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 emitter breakdown voltage, called avalanche breakdown region . This region is characterized by avalanche breakdown, a phenomena 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).

Basic theory

Static avalanche region characteristics

Bias currents and voltages for a npn bipolar transistor

In this section, the $I_{C}-V_{CE}$ static characteristic of an avalanche transistor is calculated. For the sake of simplicity, only a NPN device is considered: however, the same results are valid for PNP devices only changing signs to voltages and currents accordingly. 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 phenomena. Kirchhoff's current law applied to a bipolar junction transistor implies the following relation, always satisfied by the collector current $I_{C}$

$I_{C}=I_{E}-I_{B}\,$

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

• $I_{B}$ is the base current,
• $I_{CBO}$ is the collector-base reverse leakage current,
• $I_{E}$ is the emitter current,
• $\beta$ is the common emitter current gain of the transistor.

Equating the two formulas for $I_{C}$ gives the following result

$I_{E}=(\beta +1)I_{B}+(\beta +1)I_{CBO}\,$

and since $\alpha =\beta {(\beta +1)^{-1}}$ 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 $I_{C}$ 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

• $BV_{CBO}$ 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,
• $V_{CB}$ 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 $I_{C}$ 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 $V_{CB}=V_{CE}-V_{BE}$ and $V_{BE}=V_{BE}(I_{B})$ where $V_{BE}$ 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 $V_{CE}>>V_{BE}$: this is the expression of the parametric family of the collector characteristics $I_{C}-V_{CE}$ with parameter $I_{B}$. Note that $I_{C}$ 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 $BV_{CEO}$ is the collector-emitter breakdown voltage. Also, it is possible to express $V_{CE}$ as a function of $I_{C}$, and obtain an analytical formula for the collector-emitter differential resistance by straightforward differentiation: however, the details are not given here.

Differential dynamical model

Equivalent circuit of an avalanche npn bipolar transistor operated by a commonly used bias network.

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. The magnitude and sign of both those parameters are controlled by the base current $I_{B}$: 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

$\tau _{Ace}=r_{Ace}C_{Ace}\,$

where

• $r_{Ace}$ is the collector-emitter avalanche differential resistance and, as stated above, can be obtained by differentiation of the collector-emitter voltage $V_{CE}$ respect to the collector current $I_{C}$, for a constant base current $I_{B}$

$r_{Ace}={\frac {\partial {V_{CE}}}{\partial {I_{C}}}}{\Bigg |}_{I_{B}=const.}$

• $C_{Ace}$ 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

$\omega _{\beta }=2\pi f_{\beta }$ is the current gain angular cutoff frequency

$C_{ob}$ 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.

Applications

Avalanche transistors are mainly used as fast pulse generators, having rise and fall times of less than a nanosecond and high output voltages 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).

Avalanche mode switching

Avalanche mode switching relies on avalanche multiplication of current flowing through the collector-base junction as a result of impact ionisation 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.

Avalanche mode amplification

Avalanche mode amplification relies on avalanche multiplication as avalanche mode switching: however, for this mode of operation, the operating point of the device is stabilized by a proper choice of output impedance.

For comparison: When a diode is poled from conduction to isolation the carriers need some time to leave the diode. If the voltage is increased sufficiently fast avalanches occur amplifying the current, increasing the time needed to get into the isolating state.

See also

• Avalanche breakdown
• Bipolar junction transistor
• Pulse generator
• Avalanche diode

References

• Wolfgang Meiling and Franz Stary (1968). Nanosecond pulse techniques. Gordon & Breach. Sections 3.1.5 "Avalanche transistors", 3.2 and 3.4 "Trigger circuits containing avalanche transistors".
• Jacob Millman and Herbert Taub (1965). Pulse, digital and switching waveforms. McGraw-Hill. Sections 6.9, 6.10, 12.10, 13,16, 13.17.
• William D. Roehr (1963). High-speed switching transistor handbook (3^rd printing ed.). Motorola, Inc. Chapter 9 "Avalanche mode switching".
• The ZTX413 Avalanche Transistor Zetex Semiconductors Design Note 24, October 1995.
• The ZTX415 Avalanche Mode Transistor Zetex Semiconductors Application Note 8, January 1996.

Bibliography

• Template:Harvard reference. A paper containing an accurate analysis of the avalanche breakdown phenomena in planar pn-junctions, as those found in almost all modern transistors.
• S. L. Miller "Avalanche Breakdown in Germanium", Phys. Rev. 99, 1234 - 1241 (1955). The paper where the above formula for the avalanche multiplication coefficient $M$ first appeared.
• Владимир Павлович Дьяконов (Vladimir Pavlovich D'yakonov) (1973). Лавинные транзисторы и их применение в импульсных устройствах (Avalanche transistors and their application in pulse circuits). Советское радио (Sovetskoe Radio). A very scarce book worth a look, especially for the Russian reader.

External links

Theory

• Владимир Павлович Дьяконов (Vladimir Pavlovich D'yakonov), Анализ статических вольтамперных характеристик диодов и транзисторов с учетом лавинного пробоя (Analysis of static volt-amperometric characteristics of diodes and transistors including avalanche breakdown), www.exponenta.ru . A paper analyzing the volt-amperometric characteristic of diodes and transistors using computer algebra.
• Владимир Павлович Дьяконов (Vladimir Pavlovich D'yakonov), Расчет параметров импульсов емкостного релаксатора на лавинном транзисторе (Calculation of pulse parameters as a function of capacity in an avalanche transitor relaxation oscillator), www.exponenta.ru . A paper about the design of an avalanche transistor relaxation oscillator using computer algebra.
• Douglas J. Hamilton, James F. Gibbons and Walter Shockley (1959), "Physical principles of avalanche transistor pulse circuits", IRE Solid-State Circuits Conference, Volume II, 92 - 93. A brief description of the basic physical principles of avalanche transistor circuits: instructive and interesting but "restricted access".
• A.A. Keshavarz, C.W. Raney, and D.C. Campbell A breakdown model for the bipolar transistor to be used with circuit simulators, Report SAND--93-0241C, Sandia National Laboratories, August 1, 1993. Available from the U.S. Department of Energy Office of Scientific & Technical Information. A report describing a transistor model capable of including avalanche effects in SPICE simulations.
• Jochen Riks "Avalanche-Transistor" (in German). A brief description of the working principles of the avalanche transistor, part of the course "Impulsschaltungen F-Praktikum EXP 10", June 1996, Fachschaft Physik Uni Düsseldorf.

Applications

• Wade Biddle and David Lonobile "Sweep Deflection Circuit Development Using Computer-Aided Circuit Design for the OMEGA Multichannel Streak Camera", LLE Review, vol. 73, 6-14 (1997). A paper describing a fast sweep generator for a streak camera constructed using series connected avalanche transistor circuits.
• G.B.B. Chaplin (1958), "A method of designing transistor avalanche circuits with application to a sensitive transistor oscilloscope", IRE Solid-State Circuits Conference, Volume I, 21 - 23. A paper describing an application of avalanche transistors to the design of a sampling oscilloscope: available abstract, full paper is "restricted access".
• E. Stephen Fulkerson, Douglas C. Norman, Rex Booth "Driving Pockel cells using avalanche transistors" Report UCRL-JC--125874, Lawrence Livermore National Laboratory, May 28, 1997. Available from the U.S. Department of Energy Office of Scientific & Technical Information. A report describing the design of a driver for Pockel cells Q-switches.
• Andrew Holme "Avalanche pulse generator". A project of an avalanche transistor astable multivibrator with schematics, waveforms and photos of the layout.
• Ari Kilpelä "Pulsed time-of-flight laser range finder techniques for fast, high precision measurement applications", Academic Dissertation presented with the assent of the Faculty of Technology, University of Oulu, 2004. Acta Universitatis Ouluensis Technica C 197, ISBN 951-42-7261-7. A doctoral dissertation describing a Laser TOF (Time Of Flight) Radar and its construction using an avalanche transistor pulser.
• Ari Kilpelä, Juha Kostamovaara "A LASER pulser for a TOF Laser RADAR". A preprint describing an avalanche transistor pulser and its use as Laser driver in a TOF (Time Of Flight) LASER RADAR: published as "Laser pulser for a time-of-flight laser radar", Rev. Sci. Instrum. 68, 2253 (1997).
• "Operating the pulsed laser diode SPL LLxx", "Range finding using pulsed laser diodes" Osram Opto Semiconductors Application Notes, 2004-09-10. Two application notes from Osram Opto Semiconductors describing pulsed operation of a Laser diode, using avalanche transistors and other kind of drivers.
• J.L. Pellegrin "Increasing the Stability of Series Avalanche Transistor Circuits", SLAC-PUB-0669 Stanford Linear Accelerator Center - SLAC. A paper describing a method to enhance performances of banks of seies-connected avalanche transistor circuits.
• Jim Williams, "The taming of the slew", EDN Magazine , 57-65, 25 September 2003. (Link to PDF article) 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 "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, 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

• 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 Academic Web Page. A researcher working on theory and applications of avalanche transistor circuits.