Many-body theory of carrier capture and relaxation in semiconductor quantum-dot lasers

In quantum-dot laser devices containing a quasi-two-dimensional wetting layer, a pump process initially populates the wetting-layer states. The scattering of carriers from these spatially-extended quasi-two-dimensional states into the quantum-dot states as well as the relaxation of carriers between the quantum-dot levels are studied theoretically. Based on the wave functions for the coupled quantum-dot/wetting-layer system interaction matrix elements are calculated for carrier-carrier Coulomb interaction and carrier-phonon interaction. Scattering rates for various capture and relaxation processes are evaluated under quasiequilibrium conditions. For elevated carrier densities in the wetting layer, Coulomb scattering provides processes with capture (relaxation) times typically faster than $10\mathrm{ps}\left(1\mathrm{ps}\right)$. When energy conservation allows for interaction with LO phonons, comparable rates are obtained.

Figure 1

Schematic drawing of energy levels in the quantum dot (QD) on wetting-layer (WL) system. The quasicontinuum of WL states (grey area) has larger interband transition energies than the discrete QD states labeled with the shell index $n$ and the two-dimensional angular momentum $m$. The energetically degenerate states $m=\pm 1$ are visualized by two separated lines.

Figure 2

Examples of scattering processes: (a) and (b) capture of electrons. (c) Relaxation process $S^{\left(1\right)}$ for electrons. (d) Relaxation process $S^{\left(2\right)}$ for electrons. (e) Mixed relaxation processes. (f) Capture and (g) relaxation process $S^{\left(3\right)}$ assisted by QD carriers. The grey areas schematically show the energetic continua for delocalized states of electrons or holes while the three lines correspond to localized states.

Figure 3

Scattering rates for capture processes to QD ground states (solid and dashed-dotted lines: assisted by WL and QD carriers, respectively) and to first excited states (dashed and dotted lines: assisted by WL and QD carriers, respectively) for electrons (a), (b) and holes (c), (d) as a function of the carrier density in the WL at $300\mathrm{K}$. In-scattering rates for processes assisted by QD carriers are scaled up for better visibility.

Figure 4

Scattering rates for QD carrier relaxation processes according to Eqs. (7, 8, 9, 12). (a) and (c) represent scattering out of the QD ground state into the QD excited states while (b) and (d) show results for the reverse processes.

Figure 5

Rates for mixed scattering processes. (a) and (b) show electron in and outscattering while (c) and (d) are hole in and outscattering, respectively.

Figure 6

Scattering times for processes assisted by WL carriers. (a) Capture times for WL carriers to the QD ground states $\mid e_S⟩$ and first excited states $\mid e_P⟩$ for electrons and correspondingly for holes. (b) Relaxation times for carrier scattering from first excited states to ground states. The temperature is $300\mathrm{K}$. Different axis scaling for capture and relaxation times should be noted.

Figure 7

Same as Fig. 6 but for processes assisted by QD carriers.

Figure 8

(a), (b) Scattering rates for hole capture from the WL to the QD ground states (solid line: OPW, dashed-dotted line: PW) and to first excited states (dotted line: OPW, dashed line: PW) and corresponding capture times (c) at $300\mathrm{K}$.

Figure 9

Scattering rates for QD carrier relaxation processes $S^{1\mathrm{D}}$ similar to Fig. 4 but with different approximations for the confinement wave functions. Solid line: OPW calculation, short-dashed line: plane-wave WL states, long-dashed line: larger QD height and smaller WL thickness, dashed-dotted line: equal confinement in growth direction for QD and WL.

Figure 10

Scattering rates for carrier capture from WL to first excited QD states similar to Fig. 3 but with different approximations for the confinement wave functions. Solid line: 3D-OPW calculation, dotted line: 2D-OPW model. For other lines, see Fig. 9.