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-emitter breakdown voltage, called avalanche breakdown region. This region is characterized by avalanche breakdown, which is a phenomenon similar to Townsend discharge for gases, and negative differential resistance. Operation in the avalanche 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."Linear Technology AN47" , High-speed amplifier techniques, 1991, Appendix D: Measuring probe-oscilloscope response."Linear Technology AN94", Slew Rate Verification for Wideband Amplifiers The Taming of the Slew"
History The first paper dealing with avalanche transistors was . 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 , first introduced in the paper . 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 ).
From the beginning of the 1960s to the first half of the 1970s, several avalanche-transistor circuits were proposed. The kind 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 .
The first application of the avalanche transistor as a linear amplifier, named Controlled Avalanche Transit Time Triode, (CATT) was described in . A similar device, named IMPISTOR was described more or less in the same period in the paper of . Linear applications of this class of devices 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
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 . 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 and doping 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 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 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 .
An avalanche transistor operated by a common bias network is shown in the adjacent picture: can be zero or positive value, while 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 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 : 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 angular cutoff frequency 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 voltage 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 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 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 .
Numerical simulations 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 which relies upon the book , 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 and in the paper : the latter is a description of the Mextram model, currently used by some semiconductor industries to characterize their bipolar junction transistors.
A graphical method A graphical method for studying the behavior of an avalanche transistor was proposed in references and : 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