Ideal Diode Model

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Ideal Diode Model
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• Lets begin with an ideal diode and look at its
  characteristics

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Real PN Junction Diode I-V Characteristic
Typical PN junction diode I-V characteristic is
shown on the right. In forward bias, the PN
junction has a turn on voltage based on the
built-in potential of the PN junction. The turn
on voltage is typically in the range of 0.5V to
0.8V In reverse bias, the PN junction conducts
essentially no current until a critical breakdown
voltage is reached. The breakdown voltage can
range from 1V to 100V. Breakdown mechanisms
include avalanche and zener tunneling.
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Current Equations
The forward bias current is closely approximated
by
where VT is the thermal voltage (25.8mV at room
temp T 300K or 27C ) k Boltzmans constant
1.38 x 10-23joules/kelvin T absolute
temperature q electron charge 1.602 x
10-19coulombs n constant dependent on
structure, between 1 and 2 (we will assume n
1) IS scaled current for saturation current that
is set by diode size Notice there is a strong
dependence on temperature We can approximate the
diode equation for igtgt IS
In reverse bias (when v ltlt 0 by at least VT),
then
In breakdown, reverse current increases
rapidlya vertical line
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Mobile Carriers
Now lets look at physical mechanisms from
which the current equations come. Weve seen
that holes and electrons move through a
semiconductor by two mechanisms drift and
diffusion
In equilibrium, diffusion current (ID) is
balanced by drift current (IS). So, there is no
net current flow. Drift current comes from
(thermal) generation of electron-hole pairs (EHP).
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Band Diagrams
When the P-type material is contacted with the
N-type material, the Fermi levels must be at
equilibrium. Band bending The conduction and
valence bands bend to align the Fermi
levels. Electrons diffuse from the N-side to the
P-side and recombine with holes at the boundary.
Holes diffuse from the P-side to the N-side and
recombine with electrons at the boundary. There
is a region at the boundary of charged atoms
called the space-charge region (also called the
depletion region b/c no mobile carriers in this
region) An electric field is created which
results in a voltage drop across the region
called the barrier voltage or built-in potential
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What happens when P-type meets N-type?
Holes diffuse from the p-type into the n-type,
electrons diffuse from the n-type into the
p-type, creating a diffusion current. The
diffusion equation is given by
Once the holes electrons cross into the n-type
p-type region, they recombine with the
electrons holes. This recombination strips
the n-type p-type of its electrons near the
boundary, creating an electric field due to the
positive and negative bound charges. The region
stripped of carriers is called the space-charge
region, or depletion region. V0is the contact
potential that exists due to the electric field.
Some carriers are generated (thermally) and make
their way into the depletion region where they
are whisked away by the electric field, creating
a drift current.
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E-field and Built-in Potential
Diffusion is balanced by drift due to bound
charges at the junction that induce an E-field.
Integrating the bound charge density gives us
the E-field
Integrating the E-field gives the potential
gradient
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Junction Built-In Voltage
With no external biasing, the voltage across the
depletion region is
Typically, at room temp, V0 is 0.60.8V How
does V0 change as temperature increases? Note
that there is no measurable potential difference
between the n-type and p-type materials of pn
junction when in equilibrium. The electrochemical
potentials (Fermi levels) are the equal.
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Width of Depletion Region
The depletion region exists on both sides of the
junction. The widths in each side is a function
of the respective doping levels. Charge-equality
gives
The width of the depletion region can be found
as a function of doping and the built-in voltage
es is the electrical permittivity of silicon
11.7e0 (where e0 8.854E-14 F/cm)
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Pn Junction in Reverse Bias (1)
As the depletion region grows, the capacitance
across the diode changes.
Treating the depletion region as a parallel
plate capacitor
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Reverse Bias (2)
Reverse bias apply a negative voltage to the
p-type, positive to n-type. Increase the
built-in potential, increase the barrier
height. Decrease the number of carriers able to
diffuse across the barrier. Diffusion current
decreases. Drift current remains the same (due
to generation of EHP). Almost no current flows.
Reverse leakage current, IS, is the drift
current, flowing from n to p.
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Reverse Breakdown
Zener Breakdown The bands bend so much that
carriers tunnel through the depletion region.
This will occur in heavily doped junctions when
the n-side conduction band appears opposite the
p-side valence band. Avalanche Breakdown
carriers have enough energy to ionize an
electron-hole-pair (EHP), creating more highly
energetic carriers, which collide to form more
EHPs, which creates
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pn Junction in Forward Bias (1)
Now lets look at the condition where we push
current through the pn junction in the opposite
direction. Add more majority carriers to both
sides ?shrink the depletion region ?lower
V0?diffusion current increases Look at the
minority carrier concentration lower barrier
allows more carriers to be injected to the other
side Note that np0 ni2/NA and pn0
ni2/ND This comes from two equations
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The forward bias voltage causes excess minority
carriers to be injected across the junction.
The distribution of excess minority hole
concentration in the n-type Siis an exponentially
decaying function of distance from xn
where Lp is the diffusion length (steepness of
exponential decay) and is set by the
excess-minority-carrier lifetime, tp. The average
time it takes for a hole injected into the n
region to recombine with a majority carrier
electron
The diffusion of holes leads to the following
current density vs. x
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In equilibrium, as holes diffuse away, they must
be met by a constant supply of electrons with
which they recombine. Thus, the current must be
supplied at a rate that equals the concentration
of holes at the edge of the depletion region
(xn). Thus, the current due to hole injection is
Current due to electrons injected into the p
region is
Combined
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Minority Carrier Concentration and Current
Densities in Forward Bias
Current is due to the diffusion of holes and
electrons. Current is dominated by holes or
electrons depending on the relative doping of NA
vs. ND Is NAgt ND or NAltND in this example?
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Forward Bias (2)
Forward bias apply a positive voltage to the
p-type, negative to n-type. Decrease the
built-in potential, lower the barrier
height. Increase the number of carriers able to
diffuse across the barrier Diffusion current
increases Drift current remains the
same Current flows from p to n
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Review of Biasing
Applying a bias adds or subtracts to the
built-in potential. This changes the diffusion
current, making it harder or easier for the
carriers to diffuse across. The drift current
is essentially constant, as it is dependent on
temperature.
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Photodiodes
Diodes have an optical generation rate.
Carriers are created by shining light with photon
energy greater than the bandgap. Photodetector
should have large depletion widths and long
diffusion lengths (minority carrier lifetimes) so
that photo generatedEHPscan be collected and
swept across the junction. Solar Cell
operating in the fourth quadrant generates
current, though small.
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Light Emitting Diodes
When electrons and holes combine, they release
energy. This energy is often released as heat
into the lattice, but in some materials, known as
direct bandgap materials, they release
light. Engineering LEDs can be difficult, but
has been done over a wide range of
wavelengths. This illustration describes the
importance of the plastic bubble in directing the
light so that it is more effectively seen.
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Diode Circuits
Look at the simple diode circuit below. We can
write two equations
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Diode Small-Signal Model
Some circuit applications bias the diode at a
DC point (VD) and superimpose a small signal
(vd(t)) on top of it. Together, the signal is
vD(t), consisting of both DC and AC
components Graphically, can show that there is a
translation of voltage to current (id(t)) Can
model the diode at this bias point as a resistor
with resistance as the inverse of the tangent of
the i-v curve at that point
And if vd(t) is sufficiently small then we can
expand the exponential and get an approximate
expression called the small-signal approximation
(valid for vdlt 10mV)
So, the diode small-signal resistance is
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Perform the small signal analysis of the diode
circuit biased with VDD by eliminating the DC
sources and replacing the diode with a small
signal resistanceThe resulting voltage divider
gives
Separating out the DC or bias analysis and the
small-signal analysis is a technique we will use
extensively