A pure silicon crystal of length l (= 0.1m) and area A(10^–4m²) has the mobility of electron ( $μ_{e}$ ) and holes ( $μ_{h}$ ) as 0.135 m²/Vs and 0.048 m²/Vs, respectively, If the voltage applied across it is 2V and the intrinsic charge concentration is n_i = 1.5 × 10⁶m^–3, then the total current flowing through the crystal is:

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8.78 × 10^–17A

6.25 × 10^–17A

2.456 × 10^–17A

7.89 × 10^–17A

answer is A.

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Detailed Solution

$l = 0.1 m A = 10^{- 4} m^{- 2} μ_{e} = 0.135 m^{2} (Vs)^{- 1} μ_{h} = 0.048 m^{2} (Vs)^{- 1}$

$n_{i} = 1.5 \times 10^{6} m^{- 3}$

The conductivity is:

$σ = n_{i} (μ_{e} + μ_{h}) e = 1.5 \times 10^{6} (0.135 + 0.048) 1.6 \times 10^{- 19} = 1.5 (0.183) 1.6 \times 10^{- 13} = 0.4392 \times 10^{- 13} {Sm}^{- 1}$

$Now, the resistance is given by, R = \frac{l}{σ (A)} \Rightarrow R = \frac{0.1}{0.4392 \times 10^{- 13} (10^{- 4})} \Rightarrow R = 0.2276 \times 10^{17} Ω$

Hence, the current is:

$\begin{aligned} I = \frac{V}{R} = \frac{2}{0.2276 \times 10^{17}} \\ \Rightarrow I = 8.787 \times 10^{- 17} A \end{aligned}$

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