I'd like to Know more about Conductors

[iScience92]

Hi, I was hoping to get some pointers/ references for the following:

I'm trying to learn about the force that an electron experiences while in a conductor. When bound to a conductor, it's essentially in potential well.

My goal is be able to model this potential well to manipulate it. I'm trying to get an electron to physically leave its conductor but i don't want to just blindly "do it," i want to understand it.



Thanks in advance

[ajb]

You should look up condensed matter physics and the notion of bands.

[studiot]

 

You should look up condensed matter physics and the notion of bands.

 

 

Yes the 'drude model' would be appropriate.

 

http://en.wikipedia.org/wiki/Drude_model

[ajb]

Yes the 'drude model' would be appropriate.

 

http://en.wikipedia.org/wiki/Drude_model

Indeed, then one should look at the quantum mechanical version, the so-called Drude–Sommerfeld model.

[Enthalpy]

[...]an electron to physically leave its conductor [...]

 

If the emission of an electron is the only goal, then one doesn't need too detailed models of the conductor. All models for the emission

http://en.wikipedia.org/wiki/Field_electron_emission

http://en.wikipedia.org/wiki/Thermionic_emission

suppose only some sort of work for the electron to leave the metal

http://en.wikipedia.org/wiki/Work_function

and optionally a kinetic energy for the electrons in the metal.

 

Though, condensed matter is interesting in itself.

 

By the way, field emission is often done by one single atom at a tip (LaB6, tunnel microscopes...) but people boldly apply models of bulk materials (as far as I know) combined with field concentration at the tip. Maybe a better model, where the tip atom is not treated as bulk, could bring something.

[Enthalpy]

Models of metals or solids used for electron emission are sometimes more evolved than a potential well or an electron work function, because the anisotropy of the crystal has an important influence.

 

The work function if often measured for one or several specified crystal orientations with important differences. It still matters for polycrystalline materials since the emission zone is often tiny - even if the intended emission zone is broad, several 100meV difference in the work function mean that the emission occurs at the favoured orientations.

 

Then, the bands in semiconductors are not isotropic. In non-stresssed GaAs they are but in Si, Ge and many more the conduction "band" is a mean of several valleys where the conduction electrons at minimum energy have a strong (and oriented) wave vector. For bulk conduction, all valleys sum to the equivalent of isotropic conduction, but for electrons flowing through a surface, where the wavevector's components perpendicular and parallel to the surface count separately they don't. This is known and modelled for heterojunctions which are produced and observed accurately, less so for electron emission. Valence bands would have been simpler but are bad electron emitters. Metals, with their complicated bands, make it more difficult; free surfaces as well, because they're always dirty.

 

Electron emitters had been prototyped where avalanche (did they try heterojunctions as well?) injected hot electrons (kinetic energy well above the conduction band minimum) in a zone near the emitting surface. The hot electrons missed less energy to reach the vacuum level. These devices did show electron emission from a cold material but they didn't generalize.

 

Usual emission models like Fowler-Nordheim don't use these refinements and are known to be rough approximations, where the dependance on T and V is good to keep but the fixed coefficient is seriously inaccurate.

 

Rugosity makes it worse. Usually it's unavoidable, since polishing generally replaces few big hills by many smaller ones that concentrate the field just as well. Since electron emission is so sensitive to the field right at the surface, the rugosity is paramount but it's difficult to characterize.

 

Insulation by vacuum is presently very important to technology but poorly understood. Usual models concentrate on electron emission, especially field emission, but their inaccuracy suggests that this is not the only important effect.