Semiconductor Electron Affinity

[magfluxfield]

Hi There,

Im doing a study of MOS capacitors (Semiconductor is 4H-SiC) and I am looking at the interface trap density with respect to temperature (range 300K to around 600K) and also photonic excitation with hv<Eg.

That said, i have a question regarding the temperature dependence on electron affinity, to calculate the flatband voltage shift due to the workfunction difference between the metal and the semiconductor (this does not take into account oxide fixed charges or interface traps) we can use;

$$\phi_{ms}=\phi_{m}-\phi_{s}=\phi_{m}-\left(\chi+\frac{E_{g}}{2}-\psi_{B}\right)$$

where

$$\psi_{B}=E_{F}-E_{i}=kT\exp\left(\frac{N_{D}}{n_{i}}\right)$$

and obviously the intrinsic carrier concentration has a temperature dependance, and also the components of that determining equation also have temperature depandance;

$$n_{i}=\sqrt{n_{c}n_{v}}\exp\left(\frac{-E_{g}}{2kT}\right)$$

For 4H-SiC

$$E_{g}(T)=E_{g}(0)+6.5\times10^{-4}\frac{T^{2}}{T+1300}$$

$$n_{c}=3.25\times10^{15}T^{\frac{3}{2}}$$

$$n_{c}=4.8\times10^{15}T^{\frac{3}{2}}$$

so we can now use these to calculate $$E_{F}-E_{i}=\psi_{B}$$ for various temperatures, which means the $$\frac{E_{g}}{2}-\psi_{B}$$ part is sorted.

However, my question is, the electron affinity must change due to band gap variations with temperature, how can these values for electron affinity be calculated to get a more accurate value for the metal-semiconductor work function difference as this determines the voltage shift in the C-V curve, which is then used to determine the interface trap density.

Any help would be appreciated.

Thanks,

Chris

 

[shawl]

We can not understand the "the electron affinity must change due to band gap variations with temperature".

The electronic affinity is the difference between the bottom conduction band (CB) and the vacuum energy level.
It is independent on band gap and temperature.

 

[magfluxfield]

I agree that the electronic affinity is the difference between the bottom of the conduction band and the vacuum energy level.

However you are mistaken that the band gap is not a function of temperature, as the temperature increases from 300K, the interatomic spacing increases, which lowers the field seen by other atoms, hence reducing the band gap, this reduction can be found by;


[PLAIN]https://www.physicsforums.com/latex_images/30/3001979-3.png

**Note: + should be -, as it is a reduction, and latex for some reason isn't working for me at this second so i had to use the picture of the latex from my previous post.

Where the constant values are fitting parameters and they are valid for 4H-SiC only, there are other values for other semiconductors. Now using the value of the band gap at 300K for Eg(0), it is possible to calculate the reduction in band gap for increased temperature 'T'.

So, the band gap reduces with temperature, now, thus if the conduction band and or valence band will move. Now, if the conduction band moves due to the shrinking of the band gap (i do not know wether the valence band comes up only, the conduction band goes down only or they both change in proportion), this will have an effect on the electron affinity.

I am guessing that the conduction band stays the same and the valence band comes up, but I am not sure. That would mean the electron affinity would remain constant, which is fine, but I would like to know for sure.

Now in regard to the semiconductor work function, all of the terms in the equationmust be used as the work function is defined thus (see Schroder or Nicollian & Brews);
[PLAIN]https://www.physicsforums.com/latex_images/30/3001979-0.png

Now this assumes the only non ideality, this would be the flatband shift if the fixed oxide charge, trapped oxide charge and mobile ionic charges along with Dit were neglected.

I made a mistake in my pervious post about the work function difference being a function of the mentioned non idealities, i meant to say the flat band voltage shift!

 

[shawl]

yes, I misunderstood your problem.

I am not familiar with the SiC.

But I give a paper searched on google.

Find the attachment PLZ.

 

[shawl]

Here is a website for the 4H-SiC theory.

http://www.iue.tuwien.ac.at/phd/ayalew/node56.html

I think you may find your answer there