What Mobility is Needed for Diamond to Have Intrinsic Conductivity?

AI Thread Summary
The 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 for conductivity incorporates parameters such as effective mass, temperature, and energy gaps for each material. Initial calculations were hindered by incorrect values for conductivity and the Boltzmann constant, but the correct answer was ultimately reached. The conversation emphasizes the importance of accurate constants and values in semiconductor physics calculations. Understanding these mobilities is crucial for assessing the conductivity potential of diamond.
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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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