Mobility of holes and electrons

In summary: A long-lived particle with an effective mass m will have a smaller mean free path than a short-lived particle with an effective mass m' due to the greater Coulomb interaction between the two particles.
  • #1
jablonsky27
74
0
hi,
holes are the absence of electrons in the lattice, right? then how come we say holes have a +ve charge? shouldn't it be zero?
also, why is the mobility of electrons more than holes?
thanks
 
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  • #2
This is what I wrote for another thread:

Defennder said:
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:


[tex]J_{x} = \sum_i^N -ev_{i} = 0[/tex]

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

[tex]J_{x}=\sum_i^{N-1}-ev_{i} = \sum_i^N -ev_{i} -(-ev_{j}) = ev_{j}[/tex]

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.
 
  • #3
i should ve searched for that before posting a new thread. it makes sense, yes..

what would the effective mass of a hole be??
 
  • #4
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 into 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.
 
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1. What is the difference between holes and electrons in terms of mobility?

Holes and electrons have opposite charges and behave differently when subjected to an electric field. Electrons, which have a negative charge, are able to move freely through a material, while holes, which are essentially the absence of an electron, move in the opposite direction of the electric field.

2. How does temperature affect the mobility of holes and electrons?

Increasing the temperature of a material causes an increase in the mobility of both holes and electrons. This is because higher temperatures provide more energy for the particles to move, allowing them to move more quickly and easily through the material.

3. What factors can affect the mobility of holes and electrons?

The mobility of holes and electrons can be influenced by various factors, such as the type of material, impurities present, and the strength of the electric field. Additionally, the size and shape of the material can also affect the mobility of particles.

4. How is the mobility of holes and electrons measured?

The mobility of holes and electrons can be measured by conducting experiments, such as the Hall effect, which involves applying an electric field and measuring the resulting voltage and current. The ratio of the two values can then be used to calculate the mobility of the particles.

5. What is the significance of understanding the mobility of holes and electrons?

The mobility of holes and electrons is an important concept in the study of semiconductors and other materials used in electronic devices. Understanding the behavior of these particles allows scientists and engineers to design more efficient and effective electronic components, leading to advancements in technology.

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