Kinetic coefficients of semiconductor superlattices in high-frequency electromagnetic fields
https://doi.org/10.17586/2220-8054-2017-8-6-740-745
Abstract
Kinetic coefficients of semiconductor superlattice are obtained from the Boltzmann transport equation with Bhatnagar–Gross–Krook (BGK) collision term and Poisson equation. Using the universal analytic procedure, we found kinetic coefficient in the quasistatic limit starting from the exact solution of the Boltzmann transport equation. It is shown that the Einstein relation for the diffusion coefficient is applicable only for weak fields and it is not valid in the general case. As a consequence, a drift-diffusion model of miniband transport in the case of strong dc and ac fields should be corrected, taking into account the kinetic coefficients obtained from the Boltzmann equation.
Keywords
superlattice,
Boltzmann equation,
drift-diffusion model,
THz radiation,
diffusion coefficient,
drift velocity,
Maxwell frequency,
Einstein relation
Supporting agencies: The authors would like to thank Kirill Alekseev for collaboration and useful ideas. This work was supported by the Ministry of Education and Science of the Russian Federation (Project No. 3.6321.2017/8.9), and RFBR (Project No. 17-02-00969).
About the Authors
A. V. Shorokhov
National Research Mordovia State University
Russian Federation
Russian Federation
Bolshevistskaya, 68, Saransk, 430005
N. S. Prudskikh
National Research Mordovia State University
Russian Federation
Russian Federation
Bolshevistskaya, 68, Saransk, 430005
M. B. Semenov
Penza State University
Russian Federation
Russian Federation
Krasnaya, 40, Penza, 440026
V. D. Krevchik
Penza State University
Russian Federation
Russian Federation
Krasnaya, 40, Penza, 440026
M. A. Pyataev
National Research Mordovia State University
Russian Federation
Russian Federation
Bolshevistskaya, 68, Saransk, 430005
S. E. Golovatyuk
National Research Mordovia State University
Russian Federation
Russian Federation
Bolshevistskaya, 68, Saransk, 430005
Tian-Rong Li
Institute of Functional and Environmental Materials, Lanzhou University
China
China
Lanzhou
Yu-Hua Wang
Institute of Functional and Environmental Materials, Lanzhou University
China
China
Lanzhou
References
1. Ignatov A. A., Shashkin V. I. Bloch oscillation of electrons and instabilities of space-charge waves in semiconductor superlattices. Sov. Phys. JETP, 1987, 66, P. 526–530.
2. Ignatov A. A., Shashkin V. I. Diffusion coefficient of heated carries, spectrum of space-charge waves, and characteristic instability frequencies of semiconductor superlattices. Sov. Phys. Semicond, 1984, 18, P. 721–724.
3. Ignatov A. A., Shashkin V. I. Quasihydrodynamdice description of the instability of space charge waves and impedance of bounded superlattice structures. Sov. Phys. Semicond, 1987, 21, P. 973–976.
4. Bonilla L. L., Alvaro M., Carretero M. Theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices. Physical Review B, 84, 2011, P. 155316 1–17.
5. Bonilla L. L., Escobedo R., Perales Á. Generalized drift-diffusion model for miniband superlattices. Physical Review B, 2003, 68, P. 2413041-4(R).
6. lvaro M., Carretero M., Bonilla L. L. Numerical method for hydrodynamic modulation equations describing Bloch oscillations in semiconductor superlattices. Journal of Computational Physics, 2012, 231, P. 4499–4514.
7. Bryksin V.V., Kleinert P. Theory of quantum diffusion in biased semiconductors. J. Phys.: Condens. Matter, 2003, 15, P. 1415-1425.
8. Shorokhov A. V., Aleksev K. N. High-frequency absorption and gain in superlattices: Semiquasistatic approach. Physica E, 2006, 33, P. 284–295.
9. Shorokhov A. V., Aleksev K. N. Quantum Derivatives and Terahertz Gain in a Superlattice. JETP, 2006, 105, P. 198–200.
10. Winnerl S., Schomburg E., Grenzer J., Regl H.-J., Ignatov A. A., Semenov A. D., Renk K. F., Pavel’ev D. G., Koschurinov Yu., Melzer B., Ustinov V., Ivanov S., Schaposchnikov S., Kop’ev P. S. Quasistatic and dynamic interaction of high-frequency fields with miniband electrons in semiconductor superlattices. Physical Review B, 1997, 56, P. 10303–10307.
11. Suris R. A. and Shchamkhalova B. S. Heating of electrons in superlattice semiconductors. Sov. Phys. Semicond, 1984, 18, P. 738–742.
12. Ignatov A. A., Dodin E. P., Shashkin V. I. Transient response theory of semiconductor superlattices: connection with Bloch oscillations Mod. Phys. Lett. B, 1991, 5, P. 1087–1094.
13. Grahn H. T., von Klitzing K., Ploog K., Dohler G. H. Electrical transport in narrow-miniband semiconductor superlattices Phys. Rev. B, 1991, 43, P. 12094–12097.
Review
For citations:
Shorokhov A.V., Prudskikh N.S., Semenov M.B., Krevchik V.D., Pyataev M.A., Golovatyuk S.E., Li T., Wang Yu. Kinetic coefficients of semiconductor superlattices in high-frequency electromagnetic fields. Nanosystems: Physics, Chemistry, Mathematics. 2017;8(6):740-745. https://doi.org/10.17586/2220-8054-2017-8-6-740-745
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