Electronics: The Microscopic View of Conduction

 There is a lattice of copper balls patched together. The bonding is metallic bonding. The outermost valence electrons form "free electron clouds" free up space between metal ions. Sometimes, free electrons can rebound "off" of metal ions. The free electron model assumes 1 free electron per copper atom. The average distance than an electron travels is about 2 x 10 ^ -9 meters, and an average collision time of 2.4 x 10^-14 seconds. Quantum Mechanics help to explain why electrons are in many energy levels. It also indicates the electron speed to be higher than the free electron model. 

The work function prevents electrons from exiting particle surfaces. There are 4 types of emissions. 

1. The thermionic emission increases the temperature high enough for energy to overcome the work needed for the electron to "jump" from the conductor. 

2. The secondary emission is when the electrons are emitted from the metallic surface and bombards with other particles. 

3. The field emission happens when additional energy from an electric field provides enough positive fields to free electrons from the surface. 

4. The photoelectric emission results in the bombarding of photons to give them enough energies to overcome the work function. The photon has to be of the correct frequency, or W = hf0 where f0 is in Hertz. Planck's constant, h is 6.63 x 10^-34 Js, or 4.14 x 10^-14 eV, where f0 is in Hertz. 

Here's a diagram of the electrons vibrating with the lattice ions: 

eV is the fermi energy, and the temperature can e measured in Fermi temperature. The Fermi density ρe is measured in electrons/(m^3) and the work function is used in eV. Velocity is measured in the following:

VF = C(2EF/(me(C^2)))^(1/2)

Applying voltage is when free electrons experience force towards the positive end of the wire due to its electric field. Electrons rebound through the copper lattice and its impurities. The electrons also have a slightly parabolic trajectory. 

The charge is the product of drift velocity, time, free electron concentration, and charge. The electric field also has repulsive effect on the neighbors, which moves to the anodes towards the cathodes, almost at the speed of light. It's like water out of a hose, they will help greatly make things to accelerate. 

In the alternating current, electric fields will change direction X times a second with X hertz. Although electron motion is random; however, they still follow a general trend.