Chapter1 Diodes
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Transcript of Chapter1 Diodes
SJTU Zhou Lingling 1
ChapterChapter 11
DiodesDiodes
SJTU Zhou Lingling 2
Outline of Chapter 1
1.1 Introduction1.2 Basic Semiconductor Concepts1.3 The pn Junction1.4 Analysis of diode circuits1.5 Applications of diode circuits
SJTU Zhou Lingling 3
1.1 Introduction
• The diode is the simplest and most fundamental nonlinear circuit element.
• Just like resistor, it has two terminals.• Unlike resistor, it has a nonlinear current-
voltage characteristics.• Its use in rectifiers is the most common
application.
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Physical Structure
The most important region, which is called pn junction, is the boundary between n-type and p-type semiconductor.
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Symbol and Characteristic for 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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Characteristics
• Conducting in one direction and not in the other is the I-V characteristic of the diode.
• The arrowlike circuit symbol shows the direction of conducting current.
• Forward biasing voltage makes it turn on.
• Reverse biasing voltage makes it turn off.
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1.2 Basic Semiconductor Concepts
• Intrinsic Semiconductor• Doped Semiconductor• Carriers movement
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Intrinsic Semiconductor
• DefinitionA crystal of pure and regular lattice structure is called intrinsic semiconductor.
• MaterialsSilicon---today’s IC technology is based
entirely on siliconGermanium---early used Gallium arsenide---used for microwave circuits
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Intrinsic Semiconductor(cont’d)
Two-dimensional representation of the silicon crystal. The circles represent the inner core of silicon atoms, with +4 indicating its positive charge of +4q, which is neutralized by the charge of the four valence electrons. Observe how the covalent bonds are formed by sharing of the valence electrons. At 0 K, all bonds are intact and no free electrons are available for current conduction.
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Intrinsic Semiconductor(cont’d)
At room temperature, some of the covalent bonds are broken by thermal ionization. Each broken bond gives rise to a free electron and a hole, both of which become available for current conduction.
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Intrinsic Semiconductor(cont’d)
• Thermal ionizationValence electron---each silicon atom has four
valence electronsCovalent bond---two valence electrons from
different two silicon atoms form the covalent bond Be intact at sufficiently low temperature Be broken at room temperature
Free electron---produced by thermal ionization, move freely in the lattice structure.
Hole---empty position in broken covalent bond,can be filled by free electron, positive charge
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Intrinsic Semiconductor(cont’d)
• CarriersA free electron is negative charge and a hole is positive charge. Both of them can move in the crystal structure. They can conduct electric circuit.
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Intrinsic Semiconductor(cont’d)
• RecombinationSome free electrons filling the holes results in the disappearance of free electrons and holes.
• Thermal equilibriumAt a certain temperature, the recombination rate is equal to the ionization rate. So the concentration of the carriers is able to be calculated.
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Intrinsic Semiconductor(cont’d)
• Carrier concentration in thermal equilibrium
• At room temperature(T=300K)
carriers/cm3
inpn kTE
iGeBTn 32
10105.1 in
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Intrinsic Semiconductor(cont’d)
Important notes:• has a strong function of temperature.
The high the temperature is, the dramatically great the carrier concentration is.
• At room temperature only one of every billion atoms is ionized.
• Silicon’s conductivity is between that of conductors and insulators. Actually the characteristic of intrinsic silicon approaches to insulators.
in
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Doped Semiconductor
• Doped semiconductors are materials in which carriers of one kind predominate.
• Only two types of doped semiconductors are available.
• Conductivity of doped semiconductor is much greater than the one of intrinsic semiconductor.
• The pn junction is formed by doped semiconductor.
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Doped Semiconductor(cont’d)
n type semiconductor• Concept
Doped silicon in which the majority of charge carriers are the negatively charged electrons is called n type semiconductor.
• Terminology Donor---impurity provides free electrons, usually entirely ionized. Positive bound charge---impurity atom donating electron gives rise
to positive bound charge carriers
• Free electron---majority, generated mostly by ionized and slightly by thermal ionization.
• Hole---minority, only generated by thermal ionization.
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Doped Semiconductor(cont’d)
A silicon crystal doped by a pentavalent element. Each dopant atom donates a free electron and is thus called a donor. The doped semiconductor becomes n type.
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Doped Semiconductor(cont’d)
p type semiconductor• Concept
Doped silicon in which the majority of charge carriers are the positively charged holes is called p type semiconductor.
• Terminology acceptor---impurity provides holes, usually entirely ionized. negatively bound charge---impurity atom accepting hole give rise
to negative bound charge carriers
• Hole---majority, generated generated mostly by ionized and slightly by thermal ionization.
• Free electron---minority, only generated by thermal ionization.
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Doped Semiconductor(cont’d)
A silicon crystal doped with a trivalent impurity. Each dopant atom gives rise to a hole, and the semiconductor becomes p type.
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Doped Semiconductor(cont’d)
Carrier concentration for n typea) Thermal equilibrium equation
b) Electric neutral equation
200 inn npn
Dnn Npn 00
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Doped Semiconductor(cont’d)
Carrier concentration for p typea) Thermal equilibrium equation
b) Electric neutral equation
200 ipp nnp
App Nnp 00
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Doped Semiconductor(cont’d)
Because the majority is much great than the minority, we can get the approximate equations shown below:
for n type for p type
D
in
Dno
Nnp
Nn2
0
A
ip
Ap
Nnn
Np2
0
0
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Doped Semiconductor(cont’d)
• ConclusionMajority carrier is only determined by the
impurity, but independent of temperature.Minority carrier is strongly affected by
temperature.If the temperature is high enough,
characteristics of doped semiconductor will decline to the one of intrinsic semiconductor.
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Doped Semiconductor(cont’d)
• Doping compensation n type semiconductor is generated by
donor diffusion, then injecting acceptor into the specific area(assuming ) forms p type semiconductor. The boundary between n and p type semiconductor is the pn junction. This is the basic step for VLSI fabrication technology.
ND
NA
DA NN
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Carriers Movement
There are two mechanisms by which holes and free electrons move through a silicon crystal.
• Drift--- The carrier motion is generated by the electrical field across a piece of silicon. This motion will produce drift current.
• Diffusion--- The carrier motion is generated by the different concentration of carrier in a piece of silicon. The diffused motion, usually carriers diffuse from high concentration to low concentration, will give rise to diffusion current.
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Drift and Drift Current
• DriftDrift velocities
Drift current densities
Ev
Ev
ndrift
pdrift
np ,
EqpJ
EqnEqnJ
pdriftp
nndriftn
)()(
Where are the constants called mobility of holes and electrons respectively.
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Drift and Drift Current
• Total drift current density
• Resistivity
EpnqJ pndrift ) +(
)(1
pn pnq +
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Drift and Drift Current
• Resistivities for doped semiconductor
* Resistivities are inversely proportional to the concentration of doped impurities.
• Temperature coefficient(TC)TC for resistivity of doped semiconductor is positive due to negative TC of mobility
pA
nD
pnqN
qNpnq
1
1
)(1 For n type
For p type
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Drift and Drift Current
• Resistivity for intrinsic semiconductor
* Resistivity is inversely proportional to the carrier concentration of intrinsic semiconductor.
• Temperature coefficient(TC)TC for resistivity of intrinsic semiconductor is negative due to positive TC of .
)(1
)(1
pnipn qnpnq
in
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Diffusion and Diffusion Current
• diffusion
A bar of intrinsic silicon (a) in which the hole concentration profile shown in (b) has been created along the x-axis by some unspecified mechanism.
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Diffusion and Diffusion Current
where are the diffusion constants or diffusivities for hole and electron respectively.
* The diffusion current density is proportional to the slope of the the concentration curve, or the concentration gradient.
dxxdnqDJ
dxxdpqDJ
nn
pp
)(
)(
np DD ,
SJTU Zhou Lingling 33
Einstein Relationship
Einstein relationship exists between the carrier diffusivity and mobility:
Where VT is Thermal voltage.
At room temperature ,
qkTV
DDT
p
p
n
n
mvVT 25
SJTU Zhou Lingling 34
1.3 pn Junction
• The pn junction under open-circuit condition
• I-V characteristic of pn junctionTerminal characteristic of junction diode.Physical operation of diode.
• Junction capacitance
SJTU Zhou Lingling 35
pn Junction Under Open-Circuit Condition
• Usually the pn junction is asymmetric, there are p+n and pn+.
• The superscript “+” denotes the region is more heavily doped than the other region.
SJTU Zhou Lingling 36
pn Junction Under Open-Circuit Condition
Fig (a) shows the pn junction with no applied voltage (open-circuited terminals).
Fig.(b) shows the potential distribution along an axis perpendicular to the junction.
SJTU Zhou Lingling 37
Procedure of Forming pn Junction
The procedure of forming pn the dynamic equilibrium of drift and diffusion movements for carriers in the silicon. In detail, there are 4 steps:
a) Diffusion
b) Space charge region
c) Drift
d) Equilibrium
SJTU Zhou Lingling 38
Procedure of Forming pn Junction
• diffusionBoth the majority carriers diffuse across the
boundary between p-type and n-type semiconductor.
The direction of diffusion current is from p side to n side.
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Procedure of Forming pn Junction
• Space charge regionMajority carriers recombining with minority carriers
results in the disappearance of majority carriers.Bound charges, which will no longer be neutralized by
majority carriers are uncovered.There is a region close to the junction that is depleted of
majority carriers and contains uncovered bound charges.This region is called carrier-depletion region or space
charge region.
SJTU Zhou Lingling 40
Procedure of Forming pn Junction
• DriftElectric field is established across the space charge
region.Direction of electronic field is from n side to p side. It helps minority carriers drift through the junction. The
direction of drift current is from n side to p side. It acts as a barrier for majority carriers to diffusion.
SJTU Zhou Lingling 41
Procedure of Forming pn Junction
• EquilibriumTwo opposite currents across the junction is
equal in magnitude.No net current flows across the pn junction.Equilibrium conduction is maintained by the
barrier voltage.
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Junction Built-In Voltage
The Junction Built-In Voltage
It depends on doping concentration and temperature
Its TC is negative.
2lni
DATo n
NNVV
SJTU Zhou Lingling 43
Width of the Depletion Region
Width of the Depletion Region:
Depletion region exists almost entirely on the slightly doped side.
Width depends on the voltage across the junction.
oDA
depo VNNq
W )11(2
))11(2 VVNNq
W oDA
dep -(
SJTU Zhou Lingling 44
I-V Characteristics
The diode i–v relationship with some scales expanded and others compressed in order to reveal details
SJTU Zhou Lingling 45
I-V Characteristic Curve
Terminal Characteristic of Junction Diodes• The Forward-Bias Region, determined by
• The Reverse-Bias Region, determined by
• The Breakdown Region, determined by
ov
0 vVZK
ZKVv
SJTU Zhou Lingling 46
The pn Junction Under Forward-Bias Conditions
The pn junction excited by a constant-current source supplying a current I in the forward direction.
The depletion layer narrows and the barrier voltage decreases by V volts, which appears as an external voltage in the forward direction.
SJTU Zhou Lingling 47
The pn Junction Under Forward-Bias Conditions
Minority-carrier distribution in a forward-biased pn junction. It is assumed that the p region is more heavily doped than the n region; NA >>ND.
SJTU Zhou Lingling 48
The pn Junction Under Forward-Bias Conditions
Excess minority carrier concentration:
Exponential relationshipSmall voltage incremental give rise to great incremental
of excess minority carrier concentration.
T
T
Vv
ppp
Vv
nnn
enxn
epxp
0
0
)(
)(
SJTU Zhou Lingling 49
The pn Junction Under Forward-Bias Conditions
Distribution of excess minority concentration:
Where
are called excess-minority-carrier lifetime.
n
p
pn
Lxx
ppppp
Lxx
nnnnon
enxnnxn
epxppxp)(
00
)(
0
])([)(
])([)(+
-
nnn
ppp
DL
DL
pn ,
SJTU Zhou Lingling 50
The pn Junction Under Forward-Bias Conditions
The total current can be obtained by the diffusion current of majority carriers.
)1)((
)()((
)(
00
T
pn
VV
n
pn
p
np
xxxx
nDpD
nDpD
eLnD
LpD
Aq
dxxdnq
dxxdpqA
JJA
III
)
SJTU Zhou Lingling 51
The pn Junction Under Forward-Bias Conditions
The saturation current is given by :
)(
)(
2
00
An
n
Dp
pi
n
pn
p
nps
nLD
nLD
qAn
LnD
LpD
qAI
SJTU Zhou Lingling 52
The pn Junction Under Forward-Bias Conditions
I-V characteristic equation:
• Exponential relationship, nonlinear.• Is is called saturation current, strongly
depends on temperature.• or 2 , in general • VT is thermal voltage.
)1 TnVv
s eIi (
1n 1n
SJTU Zhou Lingling 53
The pn Junction Under Forward-Bias Conditions
assuming V1 at I1 and V2 at I2
then:
* For a decade changes in current, the diode voltage drop changes by 60mv (for n=1) or 120mv (for n=2).
1
2
1
212 lg3.2ln I
InVIInVVV TT
SJTU Zhou Lingling 54
The pn Junction Under Forward-Bias Conditions
• Turn-on voltage
A conduction diode has approximately a constant voltage drop across it. It’s called turn-on voltage.
• Diodes with different current rating will exhibit the turn-on voltage at different currents.
• Negative TC,
VV
VV
onD
onD
25.0
7.0
)(
)(
For silicon
For germanium
CmvTC /2
SJTU Zhou Lingling 55
The pn Junction Under Reverse-Bias Conditions
The pn junction excited by a constant-current source I in the reverse direction.
To avoid breakdown, I is kept smaller than IS.
Note that the depletion layer widens and the barrier voltage increases by VR volts, which appears between the terminals as a reverse voltage.
SJTU Zhou Lingling 56
The pn Junction Under Reverse-Bias Conditions
I-V characteristic equation:
Where Is is the saturation current, it is proportional to ni2
which is a strong function of temperature.
sIi
)(
)(
2
00
An
n
Dp
pi
n
pn
p
nps
nLD
nLD
qAn
LnD
LpD
qAI
Independent of voltage 。
SJTU Zhou Lingling 57
The pn Junction In the Breakdown Region
The pn junction excited by a reverse-current source I, where I > IS. The junction breaks down, and a voltage VZ , with the polarity indicated, develops across the junction.
SJTU Zhou Lingling 58
The pn Junction In the Breakdown Region
• Supposing , the current source will move holes from p to n through the external circuit.
• The free electrons move through opposite direction.
• This result in the increase of barrier voltage and decrease almost zero of diffusion current.
• To achieved the equilibrium, a new mechanism sets in to supply the charge carriers needed to support the current I.
sII
SJTU Zhou Lingling 59
Breakdown Mechanisms
• Zener effect Occurs in heavily doping semiconductor Breakdown voltage is less than 5v. Carriers generated by electric field---field ionization. TC is negative.
• Avalanche effect. Occurs in slightly doping semiconductor Breakdown voltage is more than 7v. Carriers generated by collision. TC is positive.
SJTU Zhou Lingling 60
Breakdown Mechanisms
Remember:
pn junction breakdown is not a destructive process, provided that the maximum specified power dissipation is not exceeded.
SJTU Zhou Lingling 61
Zener Diode
Circuit symbol
The diode i–v characteristic with the breakdown region shown in some detail.
SJTU Zhou Lingling 62
Junction Capacitance
• Diffusion Capacitance Charge stored in bulk region changes with the change of voltage
across pn junction gives rise to capacitive effect.
Small-signal diffusion capacitance
• Depletion capacitance Charge stored in depletion layer changes with the change of
voltage across pn junction gives rise to capacitive effect.
Small-signal depletion capacitance
SJTU Zhou Lingling 63
Diffusion Capacitance
According to the definition:
The charge stored in bulk region is obtained from below equations:
Qd dV
dQC
pp
pnonn
x nonp
I
LpxpAq
dxpxpAqQn
])([
])([
n n nI Q
SJTU Zhou Lingling 64
Diffusion Capacitance
The expression for diffusion capacitance:
Forward-bias, linear relationship
Reverse-bias, almost inexistence
0
)(
)(
][
QT
T
QT
T
VV
sTd
IV
IV
eIdVdC T
SJTU Zhou Lingling 65
Depletion Capacitance
According to the definition:
Actually this capacitance is similar to parallel plate capacitance.
QR VVRj dV
dQC
)1(
))(11(2[
0
0
o
R
j
RBA
depj
VV
C
vVNNq
AW
AC
=
SJTU Zhou Lingling 66
Depletion Capacitance
• A more general formula for depletion capacitance is :
• Where m is called grading coefficient.
• If the concentration changes sharply, • Forward-bias condition,• Reverse-bias condition,
mR
jj V
CC
)V1(0
0
21~
31
m
21
m
02 jj CC dj CC
SJTU Zhou Lingling 67
Junction Capacitance
Remember:
a) Diffusion and depletion capacitances are incremental capacitances, only are applied under the small-signal circuit condition.
b) They are not constants, they have relationship with the voltage across the pn junction.
SJTU Zhou Lingling 68
1.4 Analysis of Diode Circuit
• ModelsMathematic modelCircuit model
• Methods of analysisGraphical analysisIterative analysisModeling analysis
SJTU Zhou Lingling 69
The Diode Models
Mathematic Model :
The circuit models are derived from approximating the curve into piecewise-line.
s
nVv
s
nVv
s
IeI
eIi
T
T )1(
Forward biased
Reverse biased
SJTU Zhou Lingling 70
The Diode Models
Circuit Modela) Simplified diode model
b) The constant-voltage-drop model
c) Small-signal model
d) High-frequency model
e) Zener Diode Model
SJTU Zhou Lingling 71
Simplified Diode Model
Piecewise-linear model of the diode forward characteristic and its equivalent circuit representation.
SJTU Zhou Lingling 72
The Constant-Voltage-Drop Model
The constant-voltage-drop model of the diode forward characteristics and its equivalent-circuit representation.
SJTU Zhou Lingling 73
Small-Signal Model
Symbol convention: Lowercase symbol, uppercase subscript stands
for total instantaneous qualities. Uppercase symbol, uppercase subscript stands
for dc component. Lowercase symbol, lowercase subscript stands
for ac component or incremental signal qualities. Uppercase symbol, lowercase subscript stands
for the rms(root-mean-square) of ac.)(tId
)(tid
DI
)(tiD
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Small-Signal Model
Development of the diode small-signal model. Note that the numerical values shown are for a diode with n = 2.
SJTU Zhou Lingling 75
Small-Signal Model(cont’d)
Incremental resistance:
*The signal amplitude sufficiently small such that the excursion at Q along the i-v curve is limited to a short, almost linear segment.
DQ
Td I
Vr
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High-Frequency Model
High frequency model
rd
rs
cj
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Zener Diode Model
ZZZZ rIVV 0
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Method of Analysis
Load line
Diode characteristic
Q is the intersect point
Visualization
SJTU Zhou Lingling 79
Method of Analysis
• Iterative analysisRefer to example 3.4
• Model AnalysisRefer to example 3.6 and 3.7
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1.5 The Application of Diode Circuits
• Rectifier circuitsHalf-wave rectifierFull-wave rectifier
• Transformer with a center-tapped secondary winding• Bridge rectifier
The peak rectifier• Voltage regulator• Limiter
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Half-Wave Rectifier
(a) Half-wave rectifier.
(b) Equivalent circuit of the half-wave rectifier with the diode replaced with its battery-plus-resistance model.
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Half-Wave Rectifier
(c) Transfer characteristic of the rectifier circuit.
(d) Input and output waveforms, assuming that RrD
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Full-Wave Rectifier
(a) circuit(b) transfer characteristic assuming a constant-voltage-drop model for
the diodes
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Full-Wave Rectifier
(c) input and output waveforms.
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The Bridge Rectifier
(a) circuit
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The Bridge Rectifier
(b) input and output waveforms
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Peak Rectifier
Voltage and current waveforms in the peak rectifier circuit with .
The diode is assumed ideal.
TCR
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Voltage Regulator
We define:
s
oV
VtionLineregula
L
oI
VtionLoadregula
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Limiter
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Limiter
Applying a sine wave to a limiter can result in clipping off its two peaks.
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Soft Limiting