Shallow–deep transitions of neutral and charged donor states in semiconductor quantum dots

We carry out a detailed study of neutral $\left(D^0\right)$ and charged $\left(D^{-}\right)$ impurity states of hydrogen-like donors in spherical semiconductor quantum dots. The work is carried out within the effective mass theory, treating many-body effects within the local density approximation and the Harbola-Sahni schemes. We observe that the donor level undergoes shallow to deep transition as the dot radius is reduced. On further reduction of the dot radius it becomes shallow again. This suggests the possibility of carrier “freeze out” for both $D^0$ and $D^{-}$. Further, our study of the optical gaps also reveals a nonmonotonic shallow–deep behavior.

Figure 1

The binding energy of a neutral donor $[E_B(D^0)]$ is plotted as a function of the size $R$ of the QD. In the inset we plot the conduction band edge or lowest unoccupied molecular orbital (solid line) and the impurity level (dashed line) as a function of size. Hartree units are employed.

Figure 2

This plot shows the dependence of the binding energy of negative donor (meV) on the QD size $R$ (nm) and the potential well depth $V_0$. The materials chosen are GaAS and ZnS.

Figure 3

The eigenvalue difference of an electron in the conduction band minimum and the neutral donor $({ϵ}_0-{ϵ}_1)$ is plotted as a function of the size of QD. For comparison we plot results of the calculations of both LDA and the HS scheme. Hartree units are employed.

Figure 4

The eigenvalue difference of an electron in the conduction band minimum and the negative donor $({ϵ}_0-{ϵ}_2)$ is depicted as a function of the size of QD. We compare results of the calculations of both LDA and the HS scheme. Hartree units are employed.