2.1 Fundamentals of Avalanche Multiplication

Let us consider the following simple situation. An electron is injected into a sample of length L with a homogeneous field F (Fig. 2.1). Let us suppose that at this given field F the electron ionization rate ? _i is much larger than the hole ionization rate ( ? _i >> ? _i), so that ? _iL, >> 1 but / ? _iL << 1 This means that the electron performs numerous elementary acts of impact ionization as it passes through the sample. On the other hand, the probability of a hole making even one act of impact ionization is practically zero.

Figure 2.1: An electron is injected into a sample from the left. In travelling a distance l _i = 1/ ? _i (on average) it will create a new electron and a hole. The hole will move to the left (without ionization), while emergent electrons will move to the right and create further electron-hole pairs, and so on.

In this simplest case we have

(2.1)

and a multiplication factor M _n for electrons injected at the cathode M _n = i _n( L) /j _n(0) is equal to

(2.2)

For a non-homogeneous field distribution across the sample:

(2.3)

It is worth noting that in this simplest case ( ? _iL << 1) the multiplication factor M is always a finite value. It may be...