Currents in splice PN
1) Equation of continuity:
Draft of an equation that holds account of the current due is to the majority bearers that to the minority bearers, in order to characterize it considers a having wide region of semiconductor dx and area To, is had:
I replace the development of Taylor di Jn(x dx) and ottengo 
, replacing in essa 
obtains 
where E(x) and n(x) is both function of x
therefore demands the calculation of the derivative of composed
function, an analogous relation is had also for gaps.
2) Capture and emission from part of states localize to you:
The mechanism simpler than generation previews the emission of an electron that they give the valence band passes in the conduction band, it but it is enough improbable in the semiconductors that like the Germanium and a Silicon they possess a gap indirect, demands in fact a collision to three particles, an electron, a photon and a fonone, that that happens instead is that they come takes advantage of you of the present states to the inside of the gap which have had to impurities or to imperfections of the reticulum, they is many Firm neighbors to the level of intrinsic and has energy andt and N densityt , we suppose moreover that they are of the states accepters that is neutral when empty and denied to you when occupied.
The 4 possible processes can be had following:
R1 Capture of an
electron draft of the passage of an electron from
the band of conduction to one be empty, the rhythm to which that it
happens is 
that is is proporziona them to the
electron concentration in conduction band n, to the density of empty
states it localizes 
to you and to the product of
the thermal speed vth for the
capture section trasversa sn that measure of the efficiency of the state in the
capture of the electron is one.
R2 Emission of
elettrone a draft of
the passage of an electron from the state localized to the conduction
band, the rhythm to which ci² it happens is 
that is is proporziona them density of states localizes to you full
for the emission probability andn .
R3 Capture of
lacuna a draft of the passage of a gap from the band of valence to
one be localized occupied from an electron, the rhythm to which that
it happens is 
that is is proporziona them to the
gap concentration in valence band p, to the density of states it
localizes to you occupied from 
electrons and to
the product of the thermal speed vth for the section trasversa of capture of gaps sp .
R4 Emission of
lacuna a draft
of the passage of a gap from the state localized to the band of
valence or equivalent the passage of an electron from the band of
valence to the localized state, the rhythm to which that it happens is 
that is is proporziona them density of states
localizes empty for the probability of emission of one gap to you andp .
3) Distinction between states localizes you of type trap and type recombination center:
The distinction happens for fenomenologica way that is supposes that there is an increase of R3 therefore has an increase of the n° of gaps, can be returned to the condition of thermal equilibrium is through Rthe 1 (…in the which case localized state is a center of recombination) that through R4 (…in the which case the localized state is one trap).
4) Rate recombination clearly U:
where it has been assumed that the capture sections are
equal and that 
, it turns out to be maximum for
states localizes to you situates to you in Firm correspondence of the
level of intrinsic.
5) Time of life of the bearers in excess:
Draft of the time that elapses before that the bearers in
excess who have been inettati they come riassorbi, for its
determination uses the U function applied exactly to the bearers in
excess n' in the case of Low_Level Injection that is in the case in
which the density of the bearers they are not a lot altered from the
disturbance regarding their value to the equilibrium, is had that is
n' = n â " n0 e
p' = p â " p0
naturally poi n' = p'. The recombination rate is 
replacing the previous data and resolving the equation
it differentiates them obtains 
dove tn @t0 and therefore 
.
It is observed that the time of life of the bearers in excess tn does not depend on the concentration of the majority bearers.
6) Recombination Standard:
It is a process to two bodies, an electron and a gap annihilates mutual.
7) Auger Recombination:
It is a process to 3 bodies, an electron and a gap annihilate and a third electron or gap acquires the moment and the energy of the bearers who hit.
8) Density of minority bearers to the edge of the emptying region:
We want to determine the density of minority bearers in excess to the extremities of the emptying region therefore we are interested to the electron concentration in excess in - xp that is n'p(- xp) and to the gap concentration in excess in xn that is p'n(xn), they express like difference between the excited value and the value to the equilibrium, and can be obtained easily in how much are famous the concentration to the other end of the splice (…equal to the concentration of the impurities in vrtù of the approximation nearly neutrality) and the potential difference them equal to upgrades them of Built-In.
, analogous one obtains for p'n(- xn), the
two relations show as the concentrations of the minority bearers are
subject to the polarization while the concentrations of the majority
bearers are svincolate some.
9) Analysis of the ideal diode valve:
The course of gaps in excess to the inside of the bulk of
the n_doped can itself be gained by means of the equation of 
continuity where for semplicità of analysis the
stationary state is considered, the concentration of the donori is
constant and the electric field is null, moreover the U function is
reduced for the hypotheses previous to the 
amount, the equation is reduced to 
that has the solution 
where To and B they are
obtained from the conditions to the contour while 
.
10) Diode valve to long base:
Draft of a diode valve for which the length of L spreadp is small regarding the length
WB of the n_doped of is
followed that all are recombined before reaching in WB and therefore the B coefficient of the
reflected member is null therefore the course of gaps in excess to the
inside of the bulk is 
moreover since the
electric field in the bulk is null, the current is due exclusively to
the spread 
, draft still of a exponential that it
evidences as close to the region of Depletion the current is all due
to gaps while going away towards the contact metallic it is had
that the gap current diminishes and increases instead the current of
electrons. In analogous way 
is found and
adding it is had 
.
11) Diode valve to short base:
Draft of a diode valve in which the length of L spreadp is the much greater one of the
amplitude WB of the n_doped,
therefore in 
the first exponential makes
use 1, resolving finds 
that extension one
descrescita of linear type of the gap density in excess in the n_doped
which deriving constant gap current corresponds one that does not
demand therefore one at all majority electron current.
12) Currents in the region of load space them:
In the region of it loads spaces them are present centers
of ricombinazione/generazione, therefore it is necessary to estimate
the currents to they due, by means of function the
Polarization diretta ha U>0 therefore clean recombination, the
current total of J recombinationr obtains integrating along the region of loads spaces them 
, draft of an integral that is resolved for
numerical way or for semplicità the maximum of U is considered and
the integral one on an infinitesimal one of region of is loaded spaces
them, obtains 
that rapportata to the current J
totalt it supplies 
that extension as Jr becomes negligible to growing of the applied direct
polarization.
Polarization inversa ha U<0 therefore clean generation, the current total
of J generationg is in
approximate way 
that rapportata to the current J
totalt supplies 
that extension as in the diode valves it polarizes to
you inversely the generation current is due mostly to the region of
loads spaces them.
13) Currents in the real diode valve:
In the real diode valves beyond to the current previewed in the case of ideal diode valve the currents are had also that derive from generation and recombination in the region of loads spaces them, they mostly turn out to be important in the case of inverse polarization or active polarization but weak person, in proximity of the splice are had:
to) iniettati minority bearers that they diffuse towards the ohmmico contact
b) majority bearers who driftano towards the splice for being then diffuse in the region where they are minority
c) majority bearers who driftano towards the splice in order to recombine itself with the iniettati minority bearers
d) majority bearers whom driftano towards the region of he loads space them in order to recombine themselves with the coming from bearers from the region with opposite drogaggio.
In any case in proximity of the ohmmici contacts the current is due exclusively to the majority bearers who driftano.
14) Carica stored from a diode valve:
It loads stored in the nearly-neutral region is obtained
integrating on such region the distribution of loads minority in
excess, in the case of a diode valve to long base such distribution is that integrated supplies 
that is a lot simply loads iniettata is equal
to the product of the gap current for the time of life of the same
ones.
In the case of a diode valve to short base instead the
distribution of the bearers in excess it is 
therefore 
from which 
is obtained where according to member gap in the type region is the
time of medium transit of one n.
15) Transitory of the diode valve:
Applying to a directed polarization to a diode valve to long base initially drainage, it is had that it loads is limited from the current and therefore it is necessary a time Pò before that the diode valve cargos and is had to i its heads VD .
Applying to hour an inverse polarization we must have that the diode valve does not lead if not one small current of minority bearers, but that does not happen immediately in how much is necessary a Pò of time before that it comes riassorbita loads in the nearly neutral region, for velocizzare this time can or be reduced the direct current or to reduce the time of life of the minority bearers inserting of the centers of recombination in gold.
16) Abilities associated to a diode valve:
One ability C is hadj inherent to loads stored in the region of Depletion and one relative abilityC d to loads stored in the nearly-neutral region, this last one grows esponenzialmente with the applied direct tension while Cj assumes predominant value in the case of inverse polarization.