# Tag Info

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Any good book in Semiconductor Physics will have a description of the k.p method. Try Fundamentals of Semiconductor Physics by Peter Yu and Manuel Cardona. Another reference for Kane Model and EFA are chapters 2 and 3 of "Wave Mechanics Applied to Semiconductor Heterostructures" by Gerald Bastard. If you want a more mathematically/group theory oriented ...

6

Yes, your interpretation heuristically makes sense. As you may already know, as a consequence of Heisenberg's uncertainty principle, that an electron has a wave and particle nature. When you think of the wave nature of single particle states you are talking about Bloch states. When you're thinking about the particle nature you are talking about Wannier ...

5

If you consider a typical metal the highest energy band (i.e. the conduction band) is partially filled. The conduction band is effectively continuous, so thermal energy can excite electrons within this band leaving holes lower in the band. At absolute zero there is no thermal energy, so electrons fill the band starting from the bottom and there is a sharp ...

4

There is no proof of bulk-boundary correspondence for topological phases in general. In fact, topological phases like toric code model does not have gapless excitations on the boundary. For non-interacting fermion systems protected by internal symmetries (as in the "periodic table" classification), bulk-boundary correspondence holds. For non-interacting ...

3

which functional gives close value to the experimentally observed band gap of semiconductors Different functionals are accurate under different circumstances, so you can't make a blanket statement that one functional gives accurate band gaps for semiconductors. The only way to know when various functionals are and are not trustworthy is to use them in ...

3

It depends on who you ask. If you ask someone with solid-state physics background, they will probably answer along the lines of Colin McFaul or John Rennie: The fermi level is the same as chemical potential (or maybe one should say "electrochemical potential"), i.e. the energy at which a state has 50% chance of being occupied, while the fermi energy is the ...

3

I will ignore the confused statement "the metal Fermi Level is shown as the top of the conduction band, with the entire band filled" and focus on the main part of the question. First, I'll answer within the framework of Schottky-Mott theory, which is where this diagram comes from. In any material, the difference between vacuum level and a particular ...

2

You may think this way: take a perfect infinite crystal where Bloch theorem perfectly work and add potential which makes real crystal finite. Next question you may ask how this potential is "seen" by quasiparticles which have been obtained from infinite crystal consideration. This procedure is perfectly self-consistent and is applicable in all cases. Also, ...

2

Yes, there will be electric field and yes, the energy band will be abrupt at the interface. In general case both effects exist at the contact for any materials (even for metal-metal contact). The height of the step at the interface is equal to the difference of the electron affinities. It can be zero e.g. for p-n junction when the materials on both sides ...

2

The Fermi energy is as you describe: it is the highest occupied level at absolute zero. The Fermi level is the chemical potential. It is the energy level with 50% chance of being occupied at finite temperature T. The Fermi energy does not depend on temperature; the Fermi level does depend on temperature.

2

Surprisingly, according to Immanuel Bloch's group (no relation to F. Bloch!), the simplest topological Bloch function is the 1D staggered lattice. The topological invariant is the Zak phase, the Barry phase accrued by walking across the edge of the Brillouin zone. The article will explain it better than I can: Direct Measurement of the Zak phase in ...

2

The group velocity $v_g$ of a wave packet (that's the speed of the maximum of the wave packet) is given by $v_g=\frac{\partial\omega}{\partial k}$. In this case, $\frac{\partial\omega}{\partial k}=\frac 1 \hbar\frac{\partial E}{\partial k}$, which easily evaluates to $v_g=\frac{3ta}{2}=:v_f$ for $k=0$. That's actually the definition of $v_f$: it is the group ...

2

Wikipedia says: The eigenvalues of a Hermitian matrix depending on $N$ continuous real parameters cannot cross except at a manifold of $N-2$ dimensions. Since the Hamiltonian has $N=2$ parameters ($k_x$, $k_y$), the crossing manifold has a dimension $N-2=0$, which is a point. So it's, in principle, allowed for graphene to have degenerate states (there ...

2

Your first question- Why aren't electrons being attracted by the positive charge region? Any free charge will move in response to an electric field created by some charge distribution. So it's important to see the electric field in the region. Well, the first thing you should do is find out the where the electric fields exist and where they don't. Electric ...

2

One could write a novel about those questions... I'll try to nail down the most important facts. Regarding what you figured out so far: Basically correct. I would say: Every system of atoms has a quantum mechanical ground state. You can approximately assign an energy to each of the electrons (depending on the approximation you are using, e.g. Hartree-Fock ...

1

To my knowledge, a general formula does not exist. The modification of the band gap heavily depends on the doped material and the dopant. For moderate dopings, there seems to be an answer on this link I found with a quick google search : http://ecee.colorado.edu/~bart/book/book/chapter2/ch2_3.htm Look at section 2.3.3.4. This might fall into what you are ...

1

Both free electrons and holes in semiconductor are excitations, i.e. quasiparticles which can propagate under influence of external electric field or temperature due to diffusion or drift. Don't forget that electrons are also characterized by the effective mass. In p-doped semiconductors a gradient of the temperature creates a region where hoping of real ...

1

Your use of the no-crossing idea is correct - we do not expect level crossings in two dimension to appear unless protected by symmetry. The symmetries in this case are the symmetries of the honeycomb lattice and time reversal. The protection of level crossings by symmetry is ubiquitous in solid-state. I should add that the existence of these Dirac point is ...

1

When an electron is promoted from the valence band to the conduction band it leaves a hole in the valence band. When the electrons falls back down from the conduction band to the valence band (to fill the hole) energy is released, but not necessarily as light. A photon can be emitted only when the material has a direct band gap i.e. when the electron in the ...

1

The fourth figure is in general incorrect. If you dope semiconductor (later I'll speak of n-type, replace electrons with holes and conduction band with valence for p-type), you get a dopant level (for electrons localized on donors) in the bandgap and electrons in conduction band. If you increase doping concentration, this dopant level in the bandgap starts ...

1

Semiconductors can be split into two groups. Intrinsic semiconductors have a band gap that is around thermal energies, so a few electrons can be promoted from the valence to conduction band at room temperature. This corresponds to the third picture from the left in your post. Extrinsic semiconductors have had a dopand added, and this creates new states in ...

1

Beginner's guide to band structure follows. I've taken considerable liberties with the details to simplify this so don't take it too literally! This is going to seem an odd place to start, but consider filling up the atomic orbitals in an atom with electrons. If you take a noble gas, e.g. Xenon, you'll find each orbital is filled completely with two ...

1

The reason for this apparent contradiction is that you have two "separate" quantum effects. Fermi-Dirac distribution describes the energies of single particles in a system comprising many identical particles that obey the Pauli exclusion principle. Distribution is calculated for potential-free space and is temperature dependant. You put electrons into the ...

1

Bloch's theorem generalizes nicely to a finite size crystal if we take periodic boundary conditions (pbc). If we have pbc than the a translation by one unit cell is still a symmetry of the system and so Bloch's theorem will apply. The only difference will be that the quasimomentum $q$ will only be allowed to take certain discrete values since the ...

1

The premise is not true. Under a uniform electric field in a perfect crystal, the electron moves within a single band, with k changing at a uniform rate. The coefficients $C_G$ change in accordance with the composition of the corresponding Bloch state. You can find a detailed proof in Kittel, "Quantum Theory of Solids". See Kittel, "Quantum Theory of ...

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