chapter1 diodes

SJTU Zhou Lingling 1

ChapterChapter 11

DiodesDiodes


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


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.


Physical Structure

The most important region, which is called pn junction, is the boundary between n-type and p-type semiconductor.


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.


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.


1.2 Basic Semiconductor Concepts

• Intrinsic Semiconductor• Doped Semiconductor• Carriers movement


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


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.



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.



• 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



• 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.



• 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.



• Carrier concentration in thermal equilibrium

• At room temperature(T=300K)

carriers/cm3

inpn kTE

iGeBTn 32

10105.1 in



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


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.


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.



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.



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.



A silicon crystal doped with a trivalent impurity. Each dopant atom gives rise to a hole, and the semiconductor becomes p type.



Carrier concentration for n typea) Thermal equilibrium equation

b) Electric neutral equation

200 inn npn

Dnn Npn 00



Carrier concentration for p typea) Thermal equilibrium equation

b) Electric neutral equation

200 ipp nnp

App Nnp 00



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



• 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.



• 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


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.


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.



• Total drift current density

• Resistivity

EpnqJ pndrift ) ＋（

)(1

pn pnq ＋



• 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



• 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


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.


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 ,


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


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


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.


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.


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



• 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.



• 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.



• 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.



• 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.


Junction Built-In Voltage

The Junction Built-In Voltage

It depends on doping concentration and temperature

Its TC is negative.

2lni

DATo n

NNVV


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 －（


I-V Characteristics

The diode i–v relationship with some scales expanded and others compressed in order to reveal details


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


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.



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.



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

)(

)(



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 ,



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

）



The saturation current is given by :

)(

)(

2

00

An

n

Dp

pi

n

pn

p

nps

nLD

nLD

qAn

LnD

LpD

qAI



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



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



• 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


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.


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 。


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.


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


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.


Breakdown Mechanisms

Remember:

pn junction breakdown is not a destructive process, provided that the maximum specified power dissipation is not exceeded.


Zener Diode

Circuit symbol

The diode i–v characteristic with the breakdown region shown in some detail.


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


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


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


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

＝


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


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.


1.4 Analysis of Diode Circuit

• ModelsMathematic modelCircuit model

• Methods of analysisGraphical analysisIterative analysisModeling analysis


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


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


Simplified Diode Model

Piecewise-linear model of the diode forward characteristic and its equivalent circuit representation.


The Constant-Voltage-Drop Model

The constant-voltage-drop model of the diode forward characteristics and its equivalent-circuit representation.


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


Small-Signal Model

Development of the diode small-signal model. Note that the numerical values shown are for a diode with n = 2.


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


High-Frequency Model

High frequency model

rd

rs

cj


Zener Diode Model

ZZZZ rIVV 0


Method of Analysis

Load line

Diode characteristic

Q is the intersect point

Visualization


Method of Analysis

• Iterative analysisRefer to example 3.4

• Model AnalysisRefer to example 3.6 and 3.7


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


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.


Half-Wave Rectifier

(c) Transfer characteristic of the rectifier circuit.

(d) Input and output waveforms, assuming that RrD


Full-Wave Rectifier

(a) circuit(b) transfer characteristic assuming a constant-voltage-drop model for

the diodes


Full-Wave Rectifier

(c) input and output waveforms.


The Bridge Rectifier

(a) circuit


The Bridge Rectifier

(b) input and output waveforms


Peak Rectifier

Voltage and current waveforms in the peak rectifier circuit with .

The diode is assumed ideal.

TCR


Voltage Regulator

We define:

s

oV

VtionLineregula

L

oI

VtionLoadregula


Limiter


Limiter

Applying a sine wave to a limiter can result in clipping off its two peaks.


Soft Limiting

chapter1 diodes

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