First slide

Electrons and holes in semiconductors

Question

A block of pure Si at 300 K has a length of 10 cm and an area of cross-section 1 cm². A battery of emf 2V is connected across it. The mobility of electrons is 0.14 m²V^–1s^–1 and their number density is 1.5×10¹⁶ m^–3. The electron current is:-

Moderate

A

$6.72 \times 10^{- 4} A$
B

$6.72 \times 10^{- 5} A$
C

$6.72 \times 10^{- 6} A$
D

$6.72 \times 10^{- 7} A$

Solution

$E = \frac{V}{l} = \frac{2 V}{0.1 m} = 20 {Vm}^{- 1}$
$A = 1.0 {cm}^{2} = 1.0 \times 10^{- 4} m^{2}$
$v_{d} = μ_{e} E = 0.14 \times 20 = 2.8 {ms}^{- 1}$
$\begin{array}{l} I = n e A V_{d} = (1.5 \times 10^{16}) \times (1.6 \times 10^{- 19}) \times (1.0 \times 10^{- 4}) \times 2.8 = 6.72 \times 10^{- 7} A \end{array}$

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