Nearly free electron model

Nearly free electron model - EEE539 Solid State Electronics...

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Unformatted text preview: EEE539 Solid State Electronics 7. Nearly Free Electron Model Issues that are addressed in this chapter include: The nearly free electron model Bloch function description The Kronig-Penney model Wave equation of electron in a periodic potential EEE539 Solid State Electronics Deficiencies of the free electron model 1. The free electron model can quite accurately describe heat capacity, thermal conductivity, electrical conductivity, magnetic susceptibility and electrodynamics of metals 2. The free electron model fails in explaining the diffe- rences between metals, semimetals, insulators, etc. 7.1 The Nearly-Free Electron Model insulators metals semiconductors Energy EEE539 Solid State Electronics The nearly-free electron model 5 For the case of the free-electron model, the allowed energy values are essentially continuous and the corresponding wavefunctions are plane waves. 5 Note also that a Bragg reflection is a characteristic feature of the wave propagation. At the edge of the Brillouin zone one has reflection and the wavefunctions are composed of forward and backward propagating waves: 5 Also note that these two standing waves will pile-up electrons at different potential energy, which will then lead to the energy gaps concept. ) / sin( ) / exp( ) / exp( ) ( ) / cos( ) / exp( ) / exp( ) ( ) ( ) ( a x a x i a x i x a x a x i a x i x -- - + - + EEE539 Solid State Electronics 5 The energy expectation value difference between these two charge terms, for a potential energy term of the form U(x)=Ucos ( x/a) is [ ] U dx x x x U E a a g = - =-- + 2 / 2 / ) ( ) ( ) ( ) ( ) ( EEE539 Solid State Electronics...
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Nearly free electron model - EEE539 Solid State Electronics...

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