Bloch theorem, Bands Ekn, gaps, metals vs. insulators
Semiconductors
Small energy gap allows carriers at ordinary temperatures
Bands in typical semiconductors - understandable from
Nearly-free-electron approximation
Equation of motion and effective mass
Negative Electrons and Positive Holes
Law of mass action: np = "constant"
Concentrations of electrons and holes: law of mass action (continued)
product np = "constant" (depends upon the crystal and the temperature)
Determines directly n and p for an intrinsic crystal where n=p
Control of conductivity by doping
Donors, acceptors
Binding of electrons or hole to impurity
Like the hydrogen atom, but with m*, epsilon
Binding can be very weak
If binding is weak, carrier can escape and contribute to conductivity
Expression in simple case
When is a semiconductor a metal?
In the density of donors is so large that the electrons from
different donor overlap strongly, then the electrons are not bound to
a particular donor and the can be free to move as in a metal
Like an ordinary metal - but much less dense - since the radius
a of a donor state can be large (2-50 nm) a density of donors may be small
compared to the total number of atoms. If a = 10nm, the density needs to be roughly
1(4pi a^3/3) ~ 0.2 x 10-24m-3 ~
0.2 x 10-18cm-3 ~ 0.001 x density of atoms.
The same ideas apply to holes also
The conductivity increases as T decreases like a metal
Both electrons and holes can conduct electricity and heat
Mobilities and carrier equilibrium carrier drift velocity
Peltier Effect (Solid State refrigerator)
Thermopower - electrical power generation from heat flow
Depends on signs of carriers - can change sign with changes
in n and p and mobilities
Motion in a magnetic field Hall effect
Cyclotron resonance measures m*
Directional dependence shown anisotropy of m*
Hall effect measures signs, densities and mobilities (if one
combines conductivity information and knows that only simple bands
contribute)