Elements of physics of the semiconductors
1) Reticulum of Bravais:
The crystals are characterize to you from a regularity space them therefore are possible to describe to a whichever atom to pertaining it by means of the R carrier =1 but2 na3 , with of the R carriers constitute the reticulum of Bravais.
2) Theorem of Block:
In the solid case of crystalline a hamiltoniana it is 
where U(r) is upgrades them periodic, the
autostato one is 
that is the product of a flat
wave for a having term the same regularity of the reticulum.
3) Zone of Brillouin:
From the theorem of Block evince that in the case of a reticulum he is sufficient to know the autofunction on one determined zone of the space k said 1ª zone of Brillouin in how much us can only to it be always reduced through one translation on a carrier of the mutual reticulum.
4) Characteristics of the electron of Block:
The group velocity of an electron in the band n with wave
carrier k is 
, in presence of external forces, the
carrier of varied wave second 
the , the 
amount is the equivalent of the momentum p to pact to
consider such the effective mass M che 
.
5) Characteristics of the GaAs and of:
Crystal
The GaAs crystallizes in the structure of the zincoblenda constituted from two reticula FCC traslati along direction [ 111 ] of one equal distance to the length of the tie. Also it is crystallized in the structure of the zincoblenda that it coincides with that one of the diamond in how much all the atoms are equal.
Bands
The bands of the GaAs evidence a gap direct, moreover to the inside of the zone of Brillouin are present others two minimums, one to 0,3eV from previous and the other to 0,48eV. One is instead to gap indirect.
Effective mass
The effective mass of the GaAs is m*= 0.067m0 and is isotropa while that one of is anisotropic, in
particular the longitudinal mass is worth 
while
the cross-sectional mass is worth 
Band of Valence
The valence band is degenerate in the origin, has
in fact 3 bands characterized from parabolicità different, one of
heavy gap (HH) having effective mass 
, one of light
gap (LH) with effective mass 
and one of gap
split-off (KNOWS).
6) Characteristics of ternary compounds:
Draft of composed that they conserve the crystalline structure of the binary compounds from which they derive some but modifies the value sometimes and the nature of the gap.
7) Density of bearers in the approximation case not degeneration:
The electron density in conduction band is 
where for the function of distribution of Firm the
approximation is considered degeneration that is that the level of
Firm is had enough far away from the conduction band, in such a way
such distribution is not reduced to that one of Maxwell-Boltzmann
and 
is had where 
is the
effective density of states in conduction band that must be multiplied
for MC for i having
semiconductors more equivalent minimums in conduction band.
In analogous way it is obtained in band of 
valence con 
.
8) Level of Firm intrinsic:
9) ionizzati atom Density:
being andD the Donor Level and andTo the Acceptor Level, in particular the course of the density electronic in the band of conduction of a semiconductor drugged to varying of the temperature linearly evidences an increasing course for low temperatures, when all the donori have been ionizzati begin the saturation zone in which the concentration he is constant dopodichè for next temperatures to the 500K is had that the electrons pass from the band of valence to the conduction band giving place to one abrupt variation of the concentration in this band.
10) Law of Matthiessen:
Mobility is the constant of proportionality between the
field applied and the speed assumed from the bearers, it is worth 
, in the case that on the bearer more
mechanisms act than scattering mobility total it is 
11) Approximations used in the study of the effects induced from the thermal agitation:
The atoms of the reticulum are subject to thermal agitation, in order to facilitate of the study make the following approximations:
to) it is assumed that the medium position of atoms coincides with the crystalline reticulum
b) it is assumed that the movement regarding the equilibrium position is much minor regarding the distance between atoms.
12) Dispersion of the fononi:
It is assumed that to every atom of the crystal a harmonic oscillator is associated, that from place to acoustic dispersions characterized linear course in pressed of the origin and the optical dispersions characterized from almost constant course, to notice that the fononi they are Bosoni and therefore described from statistics of Bose-Einstein.
13) Typology of interaction processes:
to) Interaction with defects which breakups or impurities
b) Interactions with fononi are for deformation that electrostatic
c) Interaction between bearers
14) Equation of Boltzmann:
wherethe k it is said operating of collision and it describes to the temporal variation of the distribution function due to the collision phenomena.
15) Method of the moments:
It comes used the theorem according to which the
acquaintance of the infinites moments M of the function of 
distribution is
equivalent to the acquaintance of the distribution function f(r, k,
t).
16) Equations hydrodynamics:
where u it is the average speed of the bearers and w it is the medium kinetic energy of the particle.
16) Model Drift & Diffusion:
The introduced approximation is to always remain in
conditions nearly staticità that is of having 
,
is had:
17) Curve Speed - Field:
For inferior fields to 1kV/cm all the semiconductors they
have a linear course of the speed of the bearers with the field, the
proportionality constant is mobility which to low temperatures is
determined from the scattering from fononi acoustic while to high
temperatures it is determined from the scattering from fononi optical.
For fields it elevates to you, the covalenti materials which GE
and they introduce saturation due to the heating of the bearers from
part of the electric field, the saturation speed is 
,
polar materials like the GaAs instead introduce a zone to resistance
differentiates them negative due to the scattering intervalle.