Energy gap from conductivity- temperature graph

[life is maths]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

I tried to plot a graph according to the formula

E_g= -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.

 

[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,

E_g= -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?