Is the Fermi Level in Metals Crucial for Understanding Conductivity?

[Jimmy87]

Hi,

I have started looking at the fermi level and how it relates to the behaviour of conductors. It is my understanding from what I have read that the fermi level is the top of the fermi sea of filled energy states when the material is at T = 0K.

1) Is the fermi level inside the conduction band for metals? Also, when the temperature is lower it seems to say that lower energy states are filled. Would this mean there are less conduction electrons? I thought conductivity increased with a fall in temperature?

2) Some metals have greater free electron densities. Is this linked to their differences in fermi energy levels, i.e. a bigger fermi energy level would mean it would be higher in the conduction band and hence more free electrons available or is this not a good way to look at it?

Thanks.

 

[Simon Bridge]

1. For a conductor, the conduction and valence bands overlap. So, for a metal, there are always electrons in the conduction band.
The occupation of states is governed by Fermi-Dirac statistics - the effect of higher temperature is to promote electrons to higher unoccupied states, leaving empty states below. It follows that lower temperatures correspond to more filled lower energy states. Higher energy corresponds to more vigorous random motion of individual charges... so it would be harder to get them to head off in about the same direction. Compare with herding sheep (cats, small children, respectable physicists...) - it is easier to get them where you want them to go if they are not running madly all over the place.

2. All other things remianing equal, the higher densities cause the higher fermi level.
Strictly, higher fermi level metals just have a smaller work function.

In a way you can think of the metal like a swimming pool, the charges are the water, and the fermi level is the surface of the water. The height of the ground would be the external applied potential.
One pool may have a higher water surface than the one next to it, but it may be a shallower pool, or it may just be on a hill.

 

[DrDu]

1) Is the fermi level inside the conduction band for metals? Also, when the temperature is lower it seems to say that lower energy states are filled. Would this mean there are less conduction electrons? I thought conductivity increased with a fall in temperature?
.

The number of electron in the conduction band is quite independent of temperature in most metals. What changes is the distribution of electron occupancy inside the band. If the occupation were homogeneous, e.g. at high temperatures, although the band is not filled, there will be no net current.