ELE533 Mid Term Question 4

Derive Einstein's relation,

D_{n}= V_{t}u_{n}Answer

Assume

Jn = u_{n}qnE + qD_{n}(dn/dx) = 0Since n = niE

^{V/Vt}E = -(dV/dx) = -Vt(1/n)dn/dx

u

_{n}qnE = -u_{n}qnVt(1/n)dn/dx = -qD_{n}(dn/dx)

D_{n}= V_{t}u_{n}