built-in voltage

Consider a metal–p-type silicon contact with the following information: n i = 10 10 cm − 3 , N a = 10 17 cm − 3 , ϕ m = 3 V, χ s = 2.5 V, E g = 1.1 eV, q = 1.6 × 10 − 19 C, κ i = 11.9, ε 0 = 8.85 × 10 − 14 F/cm, kT = 0.0259 eV.
Determine the built-in voltage of the junction.
Determine the Schottky barrier height.

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