Electrons in the Band Gap

Karthikeyan

Hi all,
We say the energy difference between the Top of Valence band and the bottom of Conduction band as the forbidden gap or Band gap. But when we see the fermi level at zero Kelvin, its exactly at the middle of the band gap. Does this mean that there is possibility for an electron to occupy some of the energy level in the forbidden gap?? Please clarify.

ZapperZ

In the strictest sense, there really is no "Fermi level" in a semiconductor and band insulators. This is because the term "Fermi level" is defined for the occupied electron states in metals. Many books (and I do this also myself) are sloppy with their notation. In semiconductors and band insultators, what it should really be called is the "chemical potential".

So no, there are no states in the gap. However, under certain circumstance, you might have a pseudostable energy state that may be occupied in the gap, as in the case of an exiton. However, this state is NOT due to the band structure of the material (which is still empty), but rather due to the hydrogenic energy level created by the electron-hole pair. This should never be confused as the energy state originating from the material itself.

Zz.

Karthikeyan

Thanks...In most of the Semiconductor Physics Textbooks, they say that the probability of finding an electron at Fermi Energy ( Chemical Potential, as you say ) is 0.5. What does this mean?? and why should the probability curve is symmetric about the fermi level (i.e 0.5 probability) above zero Kelvin ??

ZapperZ

Again, they are using the terminology carried over from metals. Look at the Fermi level for a metal. At T>0 K, the Fermi function will start to evolve from a step function, to a rounded curve at the top and a tail at the bottom foot. At any temperature, the probability (which corresponds to the occupation number Fermi function) is always half.

So what your text is doing is to carry over that definition into the semiconductor, which is what I said before. It isn't entirely wrong if you "extrapolate" the statistics of the occupation number in the valence band and the conduction band of the semiconductor, but it is sloppy and confusing to say that, since obviously, there are NO states in the gap.

Zz.

Witchukorn

Does that mean I cannot really calculate the absolute value (number) of the so-called Fermi level in semiconductor e.g. Si, like we can in Metal? All I know are its the band gap which is 1.12 eV and the formula that relates position of the so-called Fermi level to conduction and valence band edge energy, temperature and effective density of states (in terms of effective mass).
I wonder if it is legitimate to calculate the valence band edge energy first at T = 0 K using the same method as in calculating Fermi energy for metal. We do not know the density of states of electron in bonds. It looks like free electron model that we used to derive the density of state doesn't work in this case because all electron are bonded. Can anyone confirm this for me?

ZapperZ

Wow. I hope you know that you're asking in a thread that had its last activity in 2006! Pay attention to the DATE of the post.

Secondly, I don't understand your question. All energy levels are measured with respect to something. Often one designates the energy of the Fermi level to be zero, and so everything else is measured from there. So insisting on an "absolute value" is a bit like asking for an absolute value of a potential energy. Your "zero" could be different than my "zero".

Zz.

zhanhai

So should we say that a "chemical potential" can not be truely defined such as in a semiconductor and band insulators, because it can be anywhere between the upper and lower edges of the band gap?

ZapperZ

You can define a chemical potential, but not a Fermi level, in the strictest sense.

Zz.