Fraction of valence electrons free for conduction

[jisbon]

Homework Statement

The intrisinc carrier concentration of single crystal sillcon is $(1.5*10^{10})$ per cubic centimeter.
Bandgap is 1.1eV and density is 2.33g per cubic centimeter.
How many free electron and holes are there per cubic centimeter.
Determine the fraction of valence electrons that are free for conduction at room temperature. Explain where electrons get sufficient energy from in order to be free.

Relevant Equations

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For the first part, since this is a intrisinc semiconductor, n=p= intrisinc carrier concentration. Hence free electrons and hole = $(1.5*10^{10})$ per cubic centimeter.

As for part 2, here are my steps. But I'm not sure if it's correct.
I first find the number of atoms of one cubic centimeter of sillcon, (using density and atomic mass of sillcon) then multiply it by 4 (since there is 4 valence electrons per sillcon atom?) I then take :
$(1.5*10^{10})$ divided by the number of valence electrons as calculated above. Is this thought process correct? Thanks

 

[Cutter Ketch]

The process you describe is correct except, in both parts of the question, you need to consider what it means that there are both electrons AND holes.

 

[jisbon]

The process you describe is correct except, in both parts of the question, you need to consider what it means that there are both electrons AND holes.

For the first part, isn't the n=p for an intrisinc semi conductor? Hence my answer theoretically should be correct for part 1?

For the second part, since there are only considering fraction of electrons, won't it only be just the concentration of electrons divided by the total number of electrons? Why are holes being mentioned?

Thanks

 

[Cutter Ketch]

You keep saying half of them are holes and half of them are electrons (true) and then ignoring that fact when someone asks “how many electrons are there”

 

[jisbon]

You keep saying half of them are holes and half of them are electrons (true) and then ignoring that fact when someone asks “how many electrons are there”

Pardon, but I stated that n = p = ni in an undoped semiconductor, which means three of them have the same values?

 

[haruspex]

You keep saying half of them are holes and half of them are electrons (true) and then ignoring that fact when someone asks “how many electrons are there”

Are you implying that intrinsic carrier concentration is calculated from the sum of electrons and holes? Not an area I know anything about, but that doesn't seem to match what I read on the web.

 

[Cutter Ketch]

Are you implying that intrinsic carrier concentration is calculated from the sum of electrons and holes? Not an area I know anything about, but that doesn't seem to match what I read on the web.

That is EXACTLY what I am implying! (and, as it happens, I am exactly wrong, so I’ll shut up now)

 

[jisbon]

Was a bit confused by the replies... Was just wondering if anyone could check my concepts and tell me if the steps I did were proper. Thanks

 

[haruspex]

Was a bit confused by the replies... Was just wondering if anyone could check my concepts and tell me if the steps I did were proper. Thanks

Cutter Ketch only had one objection to your method, and he has withdrawn that. Your method is fine as far as I can tell, but it's not a subject I know.