Barrier Potential of PN junction diode

Determination of Barrier Potential V0 in p-n junction

Or

Contact difference V0 in p-njunction

Or

Boltzmann Relationship

(Asked many a times in exams)

1. Consider a p-type of semiconductors with non-uniform concentration(graded)i.e. there exist a concentration gradient.

2. Let the bar be open circuited. Therefore total current because of hole is zero.

Jp = Jpdrift +Jpdiff……………………………….(drift current and diffusion current)


pqµpE = qDp (dp/dx);

Thus, E=(1/p)(Dp/µp)(dp/dx);


According to Einstein Relationship

(Dp/µp)=VT =volt equivalent of temperature


E= (1/p) VT (dp/dx);

- (dv/dx) = (1/p) VT (dp/dx);

dv = - (VT/p) dp
Integrating on both sides:


Now consider a p-n junction bar whose half side is doped with accepter impurity causing p-type material and other half is doped with donar impurity causing n-type material.

on p-side, p1=pp =NA= Accceptor ion concentration……..eqn 3

Similarly on n-side, nn = ND

pn = ni2 / ND

and we have p2= pn = ni2 / ND ……….eqn 4


V21 is the potential existing across the junction which can be identified as the barrier potential denoted by V0

Put 3 and 4 in eqn 1, we get




Thus this is the expression for barrier potential