Switching waves in asymmetric thyristor-like structures for incomplete gate turn off regime

Switching waves in asymmetric thyristor-like structures for incomplete gate turn off regime

A stationary wave of switching is considered in an infinite thyristor-like structure (TLS).This wave is initiated by the controlling gate current which differs from a certain equilibrium current Jg0(j) providing a neutrally equilibrium (translationally invariant) position of the transition layer bet...

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Datum:1998
Hauptverfasser: Gribnikov, Z.S., Gordion, I.M., Mitin, V.V.
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Sprache:English
Veröffentlicht: Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 1998
Schriftenreihe:Semiconductor Physics Quantum Electronics & Optoelectronics
Online Zugang:http://dspace.nbuv.gov.ua/handle/123456789/114676
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spelling irk-123456789-1146762017-03-12T03:02:28Z Switching waves in asymmetric thyristor-like structures for incomplete gate turn off regime Gribnikov, Z.S. Gordion, I.M. Mitin, V.V. A stationary wave of switching is considered in an infinite thyristor-like structure (TLS).This wave is initiated by the controlling gate current which differs from a certain equilibrium current Jg0(j) providing a neutrally equilibrium (translationally invariant) position of the transition layer between a blocked (OFF-) region and an open (ON-) region for a given current density j in the ON-region. The dependence of the wave velocity v(Jg, j) on the gate current Jg and the current density j is derived.We deal with structures in which the conductivity of gated base I is much higher than the conductivity of ungated base II.The injection level is considered low for base I and high for base II. It is shown that the velocity of the switching wave (i.e. the speed of transient processes in TLS) is determined mainly by parameters of base II. It is also demonstrated that a high speed of operation can be reached in structures with a moderately long base II (the length of the base should exceed 1-2 bipolar diffusion lengths) and a small lifetime of carriers in this base. This work was supported by the National Science Foundation of the USA. One of us (Z. S. Gribnikov) thanks the Ukrainian Foundation of Fundamental Researches for a partial support. We also thankful to the editorial board of the «Semiconductor Physics, Quantum Electronics & Optoelectronics» for the invitation to submit our paper to the first issue of this new journal. Розглянуто стаціонарну хвилю переключення в кінцевій тиристоро подібній структрурі (ТПС). Ця хвиля ініційована контролюючим струмом затвору I g, який відрізняється від певного рівноважного струму I g0(j), який забезпечує положення нейтральної рівноваги (трансляційно інваріантної) перехідного шару між запертою та відкритою областями для даної густини струму j у відкритій області. Виведено залежність швидкості хвилі v(I g, j) від струму 1998 Article Switching waves in asymmetric thyristor-like structures for incomplete gate turn off regime / Z.S. Gribnikov, I.M. Gordion, V.V. Mitin // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1998. — Т. 1, № 1. — С. 90-100. — Бібліогр.: 17 назв. — англ. 1560-8034 PACS 72.20; 73.61.G; 85.30.R http://dspace.nbuv.gov.ua/handle/123456789/114676 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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description A stationary wave of switching is considered in an infinite thyristor-like structure (TLS).This wave is initiated by the controlling gate current which differs from a certain equilibrium current Jg0(j) providing a neutrally equilibrium (translationally invariant) position of the transition layer between a blocked (OFF-) region and an open (ON-) region for a given current density j in the ON-region. The dependence of the wave velocity v(Jg, j) on the gate current Jg and the current density j is derived.We deal with structures in which the conductivity of gated base I is much higher than the conductivity of ungated base II.The injection level is considered low for base I and high for base II. It is shown that the velocity of the switching wave (i.e. the speed of transient processes in TLS) is determined mainly by parameters of base II. It is also demonstrated that a high speed of operation can be reached in structures with a moderately long base II (the length of the base should exceed 1-2 bipolar diffusion lengths) and a small lifetime of carriers in this base.
format Article
author Gribnikov, Z.S.
Gordion, I.M.
Mitin, V.V.
spellingShingle Gribnikov, Z.S.
Gordion, I.M.
Mitin, V.V.
Switching waves in asymmetric thyristor-like structures for incomplete gate turn off regime
Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet Gribnikov, Z.S.
Gordion, I.M.
Mitin, V.V.
author_sort Gribnikov, Z.S.
title Switching waves in asymmetric thyristor-like structures for incomplete gate turn off regime
title_short Switching waves in asymmetric thyristor-like structures for incomplete gate turn off regime
title_full Switching waves in asymmetric thyristor-like structures for incomplete gate turn off regime
title_fullStr Switching waves in asymmetric thyristor-like structures for incomplete gate turn off regime
title_full_unstemmed Switching waves in asymmetric thyristor-like structures for incomplete gate turn off regime
title_sort switching waves in asymmetric thyristor-like structures for incomplete gate turn off regime
publisher Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate 1998
url http://dspace.nbuv.gov.ua/handle/123456789/114676
citation_txt Switching waves in asymmetric thyristor-like structures for incomplete gate turn off regime / Z.S. Gribnikov, I.M. Gordion, V.V. Mitin // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1998. — Т. 1, № 1. — С. 90-100. — Бібліогр.: 17 назв. — англ.
series Semiconductor Physics Quantum Electronics & Optoelectronics
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AT mitinvv switchingwavesinasymmetricthyristorlikestructuresforincompletegateturnoffregime
first_indexed 2025-07-08T07:47:57Z
last_indexed 2025-07-08T07:47:57Z
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fulltext 90 © 1998 ²íñòèòóò ô³çèêè íàï³âïðîâ³äíèê³â ÍÀÍ Óêðà¿íè Ô³çèêà íàï³âïðîâ³äíèê³â, êâàíòîâà òà îïòîåëåêòðîí³êà. 1998. Ò. 1, ¹ 1. Ñ. 90-100. Semiconductor Physics, Quantum Electronics & Optoelectronics. 1998. V. 1, N 1. P. 90-100. I.Introduction This paper is devoted to the control of the current- conducting region in a thyristor-like structure. Here, as well as before [1, 2] we refer to TLS as a certain P+npN+ structure where two outer layers provide effective injection of their majority carriers into two inner layers (bases). One of the bases (base I) is gated. The gate transfers the controlling current into the base. This current squeezes the current-conducting region (the ON-region in fig. 1), and enlarges the OFF-region. The gated base is usually highly conducting in comparison with the second base (base II). In silicon controlled rectifiers (SCRs) [3], the gate current just turns the TLS on and off, while in light- emitting (LE) and lasing (L) thyristors the gate current can also control (or modulate) light emission [4, 5]. That is why we are interested in characteristics of stationary control of the ON-region (the position of the layer between the ON- and OFF- regions, called the ON/OFF-junction) as well as the speed of the ON/OFF-junction in the TLS. Our further consideration is based on the fact that the typical structures of LE thyristors [6, 7, 8] differ greatly from the structures of SCRs. LE thyristors should not PACS 72.20; 73.61.G; 85.30.R Switching waves in asymmetric thyristor-like structures for incomplete gate turn off regime Z. S. Gribnikov Institute of Semiconductor Physics, NAS Ukraine, 45 prospekt Nauki, Kyiv, 252028, Ukraine I. M. Gordion, and V. V. Mitin Wayne State University, Detroit, MI 48202, USA zinovi@besm6.eng.wayne.edu Abstract. A stationary wave of switching is considered in an infinite thyristor-like structure (TLS).This wave is initiated by the controlling gate current which differs from a certain equilibrium current J g0 (j) providing a neutrally equilibrium (translationally invariant) position of the transition layer between a blocked (OFF-) region and an open (ON-) region for a given current density j in the ON-region. The dependence of the wave velocity v(J g , j) on the gate current J g and the current density j is derived.We deal with structures in which the conductivity of gated base I is much higher than the conductivity of ungated base II.The injection level is considered low for base I and high for base II. It is shown that the velocity of the switching wave (i.e. the speed of transient processes in TLS) is determined mainly by parameters of base II. It is also demonstrated that a high speed of operation can be reached in structures with a moderately long base II (the length of the base should exceed 1-2 bipolar diffusion lengths) and a small lifetime of carriers in this base. Keywords: switching waves, thyristor-like structure, transient processes, controlling gate current, injection level. Paper received 22.06.98; revised manuscript received 29.07.98; accepted for publication 27.10.98. Fig. 1. a) Considered thyristor-like stucture (TLS) with b) the distributions of the current density j(y) and c) the electrical potential y(x) in it. Z. S. Gribnikov et al.: Switching waves in asymmetric thyristor-like structures... 91ÔÊÎ, 1(1), 1998 SQO, 1(1), 1998 usually resist high voltages, therefore the sum of the base widths, w I + w II , is much smaller than the initial length of the ON-region, 2a 0 , for most LE TLSs. Usually the value of w I + w II does not exceed 0.2�0.3 µm while the initial length of the ON-region is rarely less than 10 µm. Detailed descriptions of the LE and L pnpn-diodes (having different names) with gated either p- or n- bases, are presented in [10-16]. For such structures the strong inequality 2a 0 >>w I  + w II admits regimes with the width of the ON/ OFF-junction which is also much greater than w I  + w II . This means that the electrical potential changes quite smoothly along each base. The distribution of none- quilibrium carriers in the bases can be considered as nearly one-dimensional (1D) because the carrier concentrations change much slighter along pn-junction planes than in the perpendicular direction. Such distributions allow us to exploit a quasiadiabatic approach which was demonstrated earlier [1, 2, 9]. This approach assumes that the distribution of nonequilibrium carrier concentration can be represented as a function of x-coordinate and electric potentials of both bases, U I (y) and U II (y). (Here U I is the voltage drop between the anode P+-emitter) and base I, U II is the voltage drop between the anode and base II). This approximation leads to a self-consistent system of two nonlinear differential equations for U I,II (y). This system can be solved numerically [2] or can be reduced to one nonlinear differential equation [1] under the condition III σσ >> , (1) where σ I,II are the longitudinal (in-plane) conductivities of bases I,II. Here we consider a structure where base I is doped much heavier than base II, so that inequality (1) is satisfied. We also assume low injection level in base I and high injection level in base II. For real asymmetric thyristors, the second assumption is more suitable than the assumption of low injection level in both bases, as was considered before [1, 2, 9]. We also keep assuming that carrier distributions in both bases are functions of the electric potentials, U I,II (y), and of the voltage across the entire structure, U, which does not depend on y-coordi- nate. This representation for high injection level in base II is valid only if this base is not too long (w II ≤ (3-4)L, where L is the bipolar diffusion length in base II), so that the voltage across the base can be neglected in comparison with the voltage across pn-junctions. Here we consider the problem of the steady-state position of the ON/OFF- junction as well as the nonstationary problem which can be described in the framework of the stationary switching wave approach [17]. Strictly speaking, the theory of the stationary wave can be applied only if the gate current and current density in the ON-region are time-independent. This condition requires infinitely large values of a and J a . However, we can use this approach to obtain an approximate solution of the nonstationary problem with comparatively slow changes of J g (t), a(t), j(t). These changes lead to a slow change of the velocity, v(t), which should be constant for a strict stationary wave approach. II. Model and equations. Stationary theory The gate is attached to the n-base because the mobility of majority carriers (electrons) is much higher than that of holes for A III B V materials we are interested in. We consider low injection level in this base, so that carrier distribu- tion is determined by the linear equation of drift and diffu- sion of minority carriers. The boundary conditions for this equation are the following: p(x = 0) = p e I 01 ψ , (2) p(x = w I - 0) = ( )p e I II 0 2 2 ψ ψ− , (3) where ψ I,II = eU I,II /(kT) are the dimensionless electrical potentials of bases I and II; p01 is the equilibrium concentration of holes in base I at the P+n-junction (jct.1, x = 0). To derive Eq.(3) we have to use the condition of conservation of quasi Fermi-levels in the inner np-junction (jct.2): np = const, i.e. p I (w I - 0) ⋅ n I (w I - 0) = p II (w I + 0) ⋅ n II (w I + 0) (4) Because of high injection level in base II, we have p II (w I + 0) ≈ n II (w I + 0) = N eI I II− + −ψ ψ ψ0 , (5) p I (w I - 0) = ( )N eI I II− + −2 20ψ ψ ψ , (6) where N I is the donor concentration in base I at the inner pn-junction (jct.2), n I (w I - 0) e p− =2 0 0 2 ψ is the effective hole concentration there (here p02 is greater than the equilibrium concentration); and ψ 0 is the dimensionless value of equilibrium voltage across this np-junction. As the result of an approximate solution of the drift � diffusion equation in base I, we obtain: ( )j j e j eI I II 1 11 12 2= − −ψ ψ ψ , (7) )(2/ 2221 / 2 IIII ejejj ψψψ −−= (8) Since we consider that the values ψ I , (ψ I - ψ II ) are high enough, we neglect 1 in comparison with ( )e eI I IIψ ψ ψ, 2 − . In Eq.(7), j 1 is the current density through the emitter P+n-junction (jct.1). We assume that this junction � either homojunction or heterojunction � provides emission of the emitter majority carriers � holes � into base I. The current density through the inner pn-junction (jct.2) consists of two portions. The hole current density, / 2j , is given by Eq.(8). The electron current density, // 2j , will be presented below. The values of j 11 , j 12 , j 21 , / 22j can be calculated only for specified distributions of both donors and lifetimes of holes in base I. For uniformly doped base I where the drift term can be neglected, we have: IIIIIIIII zDepjzDepj tanh/,tanh/ 02 / 220111 ββ == , (9) Z. S. Gribnikov et al.: Switching waves in asymmetric thyristor-like structures... 92 ÔÊÎ, 1(1), 1998 SQO, 1(1), 1998 1 ~~ / 22121121 )(cosh,, −==== IIIII zjjjj αααα (10) where β I is the inverse diffusion length of holes in base I: β I = (D I ⋅ τ I )-1/2; D I is the coefficient of diffusion and τ I is the lifetime of holes in base I; z I = β I ⋅ w I is the dimensionless width of base I. We note that even for uniformly doped base I the concentrations p01 and p02 differ greatly because the latter is not a concentration of equilibrium holes. Since we assume high injection level in base II, we can neglect the acceptor concentration in comparison with current carrier concentration and write the electron current in base II in the form: dx dn D b b jj IIn + + = 1 , (11) where b = µ n /µ p , and µ n,p are the mobilities of electrons and holes in base II, and D II = 2D n D p /(D n +D p ) is the bipolar diffusion coefficient, D n,p are the diffusion coefficients of electrons and holes in base II, respectively. We assume that lifetime τ II in base II is constant. The continuity equation for electron current in base II has to be solved with the boundary conditions: p II (w I + 0) ≈ n II (w I + 0) = n e I II 02 ψ ψ− , (12) p II (w I + w II ) ≈ n II (w I + w II ) = n e II 03 ψ ψ− , (13) where n02 and n03 are the equilibrium concentrations in base II at junctions 2 and 3, respectively. These formulae are valid because low injection levels are considered in both base I and the N+-emitter. The expressions of current densities obtained from Eqs.(11), (12), (13) are written in the form: IIIII ejej b b wjj ψψψψ −− +− + += 23 // 22/ // 2 1 )0( , (14) IIIII ejej b b wjj II ψψψψ −− +− + = 33323 1 )( , (15) where IIIIIIIIIIII zDenjzDenj tanh/,tanh/ 033302 // 22 ββ == , (16) 1 3323 // 2232 )(cosh,, −=== IIIIIIII zjjjj ααα ; (17) IIIIIIIIIIII wzandD βτβ == − 21)( are the variables related to base II. Here we apply one of the main assumptions of our consideration: the in-plane conductivity of base I is much greater than that of base II which depends on the electron concentration n(x). This fact allows us to neglect the gate current which branches off into base II. So we assume 3 // 2 / 222 )()0( jjjjwjwj I ≅+≅=≅+ (18) From Eq. (18) we can obtain ( )[ ]IIIII ejejbjj ψψψψ −− +−+== 323232 1 (19) ( ) ( )[ ]IIIIIIIII ejejejej bjjjj ψψψψψψψ −−− +′′−+′−× ×+=′′+′== 232221 2 22 2232 1 . (20) Using Eq.(19), (20) we can express the term e I IIψ ψ− through the terms e Iψ ψ− and e Iψ . 0 2 1 2 0 BBBe III −+=−ψψ , (21) where B 0 and B 1 depend on e Iψ : / 2221 2 1 / 22 // 220 /),2(/)1)(1( jejBjejB II II ψψψα =+−= − . As a result, the current continuity equation in base I can be written in the form: ×−++−= )()~1( 0 2 1 2 01112 1 2 BBBej dy d e kT I II ψααψσ [ ( )( )] ( ).1~1 )1(~)1(( 33 // 22 IIII IIIII Rbej bj I ψαα ααα ψψ =−−+− −−++× − (22) Generally, / 2212 ~ / jjI =α can differ from α I . III. Homogeneous solution A homogeneous solution is valid when the gate current J g  = 0, and all current densities through the pn-junctions are equal: j 1 = j 2 = j 3 = j. Actually, the same equalities are valid for an inhomogeneous stationary solution in the depth of the ON-region. Thus we can treat the homogenous solution as a boundary condition for an inhomogeneous solution at y → ∞. From the particular solution of Eq.(22) (R(ψ I = 0), we obtain: 33 32 )1( /)1( jb ujjb ee I + ++ = ψψ , (23) 21 12 11     −== − j jej eu I III ψ ψψ . (24) From Eq.(20), we can calculate the dependencies ( )e jIψ and ( )e jψ (the latter being actually an expression for the voltage-current characteristic of the TLS): 2 2 2 11 / 22 11 11~         −++= rj j r j j j j e c I I αψ , (25) Z. S. Gribnikov et al.: Switching waves in asymmetric thyristor-like structures... 93ÔÊÎ, 1(1), 1998 SQO, 1(1), 1998                 +++× ×                 −++ + = rj rj j j rj j rjj jjb e c c II c I 2 // 22 2 2 2/ 22 3311 1 11~ )1( 1 α αψ (26) where )1/()1()2(/ ~ 2/ 22 // 22 IIIIjjr ααα −−⋅= and )1)1((/)1)(1( ~ / 22 −++−+= IIIIIc bbjj αααα . We consider more thoroughly two limiting cases: first, j << j c r2, and second, j >> j c r2. For the first case, the dependencies ( )e jIψ and ( )e jψ are linear (curves 1�3 in fig. 2 for the current range j/(j c r2 ) << 1): IIjjje I /)( ≅ψ , (27) 33 32 )1( 2)1( )( jbj rjbj jje II c + ++ ≅ψ , (28) Comparing Eq.(27) with Eq.(7) we note that for j << j c r2, we can neglect the second term in Eq.(7). This means that this term ( ( )e I II2 ψ ψ− instead of e I IIψ ψ− for low injection levels in both bases) does not affect TLS�s behavior. For this limiting case, the solution is very close to the solution for low injection levels in both bases (see, for example, [1]). For j >> j c r2, the dependence ( )e jIψ is still linear: )1()( 12 cII j j j j je I +≅ψ . (29) However, the proportionality coefficient here is larger than for j << j 0 r2 (see fig. 2). To increase the current density further, we have to increase U I (or e Iψ ) substantially because of a noticeable counteraction of the inner junction (jnc.2). Therefore we have to take into account the term, proportional to ( )e I II2 ψ ψ− . This dependence is strong if [ ] ( ) 1~1)1( 1)1(~ >> −+ −++ II IIII b b αα ααα . (30) Condition (30) is met in structures for which the forward and inverse transport factors in base I are large (both α I and ~α I are close to 1), and the values of b, α I,II are far from the threshold values of the thyristor effect: 01)1( >−++ III b αα , (31) i.e. α I (1 + b) + α II - 1 is not too close to 0. We stress that the multiplier (1 + b) beside α I which misses in the expression for low injection level in base II, corresponds to the transition into the ON-state due to the increasing of injection level in base II. For j >> j c r2 we get: )1( )1( )1( )( 12 3311 2123 32 c c j j bjj jjbjj je + + ++⋅ ≅ψ . (32) Expression (32) differs from expression (28) not only by the multiplier (1 + j 12 / j c ) as in Eq.(29) but also by the term 2123 cjj instead of 2rj c j in the numerator. We can introduce the parameter [ ]1)1( 1 )1( 2 2 32 −++ −= + = IIIII IIc bbj rj m ααα α to describe two different possible dependencies ( )e jψ . For m << 1 in the current range j ~ j c r2, the value of eψ becomes greater, but it is still a linear function with steeper slope up to the current density 222 32 /)1(~ rjjbjj cc >+ , where the curve becomes nonlinear: ( )e jψ ~ j3/2 (fig. 2). For m > 1 the transition from a linear dependence, ( )e jψ ~ j, to a nonlinear one, ( )e jψ ~ j3/2, occurs in the current range j ~ j c r2. Let us remind that this consideration implies low injection level in base I, so that the inequality ( ) ( )p e j nI D01 0ψ << (33) should be met (see Eq.(2)). Here n D is the donor concentration in base I at pn-junction 1. Let us discuss this condition for the simplest case of uniformly doped Fig. 2. The electrical potentials y, y I versus the current density j: 1 � y I (j); 2 � y(j) for m << 1; 3 � y(j) for m >> 1. Z. S. Gribnikov et al.: Switching waves in asymmetric thyristor-like structures... 94 ÔÊÎ, 1(1), 1998 SQO, 1(1), 1998 bases. For linear dependence ( )e jIψ , inequality (33) can be written in the form 2 2 0111 )0( i DD n n p n j j =<< On the other hand, the linear dependence ( )e jIψ is valid for the current density     −++ − ⋅⋅⋅+× ×=<< 1)1( 1 tanh tanh 4 1 2 2 2 2 2 11 2 11 III II II I III III i Dc bz z D Db n n j rj j j αα α τ τ (34) The value of the multiplier in the parentheses of Eq.(34) can differ from 1 mainly due to a large difference of τ I and τ II . The condition τ I << τ II can provide a regime of low injection level in base I up to high current density. IV. Inhomogeneous stationary solution Now we are interested in Eq.(22) with a non-zero gate current, J g , that squeezes the current-conducting region of a TLS. For 2 1 2 0 BB >> (35) Eq. (22) has the form: )( /1 )1( 1 1)1( )( 11 2 2 χ α αα χσ ψ R Ae ee e b j dy d e kT x xx II III I I = + − − −++= = ∞ , (36) where χ = ψ I - ψ I (∞) < 0, A = [1 � α II (1 � α I (1+ b)] / [α II + +α I (1+ b) −1] = ( ) ψψ ee I /∞ =(j 33 (1 + b)) / (j 33 (1 + b) α II  + +2j c r) (the second part of the expression is derived from Eqs.(27), (28) which are valid if j << j c r2). For the stationary solution, the transition from the regime with low injection level in both bases to the regime with high injection level in base II and low injection level in base I (under condition (35)) results only in a new definition for the transport factor of base I, now being equal to α I (1 + b) instead of α I for the low injection. This fact determines the choice of doping for the bases. It is clear that n-doped base I and p-doped base II structure, as we consider from the beginning, is preferable, because for most of the considered semiconductors b >> 1, and the condition of open state for the thyristor � inequality (31) � is satisfied for a wider range of α II  . For j << j c r2, inequality (35) can be modified to: 2 222 / 22 2// 22 )1)1(( )1()1( 4 )( −++ −+ ⋅<< b b j j j III III αα αα (37) while the condition j << j c r2 has the form: )1)(1)1(( )1)(1( 4 )( ~ 22 / 22 2// 22 IIIII II b b j j j αααα α −−++ −+ ⋅<< . (38) Inequalities (37) and (38) are not identical, but for most cases they differ only slightly. A detailed stationary solution for the distributions ψ I (y), j(y) for low injection level in both bases can be found in [1]. We emphasize, that eq.(36) differs from the analogous equation in [1] only by definitions of the parameters. From the solution of Eq.(36) we obtain that for infinite TLS there existsthe unique value of the gate current, J g0 , which provides steady-state position of the ON/OFF-layer for a given current density in the depth of the ON-region: jIJg ⋅= 10 (39) The current density can be presented as j = J a /(2a), where J a is the full current in the ON-region (in A/ cm) and 2a is an effective width of the ON-region (see fig. 1) where ( ) ( )[ ]11ln1 1 1)1(T2 1 1 −++ − −++ = −AAA b e k I II III l α αασ . (40) V. Stationary wave of switching We assume here that inertia of the transient processes in TLS is determined mainly by the drift-diffusion and recombination phenomena in quasineutral bases I and II; therefore we can neglect the charging processes in pn- junctions which are much faster. Therefore we have to solve two equations of continuity. The first of them is for holes in base I: div j p = -p/τ I -∂ p/∂ t, (41) The second of them is the analogous nonstationary equation for electrons in base II. Here as well as in discussed above stationary problem, we neglect (j p,n ) y in comparison with (j p,n ) x . Besides, we assume that the current density j changes slightly along y-axis over the lengths of the order of w I,II . To get the solution in the form of the stationary wave, we introduce new variables x, y/ = y - vt instead of x, y, t; thus Eq.(41) is modified to yppxj Ipx ∂∂−−=∂∂ /// υτ . (42) Equation (42) has to be solved with boundary conditions (2), (3) for ψ I,II (y). For the small velocity and for uniformly doped base I (i.e. j px = �D I ∂p/∂x, we can write the approximate solution of Eq.(42) in the form: ++ − ≅ II I I II II w x ywp w xw ypyxp β β β β sinh sinh ),( sinh )(sinh ),0(),( Z. S. Gribnikov et al.: Switching waves in asymmetric thyristor-like structures... 95ÔÊÎ, 1(1), 1998 SQO, 1(1), 1998    −−− ∂ ∂+ II II I II w xw xw y yp D β β β υ sinh )(cosh )( ),0( 2 +  −⋅ − )(sinh )(sinhcosh 2 II IIII I w xww w β ββ (43)       − ∂ ∂ + )(sinh sinhcosh sinh cosh),( 2 2 II III I II II II w xw w w x x y ywp D β ββ β β β υ . Here we have neglected terms which are proportional to v2 and the other higher degrees of v. Now we can calculate the current densities: )( |/)( )(2 1211 )(2 12110 IIII IIII ee y ejejxpeDyj xII ψψψ ψψψ λλυ − − = − ∂ ∂+ +−=∂∂−= (44) ),( |/)( )(2/ 2221 )(2/ 2221 / 2 IIII IIII I ee y ejejxpeDyj wxI ψψψ ψψψ λλυ − − = − ∂ ∂+ +−=∂∂−= (45) where j ij , / 22j are the expressions from (9), (10) and 01 02 11 / 222 01 11 , sinh sinhcosh 2 p p z zzzep I III I λλ β λ = − ⋅= , (46) 01 02 21122 01 21 , sinh sinhcosh 2 p p z zzzep I III I λλ β λ = − ⋅−= . (47) Then we can derive an expression, which is similar to Eq.(43), for distribution of electrons, n(x, y), in base II with high injection level in it, and calculate current densities: ,02 // 2 | 1 +=∂ ∂+ + = IwxII x n eD b b jj (48) III wwxII x n Dbejj +=∂ ∂+== |)1(32 , (49) As a result we can write down: ( )       − ∂ ∂+−× ×+== −−−− )( 1 32333333 32 IIIIIIIIII ee y ejej bjj ψψψψψψψψ λλυ ,(50) [ ]))()( )()( // 22322333 // 22322333 // 2 IIIII IIIII ebeb y ejbjejbjj ψψψψ ψψψψ λλλλυ −− −− +−+ ∂ ∂+ ++−+= , (51) where 03 02 33 // 222 03 33 , sinh sinhcosh 2 n n z zzzen II IIIIII II λλ β λ = − ⋅= , (52) 02 03 32232 02 32 , sinh sinhcosh 2 n n z zzzen II IIIIII II λλ β λ =−⋅−= . (53) Taking into account inequality (35) and the equation // 2 / 22 jjj += , we obtain for uniformly doped base I: ( ) ( )( )[ ] ( )( )I IIIIIII III e eeeyej e II ψψ ψψψψψψ ψψ λλα λλλυ − −− − +′′− +−′′−∂∂+ ≅ ≅ 3222 32222121 1 .(54) Using Eqs.(44), (50) and (54), we derive the equation which is similar to eq.(36) but for nonstationary case:    +⋅+= ∞ )()( )( 2 2 χυχχσ ψ II S dy d eR dy d e kT I    + −+ )( /1 / χδγ χ χ IIS dy d Ae Ae . (55) Equation (55) differ from Eq.(36) by the proportional to v term on the RHS of the equation, where ) /1 / 1 1 ()( 3332 33 21 11 11 Ae Ae j jb eSI χ χ χ λλ α λχ + − ⋅⋅ − ++= , (56) ) 1 ()( // 2232 33 21 21 II II j j eS α λλ λχ χ − − ⋅+= , (57) and )(∞−= II ψψχ , )1/()1( IIIIb ααγ −+= , )1/()1( IIb αδ −+= . We emphasize that Eq.(55) is derived under the several conditions. First, the velocity is small, i.e. we restrict our consideration by the linear on u terms. Second, the conditions Eq.(35) and j << l c r2 are met (i.e. the strong inequalities (37) and (38) are satisfied). To solve eq.(50) we can exploit the theory for nonlinear stationary waves [17]. The deviation of the gate current from its equilibrium value, δJ g = J g - J g0 , under the constant current density, j, results in the motion of the ON/OFF-junction. The velocity v is equal to ( )[ ] ( ) . 1 T 2 1 0 2 0 2 − ∞− ∞             + −+× ×−= ∫ IIII gg S dy d Ae Ae S dy d de e k jJJ I χ χ ψ δγχσ υ (58) Z. S. Gribnikov et al.: Switching waves in asymmetric thyristor-like structures... 96 ÔÊÎ, 1(1), 1998 SQO, 1(1), 1998 To calculate the integral we use the dependence dξ/dy = = f(ξ) from the stationary solution: )()( 0 jJe dy d e kT gI χχσ Φ= , (59) where ( ) ( )[ ] ( ) ( ) ( ) ( ) 21 11 11ln 111ln )(     +−+ +−−++=Φ −− AA AzAzA z , Using Eqs.(58) and (59) we can write down the formula for the velocity of the ON/OFF-junction: jJ jJJ g gg ⋅⋅ − = τ υ 0 2 0 2 2 )( , (60) Where  ∫ −− +Λ++Λ+ΛΦ⋅= 1 0 2 2 1 10 11 )/1()/1()( 1 AzAzzdz j τ , (61) )( )1( )1( 1 )1( // 2232 33 2 11 21 11 110 λαλ α α λ α α λ II II I II j jbb − − + + − + +=Λ ,     − − + − + +−=Λ )1( )( 1 1 )1( 33 // 223211 211 II I II II j j b α λλ αλ α α , )( 1 1 3332 33 11 2 λλ α α +⋅ − +−=Λ j jb II I . For small deviations of the gate current from the equilibrium value (δJ g = J g - J g0 (j)), Eq.(60) can be written in the form: j Jg ⋅ = τ δ υ . (62) The values of τ and I 1 depend on geometry and material properties of both bases. The condition A > 0 which is equivalent to inequality (31), provides the existence of the ON-state with low voltage across the structure and three forward-biased pn- junctions. The analogous condition for low injection level in both bases [1] does not include the multiplier b + 1 beside α I . That is why this condition is met for wider range of α I,II for high injection level in base II than for low injection level there. For structures with n-doped base I, the inequality b > 1 (or even b >> 1 for numerous semicon- ductor materials) is satisfied. This means that condition (31) is met for quite long bases I and II. (For example, just condition α I > (1 + b)-1 should be met for α II = 0.) We have to note, however, that the longer base II is, the higher current density is required to get high injection level over Fig. 3. The dependences of two terms of Eq.(63), f I and f II for high (dotted lines) and low (solid lines) injection level in base II, on z II for given values of z I ; b = µ n /µ p = 2. Z. S. Gribnikov et al.: Switching waves in asymmetric thyristor-like structures... 97ÔÊÎ, 1(1), 1998 SQO, 1(1), 1998 Fig. 4. The same as fig. 3 for b = µ n /µ p = 20. Fig.5. The dependences of two terms of Eq.(63), f I and f II for high (dotted lines) and low (solid lines) injection level in base II, on z I for given values of z II ; b = µ n /µ p = 2. Z. S. Gribnikov et al.: Switching waves in asymmetric thyristor-like structures... 98 ÔÊÎ, 1(1), 1998 SQO, 1(1), 1998 all length of base II, and the transition into the ON-state occurs at quite high current density j. Besides, if the length of base II exceeds 3-4 diffusion lengths, the voltage across the base would become high enough to be taken into account with the voltages across pn-junctions. For uniformly doped bases ),(),( IIIIIIIIIIII zzfzzf τττ += , (63) The dependencies f I (z I , z II ) and f II (z I , z II ) are depicted in fig. 3-6. Each figure contains two branches of curves: solid lines show the dependencies for low injection level in base II; dotted lines show the dependencies for high injection level in base II for the same dimension lengths w II of base II. The inverse diffusion lengths for high and low injection levels in base II, 21)( IIIIII D τβ = , are different. For low injection level, D II is the diffusion coefficient of minority carriers - electrons. For high injection level, D II is the bipolar diffusion coefficient, D II = 2D p D n / (D p + D n ), b = =D n /D p . Here the values of D p,n being the diffusion coefficients of electrons and holes. In case of low injection level, D I,II are just the diffusion coefficients of electrons and holes, respectively. Therefore, for the same dimension length w II , the dimensionless length for low level, )(l IIz , and the dimensionless length for high level, )(h IIz differ: 2/)1()()( bzz l II h II += . In figs. 3-6 the notation z II refers to low injection level (z II   = )(l IIz ) for the sake of convenience, because )(l IIz does not depend on the value of b. From figs. 3-6, one can see that the growth of injection level in base II does not change the form of the dependencies τ(w I, , w II ). The growth of injection level results in increasing of f I , f II for the range of parameters where the open state of TLS is possible for low injection level (i.e. condition A(l) > 0 is met). It is worth noting the following features of the dependencies f I,II (z I,II ). The functions f I,II diverge with decreasing of w II up to 0 and decrease with increasing w II . For w II → ∞ for low injection level f II decreases exponentially and goes very close to 0 while for high injection level f II is saturated for large w II . Therefore the minimum possible value of f II is much higher for high injection level than for low injection level. With decreasing w I , the value of f I goes to 0 while the value of f II increases slightly. A decrease in the value of f II with increasing w I is probably caused by failure of the P+- emitter influence on base II. VI. Discussion and Conclusion In presented paper the problem of the switching wave in an asymmetric TLS with high injection level in ungated base II is discussed; the results are compared with analogous results for a TLS with low injection level in both bases [9]. The transition to the high injection level results in re-definition of the parameters and several restricting inequalities. The field of application of the presented approach extends greatly, because the regime of the TLS with high injection level in lightly doped ungated base II is the typical regime of operation for real Fig. 6. The same as fig. 5 for b = µ n /µ p = 20. Z. S. Gribnikov et al.: Switching waves in asymmetric thyristor-like structures... 99ÔÊÎ, 1(1), 1998 SQO, 1(1), 1998 TLSs. It is partially due to the fact that the criterion of the ON-state existence can be met for much wider range of parameters in case of high injection level in base II than in case of low injection level there. Especially it is related to structures with a high value of b = µ n /µ p . Formulae (60) and (62), now being valid for wider range of parameters and regimes, allow us to describe a nonstationary beha- vior of a finite gate controlled (or gate modulated) TLS. Using the presented approach and calculations, we can point to several ways to increase the speed of operation of a TLS. 1. Base I should be n-doped. Besides, it should be as thin as possible. But base I still has to provide high in- plain conductivity which is proportional to w I . 2. A length of base II should be of the order of 1-2 diffusion length of minority carriers in this base. This range of w II provides small (almost minimum possible) values of f I and f II . The lifetime of carriers in base II should be chosen as small as possible. For this purpose the base has to be doped by effective recombination centers. It is the base that should operate as an active region in a light-emitting regime. A decrease in the values of τ II and w II is to be restricted by a given value of the breakover voltage (for a thyristor regime of operation) and a maximum value of the blocking gate voltage applied for squeezing. It is also necessary to avoid the pinch- through of base II and the growth of an ineffective transistor current (from the cathode to the gate) through this base. 3. Probably, it is better to use modulation doped structures instead of uniformly doped ungated base considered here. This structure which can avoid the pinch- through, should consist of active layers with low effective lifetime, τ II , and blocking low recombination layers. As an active region, one can use a layer with a quantum well (or quantum wells). In this work, only the calculations for uniformly doped bases I and II are presented in detail while modulation doped (layered) bases and bases with heterostructure junctions or quantum wells can be used for real light-emitting devices. To describe the modulation doped structure we just have to derive new expressions for j i,j , // 22j , j i,j , and for J g0 (j) and τ. It is worth to emphasize that we consider only asymmetric TLSs, where in-plain conductivities of bases differ greatly. If the currents through both bases are of the same order, or if both bases are gated (i.e. both bases control the current through a TLS), the calculation would be much more complicated. For these cases, the stationary wave approach which uses just one parameter, wave velocity v, may be inappropriate. However, the approach proposed here is valid for all the cases when the gate current flows mainly through the gated base and may be successfully used for real asymmetric TLSs. Acknowledgements This work was supported by the National Science Foundation of the USA. One of us (Z. S. Gribnikov) thanks the Ukrainian Foundation of Fundamental Researches for a partial support. We also thankful to the editorial board of the «Semiconductor Physics, Quantum Electronics & Optoelectronics» for the invitation to submit our paper to the first issue of this new journal. Reference 1. N. Vagidov, Z. Gribnikov, A. Korshak, V. Mitin, Semiconduc- tors, 1995, 29, 1021. 2. Z. Gribnikov, N. Vagidov, A. Korshak, V. Mitin, Solid- St. Electron., 1996, 39, 915. 3. A. Blicher, Thyristor Physics, Springer-Verlag (1976). 4. Z. Gribnikov, V. Mitin, A. Rothwarf, Proceed.1993 ISDRS, 1993, 2, 603. 5. M. Levinstein, Sov.Phys.Tech.Phys., 1981, 26, 720. 6. K. Kasahara, IEEE J. Quantum Electron., 29, 757 (1993). 7. P. Heremans, M. Kuijk, R. Vounckx, G. Borghs, J. Phys. III France, 4, 2391 (1994). 8. P. A. Evaldsson, G. W. Taylor, P. W. Cooke, S. K. Saragood, P. A. Kiely, D. P. Docter, IEEE Photon. Technol. Lett.,5, 634 (1993). 9. Z. Gribnikov, I. Gordion, V. Mitin, Solid-St.Electron., (sub- mitted). 10. K. Kasahara, J. Tashiro, N. Hamao, M. Suigimoto, T. Yanase, Appl. Phys. Lett., 52, 679 (1998). 11. J.Tashiro, K.Kasahara, N.Hamao, M.Suigimoto, T.Yanase, Japan J. Appl. Phys.,26, n6, L1014 (1987). 12. G. W. Taylor, R. S. Mand, J. G. Simmons, A. Y. Cho, Appl. Phys. Lett., 50, 338 (1987). 13. D. L. Crawford, G. W. Taylor, J. G. Simmons, Appl. Phys. Lett., 52, 863 (1988). 14. D. L. Crawford, G. W. Taylor, P. Cooke, T. Y. Chang, B. Tell, J. G. Simmons, Appl. Phys. Lett., 53, 1797 (1988) 15. G. W. Taylor, D. L. Crawford, J. G. Simmons, Appl. Phys. Lett., 54, 543 (1989). 16. P. R. Claisse, G. W. Taylor, D. P. Docter, P. W. Cooke, IEEE Transact. Electron Devices,39, 2523 (1992). 17. A. Vl. Gurevich, R. G. Mints. Sov.Phys.Usp., 27, 19 (1984). ÕÂÈ˲ ÏÅÐÅÊËÞ×ÅÍÍß Â ÀÑÈÌÅÒÐÈ×ÍÈÕ ÒÈÐÈÑÒÎÐÎ ÏÎIJÁÍÈÕ ÑÒÐÓÊÒÓÐÀÕ Â ÐÅÆÈ̲ ÂÈÊËÞ×ÅÍÍß ÐÎDzÌÊÍÓÒÎÃÎ ÇÀÒÂÎÐÓ Ç. Ñ. Ãðèáí³êîâ ²íñòèòóò ô³çèêè íàï³âïðîâ³äíèê³â ÍÀÍ Óêðà¿íè È. Ì. Ãîðä³îí, Â. Â. ̳ò³í Äåòðîéòñüêèé äåðæàâíèé óí³âåðñèòåò ³ì. À. Âåéíà, ÑØÀ Ðåçþìå. Ðîçãëÿíóòî ñòàö³îíàðíó õâèëþ ïåðåêëþ÷åííÿ â ê³íöåâ³é òèðèñòîðî ïîä³áí³é ñòðóêòðóð³ (ÒÏÑ). Öÿ õâèëÿ ³í³ö³éîâàíà êîíòðîëþþ÷èì ñòðóìîì çàòâîðó I g , ÿêèé â³äð³çíÿºòüñÿ â³ä ïåâíîãî ð³âíîâàæíîãî ñòðóìó I g0 (j), ÿêèé çàáåçïå÷óº ïîëîæåííÿ íåéòðàëüíî¿ ð³âíîâàãè (òðàíñëÿö³éíî ³íâàð³àíòíî¿) ïåðåõ³äíîãî øàðó ì³æ çàïåðòîþ òà â³äêðèòîþ îáëàñòÿìè äëÿ äàíî¿ ãóñòèíè ñòðóìó j ó â³äêðèò³é îáëàñò³. Âèâåäåíî çàëåæí³ñòü øâèäêîñò³ õâèë³ v(I g , j) â³ä ñòðóìó Z. S. Gribnikov et al.: Switching waves in asymmetric thyristor-like structures... 100 ÔÊÎ, 1(1), 1998 SQO, 1(1), 1998 çàòâîðó I g òà ãóñòèíè ñòðóìó j. Ìè ìàºìî ñïðàâó ³ç ñòðóêòóðîþ, â ÿê³é ïðîâ³äí³ñòü çàïåðòî¿ áàçè I íàáàãàòî âûùà, í³æ ïðîâ³äí³ñòü íåçàïåðòî¿ áàçè II. Ðîçãëÿíóòèé ð³âåíü ³íæåêö³¿ º íèçêèì äëÿ áàçè I òà âèñîêèì äëÿ áàçè II. Ïîêàçàíî, ùî øâèäê³ñòü õâèë³ ïåðåêëþ÷åííÿ (òîáòî øâèäê³ñòü ïåðåõ³äíîãî ïðîöåñó â ÒÏÑ) âèçíà÷àºòüñÿ ãîëîâíèì ÷èíîì ïàðàìåòðàìè áàçè II. Ïðîäåìîíñòðîâàíî òàêîæ, ùî âèñîêà øâèäê³ñòü ñïðàöþâàííÿ ìîæå áóòè äîñÿãíóòà â ñòðóêòóð³ ç ïîì³ðíî äîâãîþ áàçîþ II (äîâæèíà áàçè ïîâèííà ïåðåâèùóâàòè 1-2 á³ïîëÿðíèõ äèôóç³éíèõ äîâæèí) òà ìàëèì ÷àñîì æèòòÿ íîñ³¿â â ö³é áàç³. ÂÎËÍÛ ÏÅÐÅÊËÞ×ÅÍÈß Â ÀÑÑÈÌÅÒÐÈ×ÍÛÕ ÒÈÐÈÑÒÎÐÎ ÏÎÄÎÁÍÛÕ ÑÒÐÓÊÒÓÐÀÕ Â ÐÅÆÈÌÅ ÂÛÊËÞ×ÅÍÈß ÐÀÇÎÌÊÍÓÒÎÃÎ ÇÀÒÂÎÐÀ Ç. Ñ. Ãðèáíèêîâ Èíñòèòóò ôèçèêè ïîëóïðîâîäíèêîâ ÍÀÍ Óêðàèíû È. Ì. Ãîðäèîí, Â. Â. Ìèòèí Äåòðîéòñêèé ãîñóäàðñòâåííûé óíèâåðñèòåò èì. À. Âåéíà, ÑØÀ Ðåçþìå. Ðàññìîòðåíà ñòàöèîíàðíàÿ âîëíà ïåðåêëþ÷åíèÿ â êîíå÷íîé òèðèñòîðî ïîäîáíîé ñòðóêòðóðå (ÒÏÑ). Ýòà âîëíà èíèöèèðîâàíà êîíòðîëèðóþùèì òîêîì çàòâîðà I g , êîòîðûé îòëè÷àåòñÿ îò îïðåäåëåííîãî ðàâíîâåñíîãî òîêà I g0 (j), îáåñïå÷èâàþùåãî ïîëîæåíèå íåéòðàëüíîãî ðàâíîâåñèÿ (òðàíñëÿöèîííî èíâàðèàíòíîãî) ïåðåõîäíîãî ñëîÿ ìåæäó çàïåðòîé è îòêðûòîé îáëàñòÿìè äëÿ äàííîé ïëîòíîñòè òîêà j â îòêðûòîé îáëàñòè. Âûâåäåíà çàâèñèìîñòü ñêîðîñòè âîëíû v(I g , j) îò òîêà çàòâîðà I g è ïëîòíîñòè òîêà j. Ìû èìååì äåëî ñî ñòðóêòóðîé, â êîòîðîé ïðîâîäèìîñòü çàïåðòîé áàçû I ìíîãî âûøå, ÷åì ïðîâîäèìîñòü íåçàïåðòîé áàçû II. Ðàññìàòðèâàåìûé óðîâåíü èíæåêöèè ÿâëÿåòñÿ íèçêèì äëÿ áàçû I è âûñîêèì äëÿ áàçû II. Ïîêàçàíî, ÷òî ñêîðîñòü âîëíû ïåðåêëþ÷åíèÿ (ò.å. ñêîðîñòü ïåðåõîäíîãî ïðîöåññà â ÒÏÑ) îïðåäåëÿåòñÿ ãëàâíûì îáðàçîì ïàðàìåòðàìè áàçû II. Ïðîäåìîíñòðèðîâàíî òàêæå, ÷òî âûñîêàÿ ñêîðîñòü ñðàáàòûâàíèÿ ìîæåò áûòü äîñòèãíóòà â ñòðóêòóðå ñ óìåðåííî äëèííîé áàçîé II (äëèíà áàçû äîëæíà ïðåâûøàòü 1-2 áèïîëÿðíûõ äèôôóçèîííûõ äëèíû) è ìàëûì âðåìåíåì æèçíè íîñèòåëåé â ýòîé áàçå.

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