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This upcoming semester I'll be taking my first course in Semiconductor physics and I'm studying out of the textbook independently this summer to prepare myself.

I've been learning about energy bands and I wanted to clarify a couple of concepts that my text is rather vague on:

1. What exactly are k and crystal momentum? I know ħ*k is the crystal momentum, with units kg*m/s, and k has units kg*m/(J*s^2), but I'm not sure if I'm interpreting them correctly. I've been more or less treating k as just the momentum of the electron when I consider E versus K diagrams but is that, for want of a better word, correct?

2. How does (1/ħ)dE/dk give rise to the velocity of the particle? I've been staring at the derivation for days, and I see exactly where it comes from, but intuitively it doesn't make sense. I may be guilty of taking basic concepts of momentum too far into quantum mechanics, but isn't the velocity of the particle a component of momentum? Is the velocity given different then the velocity of the particle in k? Or do I need to readjust my concept of momentum?

3. I can see that (1/ħ)^2*d^2E/dk^2 = 1/m. If we multiply that by the electric force of the electron (-e*E, where -e is the electron charge, and E is the applied field), we have acceleration (F/m). Is it reasonable to consider the second derivative of E with respect to k proportional to the acceleration of the particle?

Any good introductory sources online I can check out to better familiarize myself with these concepts? Cheers!

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# E versus K diagrams

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