ECE 417517 Basic Semiconductor Devices

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ECE 417/517 Basic Semiconductor Devices

• Small Signal Admittance of PN diodes

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p n junctions
Large signal DC model
we will take Rs to be small, but leave it in our
model for completeness
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p n junctions
Small signal AC model
non-linear I-V characteristic
total current, I
Io
VA
V
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p n junctions
Small signal AC model
Calculating the dynamic resistance, rd
units ?
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p n junctions
Small signal AC model
Junction capacitance (majority carrier response)

Rs
Cj
VA va(t)
rd
-
junction capacitance
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p n junctions
Different Doping Profiles
Step junction
ND-NA
x
Linearly graded junction
ND-NA
?(x)
x
x
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p n junctions
Small signal AC model
More Doping Profiles
Hyperabrupt junction mlt0
Step junction m0
Linearly graded junction m1
ND-NA
ND-NA
ND-NA
x
x
x
Doping on lightly doped side.
Zero bias capacitance
Generally
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p n junctions
Small signal AC model
Now, let us consider the minority carrier
response (diffusion capacitance)
the shaded represents the total excess minority
carriers.
If bias voltage is time varying
Then Q will change with time, but response is
slow because charge redistribution is by
diffusion. This leads to an effective
Diffusion Capacitance, Cd
Cd becomes significant only at forward bias!
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p n junctions
Small signal AC model Diffusion capacitance
Use diffusion equation with time dependence
If bias voltage is time varying (sinusoidal)
Assume carrier conc. is time varying with
dc part ac part
Small signal approximation!
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p n junctions
Small signal AC model Diffusion admittance
Using
with
and taking time derivative gives
Separate into two parts
dc diffusion equation ac diffusion equation
Same as dc except
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p n junctions
Small signal AC model
Boundary conditions are also time varying
Separate dc and ac parts again
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p n junctions
Small signal AC model
Compare
Diffusion equations
ac
dc
Boundary conditions
Solution
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p n junctions
Small signal AC model
ac admittance
dc conductance
Look at real and imaginary parts
admittance
diffusion conductance
diffusion capacitance
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p n junctions
Full Small signal AC model
junction (depletion) capacitance
diffusion conductance
diffusion capacitance
dc conductance
For GD increases, CD
decreases
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p n junctions
Full Small signal AC model
diffusion conductance
diffusion capacitance
For
dc conductance
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p n junctions
CD dominates in forward bias, CJ in reverse bias
junction capacitance
CJ
diffusion capacitance
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p n junctions
SPICE Models
Our Results