Formation of a pn Junction and Junction Depth Calculations

The distance from the surface, x_j, at which the diffused impurity profile intersects the background concentration N_B, is called the metallurgical junction x_j. The net impurity concentration at x_j is zero.

Fig 4 Formation of a pn junction by diffusion (a) an example of a p-type Gaussian diffusion into a uniformly doped n-type wafer; (b) net impurity concentration in the wafer. The metallurgical junction occurs at the point x=x_j, where the net concentration is zero. The material is converted to p-type to the left of x_j and remains n-type to the right of x_j. [1]

For Gaussian Distribution

Impurity concentration at distance x and time t, that is, N(x,t) is given by

We know that at junction depth, that is, x=x_j, N(x,t)=N_B, the background concentration. Therefore, we have,

at x= x_j N(x,t) = N_B

The junction depth is given by the following expression.

For Complementary Error Function Distribution

At x=x_j N(x,t)=N_B

The junction depth is given by the following expression.