Final Exam 1998 Question 2 Answer

The impurity profile of a * pn* junction is shown in
figure 1.
Na = 10^{18}cm^{-3},
a = 10^{23}cm^{-4}

- Sketch the space charge and electric field distributions.
- If the critical electric field for breakdown is 5x10
^{5}V/cm, What is the total junction voltage(applied plus built-in) at breakdown?

Emax = qN_{a}Xp/e = q a Xn^{2}/2e = 5x10^{5}where the permittivity of silicon, e = 10

^{-12}Xp = e Emax/q Na = 3.125x10

^{-6}= 0.03125 umXn = sqrt[2e Emax/qa] = 7.9x10

^{-6}= 0.079 umVj = 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