Conductivity of a semiconductor charged with externally added electrons

[itler]

Conductivity of a semiconductor charged with "externally added" electrons

Hi,

how does it influence the conductivity of a semiconducting sphere (I take a sphere as it should make some considerations easier than for a cylindrical wire) if I add external charges to it? Don't know how this could be done, maybe by beta radiation, maybe by mechanical friction. Doing so would increase the electron density in the material and so should increase conductivity?

Some considerations about order of magnitude:

Total charge on the sphere due to intrinsic carriers in SI
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- Radius = 2.5cm --> Volume ~65cm^3
- electron density in SI ~1e10 / cm^3 --> Total charge on the sphere is about 6.5e11 electrons = 1e-7 Coulomb

Voltage needed to add an amount of charge comparable to intrinsic
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- sphere diameter 5cm --> capacitance of about 2.8e-12F

----> Voltage needed to put 1e-7 Coulomb on a 2.8e-12F capacitor is about 36.000V

So from a voltage point of view it seems realistic to add the same amount of charges onto the sphere as there is due to SI intrinsic carriers?? This should raise the conductifity significantly. I'm almost sure that I forgot something, but what??

BTW in this thought experiment, where would the "added" electrons be placed? In the sphere volume or on it's surface? And if on the surface, why do the intrinsic carriers not settle there as well?
~
"question" 16L, 947C

 

[Mapes]

I think you are confused between the idea of adding charge and increasing the number of charge carriers. We can increase the conductivity of silicon by increasing the number of carriers (for example, by shining light on the sample, which excites electrons into the conduction band) without adding charge or changing the overall neutrality. The conductivity can be expressed as $\sigma=(\mu_e n+\mu_h p)e$ where the $\mu$'s are the mobilities of electrons and holes, $n$ is the number of conducting electrons, $p$ is the number of conducting holes, and $e$ is the unit of electric charge. Does this help?

 

[itler]

Hi,

that's also an interesting aspect, yes. But wouldn't it - at least theoretically - also be possible to really increase the number of electrons in total? Maybe by putting the semiconducting sphere close to a strong corona discharge "blowing" electrons onto it? These additional electrons should also be in the conduction band and contribute to the "n" in your formula?

 

[Mapes]

It certainly seems possible. I suppose the added electrons would electrostatically repel each other towards the surface, as you suggested. Perhaps this would serve to increase the conductivity directly at the surface, but now I'm just speculating. Hopefully someone with more experience can weigh in.

It occurs to me that this is another argument against using intrinsic silicon; besides the exceptionally high purity needed, now you have a material that changes its properties if someone takes off a wool sweater nearby!

The standard argument for why the intrinsic electrons don't repel each other to the surface is that there is an equal number of intrinsic holes that attract them. In the case of extrinsic electrons (from added phosphorus, say), it's the extra proton in each nuclei of the dispersed P atoms.