Transcript Lecture 4

Lecture 4
OUTLINE
• PN Junction Diodes
– Electrostatics
– Capacitance
– I/V
– Reverse Breakdown
– Large and Small signal models
Reading: Chapter 2.2-2.3,3.2-3.4
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Lecture 4, Slide 1
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Energy Band Description
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Lecture 4, Slide 2
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PN Junction under Reverse Bias
• A reverse bias increases the potential drop across the
junction. As a result, the magnitude of the electric field
in the depletion region increases and the width of the
depletion region widens.
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Lecture 4, Slide 3
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Energy Band Description
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Lecture 4, Slide 4
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I-V characteristic from energy
band description
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Lecture 4, Slide 5
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Mathematical description of current flow in a p-n
junction diode
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Lecture 4, Slide 6
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Minority Carrier Injection under Forward Bias
• The potential barrier to carrier diffusion is decreased by
a forward bias; thus, carriers diffuse across the junction.
– The carriers which diffuse across the junction become minority
carriers in the quasi-neutral regions; they recombine with
majority carriers, “dying out” with distance.
np(x)
np0
edge of depletion region
x'
0
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x'
Equilbrium concentration n
of electrons on the P side: p 0
Lecture 4, Slide 7
ni2

NA
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Minority Carrier Concentrations
at the Edges of the Depletion Region
• The minority-carrier concentrations at the edges of
qV / kT
V
e

e
the depletion region are changed by the factor
D
D / VT
– There is an excess concentration (Dpn, Dnp) of minority
carriers in the quasi-neutral regions, under forward bias.
• Within the quasi-neutral regions, the excess minoritycarrier concentrations decay exponentially with
distance from the depletion region, to zero:
n p ( x)  n p 0  Dn p ( x)
Dn p ( x) 
2
i

VD / VT
n e
NA
e
1
Notation:
Ln  electron diffusion length (cm)
 x / Ln
J n,diff


dn p qDn ni2 VD /VT
 qDn

e
 1 e  x / Ln
dx
N A Ln
x'
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Lecture 4, Slide 8
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Diode Current under Forward Bias
• The current flowing across the junction is comprised
of hole diffusion and electron diffusion components:
J tot  J p,drift
x 0
 J n,drift
x 0
 J p,diff
x 0
 J n,diff
x 0
• Assuming that the diffusion current components are
constant within the depletion region (i.e. no
recombination occurs in the depletion region):
J n ,diff
x 0


J tot  J S e
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
qDn ni2 VD / VT

e
1
N A Ln
VD / VT
J p ,diff
x 0

qD p ni2
N D Lp
e
VD / VT

1
 Dn
Dp 

 1 where J S  qn 

N L N L 
D p 
 A n

2
i
Lecture 4, Slide 9
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Current Components under Forward Bias
• For a fixed bias voltage, Jtot is constant throughout
the diode, but Jn(x) and Jp(x) vary with position.
Jtot
-b
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Lecture 4, Slide 10
0
a
x
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I-V Characteristic of a PN Junction
• Current increases exponentially with applied forward
bias voltage, and “saturates” at a relatively small
negative current level for reverse bias voltages.
“Ideal diode” equation:


I D  I S eVD / VT  1
 Dn
Dp 

I S  AJ S  Aqn 

N L N L 
D p 
 A n
2
i
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Lecture 4, Slide 11
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Practical PN Junctions
• Typically, pn junctions in IC devices are formed by
counter-doping. The equations provided in class (and
in the textbook) can be readily applied to such diodes if
– NA  net acceptor doping on p-side (NA-ND)p-side
– ND  net donor doping on n-side (ND-NA)n-side
I D  I S (e qVD
kT
 1)
ID (A)
 Dn
Dp 

I S  Aqni 

L N

L
N
n
A
p
D


2
VD (V)
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Lecture 4, Slide 12
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Parallel PN Junctions
• Since the current flowing across a PN junction is
proportional to its cross-sectional area, two identical
PN junctions connected in parallel act effectively as a
single PN junction with twice the cross-sectional
area, hence twice the current.
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Lecture 4, Slide 13
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Diode Saturation Current IS
 Dn
Dp 

I S  Aqni 

L N

L
N
n
A
p
D


2
• IS can vary by orders of magnitude, depending on the diode
area, semiconductor material, and net dopant concentrations.
– typical range of values for Si PN diodes: 10-14 to 10-17 A/mm2
• In an asymmetrically doped PN junction, the term associated
with the more heavily doped side is negligible:
 Dp 

– If the P side is much more heavily doped, I S  Aqni 

L
N
 p D
2
 Dn 

– If the N side is much more heavily doped, I S  Aqni 
 Ln N A 
2
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Lecture 4, Slide 14
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PN Junction under Reverse Bias
• A reverse bias increases the potential drop across the
junction. As a result, the magnitude of the electric field
in the depletion region increases and the width of the
depletion region widens.
Wdep
2 si  1
1 

V0  VR 


q  N A ND 
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Lecture 4, Slide 15
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PN Junction Small-Signal Capacitance
• A reverse-biased PN junction can be viewed as a
capacitor, for incremental changes in applied voltage.
Cj 
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Lecture 4, Slide 16
 si
Wdep
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Voltage-Dependent Capacitance
• The depletion width (Wdep) and hence the junction
capacitance (Cj) varies with VR.
Cj 
VD
C j0 
C j0
VR
1
V0
 si q N A N D
1
2 N A  N D V0
si  10-12 F/cm is the permittivity of silicon.
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Lecture 4, Slide 17
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Reverse-Biased Diode Application
• A very important application of a reverse-biased PN
junction is in a voltage controlled oscillator (VCO),
which uses an LC tank. By changing VR, we can
change C, which changes the oscillation frequency.
f res
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Lecture 4, Slide 18
1

2
1
LC
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Reverse Breakdown
• As the reverse bias voltage increases, the electric
field in the depletion region increases. Eventually, it
can become large enough to cause the junction to
break down so that a large reverse current flows:
breakdown voltage
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Lecture 4, Slide 19
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Reverse Breakdown Mechanisms
a) Zener breakdown occurs when the electric field is
sufficiently high to pull an electron out of a covalent
bond (to generate an electron-hole pair).
b) Avalanche breakdown occurs when electrons and holes
gain sufficient kinetic energy (due to acceleration by the
E-field) in-between scattering events to cause electronhole pair generation upon colliding with the lattice.
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Lecture 4, Slide 20
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Constant-Voltage Diode Model
for Large-Signal Analysis
• If VD < VD,on: The diode operates as an open circuit.
• If VD  VD,on: The diode operates as a constant voltage
source with value VD,on.
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Lecture 4, Slide 21
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Example: Diode DC Bias Calculations
IX
VX  I X R1  VD  I X R1  VT ln
IS
I X  2.2mA for VX  3V
I X  0.2mA for VX  1V
• This example shows the simplicity provided by a
constant-voltage model over an exponential model.
• Using an exponential model, iteration is needed to
solve for current. Using a constant-voltage model,
only linear equations need to be solved.
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Lecture 4, Slide 22
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Small-Signal Analysis
• Small-signal analysis is performed at a DC bias point by
perturbing the voltage by a small amount and
observing the resulting linear current perturbation.
– If two points on the I-V curve are very close, the curve inbetween these points is well approximated by a straight line:
DI D
dI D

DVD dVD
2
3
x
x
ex  1 x 

 
2! 3!
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Lecture 4, Slide 23
VD VD 1
I s VD1 / VT I D1

e

VT
VT
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Diode Model for Small-Signal Analysis
• Since there is a linear relationship between the
small-signal current and small-signal voltage of a
diode, the diode can be viewed as a linear resistor
when only small changes in voltage are of interest.
Small-Signal Resistance
(or Dynamic Resistance)
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Lecture 4, Slide 24
VT
rd 
ID
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Small Sinusoidal Analysis
• If a sinusoidal voltage with small amplitude is applied
in addition to a DC bias voltage, the current is also a
sinusoid that varies about the DC bias current value.
V D(t )  V0  V p cos t
 V0
I D (t )  I 0  I p cos t  I s exp 
 VT
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Lecture 4, Slide 25
 V p cos t
 
 VT / I 0 
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