PN Junctions and Diodes
1
Definitions FYI
B: material dependent parameter = 5.4 × 1031 for Si
EG: Bandgap energy = 1.12 eV
k: Boltzmann constant=8.62×10-5 ev/K
ni: intrinsic carrier concentration
At T = 300 K, ni = 1.5 × 1010 carriers/cm3
Jp: current density A/m2
q: electron charge
Dp: Diffusion constant (diffusivity) of holes
μp: mobility for holes = 480 cm2 /V sec
μn: mobility for electrons = 1350 cm2 /V sec
ND: concentration of donor atoms
nno: concentration of free electrons at thermal equilibrium
NA: concentration of acceptor atoms
ppo: concentration of holes at thermal equilibrium
D
D
kT
Einstein Relation : n = p =
= VT : thermal voltage
q
μn μ p
PN Junction
•
When a p material is connected to an n-type material, a junction is formed
– Holes from p-type diffuse to n-type region
– Electrons from n-type diffuse to p-type region
– Through these diffusion processes, recombination takes place
– Some holes disappear from p-type
– Some electrons disappear from n-type
A depletion region consisting of bound charges is thus formed
Charges on both sides cause electric field Î potential = Vo
PN Junction
•
•
Potential acts as barrier that must be overcome for holes to diffuse into the
n-region and electrons to diffuse into the p-region
Open circuit: No external current
Junction built-in voltage
From principle of detailed balance and
equilibrium we get:
⎛ N AND ⎞
Vo = VT ln ⎜
⎟
2
⎝ ni ⎠
For Si, Vo is typically 0.6V to 0.8V
ε s : silicon permittivity
ε s = 11.7ε o = 1.04 × 10−8 F/m
xn N A
=
xp ND
Charge equality in depletion region gives:
qx p AN A = qxn AN D
A: cross-section of junction
xp: width in p side
xn : width in n side
Wdep = xn + x p =
2ε s ⎛ 1
1 ⎞
+
⎜
⎟Vo
q ⎝ N A ND ⎠
PN Junction under Reverse Bias
•
When a reverse bias is applied
– Transient occurs during which depletion capacitance is charged to new
bias voltage
– Increase of space charge region
– Diffusion current decreases
– Drift current remains constant
– Barrier potential is increased
– A steady state is reached
– After transient: steady-state reverse current = IS-ID (ID is very small) Î
reverse current ~ IS ~10-15 A
Under reverse bias the current in the diode is negligible
The Diode
+
I
V
•
Diode Properties
– Two-terminal device that conducts current freely in one direction but blocks
current flow in the opposite direction.
– The two electrodes are the anode which must be connected to a positive voltage
with respect to the other terminal, the cathode in order for current to flow.
The ideal diode: (a) diode circuit symbol; (b) i–v
characteristic; (c) equivalent circuit in the reverse
direction; (d) equivalent circuit in the forward
direction.
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ideal diodes: two modes of operation
external circuit used to limit forward
current (a) and the reverse voltage (b).
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Ideal Diode Characteristics
+
I
+
V
V
-
-
V<0
OFF
I>0
ON
I
Ideal Diode Characteristics
Diode Characteristics
•
Three distinct regions
– The forward-bias region, determined by v > 0
– The reverse-bias region, determined by v < 0
– The breakdown region, determined by v < -VZK
Diode Models
Exponential
Piecewise Linear
16
Constant-Voltage-Drop
Diodes Logic Gates
OR Function
Y = A+ B +C
AND Function
Y = A⋅ B ⋅C
Diode Circuit Example 1
IDEAL Diodes
Assume both diodes are on; then
VB = 0 and V = 0
I D2 =
10 − 0
= 1 mA
10
At node B
0 − (−10)
I +1 =
⇒ I = 1 mA, V = 0 V
5
D1 is conducting as originally
assumed
Diode Circuit Example 2
IDEAL Diodes
Assume both diodes are on; then
VB = 0 and V = 0
10 − 0
I D2 =
= 2 mA
5
At node B
I +2=
0 − (−10)
⇒ I = −1 mA ⇒ wrong
10
original assumption is not correct …
assume D1 is off and D2 is on
ID2 =
10 − (−10)
= 1.33 mA
15
VB = −10 + 10 × 1.33 = +3.3 V
D1 is reverse biased as assumed
Excercise
Find
I&V
Figure E3.4
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Vo = ?
I = ?
Figure E3.12 P3.2 V , I ??
P3.3 V=
I=
V=
I=
Analyze Circuit with load RL V0, 3 current branches
Figure 3.19 Circuit for Example 3.7. Application:
Diodes as Voltage Regulators
•
Objective
–
–
–
–
Provide constant dc voltage between output terminals
Load current changes
Dc power supply changes
Take advantage of diode I-V exponential behavior
Big change in current
correlates to small
change in voltage
Application:
Diode as Rectifier
While applied source alternates in
polarity and has zero average
value, output voltage is
unidirectional and has a finite
average value or a dc component
(a) Rectifier circuit.
(b) Input waveform
Application: Rectifier
(c) Equivalent
circuit when vI ≥ 0.
(d) Equivalent
circuit when vI !
0.
(e) Output waveform.
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Figure 3.25 (a) Half-wave rectifier. (b) Equivalent circuit: diode
replaced with battery-plus-resistance. (c) Transfer characteristic
(d) Input and output waveforms assuming that rD ! R.
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Figure 3.4 Circuit and waveforms for Example
3.1.
I=?
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Full wave rectifier
Inverts –ve half of sinusoid
Center tapped transformer
2 equal voltages across 2
halves
+ve cycle: Vs +ve, D1
conducts thru R, D2 reverse
biased
-ve cycle: Vs –ve, D1 off,
D2 conducts
Figure 3.26 Full-wave rectifier utilizing a transformer with a center-tapped secondary winding: (a) circuit; (b) transfer
characteristic assuming a constant-voltage-drop model for the diodes; (c) input and output waveforms.
Copyright © 2004 by Oxford University Press, Inc.
Bridge rectifier: (a) circuit; (b) input and output waveforms.
+ve half cycle
Vs +ve,
current conducted
thru D1, R, D2 (D3,
D4 reverse biased
-ve half cycle
Vs –ve
current conducted
thru D3, R, D4 (D1,
D2 reverse biased
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Peak Rectifier
Using filter
Capacitor
Figure 3.28 (a) A simple circuit used to illustrate the effect of a filter capacitor. (b) Input and output waveforms assuming
an ideal diode. Note that the circuit provides a dc voltage equal to the peak of the input sine wave. The circuit is therefore
known as a peak rectifier or a peak detector.
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Figure 3.29 Voltage and current waveforms in the peak rectifier circuit with CR @ T. The diode is assumed ideal.
Microelectronic Circuits - Fifth Edition
Sedra/Smith
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Figure 3.30 Waveforms in the full-wave peak rectifier.
Microelectronic Circuits - Fifth Edition
Sedra/Smith
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Table 3.1 Modeling the Diode Forward Characteristic
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Figure 3.24 Block diagram of a dc power supply.
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Diode Characteristics
•
Three distinct regions
– The forward-bias region, determined by v > 0
– The reverse-bias region, determined by v < 0
– The breakdown region, determined by v < -VZK
Zener Diode, Model, I-V
Figure 3.20, 21 The diode i–v characteristic with the breakdown region shown in some detail.
Copyright © 2004 by Oxford University Press, Inc.