Solid State Physics - Science topic

whats your domaine?

Abhisek Roy your answer is the same with chatgpt.

If you have done DFT calculations, you can use the wannier90 code to calculate the wannier function, and use the xcrysden software to plot a 3-dimensional image of the s,p,d orbitals.

Thanks Professor Merve Özcan

I am working on vanadate materials, I think they are so complex, they take a lot of time in calculations

Düzgün altıgende kenarlar eş ve oluşan eşkenar üçgenler aynı olduğu için heryerde simetriktir. Bu yüzden oluşan grafik düzgün doğrusal olur.

Fabrication Engineering at the Micro and Nanoscale by Stephen A. Campbell would be a decent starting point.

Just from the nice pic, I think the data different between MD and exp. is fairly closed from my point.

A small tip is that in exp. materials often consist of defects, vacancies, dislocation, grain boundaries and so on but in MD the materials is a perfect crystal in your case.

So I think you can accept this result.

And if you're not satisfied, I would like to propose two aspects which you can do furhter tests.

1. increase the number of atoms in the system. A big system would result in better results( or not).

2. chose a "good" potential. A good potential is critical to the properties of systems. Before you do further production run, a systematical tets of exsists potentials is essential.

This error can occur when there is an inconsistency or an issue with the input settings.

Few suggestions:

1. Verify Input Files: Double-check your input files, especially the thermo_control file. Ensure that all the required input parameters are correctly specified. Pay attention to the crystal structure information, such as lattice parameters, atomic positions, and symmetry settings.

2. Check Thermo PW Version Compatibility: Ensure that the version of thermo_pw you are using (version 1.8.2) is compatible with your QE version (7.2). Incompatibilities between different versions can sometimes lead to errors. Consider updating or matching the versions of both codes if necessary.

3. Review the Crystal Symmetry: For an FCC crystal structure (ibrav=0), it is crucial to specify the correct symmetry settings. Make sure that the crystal symmetry information, including the space group or lattice vectors, is accurately defined. Incorrect symmetry settings can lead to issues with determining the Laue class.

Hope it helps:credit AI

Hello,

here are some references about the SiO2/Si Interface:

Additionally search for "gate oxide", these are very thin oxide layers (of Si, Hf and others) used in microelectronics.

Dear Dr. Azeem,

1) What is the temperature range that you are interested.

2) What kind of samples do you have, crystals, ceramics or thin films

so that I can see if anyone can help you out.

Hello,

From my experience, I successfully performed UPS measurements and determined valence band position of a 2D perovskite thin film. It was consistent with a literature data.

However, there is a couple of tricks. As you know, He radiation penetration is about 2-3nm. So any little contamination of a surface will cause inaccurate measurements. Normally, etching ion gun is used to clean a specimen surface before measurements. Though the perovskite surface wont withstand that. Therefore your samples must be super fresh.

Also, your samples must me deposited on a conductive surface such as ITO/FTO.

My samples were disposed after measurements, so I didn't check its condition, but I wouldn't say that degradation happens immediately.

Hope it helps you

Dear Alireza Badiei

Thank you for the detailed answer. So, in principle it's possible but challenging.

I'm actually not going to be a TEM operator in the future (I'm not planning to), so I'll not need to know all the experimental problems and considerations. I mainly wanted to know how much I can rely on the data that I see in the literature (I gave a specific reference to an article in the question).

It's good anyways to have general information about it, so thank you for your time.

Yes, the Bratu equation has several applications in science, particularly in the fields of nonlinear dynamics, mathematical physics, and engineering. The Bratu equation is a second-order nonlinear differential equation that can be written as:

u'' + λe^u = 0

where u(x) is the unknown function, λ is a constant parameter, and e is the base of the natural logarithm.

Some of the applications of the Bratu equation are:

In summary, the Bratu equation has several applications in science and engineering, particularly in the study of nonlinear dynamics, pattern formation, diffusion processes, and electrical engineering.

The atomic mass of Te is 127.6 u, so you need 5x127.6x10¹⁸ u Te/cm³ assuming every Te atom creates a carrier (if not, multiply by a corresponding factor). This corresponds to 1.06x10^-3g Te/cm³. The density of InSb is 5.75g/cm³. Now, technically you would have to sum up atom numbers and divide by the overall count, but the difference is negligible when we have orders of magnitude in difference as in this case. So you can approximate by 1.06x10^-3/5.75=1.8x10^-4 which equals 0,018%.

Dear Prof. Robin Singla

In addition to the right answer by Prof. Xavier Oudet , I can advice to check the monograph by Frederick Reif "Fundamentals of Statistical and Thermal Physics", McGraw Hill, 1965

First chapters are based on the analysis of a total magnetic moment M with lots of examples worked out for different cases from the perspective of Statistical Mechanics methods of distribution (binomial and gaussian).

Kind Regards.

Vortex stat is the state at which superconductivity and magnetism coexist. It is very important for applications.

Thank you so much Khagesh Tanwar for your help!

See the following post:

Dear Shalu Pathak ,

you are right, all these peaks arise from parallel planes.

The 003 planes are paralell to the 006 planes, and paralled to the 009 planes etc, but parallel to the 002 and the 001 planes as well.

However their interplanar distances are different und thus the diffraction peaks show up at different angles

Alltogethers all these planes are multiple order planes of the 001 plane.

Please remind the Bragg law:

n*lambda= 2*d*sin(theta)

You may rewrite this equation as:

lambda= 2*d/n * sin(theta)

one also has for any d(_h,k,l)/n = d_(nh,nk,nl)

You may check the validity of this equation for all crystal systems.

The formulas for d_hkl are for example summarized in the attachment, taken from the Klug&Alexander book on 'X-Ray Diffraction Procedures'...

Ggod luck and

best regards

G.M.

Dear@Partha Pratim Nakti

Have a nice time and good day!

Please read these papers, you will find what you want:

I humbly suggest this video.. CBH fitting using Origin 2019 software is included

Agree on that point, Prof. Waldemar Łasica

Best Regards.

you can use this link for unfolding band structure:

The following blog discusses inverse problems in statistical mechanics.

One of those problems elaborated is how to establish ground zero in physics as a fundamental basis for studying the physical properties of a particular state:

https://torquato.princeton.edu/research/statistical-mechanics/

Worthly to read, I recommend it.

diffraction - some phenomena at costant freqyency

spectroscopy - as result of frequency variation

Dear S

You didn't specify any magnetic materials compounds. Find the crystal structure of nanoscale ferromagnetic materials using JCPDS CARD.

Thanks Respected Aref Wazwaz sir, for sharing helpful information.

Dear Shlu,

As shown in 4he attached figure , the charge current flows from left to right through a conductor Hall bar. If the charge current is non-polarized (with equal numbers of spin-up and spin-down electrons), the spin imbalance does not induce a charge imbalance or transverse voltage at the Hall cross. If electrons, which are polarized in the direction of magnetization M, are injected from a ferromagnetic electrode while a circuit drives a charge current (I) to the left, a spin imbalance is created. This produces a spin current (I_S) without a charge current to the right of the electrode. Spin–orbit interactions again separate spin-up and spin-down electrons, but now the excess of one spin type leads to a transverse charge imbalance and creates a spin Hall voltage, VSH. As the distance, L, between the electrode and the Hall cross increases, the voltage signal decreases, allowing the decay length of spin currents (spin diffusion length l_sf) to be measured. More details about SQHE will be presented in Chapter 9 of my Book, about spin transport in nanostructures.

Dear Shalu Pathak, in addition to all the interesting answers,

To understand the role of nonlocality between the current j_a(z) and the electrical field applied E_b(z´) to a normal metal, i.e.,

j_a(z) = (integral from 0 to infinite) K(z,z')_ab E_b(z´)

where the radius of the kernel K(z,z')_ab ~ l (the mean free path) please review section 3 of the classical work:

Best Regards.

You distinguish a normal classical Hall efect from a Quantum Hall effect.

Normal size devices exhibit the first, contain considerable number of electrons.

The magetic field acting on the current pushes electrons to one side of the device

and is counteracted by the Hall voltage set up from charge accumulation. Proportionality between magnetic field and Hall voltage for steady current.

Quantum devices contain fewer electrons in narrow or small devices (Nanostructures) . The magnetic field provokes the equivalent of Landau levels that contain the states for electrons. These pass at regular intervals as the magnetic field increases. Thus there are regular jumps

in the electron conductance as magnetic induction increases.(In single electron conductance, or normal quantum hall effect

The fractional quantum Hall effect is believed to be the consequence of electron interactions and quasi particle formation. This is an extremly complicated phenomena, and not nearly as well understood as many would have you believe.

I will second Hadi Jabbar Alagealy here, that paper is all.

Quantum materials are I believe are those materials that exhibit wave behavior, or equivalently particle-wave duality.

Please tell me more

This paper is related to this thread:

please Saravanan L can you tell me the value of DOS in metal ?

Dear Kaushick Parui , In addition to all those mentioned, the chapter VII of the book:

Statistical Physics, part II: Theory of the Condensed State, Vol. 9 by E. Lifshitz, L. Pitaevskii Elsevier, 2013.

for the Ph.D. Level - Theory. Mainly talks about magnons.

Best Regards.

Dear Satyabrata Mahapatra ,

Because this question is a basic question I would like to give an answer for it.

In solids when one applies on it an electric field the free charges in it either electrons of holes drift with a steady sate velocity which is proportional to the electric field such that vd=mu E.

The mobility itself mu= q Tau/m*

where q is the electronic charge, Tau is the relaxation time and m* is the effective mass. As said before of one wants to increase mu one has to increase Tau and decreases the effective mass.

The effective mass is a material property because it is related to the second derivative of the energy with momentum of the energy band structure at the minimum of the conduction band and maximum of the valence band.

But the quantity which can be controlled to some extent is the relaxation time Tau.

There are two main scattering mechanisms, the thermal vibration of the lattice and the other is the impurity and crystallographic defects.

One can the thermal vibration by decreasing the temperature.

And one can reduce also the impurities and crystallographic defects.

It remains one point In mosfet transistors the electrons move in a surface channel and they get scattered at the surface defects. In order to avoid such surface scattering one builds a potential well under the surface in which the electrons can move without scattering at the surface because they are not allowed to exist at the surface.

For more information about the mobility please follow the link:

Best wishes

Indeed Dear Ahmed MS Dawelbeit it is a very interesting and subtle question, refer to it as a localization phenomenon is one way since electrons can be seen as wave packets that can be or not well defined within the structure (metal, either metallic polimer).

In general, we have a kinetic criterium with three well-defined regions, the product "l . k_F", since we understand localization as the absence of diffusion of any kind of waves in a disordered medium.

Please check for the case of metallic polymers, the following reference:

Alan J. Heeger, 2003, The Critical Regime of the Metal-Insulator Transition in Conducting Polymers: Experimental Studies. Condensation and Coherence in Condensed Matter, pp. 30-35

it is very instructive

The following paper is worth mentioning in this thread:

Magnetization switching by current-induced spin-orbit torques (SOTs) is of great interest due to its potential applications for ultralow-power memory and logic devices. In order to be of technological interest, SOT effects need to switch ferromagnets with a perpendicular (out-of-plane) magnetization. Currently, however, this typically requires the presence of an in-plane external magnetic field, which is a major obstacle for practical applications. Here we report for the first time on SOT-induced switching of out-of-plane magnetized Ta/Co20Fe60B20/TaOx structures without the need for any external magnetic fields, driven by in-plane currents. This is achieved by introducing a lateral structural asymmetry into our devices during fabrication. The results show that a new field-like SOT is induced by in-plane currents in such asymmetric structures. The direction of the current-induced effective field corresponding to this new field-like SOT is out-of-plane, which facilitates switching of perpendicular magnets. This work thus provides a pathway towards bias-field-free SOT devices.

Dear Franklin Uriel Parás Hernández ,

for the exciton Bohr radius ofhexagonal boron nitride

please see the abstract of:

Solid-state Physics, go back to the old terminology, Prof. Muhammad Hamza El-Saba

I elaborate, nowadays we see many papers with titles such as "nematic supercoductors", but as far as I can recall, a solid-state crystal (solid-state) is not a nematic liquid crystal (condensed matter liquid phase, not just fluid one).

The phenomenological physics based on "free Helmholtz & Gibbs energies" for liquid crystals is something really very "very" hard to calculate and to study, and that is only the classical part of the subject. I cannot imagine how is to deal with by adding quantum correlated many-body phenomena to systems such as liquid crystals.

I can advise reading chapter VI on "the mechanics of liquid crystals" from the book: Theory of Elasticity by Lifhsitz Kosevich & Pitaelskii, 1986, Elsevier, which was previously the Landau Lifshitz VII volume, to understand what I mean.

Best Regards.

Dear Jitesh Pandya many thanks for your very interesting technical question. te synthesis and processing of lead-perovskites is an important current research topic worldwide. Thus there is a large body of scientific literature available worldwide. From the outside it is difficult to solve your specific problem without knowing the detailed reaction conditions (target compound, starting materials, solvent etc.). For an alternative synthesis of methylammonium lead bromide perovskite nanocrystals using ionic liquids please have a look at the following relevant article:

Unfortunately this paper has not been posted as public full text on RG. However, the Supplementary Information is freely available (see attached pdf file).

Also please have a look at this potentially useful paper:

There are also a number of interesting references describing the crystallization of lead bromide perovskite materials. For example, please go thorough the following Open Access articles:

and

Moreover, I strongly suggest that you use the "Search" function of RG to find and access relevant articles in this field. As an example, you could search e.g. for the term "lead bromide perovskite" and then click on "Publications":

This will provide you with a long list of useful articles.

Hello Rana Dey ,

I know that mine will be a rather late answer, but I think I'd better write my opinion.

I think your n-type doping creates a "degenerate semiconductor". If your semiconductor is silicon, if the doping concentration is above 10²⁴ m^-3, doped silicon is usually regarded as degenerate, for which the expressions you use (e.g. p=n_i²/N_D in the n-type region) will start to fail representing the behavior.

Atomic density of silicon is 5x10²⁸ atoms/m³ and the doping concentration should remain much smaller than this, however your n-type doping is not sufficiently small (N_D=3x10²⁶ m^-3, which means per 100 silicon atoms you have roughly 1 donor atom, which means the semiconductor is degenerate. However, for your p-type doping, N_A=10²⁴ m^-3, you are at the "official" limits for silicon, so it can be assumed not degenerate yet, for which the expressions can still be valid).

Best regards...

It is because SdH oscillation can only occur for those carriers with sufficiently high mobility, whereas in a Hall measurement all carriers are taken into account. So, in cases where transport happens through multi carriers with both high and low mobilities, you may notice such a difference in the value of carrier density obtained from these two measurements.

Dear Vasu Babu, You can easily plot the frequency with the number of mode and displacement plot by taking a line plot or point plot group. You can also find lots of tutorials in the COMSOL blog.

Prof.

Thank you so much for pointing out in this thread the classical textbook by Prof. S. Flugge on practical quantum mechanics, which has served well many generations of physicists.

The book definitely, treats extensively and pedagogically the elastic scattering problem in non-relativistic QM, and also there are a couple of problems dedicated to the phase shift problem and bound states.

Best Regards.

Dear Shalu Pathak,

Please look at the introduction of the following paper for the difference between TRS and inversion symmetry first :

In valleytronics, there are several open discussion on TRS, you can check-in:

If one of the two symmetries, in this case, the TRS is preserved, and the inversion not, the states are not protected, as in the case of valleytronics, please check:

Check-in addition to the following external lecture, the part on Kramers degeneracy, one should remember that spin-orbit coupling might or not play a role here:

Hello Satadal Dutta.I think you made mistake to create geometric model. You have to give coordinates of all layers truly or you must give exactly coordinates and save it for using again in sdevice file. Because this positions is used to create ray tracing in SDevice file.

Dear Sumit Bhowmick ,

You asked a very broad question, but I hope my answer will undercover the understanding of some of the subquestions =)

Due to DFT is a tool, which operates with small atomic systems up to a couple of hundreds of atoms (you can consider and larger cell up to 400-500 atoms, but you lose in CPU time or accuracy of calculations), you can consider either single-phase atomic structures (solid solution or stoichiometric phase) or supercells with an interface between two different phases.

As for mechanical properties, you can estimate them using special equations, which have bulk moduli of considered phase as input parameters.

Bulk moduli can be easily calculated using DFT.

For example, you can read how I recently did that for Mo-Ni-B-C cermet.

From experimental data and mechanical properties measurements, we obtained that precipitation of κ-phase Mo10Ni3C3B decreases a hardness with increasing of stress intensity factor.

Then we calculated elastic constants of precipitated Mo10Ni3C3B and existed Mo2NiB2 and Mo2C phases and estimated bulk properties and hardness using special equations (See Supplementary https://lettersonmaterials.com/Upload/Journals/32862/boev_et_al_supplementary_material.pdf).

The bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio were estimated according to Hooke’s law and the Voigt-Reuss-Hill (VRH) model. For hexagonal polycrystalline crystal:

B=[2(C11+C12)+4C13+C33]/9,

G=(C11+C12+2C33−4C13+12C44+12C66)/30,

E=9BG/(3B+G),

ν=(3B−2G)/2(3B+G),

The Vickers hardness (HV) was calculated according to the empirical formula: HV= 2(K^2 G)0.585−3,

K=G/B

So, we obtained that the new Mo10Ni3C3B phase has a lower hardness and is able to decrease the hardness of the whole material.

Ratio B/G is an indicator for ductility properties.

Bond analysis using electron localization functions (provided in VASP) allowed us to define the nature of the bonding in considered phases.

Covalent bonding means stronger hardness and metallic bonding - more ductility/plasticity.

Also, it is important to analyze the anisotropy factors. That will be able to undercover different useful things.

If you have any questions, do not hesitate to ask me =)

Carrier Drift and Mobility

When a free electron is perturbed by an electric field, it will be subject to forces that cause it to accelerate; it moves opposite the direction of the electric field, and would speed up with time. However, the situation in a crystal is different, because the electron is actually moving through a lattice of jiggling atoms that all exert electromagnetic forces. We cannot use the standard electron mass; we must use an effective mass for the electron in the crystal, a result of the periodic forces of the host atoms in the crystal1. The wonderful thing is that in the simple picture, we can view the electron as moving as though it were in a vacuum, but with this new effective mass that varies from material to material.

Another difference is that inside the crystal, a moving electron will not travel far before colliding with a host atom or impurity. These collisions randomize the electron’s motion; therefore, it is useful to use an average time, the relaxation time ττ, which is based on the random thermal motion of the electrons. In fact, the scattering processes of the electron bouncing around causes it to lose energy, which is given off as heat. With the addition of an applied electric field, we also have a mean free path length λλ, or a net displacement on average for a given electron.

This means free charge carriers have a drift velocity, an average speed at which they travel through the material. The average drift velocity for a single electron is the same as the average of all drift velocities of all the electrons, and is given by the following equation:

vd=12aτ=12qτm∗cE(4.1)(4.1)vd=12aτ=12qτmc∗E

where aa is the average acceleration of the carrier, qq is the charge of the carrier (including charge), m∗m∗ is the effective mass of the charge carrier, ττ is the carrier lifetime, and EE is the electric field strength2.

The movement of charge carriers in an electric field results in an electric current. We will call the current resulting from drifting carriers our field current. The current density J, or the current flow of electrons per unit volume, is given by the following:

Jn=nqvd(4.2)(4.2)Jn=nqvd

Jn=nq12qτm∗E(4.3)(4.3)Jn=nq12qτm∗E

where n is the carrier concentration (per unit volume). Furthermore, we can get rid of the factor of 2 in this equation by averaging the lifetime τ over all carrier velocities1. Therefore, we can now define a quantity called mobility, in this case electron mobility. Carrier mobility is useful as it is the ratio of drift velocity to the electric field strength. Below we will give the mathematical definition and substitute mobility (given as μn) into the current density equation.

μn=νdE=qτm∗(4.4)(4.4)μn=νdE=qτm∗

Jn=nqμnE(4.5)(4.5)Jn=nqμnE

From these equations we can then obtain the conductivity of the material in terms of the mobility2:

Jn=σE(4.6)(4.6)Jn=σE

σ=nqμn(4.7)(4.7)σ=nqμn

The same conditions hold for hole mobility and conductivity, and therefore the total conductivity, which is directly inversely related to the resistivity (the material’s resistance to being conductive, so to speak), is given below:

σ=1ρ=JEqμen+qμhp(4.8)(4.8)σ=1ρ=JEqμen+qμhp

where ρρ is the resistivity, nn and pp are the concentrations of electrons and holes respectively, and μeμe and μhμh are the electron and hole mobilities respectively.

We see that conductivity in a material is directly related to the mobility, which depends on the density of dopants, temperature, and electric field strength. Thus, as mobility decreases conductivity decreases. As materials become more heavily doped, mobility decreases because dopant atoms are very effective scatterers, and therefore decrease the average time between collisions. Similarly, as temperature increases, mobility decreases, however this effect becomes insignificant in heavily doped materials. As electric field increases, the drift velocities of carriers will eventually become comparable to the random thermal velocities. Therefore, high field strength decreases mobility; semiconductors in this way differ from conductors, which so easily generate current that only a low field strength occurs during current flow2. It is worth noting that less specialized impurities and crystal defects in the semiconductor material will also decrease the mobility, because of the scattering effects mentioned above.

The Hall Effect (and Hall mobility)

ecee.colorado.edu/~bart/book/book/chapter2/ch2_7.htm

The trends are well known, but it is difficult to say in a single sentence, why this trends exist. The following can, however, be stated:

-Mn, Fe, Co deviate from the trend because of the magnetic contribution to the thermodynamic functions.

-the total cohesive energy is much larger than the differences between the energies of the crystal structures. So there are non-obvious subtle effects which are responsible for the energy differences and which determine the observed crystal structures. Some quantitative thoughts can be found in

(quick find by google scholar)

Dear Shalu Pathak,

There are 2 classes of truly physical effects, which are originated from SO interaction:

Dr. Vadym Zayets classifies them according to the following scheme *:

Enhancement of external magnetic field, localized electrons and atomic gas experience this class of effects. In this type, time-reversed symmetry is broken by the external H.

Creation of spin polarization by an electrical current, conduction electrons experience this class of effects, time-reversed symmetry is broken by the electrical current J.

References

Dr. Vadym Zayets, “Spin-Orbit Interaction” – https://staff.aist.go.jp/v.zayets/spin3_32_SpinOrbit.html

Thank you A.O. Boev and Bojidarka Ivanova for the response. Your answers is very helpful.

I had the same problem. Did you solve this problem?

Dear Jamal M. Rzaij,

Yes, I will provide you , surely.

Please don't worry, I will send you.

Best Wishes

N Das

Hello Stam Nicolis ,

thank you very much for your answer! I tried to avoid a question with a very long description, so I wrote just some prosa here but with a link to a text with some quantitative treatment (the graphic attached to the question shows the main result). The text also contains three sketches of possible implementations. Did you have a look at it?

The main idea is that there are two volumes of space (B₀ and B_M) separated by the mirror region. The boundaries of each volume are given by the borders of the metallic specimen and by the mirror. In equilibrium, the numbers of electrons crossing the mirror in both directions have to be equal which brought me to

A₀ D₀ P₀ P_A = A_M D_M P_M P_D

with the area A of the border between the homogeneous B field and the mirror region, the density D of charge carriers, the probability P of crossing the mirror based on the Lorentz force, and the probabilities P_A and P_D based on Pauli's exclusion principle. The indices 0 and M are referring to B₀ and B_M.

One possibility would be to investigate the local structure with EXAFS. Since the interatomic distance is the basic physical quantity to which EXAFS is sensitive. From the shape and strength of the changes in X-ray absorption, it can be concluded at what distance from the ionized atom it is scattered and how strongly, thus obtaining a so-called radial distribution function. From this it can be roughly estimated at what distance which or (if the atomic types of the ligands are known) how many atoms can be located there.

Dear Jitesh Pandya, please check the following documents. My Regards

- ZnO

- PBABr

Yes. The effective work function depends on difference between Fermi level of metals and the interface. The crystallographic change / structural change at the interface plays an important role in the change in work function. However, they are usually in small range, and it becomes potential interest, by tuning the work function by suitable semiconductor or insulator in gate related applications.

Hi,

Did you find those parameters? If yes, please let me know about them. I really need it.

Thank you in advance,

Neha

it depends on what you want and you can manipulate the preparation condition , to get the optimum for your application

All recombination mechanisms can be defined as radiative or non-radiative.

Photoluminescence measurements reveal radiative recombination processes. However, if they're intentionally or unintentionally added impurities or intrinsic defects they can form deep localized energy levels in the bandgap (gap of forbidden energies between conduction and valance bands or LUMO and HOMO). These deep traps act as efficient recombination centers according to Shockley-Read-Hall (SRH) statistics. As opposite to exciton or band-to-band bimolecular recombination, trap assisted recombination is non-radiative (usually becomes radiative only at very low temperatures in the form of additional PL peak at lower photon energy than bandgap). Since one additional non-radiative recombination path is added the photoluminescence signal is quenched because the net radiative recombination rate is reduced.

This paper is a nice example.

Dear Prof. Azhar Fakharuddin ,

Last decade, it was common to use tight binding to calculate the DOS of strontium ruthenate, the first perovskite reported as been a superconductor.

Please you can look at the references within the following publication:

Dear Anton Matasov ,

In solid states there are five 2D Bravais lattices:

1 – oblique (monoclinic),

2 – rectangular (orthorhombic)

3 – centered rectangular (orthorhombic),

4 – hexagonal, and