Energy gap from conductivity- temperature graph...

[life is maths]

1. The problem statement, all variables and given/known data


Hi, I have some values of conductivity in some temperatures.


0.01 at 400 Kelvin
10 at 600 K
70 at 700 K
1000 at 1000 K

And I'm asked to find the energy gap of this intrinsic semi- conductor.


2. Relevant equations



3. The attempt at a solution

I tried to plot a graph according to the formula

Eg= -2k [''Delta''lnn/ ''Delta''(1/T)]
(I tried to put the letter delta, but it does not show up.)

I think it is a graph similar to y= 1/x, but I couldn't figure out how to calculate the energy gap. And I'm not sure my graph is true. Could you please help me? Thanks for your time and effort.
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

[Gokul43201]

Start at the beginning. What is the relationship between conductivity (or carrier concentration) and temperature in an intrinsic semiconductor?

PS: Some useful symbols to copy-paste: δερσΔΩ∑∫∂ (or you can use the built-in latex feature)

[life is maths]

As far as I know,

Eg= -2k\Deltalnn/(1/T)

I don't know any other way. I will try it again now, since the deadline is tomorrow.
I guess I will multiply the slope of lnn-1/T graph by -2k,the Boltzmann constant.

Thanks, Gokul43201. I know the latex stuff a bit, but that day my computer didn't respond well. And I would appreciate any help, since this subject really confuses me.

[Gokul43201]

I guess I will multiply the slope of lnn-1/T graph by -2k,the Boltzmann constant.That should work. Your equation above is correct in that it is generally a good approximation for intrinsic semiconductors above 300K or so.

[life is maths]

Thanks again, Gokul43201, I drew the graph, but I have another question now: Since I need to find the energy gap according to that formula, I get many values from the intervals. Which interval should I use or are there more than one value for energy gap? I'm totally lost.
Thank you.

[ideasrule]

I thought your plan was to plot ln(n) against ln(1/T) and find the slope of the line. If it wasn't, that's certainly the easiest way to do it, because the slope of the line gives Δln(n)/Δ(1/T).

[life is maths]

Yes, you're so very right, ideasrule. How can I do such a foolish mistake? :( Then what way should I use? Thank you.

[ideasrule]

Eg is just -2k times the slope, according to your equation, so that should get you directly to your answer.

[life is maths]

Thanks, but I do not have the concentration values, I only have conductivity and temperature. How am I supposed to find the energy gap from their graph?