Stability of the $D{X}^{-}$ Center in GaAs Quantum Dots

Using a first-principles band structure method, we study how the size of quantum dots affects the stability and transition energy levels of defects in GaAs. We show that, although a negatively charged $D{X}^{-}$ center is unstable in bulk $\mathrm{GaAs}:\mathrm{Si}$ with respect to the tetrahedral coordinated ${\mathrm{Si}}_{\mathrm{Ga}}^{-}$, it becomes stable when the dot size is small enough. The critical size of the dot is about 14.5 nm in diameter. The reason for the stabilization is the strong quantum-confinement effect, which increases the formation energy of ${\mathrm{Si}}_{\mathrm{Ga}}^{-}$ more than that of the $D{X}^{-}$ defect center. Our studies show that defect properties in quantum dots could be significantly different from those in bulk semiconductors.

Figure 1

A schematic plot of (a) the tetrahedral coordinated ${\mathrm{Si}}_{\mathrm{Ga}}^{-}$; (b) $D{X}^{-}$ with Si displaced along the $⟨111⟩$ direction. Panel (c) shows schematically how the $D{X}^{-}$ center can be stabilized by lowering the electronic energy and converting a shallow donor to a negatively charged deep acceptor.

Figure 2

Schematic illustration of the variation of energy levels of ${\mathrm{Si}}_{\mathrm{Ga}}^{-}$ and $D{X}^{-}$ in bulk GaAs and GaAs QDs. The numbers in parentheses indicate the projected $s/p$ characters of the defect states for bulk and QDs with $d=2.69\mathrm{nm}$.

Figure 3

(a) The formation energy of neutral ${\mathrm{Si}}_{\mathrm{Ga}}^0$ in $\mathrm{GaAs}:\mathrm{Si}$ at ${\mu }_i=0$ and (b) the transition energy $\epsilon (0/+)$ (referenced to CBM) of ${\mathrm{Si}}_{\mathrm{Ga}}$ in $\mathrm{GaAs}:\mathrm{Si}$ as a function of the QDs diameter.

Figure 4

Contour plot of the charge density distribution around Si defects for (a) ${\mathrm{Si}}_{\mathrm{Ga}}^{-}$ and (b) $D{X}^{-}$ of bulk $\mathrm{GaAs}:\mathrm{Si}$ and (c) ${\mathrm{Si}}_{\mathrm{Ga}}^{-}$ and (d) $D{X}^{-}$of $\mathrm{GaAs}:\mathrm{Si}$ QDs (diameter $d=2.67\mathrm{nm}$).

Figure 5

$DX$ formation energy as a function of the calculated band gap of GaAs QDs. The arrow indicates the band gap $E_g=1.78\mathrm{eV}$, at which the $D{X}^{-}$ is stabilized. The corresponding QD diameter is about 14.5 nm.