The final should provide an opportunity for you to show your understanding of semiconductors and metals. E vs k relationships play a big role. Where do they come from? Can you utilize them to calculate fermi velocity, fermi boundaries,…? Do you understand the significance of the Brillouin zone? Can you distinguish occupied and unoccupied states?
For semiconductors, the fermi energy is in an energy gap. Do you understand what an energy gap is and what the density of states as a function of energy typically looks like for a semiconductor? Special approximations can be used to estimate carrier density for cases where Ef is in a gap. Other approximations can often be used when Ef is not in a gap. The ability to recognize and distinguish those cases is important. Understanding the nature of those approximations, and what they rely on, is also important.
What is the essential nature and phenomenology of an n-p junction?
What role does shifting of the fermi boundary play in the conductivity of a metal?
Do you understand the origin of ferromagnetism?
I’ll post more here later. I just wanted to get the ball rolling and provide a place for questions and discussion here.Added notes: Perhaps it would be good to have a problem on illuminated n-p junctions. How do you feel about that? What about a ferromagnetism problem.
It might be a good idea to test yourself with Fermi boundaries. You may wish to test your ability to identify where a Fermi boundary crosses the kx axis, realizing that the ky term is not zero when ky=0. (Same thing for the ky axis.)
Equations are show here: (What else do we need? I can't think of very many basic equations from the second part of the class.)
This is an outstanding question. It really captures the essence of the issue. Who can answer it? This will definitely be covered on the final.
ReplyDeleteHi Zack, do you think you can post solutions to HW 8? Or will it not be covered very much?
ReplyDeleteI'll add those solutions to the HW 8 post.
DeleteAlso, the essence of what you need to know about that is also covered well in these comments already.
DeleteFreddy already already provided an excellent answer to this. To give another way of phrasing it, a ferromagnet doesn't want a higher repulsion energy or a higher band energy; it wants to minimize the total energy contribution coming from its band energy and coulomb repulsion energy. As you mentioned, spontaneous spin alignment decreases coulomb repulsion and increases band energy. Normally, a magnet's band energy (positive contribution) will be greater than its coulomb repulsion energy (negative), so the sum of the two will be positive, and spontaneous spin alignment will not occur.
ReplyDeleteHere's what makes ferromagnets behave differently from non-magnetic metals: A narrow enough bandwidth (B<2U) such that the energy contribution from the coulomb repulsion is greater than the energy contribution from the band energy, so if electrons don't spontaneously align (decrease coulomb repulsion and increase band energy), its energy will be negative (bad news). You can see this mathematically above (set band energy + coulumb energy = 0 and see that for B<2U, the total energy will be negative).
I was wondering when can we expect to get the equation sheet for the final. I know that it will expand on the previous one, but was wondering the new formula that will be on it.
ReplyDeletegood point. soon.
Deleteit's there.
DeleteWhat about the formulas for band energy and coulomb repulsion energy in terms of n-up and n-down?
ReplyDeleteAlso, what about the illuminated current formula?
DeleteI'll add those in.
DeleteIs it safe to say that if the fermi boundary shifts, then it would increase conductivity of a metal?
ReplyDeleteI do understand the fact that the fermi boundary indicates the number of occupied states, easily seen in the E vs k and E vs D(E) graphs and apart from calculating the current flow in the system, I feel like there is something more when it comes to this.
I think there will be more on unshifted fermi boundaries than on shifted ones.
DeleteOkie dokes. Thanks!
Deleteok
ReplyDelete"You may wish to test your ability to identify where a Fermi boundary crosses the kx axis, realizing that the ky term is not zero when ky=0. (Same thing for the ky axis.)"
ReplyDeleteIs the second "ky," supposed to be "kx"?
Can we also have an equation or 2 for n(x)? Such as
ReplyDeleten(x) = -n_eq + (n(x_d) - n_eq)e^-((x - x_d)/L)