How does potential barrier of a semiconductor vary with temperature?

Explanation

The barrier potential of a semiconductor increases with rise in temperature. The barrier potential `(V_B)` of a semiconductor is directly proportional to temperature in kelvin (T). The relation between barrier potential `V_B` and temperature TK in terms of the hole concentration on either side of the junction is given by
`V_(B)=(k_(B)T)/qlog_(e)(p_(p)/P_(n))`
where `k_(B)=` Boltzmann constant, `p_(p) =` hole concentration in p-side,` p_(n) =` hole concentration in n-side. The relation between barrier potential and temperature in terms of donor concentration `(N_d)` on the n-side and acceptor concentration `(N_a)` on the p-side is given by
`V_(B)=(k_(B)T)/qlog_(e)((N_a N_d)/n_(i)^(2))`
where `n_(i)` is the intrinsic carrier concentration.