Impact Ionization or Ionization Breakdown Gain and Coefficient Calculator

Semiconductor Type:	Silicon (E-field Range: 0 - 316200 V/cm) Indium Phosphide (E-field Range: 350000 - 466900 V/cm)        Gallium Arsenide:         Low Doping (E-field Range: 200000 - 326400 V/cm)         Medium Doping (E-field Range: 200000 - 325100 V/cm)         High Doping (E-field Range: 200000 - 333600 V/cm)
Voltage:	(V)
Width:	(μm)
a :	(cm-1)
b :	(cm-1)
Me, electron gain:
Mh, hole gain:
Electric Field:	(V/cm)

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1. Introduction
   1. This calculator takes a given electric field and calculates the Impact Ionization or Ionization Breakdown coefficients. This is then used to find the Electron and Hole gain for different semiconductors. Impact Ionization or Avalanching is important for Avalanche Photo Diodes and the BYU invention of the Solid-State Impact Ionization Multiplier (SIM).
2. How the Calculator Works
   1. The references listed at the bottom of this page were used to gather constants to solve for the alpha and beta impact ionization coefficients. You can either refer to those references or just view the source of this page to find the precise numbers along with the equations used. The equation for electron and hole gain was taken from Dr. Aaron Hawkin's thesis and is shown below. There are four significant digits carried in all of the calculations on this page; there are at least two but as many as four significant digits from the constants reported in the references.
   2. 

References:

Silicon:
P.P. Webb, Measurements of Ionization Coefficients in Silicon at Low Electric Fields, GE Canada Inc., Electro Optics Operations
W.N. Grant, Solid State Electronics, 16, 1189 (1973)

Indium Phosphide:
C. A. Armiento and S. H. Groves, Applied Physics Letters, Vol 43, No. 2

Gallium Arsenide:
H. David Law and Charles A. Lee, Solid-State Electronics, Vol. 21, pp. 331-340