Question

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.

(a)The velocity of electrons, v(x), moving only by diffusion with a density distribution of n(x) = no * exp(-x/2) and zero electric field is given by:

Diffusion velocity, v(x) = _______
(b) The electric field, E(x), that would lead to an electron drift velocity equal to the diffusion velocity in part (a) is:

Electric field, E(x) = _______
(c) At 300 K, what value of D would make the field in part (b) equal to 1000 V/m?

Diffusion coefficient, D = _______

Answer 1

The diffusion velocity, v(x), for electrons moving only by diffusion can be calculated using the expression -D * (dn(x)/dx). The electric field, E(x), that would lead to an electron drift velocity equal to the diffusion velocity is given by v(x) / (µ * n * q). The value of D that would make the electric field equal to 1000 V/m can be determined using the equation D = (kT) / (q * µ).

Step-by-step explanation:

The diffusion velocity, v(x), for electrons moving only by diffusion with a density distribution of n(x) = no * exp(-x/2) and zero electric field is given by:

Diffusion velocity, v(x) = -D * (dn(x)/dx)

The electric field, E(x), that would lead to an electron drift velocity equal to the diffusion velocity in part (a) is:

Electric field, E(x) = v(x) / (µ * n * q)

At 300 K, the value of D that would make the field in part (b) equal to 1000 V/m is:

Diffusion coefficient, D = (kT) / (q * µ)