Question:
The density of an electron-hole pair in a pure germanium is $3 \times 10^{16} \, m^{-3}$ at room temperature. On doping with aluminium, the hole density increases to $4.5 \times 10^{22} \, m^{-3}$. Now the electron density (in $m^{-3}$) in doped germanium will be
The density of an electron-hole pair in a pure germanium is $3 \times 10^{16} \, m^{-3}$ at room temperature. On doping with aluminium, the hole density increases to $4.5 \times 10^{22} \, m^{-3}$. Now the electron density (in $m^{-3}$) in doped germanium will be
Updated On: May 14, 2024
- $1 \times 10^{10}$
- $2 \times 10^{10}$
- $0.5 \times 10^{10}$
- $4 \times 10^{10}$
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The Correct Option is B
Solution and Explanation
$n^2_1 = n_hn_e$
$ \Rightarrow n_e = \frac{(3\times 10^{16})^2}{4.5 \times 10^{22}}= \frac{9 \times 10^{32}}{4.5\times 10^{22}} $
$= 2 \times 10^{10} \,m ^{-3}$
$ \Rightarrow n_e = \frac{(3\times 10^{16})^2}{4.5 \times 10^{22}}= \frac{9 \times 10^{32}}{4.5\times 10^{22}} $
$= 2 \times 10^{10} \,m ^{-3}$
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Concepts Used:
Semiconductors
Semiconductors are a crystalline solid materials, whose electrical conductivity lies between a conductor and an insulator. Semiconductors are mainly used in the manufacturing of electronic devices like capacitors, transistors, diodes, Integrated circuits, etc.
Properties of Semiconductor:
- Semiconductor acts like an insulator at Zero Kelvin. On increasing the temperature, it works as a conductor.
- Due to their exceptional electrical properties, semiconductors can be modified by doping to make semiconductor devices suitable for energy conversion, switches, and amplifiers.
- Lesser power losses.
Uses of Semiconductor:
- Semiconductors are widely used in manufacturing electronics devices like transistors, diodes, sensors, integrated circuits.
- Semiconductors are widely used in all electronic devices, like mobile phones, digital cameras, communication devices, trains, ATMs, etc.