Timeline for How to show that the electrons responsible for a current have an energy within $k_BT$ of the Fermi energy?
Current License: CC BY-SA 4.0
9 events
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| Jun 4, 2019 at 0:38 | comment | added | Jeffrey J Weimer | @Pieter Got it. The number density of free electrons in metals increases almost linearly with temperature. The mobility decreases linearly (or weakly with a square root of T) 1. The decrease in the mobility is greater than the increase in number density. Therefore, around room temperature in metals, conductivity decreases linearly as temperature increases. | |
| Jun 3, 2019 at 20:15 | comment | added | user137289 | @JeffreyJWeimer "Number density increases exponentially with temperature"??? You seem to be confusing metals and semiconductors. | |
| May 31, 2019 at 20:17 | comment | added | untreated_paramediensis_karnik | Thanks for the video Pieter, I'll take a look. Meanwhile I have finally figured out I think! I posted an answer... I am so happy!!! And, your picture was actually very helpful! I considered it in my answer. | |
| May 31, 2019 at 15:10 | comment | added | user137289 | @thermomagneticcondensedboson I was aware that the figure is not directly pertinent to the question. This would be a figure for $T=0$. At higher temperature there was a simulation by Silsbee. I had made a movie of that (text in Swedish), and at the frames linked it shows conduction at finit temperature: youtu.be/Y9Q2vgch490?t=158 | |
| May 31, 2019 at 11:29 | comment | added | untreated_paramediensis_karnik | Thanks for the picture Pieter, but this does not answer the question. In your picture when you calculate F+-F- where F+ is the energy associated to electrons with wavevector kf+kd (most energetic electrons creating the current) and F- is the energy associated to the least energetic electrons that create current (wavevector is kf-kd), you get an energy window around E_F of magnitude proportional to the electric field strenghth and kBT doesn't show up. Please see the Datta's reference... | |
| May 31, 2019 at 11:23 | comment | added | untreated_paramediensis_karnik | These statements are wrong @JeffreJWeimer. Please have a look at figure 1.7.2 of Datta's reference. | |
| May 30, 2019 at 22:45 | history | edited | user137289 | CC BY-SA 4.0 |
added 2 characters in body
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| May 30, 2019 at 22:40 | comment | added | Jeffrey J Weimer | The statements that only electrons above E_F contribute and that more electrons are free as T increases are not wrong. However, electron mobility goes down faster than number density goes up. Both factors are needed. I'd wonder otherwise why not just give the right explanation rather than hand-washing the integrity of the system. | |
| May 30, 2019 at 21:47 | history | answered | user137289 | CC BY-SA 4.0 |