Mobility of holes and electrons

[jablonsky27]

hi,
holes are the absence of electrons in the lattice, right? then how come we say holes have a +ve charge? shouldnt it be zero?
also, why is the mobility of electrons more than holes?
thanks

 

[Defennder]

This is what I wrote for another thread:

Consider this in 1D:

We all know that J=nev where n is the concentration of electrons, v is the drift velocity.

Suppose the valence band is completely full of N electrons, then it goes without saying there can be no current flow:


$$J_{x} = \sum_i^N -ev_{i} = 0$$

But on the other hand suppose there is one missing electron, one vacancy in the valence band where an electron should be:

$$J_{x}=\sum_i^{N-1}-ev_{i} = \sum_i^N -ev_{i} -(-ev_{j}) = ev_{j}$$

Notice that the final expression on the right can be thought of as current due to the drift of a single positive charge, since there is no minus sign. That is why we are justified in thinking that we can treat absence of negative charges as positively charged holes.

As for the other question, I'm guessing it's something to do with the magnitude of their effective masses.

 

[jablonsky27]

i should ve searched for that before posting a new thread. it makes sense, yes..

what would the effective mass of a hole be??

 

[maverick280857]

Where would you usually find a hole? And where would you usually find an electron?

Where == which band?

Yes, the effective masses of holes and electrons are different. The mobility is a function of the effective mass, which is a theoretical tool brought in to simplify the description of a charged particle in a crystal. Classically, the concept of an effective mass is analogous to that of a 'psuedo force' in Newtonian mechanics.

In the simplified, http://en.wikipedia.org/wiki/Drude_model" [Broken], for a fixed mean free time.