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ESTHER ONG PECK SUAN_A19SC0485_MINDMAP 6, Electron Theory - Coggle Diagram
ESTHER ONG PECK SUAN_A19SC0485_MINDMAP 6
Electron Theory
The Band Theory or Zone Theory
free electrons move in a periodic field
Bloch's Waves
Kronig-Penney Model
Barrier Strength:
Scattering power of potential barrier:
To determine allowed value of
Plot of E vs k:
Discontinuities occured at the boundary of Brillouin Zones
Existence of bands and gaps
Metal:
~electrons easily excited to levels above Ef
Semiconductor:
~appreciable no. of electrons can be thermally excited into the conduction band
Insulator:
~very few electrons in the conduction band
Effective mass: altered mass between electrons inside the crystal and electron in vacuum
Holes in semiconductors:
Electron moves out of the orbit, leaves a "hole" before it filled up
This vacancy considered as a hole with +ve charge
The Classical Free Electron Theory
obey law of classical mechanics
Also known as Drude-Lorentz Theory
Assumptions:
Large no. of free electrons moving freely in metals.
Free electrons behave like gas molecules (follow laws of kinetic theory of gases)
Electron conduction is due to the motion of free electrons only
Electric field is constant. Repulsion between electrons is negligible.
When an electric field is applied, electrons are accelerated in opposite direction to the electric field.
The Free Electron Model
conduction electron exists
It consist of the valance electrons from the metal atoms
Success：
It verifies Ohm's law
It explains the electric and thermal conductivities of metals
It derives Wiedemann - Franz Law
Failure:
Lorentz number - only half of the exp. value
~classical theory
Heat Capacity - fails to predict C for metal
T dependence of resistivity
The Quantum Free Electron Theory
obey quantum laws
Quantum-based free-electron theory of metals
Take into account the wave nature of electrons
Boundary conditions: electron trapped within 3D box formed by the metal surfaces
Electron represented as a particle in a box
Particles restricted to quantized energy levels
Energy
~In 1D:
~In 3D:
Density of states:
~
Number of electrons per unit volume:
~
Fermi-Dirac distribution function
Electron occupied energy levels according to Pauli exclusion principle
E = Energy occupied by 1 electron
Ef = Fermi energy (highest energy possessed by an electron in the material at 0K)
k = Boltzmann constant
T = absolute temperature in K
T = 0K
T > 0K
Sommerfeld's Model
Assumptions:
Similar to those of Drude
Free & independent electrons
~moving independently in a square well
TISE (time-independent schrodinger equation)
~
~Shorthand:
Motion of an electron in free space
~Energy of free electron:
~Wavefunction:
~Momentum:
Fermi Sphere
Fermi sphere - the boundary between occupied and unoccupied k states
Fermi radius -
Fermi Energy -
