For optoelectronic devices, the light-matter interaction is essential. In nonequilibrium Green’s function (NEGF) formalism [1], it can be included either through appropriate selfenergy [2–4] or time-dependent (ac) potential incorporated into device Hamiltonian [5]. For unipolar devices, utilizing intersubband transitions, only the “ac” approach was used [5–7]. This approach requires solving the full set of NEGF equations for several higher harmonic of fundamental frequency what generates huge numerical load. On the contrary, the selfenergy approach generates only little additional load as the light-matter selfenergy (like other selfenergies) is included into NEGF equations for the steady state. In this contribution, the selfenergy approach is used to perform simulations of quantum cascade laser.

Figure 1. (left) Gain spectra for the increasing photon flux (up-to-down) set at ℎ𝜈 = 𝐸𝛾 = 126 meV. (right) Gain at ℎ𝜈 = 𝐸𝛾 and current density as a function of photon flux set at ℎ𝜈 = 𝐸𝛾 = 126 meV calculated with the NEGF method (symbols).

Figure 2 (left) Current-voltage and light-current characteristics calculated with or without electron-photon selfenergies included into NEGF formalism; (right) gain peak for these two cases. Lines show experimental data [12].

Some results are presented in Figs. 1 and 2. In Fig. 1, the calculated gain-flux and current-flux dependencies are compared with the relations predicted by the 2-state rate equations model [6, 7] (lines). These calculations have been done for a fixed bias voltage. The current-voltage-light characteristics are shown in Fig. 2. They were calculated for electron-photon interaction turn off or on. For the latter case, the mono-chromatic field with energy 𝐸𝛾 = 0.126 eV was used, and photon flux was increased until the gain was clamped to its threshold value described by the total losses. As can be seen, the agreement with the experimental data of [12] (lines) is not bad, especially if we take into account that the only adjustable parameter of the model is the roughness of the interfaces which was assumed as one third of the monolayer spacing. The observed differences are probably due to the overestimated losses assumed in the model as well as the doping of the core in the real samples that might have been higher than the nominal value used in the simulations. Read more of this post