# Does the Fermi level change under change of temperature, voltage or other conditions?

From a previous post with similar title, (What's the difference between Fermi Energy and Fermi Level?) I think it is safe to assume that

1. In a block of material, Fermi energy is the level, up to which, electrons will fill all the available states, @ T = 0.

2. In a block of material, in room temperature, electrons will be exited and recombined all the time. at the "Fermi level" there is 50% chance that an electron can be found there.

My questions are now

1. For the same block of material, does the Fermi level change when the block is subject to temp change, external voltage, etc? I think it should.

2. For the same block of material, should the Fermi energy should remain the same, i.e. is it an intrinsic property of that material, just like mass?

3. When you write down the Fermi Function, in the exponential term $\frac{E-E_f}{KT}$, what is $E_f$? The Fermi level or the Fermi energy?

I am getting misleading information from the internet: http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html

• The hyperphysics article is a bit misleading since they always draw fermi level precisely at midgap, whereas in reality they can be higher or lower than one another depending on doping and other details. – Nanite Mar 30 '15 at 7:40

## 1 Answer

1. The Fermi level is insensitive to temperature changes. It does change upon external voltage. Strictly speaking, a Fermi level can only be defined in equilibrium. If you apply some voltage, resulting in current, you will have two or more quasi-fermi levels, associated with your external contact potentials.

2. The Fermi level is intrinsic in the sense that it is well-defined for a certain material. However, it can change with the doping or impurity level (which is also true for the effective mass).

3. The Fermi energy is just the Fermi level, expressed on an energy scale. So they are identical.

• thank you for the answer. I thought "all electrons would shift up when T>0, so that the lowest states are no longer filled, and fermi level would shift up too". So that was wrong then. The true behavior is :"when T>0, low level states remain filled, only around fermi level electrons and empty states pairs are created" My only lingering question would be: if you have a pure block of Si, and a bigger block of pure Si, will their fermi energy/level and valance band's height and thickness be absolutely identical or there will be some tiny tiny differences? thanks – YunliuStorage Mar 30 '15 at 22:21
• Fermi energy is a statistical concept, why should it depend on temperature? – Draco_1125 Aug 27 '17 at 13:16