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Electronic Devices question

2017 · 8 Apr · Shift 1 · Q53
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Electronic Devices question

2017 · 8 Apr · Shift 1 · Q53

JEE MainPhysicsElectronic DevicesMCQ+4 / −1
What is the conductivity of a semiconductor sale having electron concentration of 5×1018  m−3,5 \times {10^{18}}\,\,{m^{ - 3}},5×1018m−3, hole concentration of 5×1019  m−3,5 \times {10^{19}}\,\,{m^{ - 3}},5×1019m−3, electron mobility of 2.0 m2 V −-− 1 s-1 and hole mobility of 0.01 m2 V −-− 1 s −-− 1 ? (Take charge of electronas 1.6 ×\times× 10 −-− 19 c)
  1. A
    1.68 (Ω\OmegaΩ-m) −-− 1
  2. B
    1.83 (Ω\OmegaΩ-m) −-− 1
  3. C
    0.59 (Ω\OmegaΩ-m) −-− 1
  4. D
    1.20 (Ω\OmegaΩ-m) −-− 1
View written solutionFree

Correct answer: A

  1. Use the conductivity formula for a semiconductor

For a semiconductor with both electrons and holes contributing,

σ=e(nμe+pμh)\sigma = e\left(n\mu_e + p\mu_h\right)σ=e(nμe​+pμh​)

where:

  • e=1.6×10−19 Ce = 1.6 \times 10^{-19}\,\text{C}e=1.6×10−19C
  • n=5×1018 m−3n = 5 \times 10^{18}\,\text{m}^{-3}n=5×1018m−3
  • p=5×1019 m−3p = 5 \times 10^{19}\,\text{m}^{-3}p=5×1019m−3
  • μe=2.0 m2V−1s−1\mu_e = 2.0\,\text{m}^2\text{V}^{-1}\text{s}^{-1}μe​=2.0m2V−1s−1
  • μh=0.01 m2V−1s−1\mu_h = 0.01\,\text{m}^2\text{V}^{-1}\text{s}^{-1}μh​=0.01m2V−1s−1
  1. Calculate each contribution

Electron contribution:

nμe=(5×1018)(2.0)=1.0×1019n\mu_e = (5 \times 10^{18})(2.0) = 1.0 \times 10^{19}nμe​=(5×1018)(2.0)=1.0×1019

Hole contribution:

pμh=(5×1019)(0.01)=5×1017p\mu_h = (5 \times 10^{19})(0.01) = 5 \times 10^{17}pμh​=(5×1019)(0.01)=5×1017

Now add them:

nμe+pμh=1.0×1019+5×1017n\mu_e + p\mu_h = 1.0 \times 10^{19} + 5 \times 10^{17}nμe​+pμh​=1.0×1019+5×1017 =1.05×1019= 1.05 \times 10^{19}=1.05×1019
  1. Multiply by charge eee
σ=(1.6×10−19)(1.05×1019)\sigma = (1.6 \times 10^{-19})(1.05 \times 10^{19})σ=(1.6×10−19)(1.05×1019) σ=1.68 (Ω⋅m)−1\sigma = 1.68\, (\Omega\cdot \text{m})^{-1}σ=1.68(Ω⋅m)−1
  1. Match with the options
σ=1.68 (Ω⋅m)−1\boxed{\sigma = 1.68\,(\Omega\cdot m)^{-1}}σ=1.68(Ω⋅m)−1​

So the correct option is:

A\boxed{\text{A}}A​
  1. Comparison with stored correct answer

Stored correct answer: A

Our derived answer: A

Hence, the derived answer agrees with the stored correct answer.

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