A~new numerical method for the solution of the Boltzmann equation in the semiconductor nonlinear electron transport problem
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 6, pp. 77-97.

Voir la notice de l'article provenant de la source Math-Net.Ru

A new iterative method for solving the Boltzmann transport equation in the space-uniform case is introduced. The method is based on the use of a mesh in the momentum space to represent the distribution function. In intermediate points the function is found with the help of interpolation. The method is used to study the hot-electron transport in bulk $n$-In N, which is a promising material for optoelectronic applications.
@article{FPM_2009_15_6_a6,
     author = {N. A. Masyukov and A. V. Dmitriev},
     title = {A~new numerical method for the solution of the {Boltzmann} equation in the semiconductor nonlinear electron transport problem},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {77--97},
     publisher = {mathdoc},
     volume = {15},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_6_a6/}
}
TY  - JOUR
AU  - N. A. Masyukov
AU  - A. V. Dmitriev
TI  - A~new numerical method for the solution of the Boltzmann equation in the semiconductor nonlinear electron transport problem
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2009
SP  - 77
EP  - 97
VL  - 15
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2009_15_6_a6/
LA  - ru
ID  - FPM_2009_15_6_a6
ER  - 
%0 Journal Article
%A N. A. Masyukov
%A A. V. Dmitriev
%T A~new numerical method for the solution of the Boltzmann equation in the semiconductor nonlinear electron transport problem
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2009
%P 77-97
%V 15
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2009_15_6_a6/
%G ru
%F FPM_2009_15_6_a6
N. A. Masyukov; A. V. Dmitriev. A~new numerical method for the solution of the Boltzmann equation in the semiconductor nonlinear electron transport problem. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 6, pp. 77-97. http://geodesic.mathdoc.fr/item/FPM_2009_15_6_a6/

[1] Abrikosov A. A., Osnovy teorii metallov, Nauka, M., 1987

[2] Ashkroft N., Mermin N., Fizika tvërdogo tela, Mir, M., 1979

[3] Bass F. G., Gurevich Yu. G., Goryachie elektrony i silnye elektromagnitnye volny v plazme poluprovodnikov i gazovogo razryada, Nauka, M., 1975 | MR

[4] Bonch-Bruevich V. L., Kalashnikov S. G., Fizika poluprovodnikov, Nauka, M., 1990

[5] Gantmakher V. F., Levinson I. B., Rasseyanie nositelei toka v metallakh i poluprovodnikakh, Mir, M., 1984

[6] Davydov V. Yu., Klochikhin A. A., “Elektronnye i kolebatelnye sostoyaniya InN i tvërdykh rastvorov $\mathrm{In}_x\mathrm{Ga}_{1-x}\mathrm N$”, Fizika i tekhnika poluprovodnikov, 38:8 (2004), 897–936

[7] Zaiman Dzh., Printsipy teorii tvërdogo tela, Mir, M., 1974

[8] Kittel Ch., Vvedenie v fiziku tvërdogo tela, Nauka, M., 1978

[9] Fertsiger Dzh., Kaper G., Matematicheskaya teoriya protsessov perenosa v gazakh, Mir, M., 1976

[10] Chepmen C., Kauling T., Matematicheskaya teoriya neodnorodnykh gazov, IL, M., 1960

[11] Cherchinyani K., Teoriya i prilozheniya uravneniya Boltsmana, Mir, M., 1978 | MR

[12] Bellotti E., et al., “Ensemble Monte Carlo study of electron transport in wurtzite InN”, J. Appl. Phys., 85:2 (1999), 916–923 | DOI

[13] Ertler C., Schruerrer F., “A multicell matrix solution to the Boltzmann equation applied to the anisotropic electron transport in silicon”, J. Phys. A, 36 (2003), 8759–8774 | DOI | Zbl

[14] Foutz B. E., O'Leary S. K., Shur M. S., Eastman L. F., “Transient electron transport in wurtzite GaN, InN, and AlN”, J. Appl. Phys., 85:11 (1999), 7727–7734 | DOI

[15] Galler M., Schruerrer F., “A deterministic solution method for the coupled system of transport equations for the electrons and phonons in polar semiconductors”, J. Phys. A, 37 (2004), 1479–1497 | DOI | MR | Zbl

[16] Humphreys C. J., “Solid-state lighting”, MRS Bulletin, 33 (2008), 459–470 | DOI

[17] Jacoboni C., Reggiani L., “The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials”, Rev. Modern Phys., 55:3 (1983), 645–698 | DOI

[18] Keys R., “Cubic convolution interpolation for digital image processing”, IEEE Trans. Acoust. Speech Signal Process, 29 (1981), 1153–1160 | DOI | MR | Zbl

[19] O'Leary S. K., Foutz B. E., Shur M. S., Bhapkar U. V., Eastman L. F., “Electron transport in wurtzite indium nitride”, J. Appl. Phys., 83:2 (1998), 826–829 | DOI

[20] O'Leary S. K., Foutz B. E., Shur M. S., Eastman L. F., “Steady-state and transient electron transport within bulk wurtzite indium nitride: An updated semiclassical three-valley Monte Carlo simulation anaysis”, Appl. Phys. Lett., 87 (2005), 222103 | DOI

[21] Polyakov V. M., Schwierz F., “Low-field electron mobility in wurtzite InN”, Appl. Phys. Lett., 88 (2006), 032101 | DOI

[22] Polyakov V. M., Schwierz F., “Nonparabolicity effect on bulk transport properties in wurtzite InN”, J. Appl. Phys., 99 (2006), 113705 | DOI

[23] Rodrigues C. G., et al., “Nonlinear transport properties of III-nitrides in electric field”, J. Appl. Phys., 98 (2005), 043702 | DOI

[24] Starikov E., et al., “Monte Carlo calculations of static and dynamic electron transport in nitrides”, J. Appl. Phys., 98 (2005), 083701 | DOI

[25] Vurgaftman I., Meyer J. R., Ram-Mohan L. R., “Band parameters for III–V compound semiconductors and their alloys”, J. Appl. Phys., 89:11 (2001), 5815–5875 | DOI

[26] Zanato D., Balkan N., Ridley B. K., Hill G., Schaff W. J., “Hot electron cooling rates via the emission of LO-phonons in InN”, Semicond. Sci. Technol., 19 (2004), 1024–1028 | DOI