasing dot radius.

SHADES phenomenon observed in optical gaps, indicating complex impurity behavior.

Potential for carrier freeze-out in quantum dots due to SHADES transitions.

Abstract

We carry out a detailed investigation of neutral ($D^0$) and charged ($D^-$) impurity states of hydrogen-like donors in spherical semiconductor quantum dots. The investigation is carried out within the effective mass theory (EMT). We take recourse to local density approximation (LDA) and the Harbola-Sahni (HS) schemes for treating many-body effects. We experiment with a variety of confining potentials: square, harmonic and triangular. We observe that the donor level undergoes shallow to deep transition as the dot radius ($R$) is reduced. On further reduction of the dot radius it becomes shallow again. We term this non-monotonic behaviour \textbf{SHADES}. This suggests the possibility of carrier {\textbf{\textit{``freeze out''}}} for both $D^0$ and $D^-$. Further, our study of the optical gaps also reveals a {\textbf{SHADES}} transition.