5
OUTLINE
Lecture PN Junction Diodes
I/V
Capacitance
Reverse Breakdown
Large and Small signal
models
Reading: Chapter 2.2-2.3,3.2-3.4
EE105 Fall 2011
Lecture 5, Slide 1
Prof. Salahuddin, UC Berkeley
Recap: Law of the Junction
Law of the junction:
n(a ) p (a ) = ni2 eVD / VT
-b 0 a
EE105 Fall 2011
Lecture 5, Slide 2
Prof. Salahuddin, UC Berkeley
Recap: Minority Carrier
Concentrations
at the Edges of the Depletion Region
-b 0
x'
;x=0
x=a
n p ( x) = n p 0 + n p ( x)
(
)
ni2 eVD / VT 1 x / Ln
n p ( x) =
e
NA
J n ,diff
EE105 Fall 2011
(
Notation:
Ln electron diffusion length
(cm)
)
dn p qDn ni2 VD / VT
= qDn
=
e
1 e x / Ln
dx
N A Ln
Lecture 5, Slide 3
Prof. Salahuddin, UC Berkeley
Hole Diffusion
X
x
0
J p ,diff =
EE105 Fall 2011
qD p ni2
N D Lp
(e
VD / VT
Lecture 5, Slide 4
)
1 e
x '' / L p
Prof. Salahuddin, UC Berkeley
Distribution of Diffusion
Current
J p ,diff =
qD p ni2
N D Lp
(e
VD / VT
)
1 e
x / Lp
J n ,diff
(
)
qDn ni2 VD / VT
=
e
1 e x / Ln
N A Ln
x
-b
0
a
Assume: No Recombination in the depletion region
Known: Total Current is the same everywhere
EE105 Fall 2011
Lecture 5, Slide 5
Prof. Salahuddin, UC Berkeley
Diode Current under Forward
Bias
The current flowing across the junction is
comprised of hole diffusion and electron
diffusion J
J = components:
+J
+J
+J
tot
p , drift x = 0
n , drift x = 0
p , diff x = 0
n , diff x = 0
J_total
J p ,diff =
qD p ni2
N D Lp
(e
VD / VT
)
1 e
x / Lp
J n ,diff
(
)
qDn ni2 VD / VT
=
e
1 e x / Ln
N A Ln
x
-b
EE105 Fall 2011
0
a
Lecture 5, Slide 6
Prof. Salahuddin, UC Berkeley
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
An
2
i
EE105 Fall 2011
Lecture 5, Slide 7
Prof. Salahuddin, UC Berkeley
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
ID (A)
I D = I S (e qVD
kT
1)
Dn
Dp
I S = Aqni
+
L N
Lp N D
n
A
2
VD (V)
EE105 Fall 2011
Lecture 5, Slide 8
Prof. Salahuddin, UC Berkeley
How to make sure that current flow in a forwardbiased p-n junction diode is mainly due to
electrons?
EE105 Fall 2011
Lecture Slide 5, 9
Prof. Salahuddin, UC Berkeley
Diode Saturation Current IS
Dn
Dp
I S = Aqni
+
L N
Lp N D
n
A
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/m2
In an asymmetrically doped PN junction, the term
associated with the more heavily doped side2 negligible:
is D p
I S Aqni
L N
p D
If the P side is much more heavily doped,
Dn
I S Aqni
L N
n A
2
If the
EE105 Fall 2011
N side is much more heavily doped,
Lecture 5, Slide 10
Prof. Salahuddin, UC Berkeley
Depletion Width at Equilibrium
(see slide 3 in lecture 4)
(x)
qND
a
-b
-qNA
on the P side: E =
x
qN A
( a x ) --(1)
si
qN D
( x + b)
E=
on the N side:
si
aN A = bN D
V(x)
EE105 Fall 2011
0
--(3)
Let us set the reference point at x=a
Then V(a)=0
V(-b)=V0; Built in potential
V0
-b
--(2)
a
x
Lecture 5, Slide 11
Prof. Salahuddin, UC Berkeley
Depletion Width at Equilibrium
E=
V(x)
V0
-b
E=
0
a
x
qN A
( a x ) --(1)
si
qN D
( x + b)
si
aN A = bN D
--(2)
--(3)
V(a)=0
V(-b)=V0; Built in potential
EE105 Fall 2011
Lecture 5, Slide 12
Prof. Salahuddin, UC Berkeley
Depletion Width at Equilibrium
V(x)
V0
-b
0
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a
x
Lecture 5, Slide 13
Prof. Salahuddin, UC Berkeley
Depletion Width at biased
conditions
V(x)
V0
-b
0
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a
x
Lecture 5, Slide 14
Prof. Salahuddin, UC Berkeley
PN Junction Depletion
Capacitance
A reverse-biased PN junction can be viewed as
a capacitor, for incremental changes in applied
voltage.
si 10-12 F/cm is the permittivity of silicon
si
Cj =
Wdep
EE105 Fall 2011
Lecture 5, Slide 15
Prof. Salahuddin, UC Berkeley
Voltage-Dependent
Capacitance
The depletion width (Wdep) and hence the
junction capacitance (Cj) varies with VR.
VD
EE105 Fall 2011
Lecture 5, Slide 16
Prof. Salahuddin, UC Berkeley
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
EE105 Fall 2011
Lecture 5, Slide 17
1
=
2
1
LC
Prof. Salahuddin, UC Berkeley
Forward Bias Diffusion
capacitance
x
At small forward bias, putting a small ac signal changes the concentration
of diffused minority carriers and therefore gives a capacitance. This is
called a diffusion capacitance
EE105 Fall 2011
Lecture 5, Slide 18
Prof. Salahuddin, UC Berkeley