lesson 11 Sommerfeld model i Solid State Physics

lesson # 11: Sommerfeld model i Solid State Physics M. Casalboni 2018/’ 19 SOMMERFELD MODEL (1928) free electron model with parabolic dispersion curve Arnold Sommerfeld 1868 -1951 it describes conduction electron in metals usefull for showing thermodynamic implications 1/17

lesson # 11: Sommerfeld model i the model is an evolution of the classical Drude model for electron in solids derived by kinetic theory (1900) Solid State Physics M. Casalboni 2018/’ 19 2/17

lesson # 11: Sommerfeld model i the model is based on quantum theory of ELECTRON GAS Solid State Physics M. Casalboni 2018/’ 19 BASIC ASSUMPTION: in several metals the potential energy of a CONDUCTION electron can be considered CONSTANT 3/17

lesson # 11: Sommerfeld model i the model is based on quantum theory of ELECTRON GAS Solid State Physics M. Casalboni 2018/’ 19 free electron plane wave 4/17

lesson # 11: Sommerfeld model i Solid State Physics M. Casalboni 2018/’ 19 it implies the Pauli’s exclusion principle proposed in 1925 and the Fermi –Dirac distribution developed in 1926 5/17

lesson # 11: Sommerfeld model i Solid State Physics M. Casalboni 2018/’ 19 6/17

lesson # 11: Sommerfeld model i too simple ? Solid State Physics M. Casalboni 2018/’ 19 7/17

lesson # 11: Sommerfeld model i Solid State Physics M. Casalboni 2018/’ 19 note: as Bloch function with the periodic part = 1 we can take 8/17

lesson # 11: Sommerfeld model i how many electrons ? for Alkaline metal for Aluminium ( Solid State Physics M. Casalboni 2018/’ 19 1 ) 3 9/17

lesson # 11: Sommerfeld model i Solid State Physics M. Casalboni 2018/’ 19 bcc 2 atoms each a 3 a (Å) rs Li 3. 49 3. 25 Na 4. 23 3. 94 K 5. 23 4. 87 Rb 5. 59 5. 20 10/17

lesson # 11: Sommerfeld model i Solid State Physics M. Casalboni 2018/’ 19 11/17

lesson # 11: Sommerfeld model i Solid State Physics M. Casalboni 2018/’ 19 a little warning!! FERMI ENERGY 12/17

lesson # 11: Sommerfeld model i Solid State Physics M. Casalboni 2018/’ 19 13/17

lesson # 11: Sommerfeld model i Solid State Physics M. Casalboni 2018/’ 19 Fermi velocity 14/17

lesson # 11: Sommerfeld model i Solid State Physics M. Casalboni 2018/’ 19 typically EF = 1 to 10 e. V Fermi energy 15/17

lesson # 11: Sommerfeld model i Solid State Physics M. Casalboni 2018/’ 19 total energy of the ground state 16/17

lesson # 11: Sommerfeld model i Solid State Physics M. Casalboni 2018/’ 19 density of states 17/17