Transverse instability of a plane front of fast impact ionization waves

Abstract The transverse instability of a plane front of fast impact ionization waves in p+-n-n+ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration $ σ_{b} $ ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum sM at k = kM, then decreases, and becomes negative at k > k01. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and “smearing” of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ≳ kM have been established: at fixed $ σ_{b} $ values and the maximum field strength on the front E0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k01 ∝ N. The parameters sM, kM, and k01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Kyuregyan, A. S. [verfasserIn]

Format:	Artikel
Sprache:	Englisch

Erschienen:	2012

Schlagwörter:	Plane Front Space Charge Region Continuum Approximation Space Charge Density Soft Matter Phys

Anmerkung:	© Pleiades Publishing, Ltd. 2012

Übergeordnetes Werk:	Enthalten in: Journal of experimental and theoretical physics - SP MAIK Nauka/Interperiodica, 1993, 114(2012), 5 vom: Mai, Seite 857-866
Übergeordnetes Werk:	volume:114 ; year:2012 ; number:5 ; month:05 ; pages:857-866

Links:	Volltext

DOI / URN:	10.1134/S1063776112030168

Katalog-ID:	OLC2043164503

Internformat


LEADER	01000caa a22002652 4500
001	OLC2043164503
003	DE-627
005	20230504103935.0
007	tu
008	200820s2012 xx \|\|\|\|\| 00\| \|\|eng c
024	7		\|a 10.1134/S1063776112030168 \|2 doi
035			\|a (DE-627)OLC2043164503
035			\|a (DE-He213)S1063776112030168-p
040			\|a DE-627 \|b ger \|c DE-627 \|e rakwb
041			\|a eng
082	0	4	\|a 530 \|q VZ
084			\|a 33.00 \|2 bkl
100	1		\|a Kyuregyan, A. S. \|e verfasserin \|4 aut
245	1	0	\|a Transverse instability of a plane front of fast impact ionization waves
264		1	\|c 2012
336			\|a Text \|b txt \|2 rdacontent
337			\|a ohne Hilfsmittel zu benutzen \|b n \|2 rdamedia
338			\|a Band \|b nc \|2 rdacarrier
500			\|a © Pleiades Publishing, Ltd. 2012
520			\|a Abstract The transverse instability of a plane front of fast impact ionization waves in p+-n-n+ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration $ σ_{b} $ ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum sM at k = kM, then decreases, and becomes negative at k > k01. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and “smearing” of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ≳ kM have been established: at fixed $ σ_{b} $ values and the maximum field strength on the front E0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k01 ∝ N. The parameters sM, kM, and k01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave.
650		4	\|a Plane Front
650		4	\|a Space Charge Region
650		4	\|a Continuum Approximation
650		4	\|a Space Charge Density
650		4	\|a Soft Matter Phys
773	0	8	\|i Enthalten in \|t Journal of experimental and theoretical physics \|d SP MAIK Nauka/Interperiodica, 1993 \|g 114(2012), 5 vom: Mai, Seite 857-866 \|w (DE-627)131188410 \|w (DE-600)1146369-7 \|w (DE-576)032622368 \|x 1063-7761 \|7 nnns
773	1	8	\|g volume:114 \|g year:2012 \|g number:5 \|g month:05 \|g pages:857-866
856	4	1	\|u https://doi.org/10.1134/S1063776112030168 \|z lizenzpflichtig \|3 Volltext
912			\|a GBV_USEFLAG_A
912			\|a SYSFLAG_A
912			\|a GBV_OLC
912			\|a SSG-OLC-PHY
912			\|a GBV_ILN_22
912			\|a GBV_ILN_70
912			\|a GBV_ILN_2185
936	b	k	\|a 33.00 \|q VZ
951			\|a AR
952			\|d 114 \|j 2012 \|e 5 \|c 05 \|h 857-866

Indexfelder

author_variant	a s k as ask
matchkey_str	article:10637761:2012----::rnvrentbltoalnfotfatma
hierarchy_sort_str	2012
bklnumber	33.00
publishDate	2012
allfields	10.1134/S1063776112030168 doi (DE-627)OLC2043164503 (DE-He213)S1063776112030168-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kyuregyan, A. S. verfasserin aut Transverse instability of a plane front of fast impact ionization waves 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2012 Abstract The transverse instability of a plane front of fast impact ionization waves in p+-n-n+ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration $ σ_{b} $ ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum sM at k = kM, then decreases, and becomes negative at k > k01. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and “smearing” of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ≳ kM have been established: at fixed $ σ_{b} $ values and the maximum field strength on the front E0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k01 ∝ N. The parameters sM, kM, and k01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave. Plane Front Space Charge Region Continuum Approximation Space Charge Density Soft Matter Phys Enthalten in Journal of experimental and theoretical physics SP MAIK Nauka/Interperiodica, 1993 114(2012), 5 vom: Mai, Seite 857-866 (DE-627)131188410 (DE-600)1146369-7 (DE-576)032622368 1063-7761 nnns volume:114 year:2012 number:5 month:05 pages:857-866 https://doi.org/10.1134/S1063776112030168 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_70 GBV_ILN_2185 33.00 VZ AR 114 2012 5 05 857-866
spelling	10.1134/S1063776112030168 doi (DE-627)OLC2043164503 (DE-He213)S1063776112030168-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kyuregyan, A. S. verfasserin aut Transverse instability of a plane front of fast impact ionization waves 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2012 Abstract The transverse instability of a plane front of fast impact ionization waves in p+-n-n+ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration $ σ_{b} $ ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum sM at k = kM, then decreases, and becomes negative at k > k01. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and “smearing” of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ≳ kM have been established: at fixed $ σ_{b} $ values and the maximum field strength on the front E0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k01 ∝ N. The parameters sM, kM, and k01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave. Plane Front Space Charge Region Continuum Approximation Space Charge Density Soft Matter Phys Enthalten in Journal of experimental and theoretical physics SP MAIK Nauka/Interperiodica, 1993 114(2012), 5 vom: Mai, Seite 857-866 (DE-627)131188410 (DE-600)1146369-7 (DE-576)032622368 1063-7761 nnns volume:114 year:2012 number:5 month:05 pages:857-866 https://doi.org/10.1134/S1063776112030168 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_70 GBV_ILN_2185 33.00 VZ AR 114 2012 5 05 857-866
allfields_unstemmed	10.1134/S1063776112030168 doi (DE-627)OLC2043164503 (DE-He213)S1063776112030168-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kyuregyan, A. S. verfasserin aut Transverse instability of a plane front of fast impact ionization waves 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2012 Abstract The transverse instability of a plane front of fast impact ionization waves in p+-n-n+ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration $ σ_{b} $ ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum sM at k = kM, then decreases, and becomes negative at k > k01. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and “smearing” of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ≳ kM have been established: at fixed $ σ_{b} $ values and the maximum field strength on the front E0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k01 ∝ N. The parameters sM, kM, and k01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave. Plane Front Space Charge Region Continuum Approximation Space Charge Density Soft Matter Phys Enthalten in Journal of experimental and theoretical physics SP MAIK Nauka/Interperiodica, 1993 114(2012), 5 vom: Mai, Seite 857-866 (DE-627)131188410 (DE-600)1146369-7 (DE-576)032622368 1063-7761 nnns volume:114 year:2012 number:5 month:05 pages:857-866 https://doi.org/10.1134/S1063776112030168 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_70 GBV_ILN_2185 33.00 VZ AR 114 2012 5 05 857-866
allfieldsGer	10.1134/S1063776112030168 doi (DE-627)OLC2043164503 (DE-He213)S1063776112030168-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kyuregyan, A. S. verfasserin aut Transverse instability of a plane front of fast impact ionization waves 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2012 Abstract The transverse instability of a plane front of fast impact ionization waves in p+-n-n+ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration $ σ_{b} $ ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum sM at k = kM, then decreases, and becomes negative at k > k01. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and “smearing” of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ≳ kM have been established: at fixed $ σ_{b} $ values and the maximum field strength on the front E0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k01 ∝ N. The parameters sM, kM, and k01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave. Plane Front Space Charge Region Continuum Approximation Space Charge Density Soft Matter Phys Enthalten in Journal of experimental and theoretical physics SP MAIK Nauka/Interperiodica, 1993 114(2012), 5 vom: Mai, Seite 857-866 (DE-627)131188410 (DE-600)1146369-7 (DE-576)032622368 1063-7761 nnns volume:114 year:2012 number:5 month:05 pages:857-866 https://doi.org/10.1134/S1063776112030168 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_70 GBV_ILN_2185 33.00 VZ AR 114 2012 5 05 857-866
allfieldsSound	10.1134/S1063776112030168 doi (DE-627)OLC2043164503 (DE-He213)S1063776112030168-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kyuregyan, A. S. verfasserin aut Transverse instability of a plane front of fast impact ionization waves 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2012 Abstract The transverse instability of a plane front of fast impact ionization waves in p+-n-n+ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration $ σ_{b} $ ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum sM at k = kM, then decreases, and becomes negative at k > k01. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and “smearing” of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ≳ kM have been established: at fixed $ σ_{b} $ values and the maximum field strength on the front E0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k01 ∝ N. The parameters sM, kM, and k01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave. Plane Front Space Charge Region Continuum Approximation Space Charge Density Soft Matter Phys Enthalten in Journal of experimental and theoretical physics SP MAIK Nauka/Interperiodica, 1993 114(2012), 5 vom: Mai, Seite 857-866 (DE-627)131188410 (DE-600)1146369-7 (DE-576)032622368 1063-7761 nnns volume:114 year:2012 number:5 month:05 pages:857-866 https://doi.org/10.1134/S1063776112030168 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_70 GBV_ILN_2185 33.00 VZ AR 114 2012 5 05 857-866
language	English
source	Enthalten in Journal of experimental and theoretical physics 114(2012), 5 vom: Mai, Seite 857-866 volume:114 year:2012 number:5 month:05 pages:857-866
sourceStr	Enthalten in Journal of experimental and theoretical physics 114(2012), 5 vom: Mai, Seite 857-866 volume:114 year:2012 number:5 month:05 pages:857-866
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Plane Front Space Charge Region Continuum Approximation Space Charge Density Soft Matter Phys
dewey-raw	530
isfreeaccess_bool	false
container_title	Journal of experimental and theoretical physics
authorswithroles_txt_mv	Kyuregyan, A. S. @@aut@@
publishDateDaySort_date	2012-05-01T00:00:00Z
hierarchy_top_id	131188410
dewey-sort	3530
id	OLC2043164503
language_de	englisch
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2043164503</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230504103935.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2012 xx \|\|\|\|\| 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1134/S1063776112030168</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2043164503</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)S1063776112030168-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">33.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kyuregyan, A. S.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Transverse instability of a plane front of fast impact ionization waves</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2012</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Pleiades Publishing, Ltd. 2012</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The transverse instability of a plane front of fast impact ionization waves in p+-n-n+ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration $ σ_{b} $ ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum sM at k = kM, then decreases, and becomes negative at k > k01. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and “smearing” of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ≳ kM have been established: at fixed $ σ_{b} $ values and the maximum field strength on the front E0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k01 ∝ N. The parameters sM, kM, and k01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Plane Front</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Space Charge Region</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Continuum Approximation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Space Charge Density</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Soft Matter Phys</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of experimental and theoretical physics</subfield><subfield code="d">SP MAIK Nauka/Interperiodica, 1993</subfield><subfield code="g">114(2012), 5 vom: Mai, Seite 857-866</subfield><subfield code="w">(DE-627)131188410</subfield><subfield code="w">(DE-600)1146369-7</subfield><subfield code="w">(DE-576)032622368</subfield><subfield code="x">1063-7761</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:114</subfield><subfield code="g">year:2012</subfield><subfield code="g">number:5</subfield><subfield code="g">month:05</subfield><subfield code="g">pages:857-866</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1134/S1063776112030168</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2185</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">33.00</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">114</subfield><subfield code="j">2012</subfield><subfield code="e">5</subfield><subfield code="c">05</subfield><subfield code="h">857-866</subfield></datafield></record></collection>
author	Kyuregyan, A. S.
spellingShingle	Kyuregyan, A. S. ddc 530 bkl 33.00 misc Plane Front misc Space Charge Region misc Continuum Approximation misc Space Charge Density misc Soft Matter Phys Transverse instability of a plane front of fast impact ionization waves
authorStr	Kyuregyan, A. S.
ppnlink_with_tag_str_mv	@@773@@(DE-627)131188410
format	Article
dewey-ones	530 - Physics
delete_txt_mv	keep
author_role	aut
collection	OLC
remote_str	false
illustrated	Not Illustrated
issn	1063-7761
topic_title	530 VZ 33.00 bkl Transverse instability of a plane front of fast impact ionization waves Plane Front Space Charge Region Continuum Approximation Space Charge Density Soft Matter Phys
topic	ddc 530 bkl 33.00 misc Plane Front misc Space Charge Region misc Continuum Approximation misc Space Charge Density misc Soft Matter Phys
topic_unstemmed	ddc 530 bkl 33.00 misc Plane Front misc Space Charge Region misc Continuum Approximation misc Space Charge Density misc Soft Matter Phys
topic_browse	ddc 530 bkl 33.00 misc Plane Front misc Space Charge Region misc Continuum Approximation misc Space Charge Density misc Soft Matter Phys
format_facet	Aufsätze Gedruckte Aufsätze
format_main_str_mv	Text Zeitschrift/Artikel
carriertype_str_mv	nc
hierarchy_parent_title	Journal of experimental and theoretical physics
hierarchy_parent_id	131188410
dewey-tens	530 - Physics
hierarchy_top_title	Journal of experimental and theoretical physics
isfreeaccess_txt	false
familylinks_str_mv	(DE-627)131188410 (DE-600)1146369-7 (DE-576)032622368
title	Transverse instability of a plane front of fast impact ionization waves
ctrlnum	(DE-627)OLC2043164503 (DE-He213)S1063776112030168-p
title_full	Transverse instability of a plane front of fast impact ionization waves
author_sort	Kyuregyan, A. S.
journal	Journal of experimental and theoretical physics
journalStr	Journal of experimental and theoretical physics
lang_code	eng
isOA_bool	false
dewey-hundreds	500 - Science
recordtype	marc
publishDateSort	2012
contenttype_str_mv	txt
container_start_page	857
author_browse	Kyuregyan, A. S.
container_volume	114
class	530 VZ 33.00 bkl
format_se	Aufsätze
author-letter	Kyuregyan, A. S.
doi_str_mv	10.1134/S1063776112030168
dewey-full	530
title_sort	transverse instability of a plane front of fast impact ionization waves
title_auth	Transverse instability of a plane front of fast impact ionization waves
abstract	Abstract The transverse instability of a plane front of fast impact ionization waves in p+-n-n+ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration $ σ_{b} $ ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum sM at k = kM, then decreases, and becomes negative at k > k01. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and “smearing” of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ≳ kM have been established: at fixed $ σ_{b} $ values and the maximum field strength on the front E0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k01 ∝ N. The parameters sM, kM, and k01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave. © Pleiades Publishing, Ltd. 2012
abstractGer	Abstract The transverse instability of a plane front of fast impact ionization waves in p+-n-n+ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration $ σ_{b} $ ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum sM at k = kM, then decreases, and becomes negative at k > k01. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and “smearing” of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ≳ kM have been established: at fixed $ σ_{b} $ values and the maximum field strength on the front E0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k01 ∝ N. The parameters sM, kM, and k01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave. © Pleiades Publishing, Ltd. 2012
abstract_unstemmed	Abstract The transverse instability of a plane front of fast impact ionization waves in p+-n-n+ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration $ σ_{b} $ ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum sM at k = kM, then decreases, and becomes negative at k > k01. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and “smearing” of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ≳ kM have been established: at fixed $ σ_{b} $ values and the maximum field strength on the front E0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k01 ∝ N. The parameters sM, kM, and k01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave. © Pleiades Publishing, Ltd. 2012
collection_details	GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_70 GBV_ILN_2185
container_issue	5
title_short	Transverse instability of a plane front of fast impact ionization waves
url	https://doi.org/10.1134/S1063776112030168
remote_bool	false
ppnlink	131188410
mediatype_str_mv	n
isOA_txt	false
hochschulschrift_bool	false
doi_str	10.1134/S1063776112030168
up_date	2024-07-03T18:19:41.732Z
_version_	1803582996987510784
fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2043164503</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230504103935.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2012 xx \|\|\|\|\| 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1134/S1063776112030168</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2043164503</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)S1063776112030168-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">33.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kyuregyan, A. S.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Transverse instability of a plane front of fast impact ionization waves</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2012</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Pleiades Publishing, Ltd. 2012</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The transverse instability of a plane front of fast impact ionization waves in p+-n-n+ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration $ σ_{b} $ ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum sM at k = kM, then decreases, and becomes negative at k > k01. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and “smearing” of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ≳ kM have been established: at fixed $ σ_{b} $ values and the maximum field strength on the front E0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k01 ∝ N. The parameters sM, kM, and k01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Plane Front</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Space Charge Region</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Continuum Approximation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Space Charge Density</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Soft Matter Phys</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of experimental and theoretical physics</subfield><subfield code="d">SP MAIK Nauka/Interperiodica, 1993</subfield><subfield code="g">114(2012), 5 vom: Mai, Seite 857-866</subfield><subfield code="w">(DE-627)131188410</subfield><subfield code="w">(DE-600)1146369-7</subfield><subfield code="w">(DE-576)032622368</subfield><subfield code="x">1063-7761</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:114</subfield><subfield code="g">year:2012</subfield><subfield code="g">number:5</subfield><subfield code="g">month:05</subfield><subfield code="g">pages:857-866</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1134/S1063776112030168</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2185</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">33.00</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">114</subfield><subfield code="j">2012</subfield><subfield code="e">5</subfield><subfield code="c">05</subfield><subfield code="h">857-866</subfield></datafield></record></collection>
score	7.3990917

Nicht das Richtige dabei?

Schreiben Sie uns!

Transverse instability of a plane front of fast impact ionization waves

Nicht das Richtige dabei?

Zugang & Verfügbarkeit

Vorhandene Bände

Nicht das Richtige dabei?