Microscopic model for intersubband gain from electrically pumped quantum-dot structures

We study theoretically the performance of electrically pumped self-organized quantum dots as a gain material in the mid-IR range at room temperature. We analyze an AlGaAs/InGaAs based structure composed of dots-in-a-well sandwiched between two quantum wells. We numerically analyze a comprehensive model by combining a many-particle approach for electronic dynamics with a realistic modeling of the electronic states in the whole structure. We investigate the gain both for quasiequilibrium conditions and current injection. Comparing different structures, we find that steady-state gain can only be realized by an efficient extraction process, which prevents an accumulation of electrons in continuum states, that make the available scattering pathways through the quantum dot active region too fast to sustain inversion. The tradeoff between different extraction/injection pathways is discussed. Comparing the modal gain to a standard quantum-well structure as used in quantum cascade lasers, our calculations predict reduced threshold current densities of the quantum dot structure for comparable modal gain. Such a comparable modal gain can, however, only be achieved for an inhomogeneous broadening of a quantum-dot ensemble that is close to the lower limit achievable today using self-organized growth.

Figure 1

Confinement potential in growth direction (black), QW wave functions (blue) and optically active states (red) for structure A, which is optimized for wave-function overlap, see text. Carrier injection and extraction processes are indicated by arrows (orange).

Figure 2

Confinement potential in growth direction (black), QW wave functions (blue) and optically active states (red) for structure B, which includes a barrier between source QW and top QW. Carrier injection and extraction processes are indicated by arrows (orange). Note the additional carrier extraction from the top QW states compared to Fig. 1.

Figure 3

Schematic picture of the carrier dynamics in the QW-QD-QW system. Indicated are (i) injection/extraction process (horizontal orange arrows), (ii) transitions dipole-coupled to the optical field (red vertical arrow), (iii) scattering processes in the DWELL structure (dashed thin arrows,) and (iv) scattering processes between source/drain QWs and the QD (thin arrows).

Figure 4

Population inversion and gain for the QD transitions in structure A vs carrier densities in the top and source QWs. The lattice temperature is 150 K.

Figure 5

Same as Fig. 4 for lattice temperature 300 K.

Figure 6

Population inversion and gain for the QD transitions in structure B vs carrier densities in the top and source QW. The lattice temperature is 150 K.

Figure 7

Same as Fig. 6 for lattice temperature of 300 K.

Figure 8

Population inversion and gain for the QD transitions vs injection rate for structure A (gray lines) and structure B (black lines). The lattice temperature is 150 (solid line) and 300 K (dashed line).

Figure 9

Population inversion and gain for the QD transition vs time for structure A. The full calculation including electron-electron and electron phonon scattering (black lines) is compared with the result including only electron-phonon scattering (gray lines). The lattice temperature is 150 (solid lines) and 300 K (dashed lines).

Figure 10

Same as Fig. 9 for structure B.

Figure 11

Population inversion and gain for the QD transitions vs injection rate for structure B. The carrier density refering the pump distribution is $N^F=6\times {10}^{10}$ (solid line), $5\times {10}^{10}$ (dashes line), $4\times {10}^{10}$ (dot-dashed line), and $3\times {10}^{10}$ ${\mathrm{cm}}^{-2}$ (dotted line). The lattice temperature is 150 K.

Figure 12

Population inversion and gain for the QD states vs field intensity for the structure B. Lattice temperatures are 150 (solid line) and 300 K (dashed line).

Figure 13

Population inversion (and gain) for the QD transitions vs injection rate into the source and equal extraction rate from the drain QW (solid line) and extraction rate from the top QW (dashed line), respectively. The lattice temperature is 150 (black) and 300 K (gray).

Figure 14

Population inversion (and gain) for the QD transitions vs injection rate into the source QW (solid line) and extraction rate from the drain QW (dashed line). The lattice temperature is 300 K.

Figure 15

Modal gain vs current density for 150 (black dots) and 300 K (gray dots) without inhomogeneous broadening.

Figure 16

Modal gain vs current density for 150 (black) and 300 K (gray). The FWHM of the inhomogeneous broadening is 10 (dots), 15 (rectangles), 25 (diamonds), and 50 meV (triangles). The black line is the total loss line. (Inset) Comparison of modal gain vs current density between the QD model of this paper and a QW-QCL from Ref. [6]. For the QD model, we replot the data for 150 (black line) and 300 K (gray line) with a broadening of 15 meV. For the QW-QCL, the data for 200 (black rectangles) and 300 K (gray rectangles) are taken from Fig. 14 of Ref. [6].