Carrier Transport
Drude
- Based on kinetic theory of gas molecules
- Parallels to electron movement
- Move in straight line until collision
- No forces acting during travel
- Time between collisions
- Relaxation time
- Mean free time
- Scattering time
- Collisions randomise velocity
Assumptions
- Metal is formed of positive ions
- Number of delocalised free electrons
- Without EM field electrons move in straight line
- Only interaction is via collisions
- Electron-ion interactions usually ignored
- Free electron approximation
- Not particularly accurate
- Nearly free electron approximation is better
- Weak interactions
- Perturbations
- Electron-electron interactions ignored
- Single particle picture
- Independent electron approximation
- Hard to model because
- Don’t know wavefunctions of every electron
- Potential from interactions is not periodic
- Need to consider dynamics of all electrons at once
- Often weaker than electron-ion
- Parallel spins avoid each other
- Pauli exclusion
- Opposite spins avoid each other
- Reduce energy
- Coulomb repulsion
- Electrons distribute around ions
- Screen ions from other electrons
- Parallel spins avoid each other
- Mean free time between collisions is Tau
- Probability of collision per unit time
- 1 over Tau
- Relaxation rate
- Typically 0.1 ps
- - times per second
- Achieve thermal equilibrium via collisions with lattice
- Emerge with random direction
- Speed based on temperature of collision area
- Two temperatures
- Temperature of atoms
- What you measure
- Effective temperature of electrons
- Via Boltzmann’s
- Transfer small amount of energy to lattice
- Temperature of atoms
- Two temperatures
- Speed based on temperature of collision area
- Emerge with random direction
- Probability of collision per unit time