Band Theory of Solids: Basic Concepts Explained

[manofphysics]

I am reading the Band Theory of solids.Now, my question is on the basic concepts:
{1}When energy is given to a solid, the electrons bound to the respective atoms move from the valence band to the conduction band and hence conductivity of material increases.

{2}But we know that when we give energy to a solid, each atom as a whole starts to vibrate and finally when the energy becomes more, atoms move far apart and solid changes to liquid.

Now when we give energy to a solid, does {1} and {2} happen simultaneously or whether {1} happens first and then {2} happens?

 

[kanato]

I assume when you say 'give energy' you mean specifically increasing the temperature.

Yes, both happen simultaneously. (1) is the excitation of electrons, and (2) is the excitation of the lattice. Typically, in an insulating material the gap is so large that (1) happens very little before you reach the melting point. For semiconductors (1) can happen at temperatures reasonably well below the melting point, and of course for metals there is no gap, so (1) begins to happen right above T = 0 K.

 

[manofphysics]

Yes of course ,I meant increasing the temperature. Thanks a lot for your answer , kanato.

 

[sokrates]

I assume when you say 'give energy' you mean specifically increasing the temperature.

Yes, both happen simultaneously. (1) is the excitation of electrons, and (2) is the excitation of the lattice. Typically, in an insulating material the gap is so large that (1) happens very little before you reach the melting point. For semiconductors (1) can happen at temperatures reasonably well below the melting point, and of course for metals there is no gap, so (1) begins to happen right above T = 0 K.

Just a little correction: In metals, the fermi level is above the conduction band, and due to the exclusion principle, the conduction band is already filled with electrons at T = 0K so there's no need to excite them.

Essentially there's no (1) in metals.

 

[kanato]

Well, to clarify, in metals, the fermi level is somewhere inside the conduction band, so you get electrical conduction regardless of whether electrons are excited. But excitation of electrons in a metal still happens, and it actually dominants the heat capacity of a metal at low temperature, whereas for nonmetals the heat capacity is almost entirely due to the lattice vibrations and electronic effects are rather difficult to detect.

 

[manofphysics]

Yes,kanato, I also read that conduction band overlaps valence band( not always fully) so effectively electrons CAN excite even in metals, to the conduction band. And I assume when you say low temperature, you mean about room temperature at which conductivity is measured?

 

[kanato]

No, I mean near 0 K. At room temperature, the lattice vibrations dominate the specific heat capacity for pretty much any material.