Coulomb scattering in nitride-based self-assembled quantum dot systems

We study the carrier capture and relaxation due to Coulomb scattering in group-III nitride quantum dots on the basis of population kinetics. For the states involved in the scattering processes the combined influence of the quantum-confined Stark effect and many-body renormalizations is taken into account. The charge separation induced by the built-in field has important consequences on the capture and relaxation rates. It is shown that its main effect comes through the renormalization of the energies of the states involved in the collisions and leads to an increase in the scattering efficency.

Figure 1

Total confinement potential $U\left(z\right)$ (solid line) and modulus amplitude of the $z$-component wave function ${\mid \xi \left(z\right)\mid }^2$ (dashed line) along the growth direction $z$ for electrons (a) and holes (b) in the presence of the built-in field at a total carrier density $N_{\mathrm{sys}}={10}^{10}{\mathrm{cm}}^{-2}$. The dotted lines are the wave function amplitudes for zero field.

Figure 2

Renormalized energies as a function of the total carrier density in the system $N_{\mathrm{sys}}$, for the $s$ shell (solid lines), $p$ shell (dotted lines), $d_{\pm }$ shell (dashed lines), and WL $\mathbf{k}=0$ (dash-dotted lines). Calculations with (a),(c) and without (b),(d) electrostatic fields are shown for electrons (a),(b) and holes (c),(d). The temperature is 300 K.

Figure 3

Same as Fig. 2 for different contributions to the renormalized $p$-shell energy ${\tilde{\epsilon }}_p$ which are the free energy ${\epsilon }_p$ (dash-dotted line), screened Hartree shift ${\Delta }_p^{\mathrm{SH}}$ (dotted line), screened exchange shift ${\Delta }_p^{\mathrm{SX}}$ (solid line), and Coulomb hole shift ${\Delta }_p^{\mathrm{CH}}$ (dashed line).

Figure 4

Capture times for the $p$ shell as a function of the total carrier density in the system, $N_{\mathrm{sys}}$, using the free (unrenormalized energies), with (solid lines) and without (dotted lines) a built-in electrostatic field.

Figure 5

Capture times as a function of the total carrier density in the system, $N_{\mathrm{sys}}$, for the $s$ shell (solid lines), $p$ shell (dotted lines), $d_0$ shell (dash-dotted lines), and $d_{\pm }$ shell (dashed lines).

Figure 6

Relaxation times as a function of the total carrier density in the system, $N_{\mathrm{sys}}$, with labeling as in Fig. 5.

Figure 7

Hartree diagrams discussed in the text.