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breakdown region is called avalanche mode operation it gives avalanche transistors the ability to switch very high currents with less than a nanosecond rise and fall times transition times transistors not specifically designed for the purpose can have reasonably consistent avalanche properties for example 82 of samples of the 15v high speed switch 2n2369 manufactured over a 12 year period were capable of generating avalanche breakdown pulses with rise time of 350 ps or less using a 90v power supply as jim williams writes 1 2 history edit the first paper dealing with avalanche transistors was ebers miller 1955 the paper describes how to use alloy junction transistors in the avalanche breakdown region in order to overcome speed and breakdown voltage limitations which affected the first models of such kind of transistor when used in earlier computer digital circuits therefore the very first applications of avalanche transistors were in switching circuits and multivibrators the introduction of the avalanche transistor served also as an application of miller s empirical formula for the avalanche multiplication coefficient m displaystyle m first introduced in the paper miller 1955 the need for better understanding transistor behavior in the avalanche breakdown region not only for use in avalanche mode gave rise to an extensive research on impact ionization in semiconductors see kennedy o brien 1966 from the beginning of the 1960s to the first half of the 1970s several avalanche transistor circuits were proposed the kind which of bipolar junction transistor best suited for use in the avalanche breakdown region was studied a complete reference which includes also the contributions of scientists from ex ussr and comecon countries is the book by дьяконов dyakonov 1973 the first application of the avalanche transistor as a linear amplifier named controlled avalanche transit time triode catt was described in eshbach se puan tantraporn 1976 a similar device named impistor was described more or less in the same period in the paper of carrol winstanley 1974 linear applications clarification needed of this class of devices which started later since there are some requirements to fulfill as described below the use of avalanche transistors 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 transistors or alike made of compound semiconductors capable of switching currents of several tens of amperes even faster than traditional avalanche transistors basic theory edit static avalanche region characteristics edit bias currents and voltages for an npn bipolar transistor in this section the i c v c e displaystyle i_ c v_ ce 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 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 i c displaystyle i_ c i c i e i b displaystyle i_ c i_ e i_ b while for the same device working in the active region basic transistor theory gives the following relation i c β i b β 1 i c b o displaystyle i_ c beta i_ b beta 1 i_ cbo where i b displaystyle i_ b is the base current i c b o displaystyle i_ cbo is the collector base reverse leakage current i e displaystyle i_ e is the emitter current β displaystyle beta is the common emitter current gain of the transistor equating the two formulas for i c displaystyle i_ c gives the following result i e β 1 i b β 1 i c b o displaystyle i_ e beta 1 i_ b beta 1 i_ cbo and since α β β 1 1 displaystyle alpha beta beta 1 1 is the common base current gain of the transistor then α i e β i b β i c b o i c i c b o i c α i e i c b o displaystyle alpha i_ e beta i_ b beta i_ cbo i_ c i_ cbo iff i_ c alpha i_ e i_ cbo when avalanche effects in a transistor collector are considered the collector current i c displaystyle i_ c is given by i c m α i e i c b o displaystyle i_ c m alpha i_ e i_ cbo where m displaystyle m is miller s avalanche multiplication coefficient it is the most important parameter in avalanche mode operation its expression is the following m 1 1 v c b b v c b o n displaystyle m frac 1 1 left frac v_ cb bv_ cbo right n where b v c b o displaystyle bv_ cbo is the collector base breakdown voltage n displaystyle n is a constant depending on the semiconductor used for the construction of the transistor and doping profile of the collector base junction v c b displaystyle v_ cb is the collector base voltage using again kirchhoff s current law for the bipolar junction transistor and the given expression for m displaystyle m the resulting expression for i c displaystyle i_ c is the following i c m 1 α m i c b o α i b i c i c b o α i b 1 α v c b b v c b o n displaystyle i_ c frac m 1 alpha m i_ cbo alpha i_ b iff i_ c frac i_ cbo alpha i_ b 1 alpha left frac v_ cb bv_ cbo right n and remembering that v c b v c e v b e displaystyle v_ cb v_ ce v_ be and v b e v b e i b displaystyle v_ be v_ be i_ b where v b e displaystyle v_ be is the base emitter voltage i c i c b o α i b 1 α v c e v b e i b b v c b o n i c b o α i b 1 α v c e b v c b o n displaystyle i_ c frac i_ cbo alpha i_ b 1 alpha left frac v_ ce v_ be i_ b bv_ cbo right n cong frac i_ cbo alpha i_ b 1 alpha left frac v_ ce bv_ cbo right n since v c e v b e displaystyle v_ ce v_ be this is the expression of the parametric family of the collector characteristics i c v c e displaystyle i_ c v_ ce with parameter i b displaystyle i_ b note that i c displaystyle i_ c increases without limit if v c e b v c b o n 1 α v c e b v c e o 1 α n b v c b o b v c b o β 1 n displaystyle left frac v_ ce bv_ cbo right n 1 alpha iff v_ ce bv_ ceo sqrt n 1 alpha bv_ cbo frac bv_ cbo sqrt n beta 1 where b v c e o displaystyle bv_ ceo is the collector emitter breakdown voltage also it is possible to express v c e displaystyle v_ ce as a function of i c displaystyle i_ c and obtain an analytical formula for the collector emitter differential resistance by straightforward differentiation however the details are not given here differential dynamical model edit equivalent circuit of an avalanche npn bipolar transistor operated by a commonly used bias network the differential dynamical mode described here also called the small signal model is the only intrinsic small signal model of the avalanche transistor stray elements due to the package enclosing the transistor are deliberately neglected since their analysis would not add anything useful from the point of view of the working principles of the avalanche transistor however when realizing an electronic circuit those parameters are of great importance particularly stray inductances in series with collector and emitter leads have to be minimized to preserve the high speed performance of avalanche 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 of time constants and therefore rise and fall times of the v c e displaystyle v_ ce waveform however since avalanche transistor switching circuits are intrinsically large signal circuits the only way to predict with reasonable accuracy their real behaviour is to do numerical simulations again the analysis closely follows that of william d roehr in roehr 1963 an avalanche transistor operated by a common bias network is shown in the adjacent picture v b b displaystyle v_ bb can be zero or positive value while r e displaystyle r_ e can be short circuited in every avalanche transistor circuit the output signal 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 r c displaystyle rc circuit as shown in the adjacent picture which includes only bias components the magnitude and sign of both those parameters are controlled by the base current i b displaystyle i_ b 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 τ a c e r a c e c a c e displaystyle tau _ ace r_ ace c_ ace where r a c e displaystyle r_ ace is the collector emitter avalanche differential resistance and as stated above can be obtained by differentiation of the collector emitter voltage v c e displaystyle v_ ce respect to the collector current i c displaystyle i_ c for a constant base current i b displaystyle i_ b r a c e v c e i c i b c o n s t displaystyle r_ ace frac partial v_ ce partial i_ c bigg _ i_ b const c a c e displaystyle c_ ace is the collector emitter avalanche differential capacitance and has the following expression c a c e 1 r a c e ω β c o b displaystyle c_ ace left frac 1 r_ ace omega _ beta c_ ob right where ω β 2 π f β displaystyle omega _ beta 2 pi f_ beta is the current gain angular cutoff frequency c o b displaystyle c_ ob is the common base output capacitance the two parameters are both negative this means that if the collector load const of an ideal current source the circuit is unstable this is the theoretical justification of the astable multivibrator behavior of the circuit when the v c c displaystyle v_ cc voltage is raised over some critical level second breakdown avalanche mode edit when the collector current rises above the data sheet limit i c m a x displaystyle i_ cmax 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 the bipolar junction transistor which give rise to an exponentially increasing current through these points this exponential rise of current in turn gives rise to even more overheating originating a positive thermal feedback mechanism while analyzing the i c v c e displaystyle i_ c v_ ce static characteristic the presence of this phenomenon is seen as a sharp collector voltage 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 of silicon during this process very small but finite quantities of metals remain in localized portions of the wafer these particles of metals became deep centers of recombination i e centers where current exists in a preferred way while this phenomenon is destructive for bipolar junction transistors 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 in second breakdown regime together with some examples can be found in the paper baker 1991 numerical simulations edit avalanche transistor circuits are intrinsically large signal circuits so small signal models when applied to such circuits can only give a qualitative description to obtain more accurate information about the behavior of time dependent voltages and currents in such circuits it is necessary to use numerical analysis the classical approach detailed in the paper дьяконов dyakonov 2004b which relies upon the book дьяконов dyakonov 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 purpose numerical simulation software results obtained in this way are fairly accurate and simple to obtain however these 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 is to use the common analog circuit simulator spice together with an advanced transistor model supporting avalanche breakdown simulations which the basic spice transistor model does not examples of such models are described in the paper keshavarz raney campbell 1993 and in the paper kloosterman de graaff 1989 the latter is a description of the mextram model currently used by some semiconductor industries to characterize their bipolar junction transistors a graphical method edit a graphical method for studying the behavior of an avalanche transistor was proposed in references spirito 1968 and 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 edit avalanche transistors are mainly used as fast pulse generators having rise and fall times of less than a nanosecond and high output voltage and current they are occasionally used as amplifiers in the microwave frequency range even if this use is not mainstream when used for this purpose they are called controlled avalanche transit time triodes catt s avalanche mode switching circuits edit 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 the semiconductor crystal lattice avalanche breakdown in semiconductors has found application in switching circuits for two basic reasons it can provide very high switching speeds since current builds up in very small times in the picosecond range due to avalanche multiplication it can provide very high output currents since large currents 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 there are several more complex circuits in the literature for example in the books roehr 1963 and дья...