First slide

Types of semiconductors

Question

Find the current produced at room temperature in a pure germanium plate of area $2 \times 10^{- 4} m^{2}$ and thickness is $1.2 \times 10^{- 3} m$ when a potential of 5 V is applied across the faces. Concentration of carriers in germanium at room temperature is $1.6 \times 10^{6} m^{- 3}$ . The mobilities of electrons and holes are $0.4 m^{2} v^{- 1} s^{- 1}$ and $0.2 m^{2} v^{- 1} s^{- 1}$ respectively . The heat generated in the plate in 100 second is

Moderate

A

$2.4 \times 10^{- 11} J$
B

$3.4 \times 10^{- 11} J$
C

$5.4 \times 10^{- 11} J$
D

$6.4 \times 10^{- 11} J$

Solution

$n_{e} = n_{h} = 1.6 \times 10^{6} m^{- 3}$
$t = 100 Sec$
$A = 2 \times 10^{- 4} m^{2}$
$d = 1.2 \times 10^{- 3} m$
$\begin{array}{l} V = 5 v o l t \end{array}$
$\begin{array}{l} μ_{e} = 0.4 m^{2} v^{- 1} s^{- 1} \\ μ_{h} = 0.2 m^{2} v^{- 1} s^{- 1} \end{array}$
H = ?
H = V i t
H = V J A t $(∴ i = J A)$
$H = V σ E A t$    $(∴ J = σ E)$
$\begin{array}{l} H & = V (σ_{e} + σ_{h}) E A t & (∴ σ = σ_{e} + σ_{h}) \\ H & = V (n_{e} e μ_{e} + n_{h} e μ_{h}) E A t & (∴ σ = n μ e) \end{array}$
$\begin{array}{l} H & = V e (n_{e} μ_{e} + n_{h} μ_{h}) E A t \\ H & = V e (n_{e} μ_{e} + n_{h} μ_{h}) \frac{V}{d} A t \end{array}$
$\begin{array}{l} H = 5 \times 1.6 \times 10^{- 19} (1.6 \times 10^{6} \times 0.4 + 1.6 \times 10^{6} \times 0.2) \frac{5}{1.2 \times 10^{- 3}} \times 2 \times 10^{- 4} \times 100 \\ H = 5 \times 1.6 \times 10^{- 19} \times 1.6 \times 10^{6} (0.4 + 0.2) \frac{5}{1.2 \times 10^{- 3}} \times 2 \times 10^{- 4} \times 100 \end{array}$
$\begin{array}{l} H = 5 \times 1.6 \times 1.6 \times 0.6 \times \frac{5}{1.2} \times 2 \times 10^{- 14} \times 100 \\ H = 6400 \times 10^{- 14} \\ H = 6.4 \times 10^{- 11} J \end{array}$

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