Computation of the Spatial Distribution of Charge-Carrier Density in Disordered Media

The space- and temperature-dependent electron distribution n(r,T) determines optoelectronic properties of disordered semiconductors. It is a challenging task to get access to n(r,T) in random potentials, while avoiding the time-consuming numerical solution of the Schrödinger equation. We present sev...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2024-05, Vol.26 (5), p.356
Main Authors: Nenashev, Alexey V, Gebhard, Florian, Meerholz, Klaus, Baranovskii, Sergei D
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Carrier density
Charge distribution
Current carriers
disordered materials
Eigenvalues
Electron distribution
electron states in random potential
Electrons
Energy
Fermi-Dirac statistics
Linear equations
Localization
Low pass filters
Mathematical analysis
Methods
Optoelectronics
Random waves
Schrodinger equation
Semiconductors
Spatial distribution
Temperature
Temperature dependence
Wave functions
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Summary:The space- and temperature-dependent electron distribution n(r,T) determines optoelectronic properties of disordered semiconductors. It is a challenging task to get access to n(r,T) in random potentials, while avoiding the time-consuming numerical solution of the Schrödinger equation. We present several numerical techniques targeted to fulfill this task. For a degenerate system with Fermi statistics, a numerical approach based on a matrix inversion and one based on a system of linear equations are developed. For a non-degenerate system with Boltzmann statistics, a numerical technique based on a universal low-pass filter and one based on random wave functions are introduced. The high accuracy of the approximate calculations are checked by comparison with the exact quantum-mechanical solutions.
ISSN:1099-4300
1099-4300
DOI:10.3390/e26050356