Axel Scherer

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Solid State Devices

• Axel Scherer

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Diode Breakdown Effects
When we apply a large reverse bias (negative
voltage) onto a diode, it eventually breaks down
and conducts again. That voltage is called the
reverse breakdown voltage Vbr.
p
n
There are two common breakdown mechanisms
Tunneling and Avalanche Multiplication
p
n
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Consider the effect of irradiating a p-n junction
with light. Lets only look at the reverse bias
saturation current
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Finally, the total diode current is the sum of
the hole and electron currents across the p-n
junction and is given by
Area of junction diffusivity diffusion length
Applied voltage Temperature (K)
L?D?
Can also be substituted for L
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Instead of a light source, we can also use a
forward biased p-n junction to inject carriers
into a reverse biased junction. In this case, we
can use the forward biased (emitter-base)
junction current to modulate the reverse biased
(base-collector) current
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Since the application of a small base current can
result in a much larger amplification of the
collector current, we can use this device as an
amplifier.
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The Transistor First proposed by Lilienfeld in
1930 (but he could never really get it to work
right because of surface states)
1930
Field-effect transistor Using a gate C,
Lilienfeld thought that it should be possible to
modulate the current from A to B. This is
conceptually very similar to the vacuum triode,
which was used as the amplifier at the time
Filament cathode
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Remember the field effect transistor. This is a
completely different device!
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Schematic description of the JFET problem
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Integrating the drift equation with respect to x
and z, we can derive the total current passing
through the transistor channel
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To find the relationship W(V)/a, we need to
derive the depletion width as a function of
voltage
Note that W approaches a when the gate voltage Vg
approaches the pinchoff voltage Vp
Next, we substitute into our original equation
and obtain
Built-in potential
Gate voltage
Pinchoff voltage
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In field effect devices The electric field of a
gate or grid is used to modulate the number of
charges (i.e. electron current) moving from the
source to the drain. This is a majority carrier
device
grid
2400K
(-)
vacuum
()
anode
electrons
In a Bipolar Junction Transistor, charges are
transmitted through a Base region to influence
the depletion region of the Base/Collector
Junction. The Emitter serves as a carrier source.
This is a minority carrier device
Emitter
Base
P-doped
Collector
N-doped
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1947
In 1947, Bardeen and Brattain invented the Ge
point contact transistor. They wanted to make the
Field-Effect Transistor, but ended up with a
Bipolar Transistor, and got the Nobel Prize
anyway. Schockley then developed the bipolar
junction transistor.
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Schematic arrangement of connections to BJTs
Ciruit symbols of two types of BJTs
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IE is the emitter current IB is the base
current IC is the collector current
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Here are three possible arrangements of
connections onto a PNP bipolar transistor
The corresponding circuit diagrams would be given
on the left.
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Typical current response curves of common base
and common emitter amplifiers. Note the
difference in the scale on the common emitter
curves.
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Here is a summary of the different biasing
polarities and the operation of pnp and npn
transistors
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Typically, good bipolar junction transistors
should have narrow base regions, so that carriers
can diffuse across the base region without much
chance for recombination. It is also important
that the emitter region is doped more heavily
than the base region to reduce current from base
to emitter.
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The definition of currents
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Emitter efficiency
Base transport factor
Definition of common terms which define the
performance of a bipolar transistor
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Schematic of all of the currents which we should
consider for a PNP bipolar junction transistor
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Common Base Current Gain
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Common emitter current gain
We rearrange above equation
This is the definition of the current gain
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Some other random equations relating currents in
BJTs
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Ebers-Moll equations
Here is a much more rigorous approach
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The emitter current can be derived as
The collector current can be derived as
The base current is simply the emitter minus the
collector current
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The evolution of BJTs with higher speeds and
better gain has been mainly a result of the
introduction of new fabrication techniques
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Emitter efficiency
Base transport factor
Definition of common terms which define the
performance of a bipolar transistor
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Collector current when IE is zero this is
usually negligible.
Common Base Current Gain
This is the dc common base current gain
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Common emitter current gain
This term is the collector current when base
current is zero (usually negligible)
We rearrange above equation
This is the definition of the current gain
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BJT static characteristics
Assumptions steady state, Low-level
injection Thermal recombination/generation
negligible in junctions
The coordinate system and the material parameter
symbols employed by the ideal transistor analysis
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On the emitter/base junction
On the collector/base junction
These concentrations reduce to simpler
expressions if the emitter junction is strongly
forward biased and the collector junction is
strongly reverse biased
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By using the diffusion equation, and the
appropriate boundary conditions, we can solve for
the hole concentration in the base region
The solution for this equation is
The boundary conditions for this solution are
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We can now solve for the two parameters C1 and C2
Next, we can solve for the distribution of excess
holes in the base region for a excess hole
concentration at the collector side (pc0)
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Terminal currents
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For a pnp BJT
Remember that at a p-n junction, the excess hole
concentration ?pn varies with applied bias in an
exponential fashion. For the emitter-base
junction, we can write an equation for the number
of excess holes on the base side of the junction
p
pn
Similarly, we can write an expression for the
excess hole concentration in the base/collector
junction as
Next, we would like to determine the excess hole
concentration as a function of distance within
the base region of the pnp transistor.
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Diffusion equation in the Emitter region
Electron lifetime in emitter region
With boundary conditions shown here
Diffusion equation in the Base region
Hole lifetime in the base region
Diffusion equation in the Collector region
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In a PNP transistor, we can derive
Again, we can derive performance factors for the
BJT
Again, current conservation requires this.
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General solution to the currents in the emitter
region
We can obtain expressions for the minority
carriers concentration, delta nE, and substitute
them into our equation to get
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A general solution for the collector region can
be derived similarly
Solving again the minority carrier concentration
And substituting into the equation for the
collector current, we get
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Base region solution
This is the general solution to the diffusion
equation at the Base region.
Next, we solve for A1 and A2, and substitute the
result into the general solution
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This relationship with many exponential terms
Can be simplified by using hyperbolic
trigonometric functions (sinh(x)) to obtain
Where
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Once an expression for the excess hole
concentration has been developed, we can
substitute this expression again into these
equations
where
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Since nE0/pB0 NB/NE
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Similarly, the common emitter current gain and
the common base current gain can be obtained by
substituting
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Moreover, the emitter and collector currents can
be found by simply adding the electron and hole
current components together
A similar expression for the base current can be
obtained by subtracting the collector current
from the emitter current.
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We can even further simplify the current
equations when WltltLB (i.e. when the base width is
very narrow compared to the diffusion length) by
using the following relationships for hyperbolic
trig functions
In this case, when WltltLB, the concentration
gradient of holes in the base becomes linear with
distance, and
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For the case of WltLB, the characteristic
performance parameters can be determined from
these simple relationships
Emitter injection efficiency
Base transport factor
Common base current gain Common emitter current
gain
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Lets look at an example