What Is the Relationship Between Band Gap and Temperature in Germanium?

[physfan]

Homework Statement

[Edit: Please also see additional posts below. I have tried to clarify my question somewhat but didn't want to edit this one just incase anyone can help with the full problem.
Thanks! :) ]

I did a lab on the band gap in germanium where I measured the voltage across a germanium sample over various temperatures and my final result is in agreement with values found online - in the region of 0.74eV - which I obtained from the gradient of the graph produced when I plotted ln(V/I) against 1/T.
I haven't covered band gaps in lectures yet so don't completely understand the theory behind it, but I do know that the band gap varies with temperature, that at low temperatures the band gap is constant and that band gaps can be approximated linearly at temperatures of around room temperature and higher.
Is the value I obtained (0.74eV) the y-intercept of the linear approximation Eg against T? And why does this approximation not work for very low temperatures?

Homework Equations

I used ln(V/I)=Eg/2kT + c where V is the voltage measured at certain temperatures (T), I is 5mA, Eg is the energy gap, k is the Boltmann constant and c is a constant.

I also found Eg(T) = Eg(0)-aT^{2}/(T+B) online and found a worked example for germanium online but I'm reluctant to introduce this into my report as there is nothing like this in my lab script and I don't know how to find the constants a and B. From what I understand a is the gradient the gradient of the graph of Eg against T.

The Attempt at a Solution

I've had a look online but can't find much to help at a basic enough level. See above for bits of research attempts, though most of my attempts consist of racking my brain but not getting very far.

 

[physfan]

If there's any more information I can give to help please let me know

 

[physfan]

If the full query can't be answered can someone please just explain why the energy gap against temperature can be approximated linearly at room temperature and higher like this
http://ece-www.colorado.edu/~bart/book/book/chapter2/ch2_3.htm#tab2_3_1

but is in reality more like this
http://www.ioffe.ru/SVA/NSM/Semicond/InN/figs/guo941.gif

(The y-intercept I was referring to in my first post is the y-intercept on the graph of the first websites linked above.)