The impurity profile of a pn junction is shown in figure 1. Na = 10¹⁸cm^-3, a = 10²³cm^-4

1. Sketch the space charge and electric field distributions.

2. If the critical electric field for breakdown is 5x10⁵V/cm, What is the total junction voltage(applied plus built-in) at breakdown?

Emax = qN_aXp/e = q a Xn²/2e = 5x10⁵

where the permittivity of silicon, e = 10^-12

Xp = e Emax/q Na = 3.125x10^-6 = 0.03125 um

Xn = sqrt[2e Emax/qa] = 7.9x10^-6 = 0.079 um

Vj = V1 + V2

V1 = Emax Xp/2 = 0.78V

Integrate E from 0 to Xn to get V2

V2 = (2/3)Emax Xn = 2.64V

Vj = V1 + V2 = 3.42V