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Molecules and Crystals

Problem 6.210

The resistivity of an impurity-free semiconductor at room temperature is ρ=50Ω⋅cm,\rho=50 \Omega \cdot \mathrm{cm}, It becomes equal to ρ1=40Ω⋅cm\rho_{1}=40 \Omega \cdot \mathrm{cm} when the semiconductor is illuminated with light, and t=8 mst=8 \mathrm{~ms} after switching off the light source the resistivity becomes equal to ρ2=45Ω⋅cm.\rho_{2}=45 \Omega \cdot \mathrm{cm} . Find the mean lifetime of conduction electrons and holes.

Reveal Answer
τ=t/ln⁡(ρ−ρ1)ρ2(ρ−ρ2)ρ1=0.01 s\tau=t / \ln \frac{\left(\rho-\rho_{1}\right) \rho_{2}}{\left(\rho-\rho_{2}\right) \rho_{1}}=0.01 \mathrm{~s}
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