First slide

Types of semiconductors

Question

Mobilities of electrons and holes in a sample of intrinsic germanium at room temperature are $0.36 m^{2} / Vs$ and $0.17 m^{2} / V s$ . The electron and hole densities are each equal to $2.5 \times 10^{19} m^{- 3}$ . Electrical conductivity of Germanium is

Moderate

A

$0.47 {sm}^{- 1}$
B

$5.185 {sm}^{- 1}$
C

$2.12 {sm}^{- 1}$
D

$1.09 {sm}^{- 1}$

Solution

$\begin{array}{l} μ_{e} = 0.36 m^{2} / V s \\ μ_{h} = 0.17 m^{2} / V s \\ n_{e} = n_{h} = 2.5 \times 10^{19} m^{- 3} \\ σ = ? \end{array}$
$\begin{array}{l} C o n d u c t i v i t y, σ = n_{e} e μ_{e} + n_{h} e μ_{h} \\ \Rightarrow σ = e (n_{e} μ_{e} + n_{h} μ_{h}) \end{array}$
$\Rightarrow σ = 1.6 \times 10^{- 19} (2.5 \times 10^{19} \times 0.36 + 2.5 \times 10^{19} \times 0.17)$
$\begin{array}{l} \Rightarrow σ = 1.6 \times 10^{- 19} \times 2.5 \times 10^{19} (0.36 + 0.17) \\ \Rightarrow σ = 1.6 \times 2.5 (0.53) \\ \Rightarrow σ = 2.12 \end{array}$

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