Diode Current Equation
PN junction diode is broadly known for passing the
electric current exclusively in one direction. The measure of current passing
through the PN junction diode incredibly relies on upon the kind of material
utilized furthermore relies on upon the concentration of doping in the creation
of PN diode. The principle purpose behind the stream of current is because of
the generation or recombination of majority charge transporters in the
structure of the PN junction diode.
There are three areas where the majority charge carrier’s
flows .These areas are specifically quasi neutral P – region, quasi neutral n
region, depletion region. The separation between the depletion layers to the p
side of diode is called as the region of the quasi neutral P type. The separation
between the depletion layer and the n side of the diode is called the quasi
neutral N type. There will be no variety in the convergence of charge
transporters as we move towards the limits of the diode. The electric field
won't show in the quasi neutral regions.
Δnp(x →
-∞) = 0
Δpn(x →
+∞) = 0
The diode present in the forward bias is because of the
recombination of majority part of charge bearers. The charge carrier
recombination happens either in the P type or N type quasi neutral regions, in
depletion region (locale) or at the ohmic (resistive) contacts i.e., contact of
metal and semiconductor. The current stream in the reverse bias is because of
generation of charge bearers. This kind of charge carrier generation process
further expands the current stream in forward furthermore in reverse bias.
The passing of current in the PN junction diode is
dictated by the charge carrier density (thickness), the electric field all
through the structure of PN junction diode and the quasi Fermi level energies of
the P type and N type. The carrier density & electric field are utilized
for deciding the drift and diffusion current of the PN junction diode.
The quasi Fermi level energies of electrons & holes
inside the depletion locale and that of in the N type and P type quasi unbiased
regions are thought to be roughly equivalent in getting a systematic
arrangement.
In the event that the Fermi energy levels are thought to
be consistent in the depletion region, the minority charge carrier density
(thickness) at the limit of the depletion area would be as per the following
At the point when there is no external voltage connected,
thermal balance state is arrived at the above expressed mathematical
statements. The division between the Fermi levels increments with the external
connected voltage. This external voltage is reproduced by the charge of the
electron. The overabundance charge bearer’s exhibit in both of the quasi
regions recombines straight away when they achieve the metal and semiconductor
contact. The methodology of recombination happens quickly at the ohmic contact
and it further increments by the vicinity of metal. Thusly legitimate limit
boundary conditions can be expressed as takes after,
pn (x = wn) = pn0
np (x = -wp) = np0
now Consider the diffusion current mathematical statement
for both the quasi neutral regions of N type and P type, the current for the
ideal diode will be acquired by the
utilizing the boundary conditions to the considered diffusion current equations
Changing over the above mathematical statements as far as
hyperbolic functions, revising the above comparisons as
pn (x≥xn)
= pn0 + A cosh {(x-xn)/Lp}
+ B sinh {(x-xn)/Lp}
np (x
≤ -xp) = np0 +
C cosh {(x+xp)/Ln} + D sinh {(x+xp)/Ln}
Here A, B, C and D are the steady values to be dead set.
On the off chance that the limit conditions are connected to the above
hyperbolic comparisons, then we will have
Where the widths of the quasi neutral regions of N type
and P type are given as
w'n = wn – xn
w'p = wp – xp
The charge carrier current density in every of the quasi
neutral region is figured from the diffusion current mathematical statements
The measure of electric current passing all through the
whole structure of the PN junction diode dependably ought to be steady, on the
grounds that no charge can vanish or accumulate in whole structure of diode.
Henceforth, add up to present current through the diode is equivalent to the
aggregate of the most hole current in the N area, the greatest electron current
present in the p type and the current due to the recombination of charge
bearers in depletion region. The most extreme flows in the quasi neutral region
happens at the sides of the depletion region.
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