Splice PN
1) Analysis of a semiconductor drugged in arbitrary way:
The presence of a gradient of concentration of bearers
gives to place to one current of spread from the region to greater
concentration towards the region to smaller concentration, the bearers
who move themselves per² leave of the Ionian ones of opposite sign,
the distribution of loads that it is obtained gives to place to an
electric field who opposes to the ulterior electron flow therefore to
the equilibrium the semiconductor is characterized from a still
variable concentration of bearers with the position and from he
upgrades them of Built-In. The presence of an electric field
deduces easy observing that on the band charts the energy that
separates the level of Firm from the conduction band is energy
upgrades them while the difference of energy between the band of
conduction and the energy of the electron is kinetic energy of this
last one, therefore defining like upgrades them 
and remembering the relation between it upgrades them and field has 
in how much andf he is constant in a semiconductor to the thermal
equilibrium and therefore its derivative is null while and it is found to the center between valence band
and conduction band and therefore varies if the semiconductor has
variable drogaggio.
To the thermal equilibrium the current that slides in the
semiconductor must be in average null therefore from the equation of
Drift & Diffusion 
ottiene 
of the rest being itself 
uguagliando the two found expressions obtain 
that
integrated between two points to various concentration it supplies 
or in exponential shape 
.
2) Equation of Poisson for a semiconductor with a generic drogaggio and its simplification:
where 
e
has been replaced. The equation is
not solvable in the general case therefore often comes adopted two
simplifications:
to) Approximation of nearly-neutrality, in short it assumes itself that the concentration of bearers is pressoche equal to the concentration of the impurities, is never valid how much in the bulk where therefore to second of the drogaggio of the semiconductor ha n = Nd oppure p = Nto .
b) Approximation of Depletion, previews that the concentration of free bearers is much inferior to the concentration of the ionizzate impurities, in sostanza n < < Nd oppure p < < Nto .
3) Splice PN to the thermal equilibrium:
When a p_doped is put to contact with a n_doped has an
abrupt variation of the drogaggio in correspondence of the splice
therefore has an electron flow from the region n to the region p and a
gap flow in opposite back, therefore in the origin regions they remain
of the Ionian ones which generate an electric field who opposes itself
to the ulterior spread of loads. In order to analyze this
situation the approximation is used nearly neutrality in the bulk
and the approximation of Depletion in the region of loads spaces them
mail to ridosso of the splice, in it therefore the equation of Poisson
is reduced to 
, uses in order to find it the
electric field. In n_doped the Nto= 0 therefore 
integrating it for 0 < x
< xn that is in the region of
loads spaces them of the n_doped has 
, analogous
for the p_doped finds 
therefore having to be the
continuous field in the origin otherwise could not admit upgrades
them, finds the 
relation in short that extension
as the semiconductor mainly drugged has one smaller extension of the
region of depletion.
Integrating the field ulteriorly it is obtained in the
n_doped upgrades them 
while in p_doped 
the where xn and
xp are i it upgrades them to the
ends of the region of Depletion and their difference corresponds to
upgrades them of Built_In 
.
4) It upgrades them of Built-In for one splice p n:
this because in the case of a semiconductor much drug addict the level of Firm is much neighbor to one of the two bands.
5) polarized Splices PN inversely:
Applying to an inverse polarization that is of the
generator on the region n the dimensions of the region of Depletion
are increased, for it in fact have 
as also the
electric field for which 
is had while the ability
diminishes in how much goes away the armors, has 
that is the classic ability for small marks them.
Naturally since increasing the polarization inverse it increases to the electric field, some phenomenon must happen or breach that you limit the operation, in particular before the breach of the device the following effects can be introduced:
Effect Valanga the electric field applied accelerates a free bearer which it meets with an atom and of free a valence electron. To continuation of the collision 3 bearers have themselves, two electrons and a gap which come accelerates from the field newly giving place to you to others hits.
Effect Zener If the semiconductor is much drug addict verification the Zener effect before the effect Avalanche, in particular is had that being the region of it loads spaces them much small, the electric field so is elevated to break off of the covalenti ties and to create of the braces electron-gap.