6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-1
Lecture 15 - p-n Junction (cont.)
March 9, 2007
Contents:
1. Ideal p-n junction out of equilibrium (cont.)
2. pn junction diode: parasitics, dynamics
Reading assignment:
del Alamo, Ch. 6, §6.2 (6.2.4), §6.3
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-2
Key questions
• What happens to the majority carriers in a pn junction under
bias?
• What are the main practical issues in synthesizing pn junction
diodes?
• How does a pn junction switch? What dominates its dynamic
behavior?
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-3
1. Ideal p-n junction out of equilibrium (cont.)
� Minority carrier storage
Quasi-neutrality in QNR’s demands n� � p� . Consequences:
n, p
compensating�
compensating�
+ΔQhp
−ΔQen
holes
n(x)
p(x)
-Qen
+Qhp
NA
ND
+ΔQhn
injected�
−ΔQep
p(x)
electrons
n(x)
ni2
NA
+Qhn
-Qep
-wp
electrons
-xp
0
xn
injected�
holes
ni2
ND
wn
x
In n-QNR, quasi-neutrality implies:
Qhn � |Qen| ≡ Qn
Also, if V ↑→ Qhn ↑→ |Qen| ↑ with:
ΔQhn � |ΔQen| ≡ ΔQn
ΔQhn supplied from p-contact, ΔQen supplied from n-contact.
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-4
Looks like a capacitor ⇒ diffusion capacitance.
Diffusion capacitance (per unit area):
Cd =
dQn dQp
+
dV
dV
with:
Qn = q
� w
n
Qp = q
� −x
p
xn
p� (x)dx
− wp
n�(x)dx
• If both sides are ”long”:
Qn = qLhp� (xn ) = τhJh(xn )
Qp = qLen� (−xp) = τeJe (−xp)
and
Cd �
q
q
qV
[τhJh(xn ) + τeJe (−xp)] =
(τhJhs + τe Jes) exp
kT
kT
kT
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-5
• If both sides are short and S = ∞:
1
Qn = q p� (xn )(wn − xn) = τtnJh(xn )
2
1
Qp = q n� (−xp )(wp − xp) = τtpJe (−xp)
2
with τtn and τtp are the minority carrier transit times through QNR’s:
τtn
(wn − xn)2
=
2Dh
τtp
(wp − xp )2
=
2De
Then:
Cd �
q
q
qV
[τtnJh(xn ) + τtpJe (−xp)] =
(τtnJhs + τtpJes) exp
kT
kT
kT
Similar result to long diode!
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-6
• General expression:
Cd =
q �
kT n,p
dominant minority carrier time constant
×injected minority carrier current density
Cd grows exponentially in forward bias, negligible in reverse bias:
Cd ∼ exp
qV
kT
qV
[check that Cd ∼ exp qV
and
not
∼
exp
− 1]
kT
kT
• Total diode capacitance:
C
Cd
C
0
0
Cj
V
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-7
2. p-n junction diode
• pn junctions present in most semiconductor devices (BJTs and
MOSFETs).
• pn junction diodes used in rectifying circuits, detectors in commu­
nications applications, bias shifters, input protection devices against
electrostatic discharge.
• For integrated p-n diodes, no special process steps available.
Typical cross section of p-n diode implemented in BJT process:
p+
n+
n
n+
p
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-8
� Parasitics
� Series resistance:
• Accounts for ohmic drop in QNR’s (neglected so far).
• Reduces internal diode voltage → I ↓
I = Is[exp
q(V − IRs )
− 1]
kT
ideal
with series resistance
I
log |I|
IRs
1/Rs
0
0
V
linear scale
0
V
semilogarithmic scale
• Higher VF required to deliver desired IF → more power dissipa­
tion, potential process control problems
• RC time constant degraded.
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-9
� Minority carrier boundary conditions:
• At top surface: depending on relative depth of emitter, effective
diode area changes
– top surface=ohmic contact area (Ac, S = ∞)
+ peripheral SiO2-covered area (Ap , S = 0)
peripheral area Ap
contact area Ac
p+
n
Je
(periphery)
Wp
Je
(area)
– if Wp � Le , volume recombination only → Aeff � Ac + Ap
– if Wp � Le, surface recombination only → Aeff � Ac
• At bottom surface: high-low junction, characterized by Shl .
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-10
� Isolation:
• Parasitic substrate p-n junction → needs to be reverse biased to
avoid turning it on.
• Even reverse biased, substrate contributes parasitic capacitance.
• Additional danger: ”bipolar effect” between diode and substrate
→ minority carriers can be extracted by substrate → current
diverted away from main body of diode.
VDD
p+
n
n+
VDD
desired�
current path
hole recombination in cathode
p
hole extraction by substrate
VSS
desired result
parasitic�
current path
VSS
actual result
• Hard to make integrated pn diodes in CMOS process (unless
they hang directly from the power rail that is connected to the
substrate).
• Easier in bipolar since n+ buried layer and collector plug can
prevent minority carrier injection.
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-11
� Dynamics
Fundamental difference between p-n and Schottky diodes: minority
carrier storage slows down p-n diode.
Consider simple voltage switching:
V
I
Vf
+
V
Vf
0
t
Vr
-Vr
Vj
Vf-IfRs
0
t
-Vr
I
If(pk)=
If(Vf)
Vf+Vr
Rs
slower decay
τt
RsC
0
Ir(pk)=If-
RsC
t
Vf+Vr
Rs
trr
As in Schottky diode, delays associated with RsCj .
Additionally, delays associated with minority carrier storage.
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-12
� Switch-off transient
Evolution of excess minority carrier concentration (long diode):
excess�
minority�
carrier �
concentration
t=0­
t=
x
switch-off
At t = 0−, Vf → If ; minority carrier stored charge:
Q = τ t If
with τt , dominant minority carrier time constant.
At t = 0+, external V abruptly changes from Vf to Vr ; internal V
cannot change abruptly → need to get rid of minority carriers!
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-13
t=0-
t=0+
I
I
Rs
Rs
-
Vf-IfRs+Vr
+
If(Vf)
+
+
Vf-IfRs
C
Vf
-
Vf-IfRs
C
Vr
-
I(0− ) = If (Vf )
I(0+) = −
1
Vr
(Vf −If Rs +Vr ) � −
Rs
Rs
Two phases to discharge:
Phase I - From Vj = Vf − If Rs to Vj � 0.
Since Q ∼ exp
qVf
,
kT
as Q discharges, Vf cannot change much.
Discharge proceeds nearly at constant current Ir (pk) � − RVrs
Time to discharge (reverse recovery time):
trr �
Q
If (Vf )Rs
� τt
|Ir (pk)|
Vr
Phase II - From Vj � 0 to Vj = −Vr .
Charge depletion capacitance → Rs Cj time constant (as in Schot­
tky diode).
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-14
� Switch-on transient
t=0-
t=0+
I
I
Rs
Rs
+
Vf+Vr
-
Vr
-
C
Vr
Vr
+
C
Vf
+
I(0−) = −Is
I(0+) =
Vf + Vr
Rs
Evolution of excess minority carrier concentration (long diode):
excess�
minority�
carrier �
concentration
t=
t=0­
x
switch-on
• First, RsCj -type charge up of junction capacitance.
• Then, minority carrier charge injection → takes τt.
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-15
Example of SPICE simulations:
IS= 6e−17, N= 1, EG= 1.12, RS= 8, CJO= 1.2e−13, VJ= 0.6,
M= 0.41, XTI= 3.814, and TT= 4e − 9
Vf = +0.89 V , Vr = −5 V
0.4
0.2
41 ps
current (A)
0.0
-0.2
-0.4
-0.6
-0.8
0
1E-10
2E-10
3E-10
4E-10
5E-10
time (s)
parameter SPICE hand calculation
41 ps
46 ps
trr
2.6 ns
4 ns
τon
730 mA
736 mA
Irr
If (pk)
?
736 mA
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-16
Key conclusions
• Diffusion capacitance arises from minority carrier storage in
QNR’s and quasi-neutrality:
Cd =
q
Σn,p(dominant minority carrier time constant
kT
×minority carrier current density)
• Cd ∝ J ∝ exp qV
kT ⇒ Cd dominates in forward bias, Cj domi­
nates in reverse bias.
• Difficult to implemented integrated diodes in CMOS process:
parasitic bipolar transistor.
• Dynamics of p-n diode dominated by minority carrier storage.
• Reverse recovery time is time required to eliminate minority
carrier stored charge in switch-off transient.
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 15-17
Self study
• Diffusion capacitance in short diode.
• Equivalent circuit models for pn diode
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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