The area of safe operation of transistors for switching operation

A thermal feedback model is presented for the analytical definition of the ASO (Area of Safe Operation) for transistors in switching operations. This area is narrowed by the "second breakdown in p-n junction," and the approximate representation of the breakdown threshold is presented. This model consists of a forward and feedback energy flow with gains A and B, respectively.
A = V_{CE} \times M, B = K \times \theta \times \alpha_{R} \times I_{e}
. Therefore, the condition of the breakdown can be introduced as
1 - AB = 0
, where
M
is the current multiplication factor, θ is transient thermal resistance,
K
is a newly introduced current concentration factor, and α
R
is the temperature coefficient of I
e
. Experimental results are also reported for a germanium alloy type transistor.