## What is Avalanche Breakdown?

Avalanche breakdown is caused by the impact ionization of electron-hole pairs. When applying a high electric field, carriers gain kinetic energy and generate additional electron-hole pairs through impact ionization. As the pair of electron-hole is created in the midst of the high field, they quickly separate and attain high velocities to cause further pair generation through more collisions.This is a cumulative process and as we approach the breakdown voltage, the field becomes so large that the chain of collisions can give rise to an almost infinite current with a very slight additional increase in voltage. This process is known as *avalanche breakdown.*

The ionization rate is quantified by the ionization constants of electrons and holes,\({ \alpha }_{ n }\) and \({ \alpha }_{ p }\). These ionization constants are defined as the change of the carrier density with position divided by the carrier density or:

*dn=\({ \alpha }_{ n }\) n dx*

The ionization causes a generation of additional electrons and holes. Assuming that the ionization coefficients of electrons and holes are the same, the multiplication factor *M*, can be calculated from:

*M=\(\frac { 1 }{ { 1- }\int _{ { x }_{ 1 } }^{ { x }_{ 2 } }{ \alpha \quad dx } }\) *

The integral is taken between\({ x }_{ 1 }\) and \({ x }_{ 2 }\), the region within the depletion layer where the electric field is assumed constant and large enough to cause impact ionization. Outside this range, the electric field is assumed to be too low to cause impact ionization. The equation for the multiplication factor reaches infinity if the if the integral equals one. This condition can be interpreted as follows: For each electron coming to the high field at point \({ x }_{ 1 }\), one additional electron-hole pair is generated arriving at point \({ x }_{ 2 }\). This hole drifts in the opposite direction and generates an additional electron-hole pair at the starting point \({ x }_{ 1 }\). One initial electron, therefore, yields an infinite number of electrons arriving at \({ x }_{ 2 }\), hence an infinite multiplication factor.

The multiplication factor is commonly expressed as a function of the applied voltage and the breakdown voltage using the following relation:

*M=\(\frac { 1 }{ 1-{ \left| { \frac { { V }_{ a } }{ { V }_{ br } } } \right| }^{ n } } ,where\quad 2<n<6\)*