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Problem 3-A piece of Metal/Silicon is doped with phosphorous, 1 x 10^¹7 cm ^-³.

The metal has a work function of 6 eV. Within depletion approximation at Zero bias:

(a) Calculate barrier height

(b) Calculate build-in potential

(c) Calculate depletion thickness (in unit of micrometer)

(d) Calculate maximum electric field