I’m trying to figure out the connection between the 1-D KE equation, E=.5mv^2 and the Einstein Relation of Dn/mu=kT/q .
I know it’s got something to do with the thermal velocity of an electron but that’s as far as I can get with it. I can’t figure out how to go from the KE equation down to the ER and include the q in teh euation
Any ideas?
This form of the Einstein relation looks unfamiliar to me. First off, are you sure that’s an “n” and not an “eta” (?)? An ? term tends to show up in situations where particles are drifting through a viscous medium. The charge q, on the other hand, tends to show up when talking about electrical conduction. I can’t say as I’ve ever seen a version which includes both of them.
What you need to do first is define all these symbols you’re throwing around, and possibly tell us where this question came from in the first place. Only then do we stand a chance of saying anything sensible at all.
Also: if we can add “edit” functionality to the board can we also get it to recognize extended character sets? This is the only place I’ve seen on the web that I can’t type something as simple as an eta.
I think the “Dn” is probably D[sub]n[/sub], the diffusion constant for electrons in a semiconductor (as distinguished from D[sub]p[/sub], the hole diffusion constant).
D / mu = k T / q
is the usual form for the Einstein relation in a semiconductor (where mu is the electron mobility mu = v[sub]d[/sub] / E, E the electric field and v[sub]d[/sub] the resulting drift velocity).
It sounds as though you’re looking for some connection between this equation and the electron thermal velocity v[sub]T[/sub]. But if you know v[sub]T[/sub] I would think the answer would be fairly obvious. What is v[sub]T[/sub]? What is the electron’s thermal kinetic energy m[sub]e[/sub] v[sub]T[/sub][sup]2[/sup] / 2? Actually, what is the thermal energy of any single degree of freedom? This Wikipedia page might provide some clues.