We report a carrier transport study in a vertical-cavity surface-emitting laser (VCSEL) for gas sensing applications. The electrically pumped VCSEL under study is designed to emit at 4 μm and is highly nanostructured to optimize device performance: an antimonide-based type-II superlattice active region is used for carrier injection and confinement, and a buried tunnel junction (BTJ) is employed to realize current confinement and improve the series conductivity (see Figure).
The device displays different carrier transport regimes depending on built-in and/or applied fields, including miniband transport or sequential tunneling in the active region, Wannier-Stark hopping between localized states in the graded superlattice, and interband tunneling in the BTJ. On the one hand, a conventional drift-diffusion (DD) model would not be applicable in this case, since it lacks any description of quantum effects, and is therefore oblivious of the details of the local density of states (LDOS). On the other hand, due to the large spatial extension of the device, the application of a purely quantum technique such as the nonequilibrium Green’s functions (NEGF) formalism would not be feasible due to its staggering computational cost.
Therefore, we propose a quantum-corrected DD model inspired by NEGF calculations: a spectrally resolved LDOS in the quantum region of the device (on the left of the dashed green line) is computed from a multiband Schrödinger solver. The resulting quantum potential raises and lowers the band edges, accounting for tunneling and confinement effects. Transport parameters (mobilities and generation-recombination rates) used in the DD model are obtained from NEGF calculations. In particular, a DD model for band-to-band tunneling is derived from a NEGF analysis of the BTJ (cyan box). Trap-assisted tunneling is also included in the quantum region within SRH theory. Additional details will be presented at the NUSOD-22 conference.
Band diagram of the VCSEL under study. Shades of blue represent the spectrally resolved LDOS. The green dashed line marks the end of the quantum-corrected region, beyond which the LDOS approaches the expected bulk behaviour. The region marked by the cyan box represents the BTJ region, where the NEGF simulation is carrier out to compute the BTBT generation rate.
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