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11 views

Why are reciprocal lattice vector periodic, and time-frequency not?

k-space vectors are related to each other by $k=k'+G$, where $G$ is the reciprocal lattice vector $G=2\pi/a$. This means that the frequency of oscillation in real space of a plane wave $e^{ikx}$ is ...
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1answer
71 views

Is Chern-number for free fermion system always limited by total band number, i.e. number of orbits with a unit cell?

If so, how to see that? Also I think it has been proven that the total Chern-number for free fermion system is 0? If you know how to prove it, please make some comment or hopefully a sketch of ...
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0answers
18 views

Why graphene's substrate is important

I just have some feelings that somehow it is important what specific subtrate is used to grow graphene monolayer on. Some substrates are better, another ones are not so good. But I cannot completely ...
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1answer
80 views

Understanding electronic band structure diagrams

Currently I'm trying to understand electronic band structures such as depicted below: And following questions were arisen. Why are there multiple lines in valence side and conduction side? Where ...
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0answers
36 views

Problem with energy bands

I am getting confused by the energy bands. As far as I know, the outermost shell of an atom is called valence shell. The electrons residing in that shell participate in reactions and conduction of ...
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2answers
50 views

Does exciting an electron across the band gap change either its position or its localization?

I suspect that exciting an electron from its valence band to conduction band doesn't change its position, since the difference between the two bands are just their energies, but I want to know for ...
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1answer
98 views

band structure of Topological insulators

The above figure is Rashba-split free electron-like surface state in a projected bulk band gap. The bellow figure is the band structure of Topological insulators. x axis is the wave vector, y axis ...
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2answers
33 views

Shining light (of a particular frequency) on an insulator to make it into a conductor

Recently I read about band theory of solids. The energy difference between valence band and conduction band determines the conductive property of solids. Suppose I take an insulator and shine it with ...
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0answers
15 views

Strain effects on conduction band edge in k.p theory

While including strain effects into the k.p theory, I often see that the heavy- and light-hole band edges are modified due to the strain, but not the split-off or conduction band edges (e.g. this ...
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1answer
33 views

Why does band gap form for Silicon?

The image on the right shows that as the interatomic distance becomes closer together, the 3P and 3S band that joined together begins to split up forming a gap in allowed energies. Why does this ...
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3answers
83 views

Do electrons in the conduction band have a quantum number?

Sorry if this is a silly question, but I haven't seen the concept anywhere and was wondering why. If valence electrons can have a quantum number, why can't conduction electrons? Is there something ...
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1answer
71 views

Factors on which barrier potential in a p n junction depends

I have a few queries regarding the barrier potential in a p-n junction diode. Is the barrier potential dependent on temperature? Why/why not? Does the barrier potential depend on doping ...
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0answers
176 views

Problems while numerically computing band structure using k.p theory

I want to use k.p theory to numerically compute the band structure of a bulk semiconductor. The band I like to include are the lowest conduction band (cb), the heavy-hole (hh), the light-hole (lh) and ...
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1answer
40 views

What do we get from the diagonalization of the $k\cdot p$ matrix?

In k.p theory, we expand the wave function around a known point ${\bf k}_0$ $$u_{\lambda}({\bf k})=\sum_{\nu} c_{\lambda,\nu}({\bf k})u_{\nu}({\bf k}_0).$$ If we now consider 8 bands (conduction, ...
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1answer
27 views

Silicon: conduction band minima

Why do the energetic minima of the silicon conduction band lie not in a high-symmetry point like a $X$-point, but somewhere in $\Delta$-direction between points $\Gamma$ and $X$? What is the physical ...
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0answers
13 views

What is the effect of doping silicon with an excessive amount of group V donors?

What is actually the effect of doping silicon with an excessive amount of group V / donor atoms? I read it reduces the conductivity but I dont understand why.
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1answer
38 views

Finite vs. infinite systems, band structure and wave functions

Why do we need a finite system to find the find the wave function and a infinite system to find the band structure?
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0answers
36 views

What is a simple example of band structure having varying “orbital character”?

I'm trying to understand exactly what orbital character is in the band structure of a solid, such as that described in this paper and many others. I'm having trouble finding references online that ...
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1answer
55 views

Where does Fermi energy place?

As you can see, this diagram determines the place of Fermi energy in different types of matter. I don't understand the later part which is related to semiconductors and insulators? Why do we set ...
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0answers
39 views

electron-electron interactions in 1-D electron gas

The electron-electron interaction contribution to the hamiltonian in $k$-space representation is given by ...
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2answers
305 views

Floquet and Bloch's theorems : connection?

It is often stated that Bloch's theorem and Floquet's theorem are equivalent, even the Bloch's theorem is often referred as Floquet-Bloch theorem. However, it seems quite confusing to me since the ...
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2answers
62 views

What can we learn from a band structure diagram?

Other than the band gap and its magnitude, what are the things that we can immediately learn about the properties of the material just by glancing at its band structure? Can we say something about ...
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1answer
121 views

Why according to Hund's first rule all electron with same spin should occupy orbitals when partially filling?

I get that because of coulomb repulsion initially all the electrons will not occupy the same site but will single occupy the orbitals.But while doing so how do they know to keep their spins aligned ...
3
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1answer
65 views

Can a strained diamond actually become conductive?

According to about.com, "The electrical resistivity of most diamonds is on the order of 1011 to 1018 Ω·m" (source) However, according to the diamond band diagram, it seems that under a certain ...
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0answers
29 views

What's the elementary reason for the formation of a band gap?

Bohr's solution for an isolated hydrogen atom showed that there are only discrete allowed energy levels, $E_n = -{E_0\over n^2}$ and the solution of the Schreodinger equation provided a certain ...
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0answers
283 views

How are band gap energy, dielectric constant (permittivity) and resistance related to each other?

The following three properties are related to current flow: Band gap energy Dielectric constant Resistance I would expect them all to have the same trend (i.e. higher band gap energy would cause ...
3
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1answer
82 views

Semiconductors and energy bands

The valence and conduction band of a semi-conductor are often drawn as here click. This plot has essentially two features and I would like to understand them. The peak and the valley of the two ...
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3answers
182 views

What does $m^*>m_e$ imply? (the effective mass of electron is larger than its rest mass)

From what I understand, the concept of effective mass is just something people come up with to make electrons and holes obey the equation of motion $$ \vec{F}=m^* \vec{a} $$ without dealing with the ...
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1answer
73 views

How to calculate the speed of electrons in a metal

According to the Sommerfeld model, the electrons on the Fermi level has the relation $$ \epsilon_F=\frac{\hbar^2k_F^2}{2m_e}=\frac{1}{2}m_ev_F^2 $$ i.e. $\hbar k_F=m_ev_F$ with $k_F=(3\pi^2n)^{1/3}$ ...
3
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1answer
51 views

Periodic momentum space in band structure

I often see pictures like this in physics, this one for Silicon band structure. (source, NB: it's the German page for Silicon). There you see the plot of the energy in terms of the momentum $k$. ...
3
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1answer
148 views

Hartree-Fock correction to $e$-$e$ interaction

The corrections to the energy per electron in a jellium model (uniform distribution of positive ion charge approximation to the regulated long range order ionic array) is given by (in units of Ry) ...
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1answer
23 views

Why an undoped heterojunction causes potential barrier?

In this image (source) a potential double-barrier was created using GaAs and AlAs lattices (undoped). Why would any potential barrier be formed, if all the bonds are electrostatically balanced (i.e. ...
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0answers
135 views

Why the current through a resonant tunnel diode drops when the bound state goes below the conduction band?

The IV curve of a resonant tunneling diode is N-shaped. The rise in current flow happens because the bound state (the energy state in the well) enters the thermal area of the conductor ($\mu_1 + ...
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1answer
80 views

What's the difference between tunnel diode (TD) and resonant tunneling diode (RTD)?

According to wikipedia, a tunnel diode is a PN junction whose energies are shifted with bias, while a resonant tunneling diode is a quantum well between a double barrier, whose energies change with ...
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42 views

Symmetry breaking and band gaps?

Can the discontinuity in the E-K dispersion relation of a periodic lattice (at the boundary of a Brillouin zone) be understood as a consequence of breaking continuous translation symmetry into ...
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0answers
52 views

How come graphene is considered to have two valleys?

The typical graphene band-structure is a double-cone (in opposite directions to each other) with Dirac point in the middle. I assume the bottom cone is like the valence band, while the top cone is ...
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2answers
117 views

Why does the “counting rule” of band theory fail to predict the conduction properties of some materials?

I'm a little confused by the description I commonly hear about the electron counting rule in band theory. The general statement I find is that a "solid with an odd number of electrons per unit cell ...
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0answers
24 views

Couting the occupied states in band structure

I work with several dft codes and I have produced the band structures of some doped semiconductors with their plots. The problem I have is that I do not know how I can analyze the band structure and ...
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0answers
28 views

Quantum Forbidden Regions-Band Theory

In systems where certain regions are classically forbidden for a particle, quantum mechanics permits a finite probability of finding the particle in those regions. However, in band theory of metals, ...
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1answer
515 views

Effect of doping on the width of depletion layer of PN-junction diode

I've read that if there is very low doping in a pn-junction diode, the depletion region will be large because a large volume of depleted semiconductor is needed to generate enough electric field to ...
2
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1answer
99 views

Electron density in metals at non zero temperature

When computing the electron density in metals, the usual crude result is computed for zero temperature. That is, we integrate \begin{equation} n=\frac{8\sqrt{2}\pi m^{3/2}}{h^{3}} ...
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1answer
38 views

Indirect band gap and additional momentum?

For indirect band gaps, an electron needs both energy and momentum in order to be excited from the conduction band. I am not sure I understand the momentum requirement. What does it mean physically? ...
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1answer
78 views

Effective masses for different direction

Assume we have an indirect semiconductor where the effective mass becomes anisotropic in different directions. Usually, one talks about a mass in parallel and perpendicular direction referring to ...
2
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1answer
67 views

How to check the ohmic contact to the film?

I have a thin semiconductor film deposited on an isolating substrate. I would like to check different metals to find out do they form the ohmic contact or Schottky barrier. What is the best way to do ...
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0answers
32 views

How can we determine the inbuilt barrierpotential and electric feld for a given band diagram?

Suppose I have got two p type silicon materials of different concentrations (the difference in thier concentrations is small but considerable enough that their fermi levels differ by noticeable ...
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4answers
123 views

The conduction electrons in metals is a thermal phenomenon?

When applying an external electric field in a metal at absolute zero, there is electrical current? There must be thermal fluctuations in the electron's band to be occurs current?
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1answer
323 views

Sold-State Band Structure - connection between Fermi Energy, Fermi Level and Work Fuction

I've been struggling with the concepts of these three terms - Fermi Energy, Fermi Level and work fuction. Now, I was given these definitions (in the context of semi-conductors): Fermi Level is the ...
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0answers
27 views

Computing Parity by numerical tables of characters

I have a table of the characters of a set of wavefunctions for different points in reciprocal space and for different band indices (this is for a solid). For the case of a single irreducible ...
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1answer
95 views

Calculating band gap from band structure

If while calculating a band gap, the band just below the Fermi level touches the Fermi level, can we say the material is semiconducting?
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1answer
257 views

Plotting a bandstructure along High-symmetry points when kx,ky,kz is known

Suppose you know kx,ky,kz points along with the corresponding energies. Basically, you know about the 4-D E(k) dispersion. How you do then convert that data into the bandstructure plots you commonly ...