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The first well is delta-doped with Si to \(n_s=3.45\times 10^\). The design utilizes a GaAs/AlGaAs material system and contains layers with widths of 4.4/6.45/ 1.62/7.15/ 2.79 /10.455/ 0.6/4.965 nm, where the bold font indicates the barriers. Each module of the cascade consists of four wells and four barriers, with the widths tuned to tenths-of-nanometer precision. This laser emits radiation at 2.4 THz frequency and uses an indirect phonon-photon pump scheme to achieve the population inversion. The THz QCL selected for the simulations was described in. 4, the results obtained for uniformly and non-uniformly sampled THz QCL devices are compared in order to demonstrate the benefits one can gain when using smart non-uniform sampling of the device potential in real space. 3), which can also be used in other device-oriented NEGF solvers. We provide the detailed formulation for current density and scattering energies for the case of non-uniform mesh discretization (Sect. Our paper aims to implement a non-uniform mesh to study scattering transport in QCLs. This study concerns ballistic, scattering-free transport in a high-electron-mobility transistor (HEMT). Non-uniform sampling of real space within NEGF implementation has already been reported. In both cases, non-uniform sampling of device potential in the real space can significantly limit the size of the discretized Hamiltonian and make the method numerically efficient. This is a concern for both mid-infrared (mid-IR) devices, whose structures utilize fine layers of sub-nanometer width, and THz devices, which have a high well-to-barrier width ratio. However, obtaining results with quantitative accuracy requires a very dense grid, making for a huge numerical load with this approach. Using a real-space basis does not have this limitation. The major simplification of the approach is that in reality, the basis is field-dependent, which is not taken into account when obtaining a self-consistent Schrödinger–Poisson solution. Because of this, many important results, both theoretical and application-oriented, have been obtained with this approach. The former uses several quantum states per QCL period and thus benefits from a relatively low numerical load, making this approach numerically efficient. QCL NEGF simulators utilize either the eigenfunction-like basis or the real-space basis. As QCLs are purely unipolar devices, they all use effective-mass Hamiltonians limited to at most two bands, so the effect of band mixing is also simplified. For example, existing approaches implementing NEGF to simulate quantum cascade lasers (QCLs) that involve the basis being cut to several quantum states per QCL period do not fully resolve for in-plane momentum, and all limit the analysis to at most three device modules. They must be introduced in order to keep the numerical load, in terms of both time and memory, at a size achievable by currently available computers. However, this method is highly demanding, both conceptually and computationally, so in order to model real devices, a few simplifications must be made. The non-equilibrium Green’s function (NEGF) formalism is a powerful semiconductor device simulation method, which allows for the simultaneous consideration of carrier scattering and quantum coherence.