Avalanche transistor

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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, 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).

Contents

[edit] History

The first paper dealing with avalanche transistor was (Ebers & Miller 1955): the paper describes how to use alloy-junction transistor 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 transistor 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, first introduced in the paper (Miller 1955): the need of better understanding transistor behavior in the avalanche breakdown region, not only for using them in avalanche mode, gave rise to a 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, and also it was studied what kind of bipolar junction transistor is best suited for the use in the avalanche breakdown region: a complete reference, which includes also the contributions of scientists from ex-USSR and COMECON countries, is the book (Дьяконов (D'yakonov) 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 (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 of compound semiconductors, being capable of switching currents of several tens of amperes even faster than "traditional" avalanche transistors.

[edit] Basic theory

[edit] Static avalanche region characteristics

Bias currents and voltages for a npn bipolar transistor
Bias currents and voltages for a npn bipolar transistor

In this section, the IC − VCE 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 flowing 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 IC

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=\beta I_B+(\beta+1)I_{CBO}\,

where

  • IB is the base current,
  • ICBO is the collector-base reverse leakage current,
  • IE is the emitter current,
  • β is the common emitter current gain of the transistor.

Equating the two formulas for IC gives the following result

I_E = (\beta + 1)I_B + (\beta + 1)I_{CBO}\,

and since α = β(β + 1) − 1 is the common base current gain of the transistor, then

\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 IC is given by

I_C=M(\alpha I_E +I_{CBO})\,

where M is Miller's avalanche multiplication coefficient. It is the most important parameter in avalanche mode operation: its expression is the following

M = {\frac{1}{1-\left(\frac{V_{CB}}{BV_{CBO}}\right)^{n}}}\,

where

  • BVCBO is the collector-base breakdown voltage,
  • n is a constant depending on the semiconductor used for the construction of the transistor and doping profile of the collector-base junction,
  • VCB is the collector-base voltage.

Using again Kirchhoff's current law for the bipolar junction transistor and the given expression for M, the resulting expression for IC is the following

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 VCB = VCE − VBE and VBE = VBE(IB) where VBE is the base-emitter voltage

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 VCE > > VBE: this is the expression of the parametric family of the collector characteristics IC − VCE with parameter IB. Note that IC increases without limit if

\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 BVCEO is the collector-emitter breakdown voltage. Also, it is possible to express VCE as a function of IC, and obtain an analytical formula for the collector-emitter differential resistance by straightforward differentiation: however, the details are not given here.

[edit] Differential dynamical model

Equivalent circuit of an avalanche npn bipolar transistor operated by a commonly used bias network.
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 wolud not add anything useful from the point of view of the working principles of the avalanche transistor. However, when realizing a electronic circuit, those parameters are of great importance: particularly stray inductances in series to collector and emitter leads 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 of time constants and therefore rise and fall times of the VCE 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 picture on the right: VBB can be zero or positive value, while RE 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 RC circuit as shown in the picture on the right, which includes only bias components The magnitude and sign of both those parameters are controlled by the base current IB: 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

\tau_{Ace}=r_{Ace}C_{Ace}\,

where

  • rAce is the collector-emitter avalanche differential resistance and, as stated above, can be obtained by differentiation of the collector-emitter voltage VCE respect to the collector current IC, for a constant base current IB
r_{Ace}=\frac{\partial{V_{CE}}}{\partial{I_C}}\Bigg|_{I_B=const.}
  • CAce is the collector-emitter avalanche differential capacitance and has the following expression
C_{Ace}=-\left(\frac{1}{r_{Ace}\omega_\beta}-C_{ob}\right)
where
ωβ = 2πfβ is the current gain angular cutoff frequency
Cob 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 VCC voltage is raised over some critical level.

[edit] Second breakdown avalanche mode

When the collector current rises above the data sheet limit ICMAX 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 flow of current through this points: this exponential rise of current in turn give rise to even more overheating, originating a positive thermal feedback mechanism. While analyzing the IC − VCE 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 flows 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).

[edit] 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 (Дьяконов (D'yakonov) 2001 (?)) which relies upon the book (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 purpose numerical 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 analog circuit simulator SPICE together with an advanced transistor model supporting avalanche breakdown simulations, since 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.

[edit] A graphical method

A graphical method for studying the behavior or 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 dynamical 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.

[edit] Applications

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 (CATTs).

[edit] 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 the semiconductor crystal lattice. Avalanche breakdown in semiconductors and 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. It is possible to find several more complex circuits in the literature, for example in the books (Roehr 1963) and (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:

Simplified collector trigger circuit of an avalanche npn bipolar transistor operated by a commonly used bias network.
Simplified collector trigger circuit of an avalanche npn bipolar transistor operated by a commonly used bias network.
Simplified base trigger circuit of an avalanche npn bipolar transistor operated by a commonly used bias network.
Simplified base trigger circuit of an avalanche npn bipolar transistor operated by a commonly used bias network.
  • Collector triggering input circuit: the input trigger signal is fed to the collector via a fast switching diode DS, possibly after being shaped by a pulse shaping network. This way of driving an avalanche transistor was extensively employed in first generation circuits since the collector node has a high impedance and also collector capacitance Cob behaves quite linearly under large signal regime. As a consequence of this, the delay time from input to output is very small and approximately independent of the value of control voltage. However, this trigger circuit requires a diode capable of resist to high reverse voltages and switch very fast, characteristics that are very difficult to realize in the same diode, therefore it is rarely seen in modern avalanche transistor circuits.
  • Base triggering input circuit: the input trigger signal is fed directly to the base via a fast switching diode DS, possibly after being shaped by a pulse shaping network . This way of driving an avalanche transistor was relatively less employed in first generation circuits because the base node has a relatively low impedance and an input capacitance Cib which is highly nonlinear (as a matter of fact, it is exponential) under the large signal regime: this causes a fairly large, input voltage dependent, delay time, which was analyzed in detail in the paper (Spirito 1974). However, the required inverse voltage for the feed diode is far lower respect diodes to be used in collectior trigger input circuits, and since ultra fast Schottky diodes 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 DS in the following applicative circuits is symbolized as a Schottky diode.

Avalanche transistor can also be triggered by lowering the emitter voltage VE, but this configuration is rarely seen in the literature and in practical circuits.: in reference (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 (Дьяконов (D'yakonov) 1973, pp. 185) a balanced level discriminator where a common bipolar 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, Vout1 is a positive going output while Vout2 is a negative going output: using a pnp transistor reverses the polarities of outputs. The descripion of their simplified versions, where resistor RE or RL is set to zero ohm (obviously not both) in order to have a single output, can be found in reference (Millman & Taub 1965). Resistor RC recharges the capacitor CT or the transmission line \scriptstyle TL_{t_f} (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 are patented 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 the avalanche breakdown between the collector and emitter lead. The capacitor CT starts to be discharged by a current flowing through the resistors RE and RL: 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 fast rise time, of the order of fractions of nanosecond. Peak current depends on the size of the capacitor CT: when its value is raised over a few hundred picofarads, transistor goes in to second breakdown avalanche mode, and peak currents reach values of several amperes if not tens of amperes.
  • Transmission line avalanche pulser: a trigger signal applied to the base lead of the avalanche transistor cause the avalanche breakdown between the collector and emitter lead. The fast rise time of the collector current generates a current shock wave of approximatively the same amplitude, which propagates along the transmission line: the wave reaches the open circuited end of the line after the characteristic delay time tf of the line has elapsed, and then is reflected backward. If the characteristic impedance of the transmission line is equal to the resistances RE and RL, 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
t=2t_f\,

In practical designs, an adjustable impedance like a two terminal Zobel network (or simply a trimmer 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 output voltages.

Simplified capacitor discharge avalanche transistor pulser.
Simplified capacitor discharge avalanche transistor pulser.
Simplified transmission line avalanche transistor pulser.
Simplified transmission line avalanche transistor pulser.

It is possible to turn those circuits into astable multivibrators by removing their trigger input circuits and

  1. raising their power supply voltage VCC until a relaxation oscillation begins, or
  2. connecting the base resistor RB to a positive base bias voltage VBB and thus forcibly starting avalanche breakdown and associated relaxation oscillation

A well detailed example of the first procedure is described in reference (Holme 2006). It is also possible to realize avalanche mode bistable multivibrators, but their use is not as common as other tipes described of multivibrators, one important reason being that they require two avalanche transistors, one working continuously in avalanche breakdown regime, and this can give serious problems from the point of wiev of power dissipation and device operating life.

[edit] 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 M 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 the negative resistance of the avalanche breakdown region for the same reason

These 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 BVCEO respect to bipolar transistors having the same geometry. The current amplification mechanism is the same of the avalanche transistor, i.e. carrier generation by impact ionization, but there is also a transit-time effect as in IMPATT and TRAPATT diodes, where a high field region travels along the avalanching junction, precisely in along the intrinsic region. The device structure and choice of bias point imply that

  1. Miller's avalanche multiplication coefficient M is limited to about 10.
  2. The transit-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 (Eshbach, Se Puan & Tantraporn 1976): in this paper it is also showh that this semiconductor device structure is well suited for microwave power amplification. It can deliver several watts of radio frequency power at a frequency of several gigahertz 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 200 volts) to work properly, while nowadays gallium arsenide or other compound semiconductors 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 (Carrol & Winstanley 1974), was the IMPISTOR, being a transistor with IMPATT collector-base junction.

Schematic of a CATT microwave amplifier.
Schematic of a CATT microwave amplifier.

[edit] See also

[edit] References

[edit] Bibliography

[edit] External links

[edit] Theory

[edit] Applications

[edit] Varia