12/9/12 Band theory of the electronic properties of solids

1/2zasoby1.open.agh.edu.pl/dydaktyka/f izyka/c_teoria_pasmow a/6.php

6th SUMMARY: POSSIBILITIES AND LIMITS band theory

Presented in Chapters 2-5 examples of calculations on the electronic structureof the elements, which generally have one atom in the primitive cell. Of course,the band theory formalism covers the case of a number of different atoms in thecell, which allows the calculation of the chemical compounds and alloysarranged. For the substances obtained numerous results, which are not presentdue to the lack of space. It has long been carried out a calculation of theelectronic properties of the surface of pure crystals. best results of thecalculations agree with the experiment for metals. The accuracy of calculationsallowed in many cases the "design" on a computer compounds which then onlyhave been produced experimentally. Values of cohesive energy and elasticconstants are played with moderate accuracy of 10%, while those with goodaccuracy in the order of 1%, fixed networks are played. Description of complexelectronic properties of semiconductors is very successful band theory. Forsemiconductor discordances for calculations from first principles are greaterthan for metals, for example, stadardowe calculation gives the value of theenergy gap of silicon less than two experimental. When you need to recreatethe exact shape of the bands are useful semiempirical methods. fundamentalrestrictions apply to systems where the theory breaks down band. We shouldmention:

(I) the disordered structure.potential periodicity assumption is that the results of band theory may bewrong for a non-crystalline structure of condensed matter such asinterest disordered, amorphous materials, structures or kwazikryształymodulated. For systems not apply Bloch theorem - jednoelektronowymstates can not have a value kwazipędu . There are theoretical

methods allowing to calculate the band structures of alloys and otherdisordered if electrons are delocalized states. Band theory breaks down,however, if the random fluctuations cause the location of potentialelectronic states ( Anderson localization ).

(Ii) the impact of network elestycznościThe lattice band theory, by the potential U ( r ), affects the electrons,and the formalism of the theory does not foresee the impact of electronson the network. Interaction of an electron or hole to the network can leadto samopułapkowania: charged particle accompanied by local deformationcreates little mobility networks POLARON . Such "trapped" Mediaconsumption is one of the reasons insulators distinguish from "good"semiconductors. (No coincidence that most of the important tech

semiconductor crystallizes in a very "rigid" structure of the diamond.)

(Iii) non-trivial effects of electron-electron interaction.Taking into account the electron-electron interaction with the exchange-correlation potential is substantially effective as long as they cause onlyquantitative changes in band structure, and does not change the qualityof the physical image. Such as, for example, the effects induced Mottlocalization . For this reason, doubtful value to calculate the bandstructure of insulators. You can calculate the band structure of NaCl, forexample, so that it does not explain the experimental facts hardly any,

What is the theory of band?

Solution to the Schrödinger equationfor a periodic potential

Populating bands by electrons. metals and non-metals

Computer calculations ab initio band structure

The evolution of the electronicstructure of the periodic table ofelements in the crystalline state.Summary: possibilities and limits of band theory

Dictionary Pol-Eng-mat

Test questions

Site Map

Literature

About the site

Designed by: Rafał Kosturek

12/9/12 Band theory of the electronic properties of solids

2/2zasoby1.open.agh.edu.pl/dydaktyka/f izyka/c_teoria_pasmow a/6.php

example, so that it does not explain the experimental facts hardly any,even the cohesive energy can be accurately calculated from the classical

electrostatic interaction of ions on the + and Cl - .

(Iv) rare earths and actinides.isolated atoms of the elements is characterized by partially filled level,respectively, 4 f and 5 f . Rare earths and actinides and their compoundswith the "normal" range of metals have not fully understood phenomena.For example, the phenomenon of "heavy fermions" lies in the fact that themeasured values of the masses effective in some compounds (UBE 13 ,

Ceal 3 ) is a factor of 10 3 times higher than the free electron mass. Band

theory of such growth can not be explained. So far, there is no goodtheory takes into account the coexistence of localized electrons 4 f or 5 felectrons and itinerant bands.

(V) the effect of temperature.discrete translational symmetry of the crystal is disturbed under theinfluence of temperature, due to the vibration of atoms around theequilibrium position. In most cases, the influence of temperature can beseen as a small disturbance band structure. However, it must be recalledthat the claims relate to density functional theory, the ground state, ieT = 0 K. As a result, there is no coming out of the first principles,calculation methods and the melting temperature ferromagnetic Curietemperature.

Limitations of band theory does not change the fact that it remains the mostimportant tool as a qualitative understanding and quantitative calculation ofproperties of condensed matter , such as property optical, thermal, magnetic,electrical and even mechanical . Works best for crystalline metals andsemiconductors, but it is also a necessary starting point for the description ofthe electronic structure of materials that do not have discrete translationalsymmetry and phenomena "do not fit" in the image jednoelektronowym.