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M I N D M A P 6 - Coggle Diagram

- - - - In metals, there are a large number of free electrons moving freely within the metals. The electrons revolve around the nucleus in an atom
      - The free electrons are assumed to behave like gas molecules, obeying the laws of kinetic theory of gases.
      - Electric conduction is due to motion of free electrons only. The +ve ion cores are at the fixed positions. The free electrons undergo incessant collisions with the ion core
      - The electric field due to the ion cores in constant through the metal. The repulsion between the electrons is negligible
      - When an electric field is applied to the metals, the free electrons are accelerated in the direction opposite to the direction of applied electric field
    - - Ohm's law
      - Relationship between
      - Wiedemann-Franz law
    - - Lorentz number
        
        L for several type of metals
        
        it is found that the classical value of Lorentz number is only half of the experimental value,
      - Heat capacity
        
        It is found that the electronic contribution is only 1% of this. (only small fraction of electron can be excited to higher level)
        
        C contributed by electron is much smaller than the calculated results
        
        Drude model fails to predict C for metal
      - To correctly account for the T dependence of resistivity in metals
        
        At very low T, and the resistivity usually reaches some finite value as the T approaches absolute zero
        
        At high T resistivity (the linear region) is predominantly characterized by collisions between electrons and metal atoms
      - To correctly account for the T dependence of thermal conductivity
        
        k behaves in a more complex manner
  - - - Valence electrons are responsible for the conduction of electricity and are called conduction electrons
  - - - Neglect electron - ion core interaction
      - Neglect electron - electron interaction
    - - Assumes electrons bouncing off the ion core
      - Assumes some from the scattering
    - - Collision mean free time
      - Independent of electron position and velocity
- - - - At 0 K, all states having energies less than the Fermi energy are occupied and all states having energies greater than the Fermi energy are vacant
    - - As T increases, the distribution rounds off slightly causing states near and below EF lose population and states near and above EF gain population
      - The Fermi energy depends on temperature, but the dependence is weak in metals
      - If
        
        Thus, valid
      - If
        
        Thus, valid
- - - - Most are similar to those of Drude
      - Free & independent electrons, but no assumptions about the nature of the scattering
      - Starting point: time-independent Schrödinger equation (TISE).
  - - - wave vector plays the same role as the momentum of an electron
      - Reciprocal space referred to as momentum space
  - - - Next, twelve electrons can go to the next lowest energy states, which are given by the following six identical values (1, 0, 0), (0, 1, 0), (0, 0, 1), (-1, 0, 0), (0, -1, 0) and (0, 0, -1)
        
        continued until all electrons up to the Avogadro number fill the reciprocal space
    - - Fermi radius,
      - Fermi velocity,
        
        Energy of a free electron,
- - - - At T = 0, all levels in the conduction band below EF are filled with electrons while those above EF are empty
      - For T > 0, some electrons can be thermally excited to energy levels above EF, but overall there is not much difference from the T = 0 case
      - metals have high electrical conductivity
    - - At T = 0, the valence band is filled and the conduction band is empty
      - the band gap energy Eg is relatively large (~ 10 eV)
      - there are very few electrons in the conduction band and the electrical conductivity is low
    - - At T = 0, the valence band is filled and the conduction band is empty
      - the band gap energy is relatively small (1-2 eV) so appreciable numbers of electrons can be thermally excited into the conduction band.
      - the electrical conductivity of semiconductors is poor at low T but increases rapidly with temperature
  - - - If there is only one electron in the band,
      - If the bands are full,