Abstract
The main goal of this work is to determine a statistical non-equilibrium distribution function for the electron and holes in semiconductor heterostructures in steady-state conditions. Based on the postulates of local equilibrium, as well as on the integral form of the weighted Gyarmati’s variational principle in the force representation, using an alternative method, we have derived general expressions, which have the form of the Fermi–Dirac distribution function with four additional components. The physical interpretation of these components has been carried out in this paper. Some numerical results of a non-equilibrium distribution function for an electron in HgCdTe structures are also presented.
Highlights
In order to completely specify the operation of a device, we should ask what is the probability of finding a carrier with crystal momentum ~k at location ~r at time t? The answer is the distribution function f = f (~k, ~r, t), a number between zero and one
By coupling the basic postulate of the thermodynamics of irreversible processes referring to entropy generation with the weighted Gyarmati’s principle in the forces representation, we have derived functionals adopting their extreme values in a steady state
Euler–Lagrange equations formulated for these functionals enable the determination of the distribution function for an electron in a conduction band (CB) and in a valence band (VB), which may be used in the case where strong gradients of temperature and those of quasi-Fermi energies occur
Summary
Progress in molecular beam epitaxy (MBE) and metal organic chemical vapor deposition (MOCVD) epitaxial techniques makes it possible to fabricate heterostructures used to manufacture numerous new devices, such as two-color photodiodes matrices, super lattices, quantum dots, etc. The modeling of these devices is based on specialized computer software, whose key task is to calculate the distribution functions mentioned above. In order to find a non-equilibrium distribution function for the electron and holes, the Boltzmann transport equation (BTE) is solved with a relaxation time approximation [1,2,3,4]. Euler–Lagrange equations formulated for these functionals enable the determination of the distribution function for an electron in a conduction band (CB) and in a valence band (VB), which may be used in the case where strong gradients of temperature and those of quasi-Fermi energies occur
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