Question:
If the resistivity of pure silicon is $3000 \, \Omega m$ and the mobilities of electrons and holes are $0.12 \, m^{2}V^{- 1}s^{- 1}$ and $0.045 \, m^{2}V^{- 1}s^{- 1}$ respectively, then what will be the resistivity of a specimen of silicon when $10^{19}$ atoms of phosphorous are added per cubic metre?
If the resistivity of pure silicon is $3000 \, \Omega m$ and the mobilities of electrons and holes are $0.12 \, m^{2}V^{- 1}s^{- 1}$ and $0.045 \, m^{2}V^{- 1}s^{- 1}$ respectively, then what will be the resistivity of a specimen of silicon when $10^{19}$ atoms of phosphorous are added per cubic metre?
Updated On: Jul 28, 2022
- $2.21\Omega m$
- $3.21\Omega m$
- $4.21\Omega m$
- $5.21\Omega m$
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The resistivity of pure $S$ is given by
$\rho =\frac{1}{\sigma }=\frac{1}{e \left(n_{e} \left(\mu \right)_{e} + n_{h} \left(\mu \right)_{h}\right)}=\frac{1}{\left(en\right)_{1} \left(\left(\mu \right)_{e} + \left(\mu \right)_{h}\right)}$
or $n_{1}=\frac{1}{e? \left(\left(\mu \right)_{e} + \left(\mu \right)_{n}\right)}=\frac{1}{1 . 6 \times \left(10\right)^{- 19} \times 3000 \left(\right. 0 . 12 + 0 . 045 \left.\right)}$
$=1.26\times 10^{16}m^{- 3}$
When $10^{19}$ atoms of phosphorous (donor atoms of valence five) are added per $m^{3},$ the semiconductor becomes $n$ - type semiconductor.
$\therefore n_{e}-n_{h}\approx n_{e}=N_{d}=10^{19}\because n_{n}=1.26\times 10^{16}$
Resitivity $\rho =\frac{1}{n_{e} \mu _{e} e}=\frac{1}{1 . 6 \times 10^{- 19} \times 10^{19} \times 0 . 12}=5.21\Omega m$
Was this answer helpful?
0
0
Top Questions on Semiconductor electronics: materials, devices and simple circuits
- The range of electrical conductivity \( \sigma \) and resistivity \( \rho \) for metals, among the following, is:
- KCET - 2025
- Physics
- Semiconductor electronics: materials, devices and simple circuits
- The reverse saturation current (I0) of a silicon diode at 27°C is \( 10^{-6} \) A. What will be the approximate value of I0 at 67°C? (Assume \( I_0 \) doubles for every 10°C rise in temperature)
- MHT CET - 2025
- Physics
- Semiconductor electronics: materials, devices and simple circuits
- In a silicon semiconductor at room temperature, the intrinsic carrier concentration is \( 1.5 \times 10^{16} \, \text{m}^{-3} \). Calculate the energy band gap of the silicon if the intrinsic carrier concentration is given by: \[ n_i = \sqrt{N_c N_v} e^{-E_g / 2kT} \] Where: - \( N_c = 2.8 \times 10^{25} \, \text{m}^{-3} \) is the effective density of states in the conduction band, - \( N_v = 1.04 \times 10^{25} \, \text{m}^{-3} \) is the effective density of states in the valence band, - \( k = 1.38 \times 10^{-23} \, \text{J/K} \) is the Boltzmann constant, - \( T = 300 \, \text{K} \) is the temperature.
- MHT CET - 2025
- Physics
- Semiconductor electronics: materials, devices and simple circuits
- In a p-n junction diode, what happens to the width of the depletion region when the forward bias is increased?
- MHT CET - 2025
- Physics
- Semiconductor electronics: materials, devices and simple circuits
Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance \( R_p = 1 \, \Omega \) as shown in the figure. An external resistance of \( R_e = 2 \, \Omega \) is connected via the sliding contact.
The current \( i \) is :
- JEE Main - 2025
- Physics
- Semiconductor electronics: materials, devices and simple circuits
View More Questions
Notes on Semiconductor electronics: materials, devices and simple circuits
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.