What Mobility is Needed for Diamond to Have Intrinsic Conductivity?

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SUMMARY

This discussion focuses on calculating the mobilities of electrons and holes in grey tin, silicon, and germanium, as well as determining the necessary mobility for diamond to achieve an intrinsic conductivity of 10-12 S m-1. The formula used is σ = Nc (eμnμp)exp(−Eg/2kT), where σ represents conductivity, Nc is the effective density of states, e is the elementary charge, and Eg is the bandgap energy. The correct values for conductivity and the Boltzmann constant were initially misapplied, but the correct calculations were confirmed, leading to accurate mobility results.

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Problem:
Calculate mobilities of electrons and holes (assuming equal) in grey tin, silicon and germanium. Calculate also the mobility that would be necessary for diamond to have an intrinsic conductivity of 10-12 S m-1 if the hole and electron mobilities were equal.

Working:
\sigma = Nc (e\mun*e\mup)exp(−Eg /2kT)

\sigma= 10-12
e = 1.6*10 -19
k = 1.38*10 -23
T = 300K
Nc = 2.5*1025
Eg(tin) = 0.08
Eg(silicon) = 1.11
Eg(germanium) = 0.66

For tin
Rearrange to give:

\munp = \sigma / 2e Nc exp(−Eg /2kT)

The exponential becomes equal to zero...

I'm quite sure I'm missing something relatively simple here but not sure what
 
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It appears i was using wrong values for the conductivity and Boltzmann constant, got the correct answer now.
 

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