- Avalanche transistor
An Avalanche Transistor is a
bipolar junction transistor designed for operation in the region of its collector-current/collector-to-emitter voltage characteristics beyond the collector to emitterbreakdown voltage , calledavalanche breakdown region . This region is characterized byavalanche breakdown , a phenomenon similar toTownsend discharge for gases, andnegative differential resistance . Operation in theavalanche breakdown region is called avalanche mode operation: it gives avalanche transistors the ability to switch very high currents with less than ananosecond rise andfall time s (transition time s).History
The first paper dealing with avalanche transistor was Harv|Ebers|Miller|1955: the paper describes how to use
alloy-junction transistor in theavalanche breakdown region, in order to overcome speed andbreakdown voltage limitations which affected the first models of such kind oftransistor when used in earliercomputer digital circuits . Therefore the very first applications of avalanche transistor were inswitching circuit s andmultivibrator s. The introduction of the avalanche transistor served also as an application of Miller's empirical formula for the avalanche multiplication coefficient , first introduced in the paper Harv|Miller|1955: the need of better understanding transistor behavior in theavalanche breakdown region,not only for using them in avalanche mode, gave rise to a extensive research onimpact ionization insemiconductors (see Harv|Kennedy|O'Brien|1966). From the beginning of the 1960s to the first half of the 1970s, several avalanche transistor circuits were proposed, and also it was studied what kind ofbipolar junction transistor is best suited for the use in theavalanche breakdown region: a complete reference, which includes also the contributions of scientists from ex-USSR andCOMECON countries, is the book Harv|Дьяконов (D'yakonov)|1973. The first application of the avalanche transistor as alinear amplifier , named Controlled Avalanche Transit Time Triode, (CATT) was described in Harv|Eshbach|Se Puan|Tantraporn|1976: a similar device, named IMPISTOR was described more or less in the same period in the paper Harv|Carrol|Winstanley|1974. Linear applications of this class of devices started later since there are some requirements to fulfill, as described below: also, the use of avalanche transistor in those applications is not mainstream since the devices require high collector to emitter voltages in order to work properly. Nowadays, there is still active research on avalanche devices (transistors or other) made ofcompound semiconductor s, being capable of switching currents of several tens ofampere s even faster than "traditional" avalanche transistors.Basic theory
Static avalanche region characteristics
In this section, the static characteristic of an avalanche transistor is calculated. For the sake of simplicity, only an NPN device is considered: however, the same results are valid for PNP devices only changing signs to voltages and currents accordingly. The analysis closely follows that of William D. Roehr in Harv|Roehr|1963.Since "avalanche breakdown multiplication is present only across the collector-base junction", the first step of the calculation is to determine collector current as a sum of various component currents "though the collector" since only those fluxes of charge are subject to this phenomenon. Kirchhoff's current law applied to a
bipolar junction transistor implies the following relation, "always" satisfied by the collector current:
while for the same device working in the active region, basic transistor theory gives the following relation
:
where
* is the "base current",
* is the "collector-base reverse leakage current",
* is the "emitter current",
* is the "common emitter current gain" of the transistor.Equating the two formulas for gives the following result:
and since is the "common base current gain" of the transistor, then
:
When avalanche effects in a transistor collector are considered, the collector current is given by
:
where is Miller's avalanche multiplication coefficient. It is the most important parameter in avalanche mode operation: its expression is the following
:
where
* is the "collector-base breakdown voltage",
* is a constant depending on the semiconductor used for the construction of the transistor anddoping profile of the collector-base junction,
* is the collector-base voltage.Using again Kirchhoff's current law for the
bipolar junction transistor and the given expression for , the resulting expression for is the following:
and remembering that and where is the "base-emitter voltage"
:
since : this is the expression of the "
parametric family of the collector characteristics " with parameter . Note that increases without limit if:
where is the "collector-emitter breakdown voltage". Also, it is possible to express as a function of , and obtain an analytical formula for the "collector-emitter differential resistance" by straightforward differentiation: however, the details are not given here.
Differential dynamical model
The differential dynamical mode described here, also called the
small signal model , is the only intrinsicsmall signal model of the avalanche transistor. Stray elements due to the package enclosing the transistor are deliberately neglected, since their analysis wolud not add anything useful from the point of view of the working principles of the avalanche transistor. However, when realizing aelectronic circuit , those parameters are of great importance: particularly strayinductance s in series to collector and emitterlead s have to be minimized to preserve the high speed performance of avalache transistor circuits. Also, this equivalent circuit is useful when describing the behavior of the avalanche transistor near its turn on time, where collector currents and voltages are still near their quiescent values: in the real circuit it permits the calculation oftime constant s and therefore rise andfall time s of thewaveform . However, since avalanche transistorswitching circuit s are intrinsically large signal circuits, the only way to predict with reasonable accuracy their real behaviour is to donumerical simulation s. Again, the analysis closely follows that of William D. Roehr in Harv|Roehr|1963.An avalanche transistor operated by a common bias network is shown in the picture on the right: can be zero or positive value, while can be
short circuit ed. In every avalanche transistor circuit, the outputsignal is taken from the collector or the emitter: therefore the small-signal differential model of an avalanche transistor working in the avalanche region is always seen from the collector-emitter output pins, and consist of a parallel circuit as shown in the picture on the right, which includes onlybias component sThe magnitude and sign of both those parameters are controlled by the base current : since both Base-Collector and Base-Emitter junctions are inversely biased in the quiescent state, the equivalent circuit of the Base input is simply a current generator shunted by Base-Emitter and Base-Collector junction capacitances and is therefore not analyzed in what follows.The intrinsic time constant of the basic equivalent small signal circuit has the following value:
where
* is the "collector-emitter avalanche differential resistance" and, as stated above, can be obtained by differentiation of the collector-emitter voltage respect to the collector current , for a constant base current :
*"" is the "collector-emitter avalanche differential capacitance" and has the following expression::where :"" is the "current gain angularcutoff frequency " :"" is the "common base output capacitance"The two parameters "are both negative": this means that if the collector load const of an idealcurrent source , the circuit is unstable. This is the theoretical justification of the astable multivibrator behavior of the circuit when thevoltage is raised over some critical level.Second breakdown avalanche mode
When the collector current rises above the data sheet limit a new breakdown mechanism become important: the
second breakdown . "This phenomenon is caused by excessive heating of some points (hot spots) in the base-emitter region of thebipolar junction transistor , which give rise to an exponentially increasing current through this points": this exponential rise of current in turn gives rise to even more overheating, originating a positive thermal feedback mechanism. While analyzing the static characteristic, the presence of this phenomenon is seen as a sharp collectorvoltage drop and a corresponding almost vertical rise of the collector current. At the present, it is not possible to produce a transistor without hot spots and thus without second breakdown, since their presence is related to the technology of refinement ofsilicon . During this process, very small but finite quantities ofmetal s remain in localized portions of thewafer : these particles of metals became deep centers of recombination, i.e. centers where current exists in a preferred way. While this phenomenon is destructive forBipolar junction transistor s working in the usual way, "it can be used to push-up further the current and voltage limits of a device working in avalanche mode" by limiting its time duration: also, the switching speed of the device is not negatively affected. A clear description of avalanche transistor circuits working insecond breakdown regime together with some examples can be found in the paper Harv|Baker|1991.Numerical simulations
Avalanche transistor circuits are intrinsically large signal circuits, so
small signal model s, when applied to such circuits, can only give a "qualitative" description. To obtain more accurate information about the behavior of time dependentvoltage s and currents in such circuits it is necessary to usenumerical analysis . The "classical" approach, detailed in the paper Harv|Дьяконов (D'yakonov)|2001 (?) which relies upon the book Harv|Дьяконов (D'yakonov)|1973, consists in considering the circuits as a system of nonlinear ordinary differential equations and solve it by a numerical method implemented by a general purposenumerical simulation software : results obtained in this way are fairly accurate and simple to obtain. However this methods rely on the use of analytical transistor models best suited for the analysis of the breakdown region: those models are not necessarily suited to describe the device working in all possible regions. A more modern approach consist in using the common analogcircuit simulator SPICE together with an advancedtransistor model supporting avalanche breakdown simulations, since the basicSPICE transistor model does not. Examples of such models are described in the paper Harv|Keshavarz|Raney|Campbell|1993 and in the paper Harv|Kloosterman|De Graaff|1989: the latter is a description of theMextram model, currently used by some semiconductor industries to characterize theirbipolar junction transistor s.A graphical method
A graphical method for studying the behavior or avalanche transistor was proposed in references Harv|Spirito|1968 and Harv|Spirito|1971: the method was first derived in order to plot the static behavior of the device and then was applied also to solve problems concerning the dynamic behavior. The method bears the spirit of the graphical methods used to design tube and transistor circuits directly from the characteristic diagrams given in data sheets by producers.
Applications
Avalanche transistors are mainly used as fast
pulse generator s, having rise andfall time s of less than ananosecond and high outputvoltage and current. They are occasionally used as amplifiers in themicrowave frequency range, even if this use is not mainstream: when used for this purpose, they are called Controlled Avalanche Transit-time Triodes (CATTs).Avalanche mode switching circuits
Avalanche mode switching relies on avalanche multiplication of current flowing through the collector-base junction as a result of impact
ionization of the atoms in thesemiconductor crystal lattice. Avalanche breakdown insemiconductor s and has found application inswitching circuit s for two basic reasons
*it can provide very high switching speeds, since current builds-up in very small times, in thepicosecond range, due to avalanche multiplication.
*It can provide very high output currents, since largecurrents can be controlled by very small ones, again due to avalanche multiplication.The two circuits considered in this section are the simplest examples of avalanche transistor circuits for switching purposes: both the examples detailed are monostable multivibrators. It is possible to find several more complex circuits in the literature, for example in the books Harv|Roehr|1963 and Harv|Дьяконов (D'yakonov)|1973. First, it is worth noting that the largest part of circuits employing an avalanche transistor is activated by the following two different kind of inputs:*Collector triggering input circuit: the input
trigger signal is fed to the collector via a fast switchingdiode , possibly after being shaped by apulse shaping network . This way of driving an avalanche transistor was extensively employed in first generation circuits since the collector node has a highimpedance and also collector capacitance behaves quite linearly underlarge signal regime. As a consequence of this, thedelay time from input to output is very small and approximately independent of the value of controlvoltage . However, this trigger circuit requires adiode capable of resist to high reversevoltage s and switch very fast, characteristics that are very difficult to realize in the samediode , therefore it is rarely seen in modern avalanche transistor circuits.
*Base triggering input circuit: the inputtrigger signal is fed directly to the base via a fast switchingdiode , possibly after being shaped by apulse shaping network . This way of driving an avalanche transistor was relatively less employed in first generation circuits because the base node has a relatively lowimpedance and an input capacitance which is highly nonlinear (as a matter of fact, it is exponential) under thelarge signal regime: this causes a fairly large, inputvoltage dependent,delay time , which was analyzed in detail in the paper Harv|Spirito|1974. However, the required inverse voltage for the feeddiode is far lower respectdiode s to be used in collectior trigger input circuits, and since ultra fastSchottky diode s are easily and cheaply found, this is the driver circuit employed in most modern avalanche transistor circuit. This is also the reason why the diode in the following applicative circuits is symbolized as aSchottky diode . Avalanche transistor can also be triggered by lowering the emitter voltage , but this configuration is rarely seen in the literature and in practical circuits.: in reference Harv|Meiling|Stary|1968, paragraph 3.2.4 "Trigger circuits" it is described one of such configuration where the avalanche transistor is used itself as a part of the trigger circuit of a complex pulser, while in reference Harv|Дьяконов (D'yakonov)|1973| pp=185 a balanced level discriminator where a commonbipolar junction transistor is emitter-coupled to an avalanche transistor is briefly described.The two avalanche pulser described below are both base triggered and have two outputs. Since the device used is a npn transistor, is a positive going output while is a negative going output: using a pnp transistor reverses the polarities of outputs. The descripion of their simplified versions, where
resistor or is set to zeroohm (obviously not both) in order to have a single output, can be found in reference Harv|Millman|Taub|1965. Resistor recharges the capacitor or thetransmission line (i.e. the energy storage components) after commutation: it has usually a high resistance in order to limit the static collector current, so the recharging process is slow. Sometimes this resistor is replaced by an electronic circuit which is capable of charging faster the energy storage components: however this kind of circuits usually arepatent ed so they are rarely found in mainstream application circuits.*Capacitor discharge avalanche pulser: a
trigger signal applied to the base lead of the avalanche transistor cause theavalanche breakdown between the collector and emitter lead. The capacitor starts to be discharged by a current flowing through the resistors and : the voltages across those resistors are the output voltages. The current waveform is not a simple RC discharge current but has a complex behavior which depends on the avalanche mechanism: however it has a very fastrise time , of the order of fractions ofnanosecond . Peak current depends on the size of the capacitor : when its value is raised over a few hundredpicofarad s, transistor goes in tosecond breakdown avalanche mode, and peak currents reach values of severalampere s if not tens ofampere s.
*Transmission line avalanche pulser: atrigger signal applied to the base lead of the avalanche transistor cause theavalanche breakdown between the collector and emitter lead. The fastrise time of the collector current generates a currentshock wave of approximatively the same amplitude, which propagates along thetransmission line : the wave reaches the open circuited end of the line after the characteristic delay time of the line has elapsed, and then is reflected backward. If thecharacteristic impedance of thetransmission line is equal to the resistances and , the backward reflected shock wave reaches the beginning of the line and stops. As a consequence of this traveling wave behavior, the current flowing through the avalanche transistor has a rectangular shape of duration::
In practical designs, an adjustable impedance like a two terminal
Zobel network (or simply atrimmer capacitor ) is placed from the collector of the avalanche transistor to ground, giving to the tramission line pulser the ability of reduce ringing and other undesidered behavior on the outputvoltage s.It is possible to turn those circuits into astable multivibrators by removing their trigger input circuits and
#raising their power supply voltage until a relaxation oscillation begins, or
#connecting the base resistor to a "positive" base bias voltage and thus forcibly starting avalanche breakdown and associated relaxation oscillationA well detailed example of the first procedure is described in reference Harv|Holme|2006. It is also possible to realize avalanche mode bistable multivibrators, but their use is not as common as other tipes described ofmultivibrator s, one important reason being that they require two avalanche transistors, one working continuously inavalanche breakdown regime, and this can give serious problems from the point of wiev of power dissipation and device operating life.The Controlled Avalanche Transit-time Triode (CATT)
Avalanche mode amplification relies on avalanche multiplication as avalanche mode switching. However, for this mode of operation, it is necessary that Miller's avalanche multiplication coefficient be kept almost constant for large output voltage swings: if this condition is not fulfilled, significant
amplitude distortion arises on the output signal. This implies that*avalanche transistors used for application in switching circuits cannot be used since Miller's coefficient varies widely with the collector to emitter voltage
*the operating point of the device cannot be in thenegative resistance of theavalanche breakdown region for the same reasonThese two requirements imply that a device used for amplification need a physical structure different from that of a typical avalanche transistor. The Controlled Avalanche Transit-time Triode (CATT), designed for
microwave amplification , has a quite large lightly doped region between the base and the collector regions: this implies that the device has fairly high collector-emitter breakdown voltage respect to bipolar transistors having the same geometry. The current amplification mechanism is the same of the avalanche transistor, i.e. carrier generation byimpact ionization , but there is also atransit-time effect as in IMPATT andTRAPATT diode s, where a high field region travels along the avalanching junction, precisely in along the intrinsic region. The device structure and choice ofbias point imply that#Miller's avalanche multiplication coefficient is limited to about 10.
#Thetransit-time effect keep this coefficient almost constant and independent of the collector to emitter voltage.A complete description of the theory for this kind of avalanche transistor is available in the paper Harv|Eshbach|Se Puan|Tantraporn|1976: in this paper it is also showh that this
semiconductor device structure is well suited formicrowave power amplification. It can deliver severalwatt s ofradio frequency power at a frequency of severalgigahertz and it also features a control terminal (the base). However its use is not mainstream as already said,since it requires high voltages (greather than 200volt s) to work properly, while nowadaysgallium arsenide or othercompound semiconductor s FETs deliver a similar performance while being easier to work with. A similar device structure, proposed more or less in the same period in the paper Harv|Carrol|Winstanley|1974, was the IMPISTOR, being a transistor with IMPATT collector-base junction.See also
*
Avalanche breakdown
*Avalanche diode
*Bipolar junction transistor
*Multivibrator
*Pulse generator
*Second breakdown References
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Given = Paolo
Title = [http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=1049655&isnumber=22493&punumber=4&k2dockey=1049655@ieeejrns&query=%28+%28%28spirito%29%3Cin%3Eau+%29+%3Cand%3E+%28%28transistor%29%3Cin%3Eti+%29+%29&pos=2&access=no Static and dynamic behaviour of transistors in the avalanche region]
Journal = [http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4 IEEE Journal of Solid State Circuits]
Volume = 6
Issue = 2
Year = 1971
Page = 83-87. A paper pushing further the study of avalanche transistor by a graphical method proposed in the preceding work ("restricted access").
*Harvrefcol
Surname = Spirito
Given = Paolo
Title = [http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=1050518&isnumber=22538&punumber=4&k2dockey=1050518@ieeejrns&query=%28+%28%28spirito%29%3Cin%3Eau+%29+%3Cand%3E+%28%28transistor%29%3Cin%3Eti+%29+%29&pos=4&access=no On the trigger delay of avalanche transistors]
Journal = [http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4 IEEE Journal of Solid State Circuits]
Volume = 9
Issue = 5
Year = 1974
Page = 307-309. A paper analyzing the trigger delay time of avalanche transistors by means ofnumerical analysis ("restricted access").
*Harvrefcol
Surname1 = Spirito
Given1 = Paolo
Surname2 = Vitale
Given2 = G.F.
Title = [http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=1050310&isnumber=22526&punumber=4&k2dockey=1050310@ieeejrns&query=%28+%28%28spirito%29%3Cin%3Eau+%29+%3Cand%3E+%28%28transistor%29%3Cin%3Eti+%29+%29&pos=5&access=no An analysis of the dynamic behavior of switching circuits using avalanche transistors]
Journal = [http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4 IEEE Journal of Solid State Circuits]
Volume = 7
Issue = 4
Year = 1972
Page = 315-320. A paper where an analytical model of the behavior of an avalanche transistor is derived after suitable approximations ("restricted access").Applications
*Harvrefcol
Surname1 = Biddle
Given1 = Wade
Surname2 = Lonobile
Given2 = David
Title = [http://www.lle.rochester.edu/pub/review/v73/2_sweep.pdf Sweep Deflection Circuit Development Using Computer-Aided Circuit Design for the OMEGA Multichannel Streak Camera]
Journal = [http://www.lle.rochester.edu/03_publications/03_01_review/03_llereview.html LLE Review]
Volume = 73
Year = 1997
Page = 6-14. A paper describing a fast sweep generator for astreak camera constructed using series connected avalanche transistor circuits.
*Harvrefcol
Surname = Chaplin
Given = G.B.B.
Chapter = [http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=1155606&isnumber=25923&punumber=8291&k2dockey=1155606@ieeecnfs&query=%28%28transistor+avalanche+circuits%29%3Cin%3Emetadata%29&pos=0 A method of designing transistor avalanche circuits with application to a sensitive transistor oscilloscope]
Title = IRE [http://ieeexplore.ieee.org/servlet/opac?punumber=8291 Solid-State Circuits Conference] , Volume I
Year = 1958
Page = 21-23. A paper describing an application of avalanche transistors to the design of a sampling oscilloscope: available abstract, full paper is "restricted access".
*Harvrefcol
Surname1 = Fulkerson
Given1 = E. Stephen
Surname2 = Norman
Given2 = Douglas C.
Surname3 = Booth
Given3 = Rex
Title = [http://www.scienceaccelerator.gov/dsa/resultNavFrameset.html?ssid=-b88956d%3A11a3450b593%3A69b0&requestType=USER&displayMode=RANK&startPosition=0&resultItem=3&resultCount=17&resultId=103643504&ranked=true&index=3&mode=RESULT Report UCRL-JC--125874 - Driving Pockels cells using avalanche transistors]
Publisher =Lawrence Livermore National Laboratory
Year = 1997, May 28. Available from [http://www.osti.gov/ the U.S. Department of Energy Office of Scientific & Technical Information] . A report describing the design of a driver forPockels cell s Q-switches.
*Harvrefcol
Surname = Holme
Given = Andrew
Title = [http://www.holmea.demon.co.uk/Avalanche/Avalanche.htm Avalanche transistor pulse generator]
Accessed = 23/04/2008
Year = 2006. A project of an avalanche transistor astable multivibrator with schematics, waveforms and photos of the layout.
*Harvrefcol
Surname = Kilpelä
Given = Ari
Title = [http://herkules.oulu.fi/isbn9514272625/ Pulsed time-of-flight laser range finder techniques for fast, high precision measurement applications]
Journal = [http://herkules.oulu.fi/issn03553213/index.html?lang=en Acta Universitatis Ouluensis Technica]
Volume = 197
Year = 2004, Academic Dissertation presented with the assent of the Faculty of Technology, University of Oulu, ISBN 951-42-7261-7. A doctoral dissertation describing aLaser TOF ("Time Of Flight")Radar and its construction using an avalanche transistor pulser.
*Harvrefcol
Surname1 = Kilpelä
Given1 = Ari
Surname2 = Kostamovaara
Given2 = Juha
Title = [http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=RSINAK&ONLINE=YES&smode=strresults&sort=chron&maxdisp=25&threshold=0&possible1zone=article&possible4=Kilpela&possible4zone=author&bool4=and&OUTLOG=NO&viewabs=RSINAK&key=DISPLAY&docID=5&page=1&chapter=0 Laser pulser for a time-of-flight laser radar]
Journal = [http://rsi.aip.org/rsi Review of Scientific Instruments]
Publisher = [http://www.aip.org The American Institute of Physics]
Volume =68
Issue = 6
Page = 2253-2258
Year = 1997 (preprint version [http://www.ee.oulu.fi/~arik/Pulse.pdf here] ). A paper describing an avalanche transistor pulser and its use asLaser driver in a TOF ("Time Of Flight")LASER RADAR .
* [http://www.nxp.com/models/bi_models/mextram/ NXP Mextram home page] A very rich repository of documents about theMextram bipolar junction transistor SPICE model, capable ofavalanche breakdown behavior simulation.
*" [http://catalog.osram-os.com/media/_en/Graphics/00018291_0.pdf Operating the pulsed laser diode SPL LLxx] ", " [http://catalog.osram-os.com/media/_en/Graphics/00018297_0.pdf Range finding using pulsed laser diodes] "OSRAM Opto Semiconductors GmbH Application Notes, 2004-09-10. Two application notes from Osram Opto Semiconductors describing pulsed operation of aLaser diode , using avalanche transistors and other kind of drivers.
*Harvrefcol
Surname = Pellegrin
Given = J.L.
Title = [http://www.slac.stanford.edu/pubs/slacpubs/0000/slac-pub-0669.html SLAC-PUB-0669 - Increasing the Stability of Series Avalanche Transistor Circuits]
Publisher = [http://www.slac.stanford.edu/ Stanford Linear Accelerator Center - SLAC]
Year =1969, September. A paper describing a method to enhance performances of banks of seies-connected avalanche transistor circuits.
*Harvrefcol
Surname = Williams
Given = Jim
Title = [http://www.edn.com/article/CA323017.html The taming of the slew] ,(.pdf copy [http://www.edn.com/contents/images/323017.pdf here] )
Journal = [http://www.edn.com EDN Magazine]
Page = 57-65
Issue = 25 September
Year = 2003 A detailed paper describing the construction and performance of an avalanche transistor pre-trigger pulse generator to test the slew-rate of very fast operational amplifiers. Also appeared under the title " [http://www.linear.com/pc/downloadDocument.do?navId=H0,C1,C1154,D4183 Slew Rate Verification for Wideband Amplifiers - The Taming of the Slew] ", application note AN94, Linear Technology, May 2003. See also, from the same author, Linear Technology application note AN47, " [http://www.linear.com/pc/downloadDocument.do?navId=H0,C1,C1154,C1009,C1028,P1219,D4138 High speed amplifier techniques] ", August 1991, where an astable circuit similar to that described by Holme is detailed in appendix D, pages 93-95.Varia
*Russel Jacob Baker [http://cmosedu.com/jbaker/jbaker.htm Academic Web Page] at
Boise State University . A contributor to the theory and applications of avalanche transistors.
* [http://www.spek.keytown.com/rasIIIProg/5_tvorch/Voc%602000/bib_spis/liste/diakonov.htm Владимир Павлович Дьяконов (Vladimir Pavlovich D'yakonov)] (in Russian). Some biographical notes about one of the leading contributors to the theory and application of avalanche transistors.
*Ari Kilpelä [http://www.ee.oulu.fi/~arik/index.html Academic Web Page] at theUniversity of Oulu . A researcher working on theory and applications of avalanche transistor circuits.
*Paolo Spirito [http://www.docenti.unina.it/docenti/web/index.php?id_prof=25 Academic Web Page] atUniversity of Naples Federico II . One of the leading contributor to the theory of avalanche transistors and avalanche process in semiconductors.
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