Electrical Conductivity in Intrinsic Semiconductor

Expression for electrical conductivity in intrinsic semiconductor

The general expression for the electrical conductivity, σ = neμ

The intrinsic electrical conductivity, σ_i = [neμ_e+ peμ_h]

But n = p = n_i

Therefore σ_i = [n_ieμ_e+ n_ieμ_h]

σ_i= n_ie [μ_e+ μ_h]

where, μ_e electron mobility and μ_h hole mobility

$\sigma_i=\left(\mu_e+\mu_h\right) e \cdot 2\left(\frac{2 \pi K T}{h^2}\right)^{\frac{3}{2}}\left(m_e^* m_h^*\right)^{\frac{3}{4}} \exp \left[\frac{-\left(E_g\right)}{2 K T}\right]$

The electrical conductivity depends on the negative exponential of and the mobilities μ_e and μ_h . But the [μ_e+ μ_h] is found to be proportional to T ^-3/2 . So that we can neglect [μ_e+ μ_h] .

The Electrical conductivity

eqn(1)

$\sigma_{\mathrm{i}}=\mathrm{Cexp}\left[-\frac{\mathrm{E}_{\mathrm{g}}}{2 \mathrm{KT}}\right]$