# Semiconductor band structure, electrons moving between valleys from thermal energy

1. Jan 22, 2012

### cr2504life

I dont really understand the valleys in the conduction band, in the E vs. k diagram, there is the L-valley, r-valley and X-valley. Each has a different momentum... and are at different energy levels.

I understand that at any temperature above absolute zero, a small fraction of electrons will acquire enough energy to jump to the conduction band (overcome the energy gap Eg).

The GaAs bandstructure here:

http://www.ioffe.ru/SVA/NSM/Semicond/GaAs/bandstr.html

I assume most electrons which acquire enough energy will jump to the lowest valley in the conduction band (r-valley for GaAs).

Ive been trying to determine what is the 'effective' temperature necessary to move an electron from the r-valley to the L-valley, the difference is 0.29 eV in GaAs.
Is the additional thermal energy comming from E = kT ?
... therefore T = 0.29eV*q/(k) ??? this is a large temperature .... this seems too large ~3,600 °K.

How do the electons move between valleys ? And how does one find the required energy for this to take place ?

Last edited: Jan 22, 2012
2. Jan 27, 2012

### Kholdstare

Re: semiconductor band structure, electrons moving between valleys from thermal energ

Although you can tell the required amount of energy an electron needs to jump from valance band top to the conduction band top, you cannot straightforward associate a temperature for this using E=kT. The electrons in a solid are distributed according to Fermi distribution function. And even in the room temperature (kT=0.026meV) a portion of the the Fermi function will reach conduction band. Hence quite handful of electrons will occupy above the conduction band.
http://en.wikipedia.org/wiki/Fermi–Dirac_statistics

3. Feb 1, 2012

### cr2504life

Re: semiconductor band structure, electrons moving between valleys from thermal energ

I see from the solution now that the 'effective' temperature of an electron which moves from the r-valley to the L-valley is equal to T = 0.29eV*q/k ~ 3600 K, I had done this correctly.

4. Feb 1, 2012

### Dr Transport

Re: semiconductor band structure, electrons moving between valleys from thermal energ

Math correct, physics wrong. Think about it, 3600 K, most likely GaAs is a vapour at that temperature, the melting point is 1240 C (1530 K). For an electron to move between the $\Gamma$-point and L-point of a lattice requires a phonon assist.