Broadening effects due to alloy scattering in a quantum cascade laser

We report on calculations of broadening effects in a quantum cascade laser due to alloy scattering. The output of numerical calculations of alloy-broadened Landau levels compare favorably with calculations performed at the self-consistent Born approximation. Results for Landau level width and optical absorption are presented. A disorder activated forbidden transition becomes significant in the vicinity of crossings of Landau levels which belong to different subbands. A study of the time dependent survival probability in the lowest Landau level of the excited subband is performed. It is shown that at resonance, the population relaxation occurs in a subpicosecond scale.

Figure 1

Density of states for different values of the magnetic field: $B=18\mathrm{T}$ (top), $B=B_r=30.9\mathrm{T}$ (center), and $B=35\mathrm{T}$ (bottom). Solid lines correspond to the DOS considering both the (2, 0) and (1, 2) LL states; dashed lines are associated with the DOS with only (1, 0) LL states. For $B=18\mathrm{T}$ and $B=35\mathrm{T}$, we show the $(l,n)$ index of the states that mainly contribute to each DOS peak. Away from the resonance field $B_r$ (top and bottom figures), the shape of DOS depends neither on the LL nor on the subband.

Figure 2

Absorption for different values of the magnetic field: $B=22\mathrm{T}$ (top), $B=B_r=30.9\mathrm{T}$ (center), and $B=35\mathrm{T}$ (bottom).

Figure 3

Absorption width as a function of the magnetic field. The solid line is a guide for the eyes.

Figure 4

Survival probability $P_s$ of states for different values of the magnetic field: $B=18\mathrm{T}$ (top), $B=B_r=30.9\mathrm{T}$ (center), and $B=35\mathrm{T}$ (bottom). The initial state is taken at the central level of the broadened (2, 0) LL’s.