Electrical Conductivity in Intrinsic Semiconductor

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Expression for electrical conductivity in intrinsic semiconductor

The general expression for the electrical conductivity, σ = neμ

The intrinsic electrical conductivity,  σi = [neμ+ peμh]

But n = p = ni

Therefore                     σi = [ni+ nih]

σ= nie [μ+ μh]

where, μe electron mobility and μh 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 μe and μh . But the [μ+ μh] is found to be proportional to  T -3/2 . So that we can neglect [μ+ μh] .

The Electrical conductivity

eqn(1)

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

where, C is a constant.

Taking  log on both sides of equation (1),

Equation

Intrinsic Semiconductor

Fig (1)

From the graph, we know that the electrical conductivity increases when temperature increases.

Read More Topics
Mobility and conductivity in semiconductors
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