Transcript No Slide Title

Diodes under Bias
Qualitatively the function of the diode
under bias can be described best in terms
of energy band levels.
In the intrinsic case, the diffusion current
is matched by a drift current in the
opposite direction, which is driven by the
contact potential.
In biased conditions, the driving voltage is
combined with the contact potential. In
the forward biased condition it acts to
minimise the contact potential or even
reverse it. In the reverse bias situation it
increases the effective contact potential.
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Diodes under Bias
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Diodes under Bias
Diffusion Current
The effect of the reduced energy barrier in
the forward bias condition is that the
diffusion current increases as more
majority holes and majority electrons have
the energy to jump the now reduced
energy barrier. In forward bias conditions,
the diffusion current can be quite large.
In the reverse bias situation, there is a
higher energy wall and there are almost no
particles with sufficient energy to jump the
barrier and hence the diffusion current is
almost zero.
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Diodes under Bias
Drift Current
The drift current however is relatively
insensitive to the height of the energy
barrier as it is more dependent on the
quantity of available electrons and holes
to acts as carriers.
Drift current across the junction is
dependent on electrons falling down the
energy bands from the P side to the N,
and similarly for holes. The problem is
the quantity of minority carriers
available for the drift current to use, for
example electrons on the P side, which
depends primarily on thermal generation.
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Diodes under Bias
Diffusion
Drift
At zero voltage, the drift and diffusion
currents equal zero, the unbiased case.
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Carrier Injection
The equilibrium level for minority
carriers on each side of a pn junction
varies with the applied bias because of
variations in diffusion current across the
junction while drift remains about the
same.
The hole concentration on either side is
given by the following equation in
unbiased cases
Under bias conditions, this changes to
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Carrier Injection
For low bias levels we can ignore changes
in the majority carrier concentrations.
The increase in majority carriers is the same
as the minority carriers, in order to maintain
charge neutrality.
However the relative increase of the minor
carriers with respect to their equilibrium
values is significantly greater.
This is demonstrated by the following
expression where  is same order of
magnitude as a
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Carrier Injection
The ratio of increase in minority hole
concentration is given by
Thus there is a significant increase in
minority hole concentration with increasing
forward bias voltage.
This is also true for minority electron
concentrations on the P side, near the
junction.
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Carrier Injection
The increase in minority carriers is given by
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Diode Diffusion Current
Now as we know the diffusion current is
going to be a dominant current mechanism
in the diode under bias conditions, we’ll
proceed to ascertain the diffusion current.
The first stage is to calculate the distribution
of excess carriers on each side and hence
work out the current using the equations
from earlier.
From our previous work we expect that as
the excess carriers move away from the
junction they’ll recombine with the
opposing type, for example holes will
recombine with elections.
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Diode Diffusion Current
The diffusion equation can give the distribution
but if the length of the material on each side of
the junction is long compared to the diffusion
length, then the decay rate is exponential.
We’ll use new reference co-ordinates, measuring
from the edge of the depletion bands in each
regard, where xn is now the distance from the
depletion band in the n-doped material
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Schockley Ideal Diode Approximation
In the following analysis, we will assume that
there is no recombination of the carriers in the
depletion region. This is the Schockley Ideal
Diode Approximation. It’s premise is that
there are no un-recombined carriers in the
depletion region left.
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Diode Diffusion Current
From before, we have the equations
So combining with the expression for the
increase in carriers, we can get their
distribution as they recombine away from the
junction.
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Diode Diffusion Current
The diffusion current at any point xn in the ndoped material can then be calculated from the
diffusion equation current.
so
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Diode Diffusion Current
A similar equation can be found for the electron
current in the P type material
(minus sign is due to difference in carrier charge)
Assuming a junction of cross-sectional area A
the junction diffusion current is given by
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Diode Equation
So quickly replacing the expression for p and
n, and evaluating at the edge of the depletion
region.
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Diode Equation
So subtracting In from Ip (due to charge direction)
will give the total diffusion current across the
junction.
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Diode Equation

I  I 0 eqV
kT

1
This is the familiar diode equation.
Some important points worth noting
• The equation makes no statement on the bias
voltage, so this equation is applicable for
diffusion current for forward and reverse bias.
It will be very small in reverse bias.
• If the bias voltage is more than a few kT
negative, then Io must equal to the total
reverse saturation current.
I Re verse
 Dp
Dp 
 qA
pn 
np 
L

L
p
p


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A Quick Way to the Diode Equation
A quicker instructive way of
developing the hole current is to think
of it as the current is the current
required to maintain the distribution
of excess carriers that was predicted
by the Poisson’s equation as they
recombine.
i.e. recombination rate must be
matched by injection of new carriers
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A Quick Way to the Diode Equation
The total positive charge of excess
carriers at any instant of time is
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A Quick Way to the Diode Equation
The average lifetime for a hole is  p,
thus the current must replenish this
quantity of holes every p seconds,
giving
This is back to the equation that we
had earlier. From here we can proceed
as before.
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Diode Diffusion Current
Outside of the depletion region, the
diffusion current tends to zero as
the number of minority carriers is
very low.
The current is then carried by
majority carrier drift current.
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Assumptions and Drawbacks
It is important to note a couple of
inaccuracies in the above approaches.
• First it assumes that all the voltage is
dropped across the junction.
• However if this were the case then there
would be no voltage in the neutral areas
to cause the majority carriers to drift, but
there is a current, so there must be some
voltage dropped across the neutral area.
• In reality there is a resistance in the
neutral area which means that voltage is
dropped in these areas.
• This means that the applied junction
voltage is less than assumed in the
derivation so the currents will be less.
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Assumptions and Drawbacks
• The next problem is that normally the
diodes are not long with respect to the
diffusion length and so the excess
carrier distribution is no longer
exponential.
• The behaviour is more complicated
than our simple models and equations
indicate. However they do provide a
good approximation to the behaviour,
sufficient for a feeling of how diodes
work.
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Assumptions and Drawbacks
• One common practical difference between
what we’ve been talking about and real
diodes is that normally one side of the
junction is much more heavily doped than the
other, normally.
• What this means is that on one side the
depletion layer is very thin (the heavily doped
side) and the other side contains most of the
depletion layer.
• This is common in manufacturing of these
devices as you would use a lightly doped
substrate and then heavily dope it to turn it to
the other type of semiconductor, then cut it
and start again.
• In terms of our derivation, with this
knowledge halve of the equations, the lightly
doped side, can be discarded as being
insignificant in terms of current contribution.
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Assumptions and Drawbacks
• One common practical difference between
what we’ve been talking about and real
diodes is that normally one side of the
junction is much more heavily doped than the
other, normally.
• What this means is that on one side the
depletion layer is very thin (the heavily doped
side) and the other side contains most of the
depletion layer.
• This is common in manufacturing of these
devices as you would use a lightly doped
substrate and then heavily dope it to turn it to
the other type of semiconductor, then cut it
and start again.
• In terms of our derivation, with this
knowledge halve of the equations, the lightly
doped side, can be discarded as being
insignificant in terms of current contribution.
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Reverse Bias
• In reverse bias the electric field is such
that minority carriers in each depletion
region is swept out down the energy
barrier across the junction.
• However due to the increased energy
barrier at the junction, diffusion back
across the junction is not possible and
so the density of excess carriers at the
junction tends to zero very quickly.
• The minority carriers are only restored
by a diffusion current from the neutral
regions into the depletion region.
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Reverse Bias
• Electrons “fall down” the electric field
gradient, from left to right
• Holes “fall up” the electric field curve,
from right to left
Diffusion
electrons
Drift
Drift
holes
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Reverse Bias
• Free carrier concentration near the
depletion region is effectively zero
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Reverse Bias
• The drift current rate could be much
greater but it doesn’t have the free
carriers near the junction
• The free carriers are provided by
diffusion from the bulk of the diode.
• The junction is too great for diffusion
across the junction.
• Bulk diffusion rate limited by thermal
generation of electron-hole pairs.
• It is very small.
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Reverse Bias
The rate of thermal generation of holes
within a volume (Area A * one hole
diffusion length) is given by
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Reverse Bias
This simplifies down to a reverse-bias
hole current of
This is one half of the current across the
reverse bias junction. It is easy to see
that this is the same as Io from the
diffusion current equation from before.
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Reverse Bias Breakdown - Zener
When there is sufficient reverse bias and
heavily doped material, the energy
levels are so shifted that the conduction
band on the N side dips below the
energy requirement of the valence band
on the P side. When this happens
current still cannot flow because there is
a forbidden energy gap.
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Reverse Bias Breakdown - Zener
However if the gap between the bands,
the depletion region, is narrow it is
possible for electrons to tunnel across
the gap from P to N and provide a
conduction path.
This requires very heavy doping and a
very abrupt change in doping across the
junction to keep the width of the
depletion region small. The width of the
depletion region is very important.
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Reverse Bias Breakdown - Zener
• An easy way to understand the mechanism is that
the heavily doped P side of the junction has a
large voltage across it which ionises the atoms
and strips out electrons which are accelerated
towards the N side. These high energy electrons
have sufficient energy to jump the gap.
• A more quantum physics explanation is to say
that the higher energy electrons have a more
energetic wave which can extend across the
energy gap and where it may find a lower energy
state. In this case the electron will transfer to the
lower energy state.
• The sort of electric field required for this behavior
is typically of the order of 106 V/cm
• With controlled doping it is possible to set the
required voltage to cause tunneling to some
desired value, normally about 6V typically. This
is not a precise value as it will begin to turn on
before and after and is temperature and process
dependent.
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Reverse Bias Breakdown - Avalanche
Basically, electrons and holes are so accelerated
near junction that when they hit another atom
they ionise it and bounce off and repeat the
process on the next collision.
This process rapidly increases the number of
carriers at the junction, allowing the drift current
to climb significantly.
This process is not harmful to the diode unless it
melts.
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Reverse Bias Breakdown - Avalanche
In lightly doped junctions, the depletion
width is too great to allow tunnelling so
the breakdown mechanism is impact
ionisation.
In any lattice scattering event where an
energetic carrier hits an atom it is
possible, if there is sufficient energy, to
create an electron-hole pair. If the new
electron-hole pair has sufficient energy
each half of the pair may cause another
ionising impact and an exponential effect
can occur
Under these circumstances the diode
places no limit on the maximum current
that can be passed.
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Diode Models
• The model for the diode depends on how
you want to imagine the diode. Many
people consider the diode to be ideal when
it says no reverse current, infinite forward
current. (Figure a).
• Another model is to assume that
significant current flows after a certain
voltage, this is where unlimited current
begins to flow, zero resistance. (figure b).
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Diode Models
• A more realistic one is to add in a
resistance to indicate that the neutral
regions do have a resistance which takes
away some voltage (with increasing
current) from the junction.
• There is no right or wrong model, all
usable models are inaccurate. It depends
on your application.
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PN Junction Capacitance
• In reverse bias, the dominant capacitance
source is the charge distribution in the
depletion region.
• The junction capacitor of a reverse biased
PN junction is quite commonly used in
varactor diodes.
• In many circuits diodes are placed in
reverse bias to prevent voltage spikes from
reaching sensitive components. In these
cases the reverse bias diode capacitance is
visible to the circuit and needs to be
considered.
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PN Junction Capacitance
C
dQ
dV
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PN Junction Capacitance
However the charge in the depletion
region changes with applied voltage.
From earlier we have the equation for the
depletion layer width
and with an applied voltage, this becomes
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PN Junction Capacitance
The charge in the depletion region on each
side is given from before as
where the width of each region is defined
by the doping and the depletion width.
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PN Junction Capacitance
The charge on each side of the junction
can be given by
Now we have Q in terms of V, and using
the original definition we can proceed to
get the junction capacitance.
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PN Junction Capacitance
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PN Junction Capacitance
But the term in the brackets is the formula
for the depletion layer width. Swapping
this for 1/W brings us neatly back to the
structure of the parallel plate capacitor
formula, where W is the width, A the area
and e corresponds to the charge. Note,
NOT the SAME, just similar form.
C
A
W
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PN Junction Capacitance
C
A
W
We’ll encounter this phenomenon again
and again in semiconductor devices, the
capacitance of device junctions is highly
voltage dependent.
The depletion layer width is voltage
dependent, hence the capacitance is
voltage dependent.
This can be used to our advantage in
some applications, but in many cases,
especially with parasitic capacitances, it
can lead to increased complexity in our
circuit models. This is particularly
critical for high frequency applications
where even fento-farads can have a
significant effect..
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