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Abstract
An efficient method for simulating quantum transport in quantum cascade lasers is presented. The calculations are performed within a simple approximation inspired by Buttiker probes and based on a finite model for semiconductor superlattices. The formalism of non-equilibrium Green’s functions is applied to determine the selected transport parameters in a typical structure of a terahertz laser. Results were compared with those obtained for a infinite model as well as other methods described in literature.
Highlights
Quantum cascade lasers (QCLs) are relatively new semiconductor devices [1]-[3]
The method used by other authors [12, 15] to calculate quantitatively QCLs parameters was a non-equilibrium Green's function method (NEGF) operating in a real space
That the Bloch theorem was created to describe phenomena occurring in crystal lattices, where the number of cells is incomparable with the number of semiconductor layers in the superlattice heterostructurem which are usually of several dozen, so it is difficult to properly assess the extent to which the assumed infinite dimensions of the model may affect the accuracy of QCL simulations
Summary
Quantum cascade lasers (QCLs) are relatively new semiconductor devices [1]-[3]. they have been successfully used both in scientific research [4,5] and industry applications [6] due to their properties such as high optical power output, wide tuning range of the emitted radiation and room temperature operation. The method used by other authors [12, 15] to calculate quantitatively QCLs parameters was a non-equilibrium Green's function method (NEGF) operating in a real space Another known method based on Wannier functions is applied to QCL simulations [16, 17]. In the present study an efficient method for simulating quantum transport in QCL, based on the finite model is demonstrated The performance of this method consists of several elements. (i) A quantum states base, inspired by Wannier functions for superlattice properties, is used which allows to limit the Hamiltonian representation solely to the space of energy [22] For such cases nano-device Hamiltonian matrices are small, so computations run fast. For such cases nano-device Hamiltonian matrices are small, so computations run fast. (ii) The scattering process is treated as just a contact described by diagonal matrix with phenomenological parameters η related to the scattering time [23]. (iii) In the calculation scheme where nonequilibrium Green’s function equations are solved, a simple approximation inspired by the Büttiker probes common in mesoscopic physics is applied [2329]
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