A general relationship for the current density carried by electrons of density n is J = qnv, where q is the electronic charge and v is the electron velocity due to drift and/or diffusion.
(a) Find the velocity of electrons, v(x), that are moving only by diffusion if they have a density distribution of n(x) = (n_o)exp(-x/f). The electric field is zero.
(b) What would be the electric field, f(x), that would lead to an electron drift velocity equal to that of the diffusion velocity in part (a)?
(c) At 300K, what value of f would make the field in part (b) to be 1000 V/cm?