Reciprocal lattice: The three vectors defining lattice translations. Any point on lattice
- linear combination of lattice vectors a1,
a2, a3. Reciprocal vectors are defined as vectors
which give the exponential as 1, i.e. multiples of 2 pi.
For this, they must be orthogonal and normalized as indicated.
A vector product is orthogonal to both of the multiplied
Resulting reciprocal lattice vectors.
The combined vector and scalar product gives a volume of the parallelpiped
formed by the three vectors. If the original lattice is in the
normal position space, the reciprocal lattice is in the wavevector
(wavenumber) space. The first has dimension length,
the reciprocal has dimension 1/length.
What about other cells? If the lattice is not
Bravais lattice, like the hexagonal? It can be made to a lattice where the hexagons are
single elements - not the atoms. Wigner Seitz cells on a lattice are connected
with the Brillouin zones. WIgner Seitz: cut all the distance to nearest neighbours
by an orthogonal plane (line in 2dim).
Semiconductor equation: 2 expressions for
ni. Set them equal and obtain expression
for the parameter mu, temperature dependent Fermi level.
Discuss the influence of the effective mass,
i.e. the curvature (second derivative) of the band E(k).
Relation of Semiconductor equation, Law of mass action,
(massevirkningsloven) as it relates to the chemical
kinetics - pH-factor mentioned.
Pure, p-doped and n-doped situations.
Position of the parameter mu
for the doped semiconductors. They must be strongly doped,
otherwise the mu is not influenced.
Overview of the results. The mu is indicated
for pure, p and n doped semiconductor
Next time: The inhomegeneous conductor: adjacent p- and n-doped regions.