Two-period model for calculation of level populations in subbands of multi-period quantum-cascade superlattice structures
| Autor: | Dmitrii V. Ushakov, Ivan S. Manak |
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| Rok vydání: | 2007 |
| Předmět: | |
| Zdroj: | Journal of Applied Spectroscopy. 74:892-896 |
| ISSN: | 1573-8647 0021-9037 |
| DOI: | 10.1007/s10812-007-0138-0 |
| Popis: | For two periods of quantum-cascade laser structures, we propose a system of closed balance equations that make it possible to calculate the occupancy of the energy levels, the quasi-Fermi levels, and also the injection current density taking into account different charge carrier scattering mechanisms. equations. Introduction. Development of lasers based on quantum-cascade superlattice structures is a promising direction in design of compact and reliable radiation sources in the mid-IR (1-5) and far IR (6, 7) ranges. The design concept for a quantum-cascade laser (QCL) was discussed in (8), but the first practical realization is described in (1). Modern QCLs are grown using the molecular beam epitaxy method and are complicated structures with several tens of repeat- ing cascades, consisting of a system of potential wells and barriers. The populations of the energy subbands are calcu- lated based on solution of balance equations in the approximation of two or three (4, 9, 10) minisubbands or in the multi-subband self-consistent approximation (11, 12). In this case, calculations of the scattering rates use the Monte Carlo method (13) and also the Green's function method (14), incurring significant computation costs. In this paper, we propose a system of closed balance equations to determine the energy level populations for only two periods of the QCL, which allows us to take into account all possible transitions between levels and the coupling between cascades, and also to reduce computation costs and shorten calculation time. Calculation. The algorithm for calculating the optoelectronic properties of QCLs includes the following steps: solution of the Schrodinger equation and determination of the energy levels and wavefunctions; calculation of the di- pole transition matrix elements; calculation of the rates of scattering off optical phonons and electron-electron scatter- ing; determination of the surface concentrations of charge carriers and quasi-Fermi levels for the corresponding energy subbands from a system of closed balance equations; calculation of threshold currents and spectral characteristics. Figure 1a shows the results of a numerical calculation of the conduction band diagram Ec(z) and the modulus squared of the electron wavefunctions for two periods of the QCL. The parameters of the band structure and the thick- nesses of the layers are taken from (2). The values of the modulus squared of the wavefunctions corresponding to the N-th period are numbered. For convenience in calculating the level populations of the subbands, the QCL period should be understood to mean the repetition period of the system of wavefunctions, which may be greater than the thickness of one cascade (the repetition period of the potential wells and barriers), since the wavefunctions extend over several cascades. As we see, two periods of the squares of the wavefunctions corresponds to about three cascades in |
| Databáze: | OpenAIRE |
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