Physics of Semiconductor Devices

MIT 6.012, problem 1.3

The Massachusetts Institute of Technology maintains an Open Course Ware site, "a free and open educational resource (OER) for educators, students, and self-learners around the world." All of the problems with a title like 'MIT ... ' were taken from that site.

In a certain n-type region of a semiconductor in thermal equilibrium, there is a hole concentration with the following spatial distribution:

p_o = 10³(1 - 2 × 10³x) 1/cm³ for 0 < x < 10^-4 with x in cm.

Assume that in this region, the electron mobility is μ_n = 500 cm²/V·s and the hole mobility is μ_p = 400 cm²/V·s.

a) Derive an expresion for and sketch the hole diffusion current in this region.

b) Derive an expresion for and sketch the electric field distribution in this region.