Question

In this 3 exercise, we consider a 10 problem. We have a metallic object so that the theory of free electrons will be used. 1) Recall in 10 lines (maximum), the hypotheses and consequences for the energy of the 4 types of electrons (free electrons, electron confinement, nearly free electrons and the tight biding methods).

Answer 1

election 0 free electon model hypothenst- According to this model metallic solid is a containe having gas. The interaction blu electron and in was not considered except for brundary condition. The interactics blw leaton-election is ignored. Electric field is weak due to screening effect. - Metal conducs elecdicity due to these colliding free ei The allowed energy states of e are quantized which depends on effective electron mass and electen no- deurity of metal. - only two e- (ab 8pm) can occupy same enersy level.

for banday conditions ). Portential energy is assumed rew and rufnity otheusse Pelection こ 1274² Im L2 for go} & But on ve sin mas E broaden Jewel this model falls as it dogsnot take into account interactions b/w elecken- in and electon-electen. It is replaced by Band theory. cii) Elecben confinement : = It means the e is confined ma spree for motion. 54 gives rise to quatum esse, quantum well and quantum dots. The energy of e confined in AD:- The gires rise to discrete enagy levels of electon. E = 22² 1 2 2 h2 m2 the + 2 m* Synt 2m* band e- is op = 0(2) Aly) exp Cikxx). - It leads to formation of jopo The energy sperdun is continuas in system with larger dimensions but when confined its energy levels become discrete and the gap bw these levels is called band gap. iii) Nearly foce electron model: This model is modification of free e- model. In this the interactions blo conduction election and ions is and considered by including a weak periodic beatusbatén. But still e=é Interaction is not taken into account Yo- 돔 Vlo) Cholks & Unelar

ane of an 14 Tight Binding model: It is e- model in which calculation electronic bound Structure is done using approximate set of wavefructing which are supe imposed atenie site. In this e- is tightly bounded to an atom and has limited interaction with subranding atens. Que to which the ware function of er becomes similarto that of odense ssital, Ereigy of S-band (10) cucing Light broling modela- Elk) = fo- La Coseka) It as coska