page_title: Avalanche transistor
section_title: Static avalanche region characteristics
hierarchical_section_title: Avalanche transistor / Basic theory / Static avalanche region characteristics
caption_attribution_description: English: I created this image for the "avalanche transistor" voice by using "Circuit_macros" for LaTeX and PSTricks. Summary I created this image for the "avalanche transistor" entry by using "Circuit_macros" for LaTeX and PSTricks.
context_page_description: 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. 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.
context_section_description: 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 (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 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.
caption: Bias currents and voltages for an NPN bipolar transistor
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