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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
29 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
19 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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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
28 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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25 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
41 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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35 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
102 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
56 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
85 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 ...
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1answer
42 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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23 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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102 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 ...
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1answer
70 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
99 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
62 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 $k_F=(3\pi^2n)^{1/3}$ ...
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1answer
42 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 $k$. ...
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1answer
102 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
18 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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74 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
34 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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34 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
42 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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1answer
67 views

Metals/Insulators and Electron Counting

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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22 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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25 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
305 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 ...
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1answer
81 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
31 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
64 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 ...
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0answers
39 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
113 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
207 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
26 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
71 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
230 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 ...
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3answers
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Reverse bias P-N junction [duplicate]

I am not able to understand why the PN junction does not conduct when reverse biased. Can't electrons travel from the N side through the power supply to the P side where they can jump from one hole to ...
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3answers
135 views

How does temperature affect photovoltaics (PV) efficiency?

I know that photovoltaic panels are more efficient at lower temperatures: As the temperature increases, the output voltage decreases. I am looking for an explanation of the mechanism behind this ...
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1answer
524 views

What is an electron/hole pocket and what is the significance?

What is an electron/hole pocket and what is the significance? I'm trying to get my head around this. I've read what Ashcroft and Mermin have to say on the subject, but it's a little convoluted. They ...
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0answers
23 views

What is Fermi energy and Fermi level? [duplicate]

What is meant by Fermi level and Fermi energy? And what is the difference between the two?
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1answer
104 views

Electron degeneracy pressure

Why is it that in stars undergoing gravitational collapse electron degeneracy kicks in? Why couldn't the electrons form energy bands like in semiconductors?
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0answers
26 views

How to model a nonperiodic supercell as a periodic one?

Some researchers use Hydrogen atom termination, to model a non periodic finite sized 2D and 1D structures as periodic one. How far this approach is useful in predicting the properties of periodic ...
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1answer
171 views

How to obtain band dispersion from a band structure diagram?

Reading about bands dispersion, I came across the following (Computational Chemsitry of Solid State Materials): ...
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2answers
113 views

List of experimental band gap

does anyone know where one can find a list, database, book of experimental bandgap values of semiconductors? Is there such a collection? Or do I need to scour papers one at a time to get the values?
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1answer
358 views

Band gaps: are they at the centre or at the edge of the Brillouin zone?

Reading about electronic band structures, I came across the following: Band gaps open at the edges of the Brillouin zone (BZ), since that is where the Bragg scattering occurs. I am slightly ...
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0answers
21 views

Is there a way to quantify how similar a polycrystal should behave to a single crystal?

So in solid state classes we learned about phenomena like band structure and others arising from a periodic potential. Then we get to doing actual experiment and find out that materials being single ...
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1answer
510 views

Fermi level and conductivity

Can someone in a simple way explain me what the Fermi level is and what does it have to do with conductivity. My teacher said that Cu conducts electric current better than Al because of something in ...
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0answers
207 views

Derivation of existence of energy band gap in semiconductor (solid State)

I am looking for both a mathematical and a physical reason for energy band gap in metals. For Physical reason, I was told that at each reciprocal lattice, you could have Bragg scattering, that would ...