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11

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 ...


8

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 ...


8

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 ...


7

In calculating the electron dispersion you probably obtained the diagonalized Hamiltonian in the momentum space $$ H=\sum_\mathbf{k}\left[c^{\dagger}_{\mathbf{k}A},c^{\dagger}_{\mathbf{k}B}\right]\left[\begin{array}{cc}0 & \Delta(\mathbf{k})\\ \Delta^{\dagger}(\mathbf{k}) &0\end{array}\right]\left[\begin{array}{c}c_{\mathbf{k}A} \\ ...


6

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 ...


5

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

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 ...


3

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.


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 ...


3

They are shown at the $\Gamma$ point in special diagrams called the reduced zone scheme in which a band will be shown folded back on itself. This way of showing the band structure is convenient for a few reasons, one of which is that it saves space on the page. If you look at that band gap at $\Gamma$ and follow the lower band down to lower energies, you ...


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 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 ...


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

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

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

I was lucky to study the kp-method from sources. You will find a lot of inspiration in these early works. Here is the list of authors: Schokley, Kane, Cardona and Pollak, Luttinger and Kohn. All of them published remarkable papers concerning the kp-method in Phys Rev.


2

TB method uses the atomic orbitals as a basis function to get the matrix representation of the crystal Hamiltonian. The matrix elements of this Hamiltonian are usually computed using fitting parameters. KP-method is based on the matrix version of the perturbation theory derived by Lowdin. It states that the energy spectrum at some point of the Brillouin zone ...


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 ...


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

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

Firstly there is a table on wikipedia with some of this data: http://en.wikipedia.org/wiki/List_of_semiconductor_materials. It sounds like you have a little more information so if you want to post in your answer that would be nice. If you want to be a really good Samaritan you could add it to Wikipedia There are maybe two things being asked here: 1) Why ...


2

The answer to your 1st question is that it depends on the Fermi energies of separated each materials. If $E_{f1}>E_{f2}$, your concerning case, electrons move from 1 to 2 regardless of the other parameters. The migration of electrons make the charge distribution and the electron potential change. To calculate the charge distribution, we assume charge ...


2

Take the solutions of the potential problem of an atom and look at the energy levels. Between the n=1 energy level and the n=2 energy level there is a forbidden gap in energy, i.e. you will not find the electron of the hydrogen atom there. Note the thick line for large n where the energy gaps become so tiny leading to a continuum , i.e. an energy "band" ...


2

Hole as a particle First, hole can really be treated as a particle. For electrons, there are Pauli exclusion principle, so there are only one electron per state(state can be described by momentum $\vec p$, band index and spin). In semiconductors, there are valence band and conduction band. In ground state, valence band is completely occupied by electrons, ...


2

------------The Fermi-Energy------------ If you operate at T=0K and fill the energy-states of a system according to the Pauli-exclusion-principle, the Fermi energy is the boundary at which all lower states are full and all higher states are empty. At the T=0 this boundary is a sharp line. For example: say you have ladder with five steps which you have to ...


1

The deep insight of Anderson is that the difference between insulators and conductors is not the energy spectrum. In fact the entire picture we are taught in introductory courses is highly misleading. [Note: Everything I am going to talk about will be about single particle effects, so no interaction.] First lets just remember the introductory picture. We ...


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

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 ...



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