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

In summary, the student attempted to find the y-intercept of a linear approximation of the energy gap against temperature, but found that it was more complicated than that. At low temperatures the energy gap is constant, but at higher temperatures it is more approximate.
  • #1
physfan
13
0

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[tex]^{2}[/tex]/(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.
 
Last edited:
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  • #2
If there's any more information I can give to help please let me know :smile:
 
  • #3
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.)
 

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

1. What is the purpose of studying the band gap in germanium?

The band gap in germanium is an important property to understand because it affects the electrical properties and performance of devices made from this material. By studying the band gap, scientists can gain insight into the behavior and potential applications of germanium in various technologies.

2. How is the band gap in germanium typically measured in experiments?

The band gap in germanium is typically measured using techniques such as optical absorption, photoluminescence, and electrical conductivity measurements. These methods involve exposing the germanium sample to light or an electric field and measuring the resulting changes in energy levels.

3. What factors can affect the band gap in germanium?

The band gap in germanium can be affected by factors such as temperature, stress, and impurities. For example, at higher temperatures, the band gap decreases due to increased thermal energy, and the presence of impurities can also alter the energy levels in the material.

4. What is the relationship between the band gap in germanium and its electrical conductivity?

The band gap in germanium is inversely related to its electrical conductivity. This means that as the band gap decreases, the material becomes more conductive. In other words, the smaller the band gap, the easier it is for electrons to move through the material and conduct electricity.

5. How does the band gap in germanium compare to other materials?

The band gap in germanium is smaller compared to other commonly used semiconductors such as silicon. This makes germanium useful for certain applications where a smaller band gap is desirable, such as in infrared detectors. However, its smaller band gap also means that germanium is not as efficient in converting light into electricity as some other materials.

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