EDC Notes Part 1 by S S Kiran

Introduction about EDC, Review of Semiconductor Physics and PN Junction Diode Characteristics.

1. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
1
ELECTRONIC DEVICES andCIRCUITS
II B.TECH ISEMESTER-ECE
DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING
LENDI INSTITUTE OF ENGINEERING AND TECHNOLOGY
(An Autonomous Institute,Approved by A.I.C.T.E & Permanently Affiliated to JNTUK, Kakinada)
(Accredited By NAAC with A Grade and Accredited by NBA)
Jonnada (Village), Denkada (Mandal), VizianagaramDist–535 005
Phone No. 08922-241111, 241112
E-Mail:[email protected] website:www.lendi.org
EDCTextbookPrepared by
Mr. S S Kiran, Dr. M Rajanbabuand Dr. B Kiranmai
Electronic Devices and Circuits

2. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Subject Code SubjectName LTP C
R19ECE-PC2101 ElectronicDevices and Circuits 300 3
Course Objectives:
1. Study the physical phenomena such as conduction, transport mechanism and V-I
characteristics of different diodes.
2. To learn and understand the application of diodes as rectifiers with their operation and
characteristics are discussed.
3. Understand the switching characteristics of diode and its application in non linear wave
shaping circuits.
4. Acquire knowledgeabout the principle of working and operation of Bipolar Junction
Transistor and Field Effect Transistor and their characteristics.
5. To learn and understand the purpose of transistor biasing and its significance.
Course Outcomes:
At the end of thecourse, students will be able to:
1.Understand the formation of p-n junction and how it can be used as a p-n junction diode in
different modes of operation (L2).
2.Demonstrate the basic applications of Diodes as rectifier with and without filters (L3).
3.Implement the non linear wave shaping circuits using diodes (L3).
4.Understand the construction, principle of operation of BJT and FET and compare their V-I
characteristics in different configurations (L2).
5.Examine the various stability parameters of a Bipolar Junction Transistor in different biasing
methods (L4).
UNIT-I
S.NOTopic name Page No
1 Introduction about Course 3
2. Review of Semi Conductor Physics 3
3. Fermi DiracFunction 18
4. ContinuityEquation 20
Junction DiodeCharacteristics,Special Semiconductor Diodes
S.NoTopic Name Page No
1. OpenCircuited P-N Junction 22
2. BiasedP-N Junction,,P-N JunctionDiode 26
3. CurrentComponents in PNJunction Diode 30
4. DiodeEquation 35
5. V-I Characteristics 36
6. TemperatureDependence on V-ICharacteristics 38
7. DiodeResistance 39
8. DiodeCapacitance 42
9. EnergyBandDiagram of PNJunction Diode 43

3. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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10.Zener Diode 46
11.Tunnel Diode 50
12.LED 54
Applications: 1.Detection signals in digitalnetworks.
2.Lighting systems in various display boards
3.As switches in logic circuits
4.Diodes in Voltage Multiplier Circuits
5.Diodes in Reverse Current Protectionbased on their PIV.
6.Diodes in Voltage Spike Suppression
Introduction about Course:
ElectronDefinition:
Anelectronis a negatively charged subatomic particle. It can be either free or bound to the
nucleus of an atomasshown in figure 0.0.It is a charged particle, the charge, or quantity, of
negative electricity and the mass of the electron have been found to be 1.60X10
-19
C
(Coulombs)and 9.11X10
-31
kg respectively.
Figure 0.0:Mechanics of Electron
DeviceDefinition:A thing(System)is designedfor a particular purpose, especially a piece of
Mechanical or Electrical orElectronic Equipment. Thisis taken input and givesoutput.
These Devices are generally categorized into various types like Electronic Devices, Electrical
Devices and Mechanical Devicesshown in following figure 0.1
Figure 0.1: Different devices.

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Electronic Devices Definition:a device which is havingelectronic components forcontrolling
the flow of electrical currents for the purpose of information processing and system control.
Electronic devices (Control Systems)are usually small and can be grouped together into
packages called integrated circuits.This is taken input andproduces desired electronic DC
output.
Figure 0.2a: Electronic Devices.
CircuitDefinition:
A roughly circular line, route, or movement that starts and finishes at the same place, in general
wayevery electronic component having terminals, joining of these terminals can design circuit
as shown in following circuit Figure 0.2b.It is very necessary for making Electronic Devices.
Figure 0.2b:Different circuits.
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Electronic Devices Definition:a device which is havingelectronic components forcontrolling
the flow of electrical currents for the purpose of information processing and system control.
Electronic devices (Control Systems)are usually small and can be grouped together into
packages called integrated circuits.This is taken input andproduces desired electronic DC
output.
Figure 0.2a: Electronic Devices.
CircuitDefinition:
A roughly circular line, route, or movement that starts and finishes at the same place, in general
wayevery electronic component having terminals, joining of these terminals can design circuit
as shown in following circuit Figure 0.2b.It is very necessary for making Electronic Devices.
Figure 0.2b:Different circuits.
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Electronic Devices Definition:a device which is havingelectronic components forcontrolling
the flow of electrical currents for the purpose of information processing and system control.
Electronic devices (Control Systems)are usually small and can be grouped together into
packages called integrated circuits.This is taken input andproduces desired electronic DC
output.
Figure 0.2a: Electronic Devices.
CircuitDefinition:
A roughly circular line, route, or movement that starts and finishes at the same place, in general
wayevery electronic component having terminals, joining of these terminals can design circuit
as shown in following circuit Figure 0.2b.It is very necessary for making Electronic Devices.
Figure 0.2b:Different circuits.

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The motion of electrons through aconductor gives us electric current. This electric
current can be produced with the help of batteries and generators. The device which controls the
flow of electrons is called electronic device. These devices are the main building blocks of
electronic circuits.
What is electronics?
The word electronics is derived from electron mechanics, which means to study the
behavior of an electron under different conditions of appliedelectric field.
Electronics Definition
The branch of engineering in which the flow and control of electrons in vacuum or
semiconductor are studied is called electronics.Electronics can also be defined as the branch of
engineering in which the electronic devices and their utilization are studied.
Electronics have various branches include, digital electronics, analog electronics, micro
electronics, nano-electronics, optoelectronics, integrated circuit and semiconductor device.
History ofElectronics
Diode vacuum tube was the first electronic component invented by J.A. Fleming. Later, Lee De
Forest developed the triode, a three element vacuum tube capable of voltage amplification.
Vacuum tubes played a major role in the field of microwave and high power transmission as well
as television receivers.
In 1947, Bell laboratories developed the first transistor based on the research of Shockley,
Bardeen and Brattain. However, transistor radios are not developed until the late 1950’s due to
the existing huge stock of vacuum tubes.
In 1959, Jack Kilby of Texas Instruments developed the first integrated circuit. Integrated
circuits contain large number of semiconductor devices such as diodes and transistors in very
small area.
Advantages ofElectronics:
Electronic devices are playing a major role in everyday life. The various electronic devices we
use in everyday life include
Computers
Today, computers are using everywhere. At home, computers are used for playing games,
watchingmovies, doing research, paying bills and reservation of tickets for railways and airlines.
At school, students use computers to complete their assignments.
Mobile phones
Mobile phones are used for variety of purposes such as for sending text messages,making voice
calls, surfing internet, playing games, and listening songs.
ATM
ATM is an electronic telecommunication device particularly used for withdrawing money at
anytimefrom anywhere. ATM stands for automated teller machine. The customer can withdraw
money up to a certain limit during anytime of the day or night.
Television

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Television is an electronic device primarily used for entertainment and knowledge. It is used for
watching movies for entertainment, news for knowledge, cartoons for children’s.
Digital camera
Digital camera is a camera used for taking pictures and videos. This images and videos are stored
for later reproduction.
Review of Semi Conductor Physics:
Semiconductor Materials: Ge, Si,andGaAs
The construction of every discrete(individual) solid-state (hard crystal structure)
electronicdevice or integrated circuit begins with a semiconductor material of the highest
quality.
Semiconductors are a special class of elements havingconductivitybetween that of agood
conductor andthat of an insulator.
In general, semiconductor materials fall into one of two classes:single-crystaland
compound.Single-crystal semiconductors such as germanium (Ge) and silicon (Si) have a
repetitive crystal structure, whereas compound semiconductors such as gallium arsenide(GaAs),
cadmium sulfide (CdS), gallium nitride (GaN), and gallium arsenide phosphide(GaAsP) are
constructed of two or more semiconductor materials of different atomicstructures.
Figure0.3: Atomic structure of (a)silicon; (b) germanium; and(c) gallium and arsenic.
As indicated inFig.0.3, silicon has 14 orbiting electrons1s2 2s2 2p6 3s2 3p2, germanium has 32
electrons1s22s22p63s23p63d104s24p2, gallium has 31 electrons, and arsenic has 33
orbitingelectrons (the same arsenic that isa very poisonous chemical agent). For germanium and

7. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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silicon there are four electrons inthe outermost shell, which are referred to asvalence electrons.
Gallium has three valenceelectrons and arsenic has five valence electrons. Atoms that have four
valence electronsare calledtetravalent, those with three are calledtrivalent, and those with five
are calledpentavalent.The termvalenceis used to indicate that the potential (ionization
potential)required to remove anyone of these electrons from the atomic structure is significantly
lower than that required for any other electron in the structure.
Figure0.4:Covalent banding of the silicon atom
In a pure silicon or germanium crystal the four valence electrons ofone atom form abonding
arrangement with four adjoining atoms, as shown in Fig.0.4.
The three semiconductors used most frequently in the construction of electronicdevices are
Ge, Si, and GaAs.
Figure0.5:Electronic Panel boards using Semiconductor Materials

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GaAs was more difficult to manufacture at high levels of purity, was more expensive,and
had little design support in the early years of development. However, in timethedemand for
increased speed resulted in more funding for GaAs research, to the point thattodayit is often
used as the base material for new high-speed, very large scale integrated(VLSI)circuit designs.
Insulators, Semi Conductors, and Metals
Types of Materials:
1.Insulators
2.SemiConductors
3.Metals
Definition:A Very poor Conductor of electricity is called anInsulator: an excellent conductor
is aMetaland a substance whose conductivity lies between these extremes is aSemiconductor.
Table 1.Comparison table between ConductorSemiconductor and Insulator
#CharacteristicsConductoror Metal Semi-Conductor Insulator
1Conductivity High Moderate Low
2Resistivity Low Moderate Very High
3ForbiddenGap No forbidden gap Small forbidden gapLarge forbidden gap
4Conduction
Largenumber of
Electrons for Conduction
Very small number of
Electrons for Conduction
Moderate number of
Electrons for
Conduction
5Conductivity valueVery high10-7mho/m
Between those of
conductors and insulators
i.e.10-7 mho/m to10-
13mho/m
Negligiblelike10-
13mho/m
6Resistivity value
Negligible; less than10-
5Ω-m
Between those of
conductors and insulators
i.e.10-5Ω-mto105Ω-m
Very high; more
than105Ω-m
7Current flow Due to free electrons
Due to holes and free
electrons
Due to negligiblefree
electrons
8
Number of current
carriers at normal
temperature
Very high Low Negligible
9
Band Overlap
(Energy Gap)
Both Conduction and
Valence bands are
Overlapped.
Both bands are separated
by an energy gap of
1.1eV
Both bands are
separated by an energy
gap of6eV to 10eV
100 Kelvin Behavior
Acts like a
superconductor
Acts like an insulatorActs like an insulator
11Formation
Formed by metallic
bonding
Formed by covalent
bonding
Formed by ionic
bonding

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12ValenceElectrons
One valence electron in
outermost shell
Four valence electron in
outermost shell
Eight valence electron in
outermost shell
13Examples
Copper, Mercury,
Aluminum, Silver
Germanium, Silicon
Wood, Rubber, Mica,
Paper
Insulators:
Figure0.6InsulatorMaterialsUsingPlasticRubber Material
Figure0.7Insulator Materials Using CeramicMaterials
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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12ValenceElectrons
One valence electron in
outermost shell
Four valence electron in
outermost shell
Eight valence electron in
outermost shell
13Examples
Copper, Mercury,
Aluminum, Silver
Germanium, Silicon
Wood, Rubber, Mica,
Paper
Insulators:
Figure0.6InsulatorMaterialsUsingPlasticRubber Material
Figure0.7Insulator Materials Using CeramicMaterials
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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12ValenceElectrons
One valence electron in
outermost shell
Four valence electron in
outermost shell
Eight valence electron in
outermost shell
13Examples
Copper, Mercury,
Aluminum, Silver
Germanium, Silicon
Wood, Rubber, Mica,
Paper
Insulators:
Figure0.6InsulatorMaterialsUsingPlasticRubber Material
Figure0.7Insulator Materials Using CeramicMaterials

10. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Figure0.8Different types of Insulating Materials
Metals(Conductors):
Figure0.9Different types ofMetals
Figure0.10CopperConductors
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Figure0.8Different types of Insulating Materials
Metals(Conductors):
Figure0.9Different types ofMetals
Figure0.10CopperConductors
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Figure0.8Different types of Insulating Materials
Metals(Conductors):
Figure0.9Different types ofMetals
Figure0.10CopperConductors

11. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Energylevels:
Within the atomic structure of each andevery isolated atomthere are specific energy
levelsassociated with each shell and orbiting electron, as shownin Fig.1.1. The energy levels
associated with each shell will be differentfor every element.
However, in general,
The farther an electron is from the nucleus, the higher is the energy state, and any
electron that has left its parent atom has a higher energy state than any electron inthe atomic
structure.
Notein Fig.0.11that only specific energy levels can exist for the electrons in the atomic
structure of an isolated atom. The result is a series of gaps between allowed energy levels
Figure0.11Energy BandDiagramsof Insulator, Semiconductor and Metal
A materialmay be placed in one of these three classes, depending upon its Energy-Band
Structure as shown in above figure.
Insulator:
The energy band structureis indicatedschematicallyshown in figure 1.4a(Energy Gap isEg=
6eV).The largeforbidden band separates the filled valence regionfrom the vacantconduction
band.Hencethe electron cannot acquire sufficient applied energy so that conductionis not
possible i.e insulator.The number of free electrons in an insulator is very small, roughly around
10
7
electrons /m
3

12. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Semiconductor:
A substancefor which the width of the forbidden energyregion is relatively small (Energy Gap
is1 eV)is called Semiconductor. The number of free electrons in semiconductor lies between
10
7
electrons /m
3
to 10
28
electrons /m
3
.
Metal (Conductor):
A solidwhich contains a partlyfilled band structure is called a metal.Under the influence of an
applied electric field the electrons may acquire additional energyand move into higher states.
Here there is energy gap between form valancebandsto conduction band isoverlappedeach
other.The number of free electrons in an Metal is very high, roughly around 10
28
electrons /m
3

13. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Types ofSemiconductors:
1)Intrinsic Semiconductor(Pure Semiconductor)
2)Extrinsic Semiconductor(Impure Semiconductoror Doped Semiconductor)
Intrinsic Semiconductor:A pure semiconductor is called intrinsic semiconductor, even at the
room temperature, some of the valence electrons may acquire sufficientenergy to enter the
conduction band to form free electrons. Under the influence of electric field, these electrons
constitute electric current. A missing electron in the valence band leaves a vacant space there,
which is known as a hole, as shown in following figure. Holes also contribute to electric current.
Figure 0.12 Creation of electron-hole pair in a semiconductor
In an intrinsic semiconductor, even at room temperature, electron-hole pairs are created. When
electric field is applied across an intrinsic semiconductor, the current conduction takes place by
two processes, namely, free electrons and hole. Under the influence of electric field, total current
through the semiconductor is the sum of currents due to free electrons and hole.
Though the total current inside the semiconductor is due to free electrons and holes, the
current in the external wire is fully by electrons. In following figure holes being positively
charged move towards the negative terminal of the battery. As the holes reach the negative
terminal of the battery, electrons enter the semiconductor near the terminal (X) and combine with
holes. At the same time, the loosely held electrons near the positive (Y) are attracted away from
their atoms into the positive terminal. This creates new holes near the positive terminal which
again drift towards the negative terminal.
Figure 0.13: Current conductionin Semiconductor

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Extrinsic Semiconductor (Impure Semiconductor or Doped Semiconductor):
A semiconductor material that has been subjected to the doping process is called an
Extrinsicmaterial.
There are two extrinsic materials of immeasureable importance to semiconductor device
fabrication:n-type andp-type materials. Each is described in some detail in the following
subsections.
n-Type Material:
Bothn-type andp-type materials are formed by adding a predetermined number of impurity
atoms to a silicon base. Ann-type material is created by introducing impurity elements that have
fivevalence electrons (Pentavalent), such asantimony,arsenic, andphosphorus.Each is a
member of a subset group of elements in the Periodic Table of Elements referred to as Group V
because each has five valence electrons. The effect of such impurity elements is indicated in Fig.
0.14(using antimonyas the impurityin a silicon base). Note that the four covalent bonds are still
present. There is, however, an additional fifth electron due to the impurity atom, which is
unassociatedwith any particular covalent bond. This remaining electron, loosely bound to its
parent (antimony) atom, is relatively free to move within the newly formedn-type material.
Since the inserted impurity atom has donated a relatively “free” electron to the structure:
Figure 0.14 Antimony impurity in n-type material
p-Type Material
Thep-type material is formed by doping a pure germanium or silicon crystal with impurity
atoms havingthreevalence electrons. The elements most frequently used for this purposeare
boron,gallium, andindium. Each is a member of a subset group of elements inthe Periodic
Table of Elements referred to as Group III because each has three valence electrons. The effect
of one of these elements, boron, on abase of silicon is indicated inFig.0.15
Note that there is now an insufficient number of electrons to complete the covalent bondsof the
newly formed lattice. The resulting vacancy is called aholeand is represented by asmall circle
or a plus sign, indicating the absence of a negative charge. Since the resultingvacancy will
readilyaccepta free electron

15. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Figure 0.15Boron impurity in p-type material
Mobility and Conductivity:
Mobility: In some materials, ability to movement of electrons freely and easily with a drift
velocity due to the electric field is applied.
vdis the drift velocity for electrons so thatVdαE
Vd=µE
µis the mobility constant unit is m
2
/V-sec
# Si Ge GaAsInAs
mn(cm
2
/Vs)14003900850030,000
mp(cm
2
/Vs)4701900400 500
Conductivity:The degree to which a specified materialconducts electricity, calculated as the
ratio of the current density in the material to the electric field which causes the flow of current
and it is property of a material
i= neAvd
J == nevd
J = neµE
J=σE(where σ = neµ)
σis conductivity, unit is mho/cm, we can also write in (nµn+pµp)e for semiconducting material.
J is also called conduction current density,
When an electric fieldEis applied, the force on an electron with charge–e is
F=-eE
If the electron with mass ‘m’ is moving in an electric field with an acceleration ‘a’
F=ma
According to Newton’s law, the average change in momentum of the free electron must match
the applied force, thus
=-eE
u=-E
ρv=-ne

16. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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J=ρvu =E
Whereσ=
J=σE
σis conductivity
Resistivity:Reciprocal of conductivity is called Resistivity (ohm-m).
R=
ρ =
σ
R=
Conductivity property in Materials
Metal: The conduction in metals is only due to the electrons. When an electric field is applied,
few electrons may acquire enough additional energy and move to higher energy within the
conduction band. Thus the electrons become mobile. Since the additional energy required for
transfer of electrons from valence band to conduction band is extremely small, the conductivity
of metal is excellent.
σ =neµ
For a good conductornis very large, approximately, 10
28
electrons/m
3
Semiconductor: The conductivity of a material is proportional to the concentration of free
electrons in a semiconductor lies between10
7
electrons /m
3
to 10
28
electrons /m
3
. Thus, a
semiconductor has conductivity much greater than that of an insulator but much smallerthan that
of a metal.
Insulator: In this material no electrical conduction is possible due to the number of free
electrons in insulator is very small, roughly about 10
7
electrons/m
3
.
Problem : A cylindrical shaped section of n-Type silicon has a 1 mmlength and 0.1 mm2 cross
sectional area. Calculate its conductivity and resistance when free electron density of n= 8 X 10
13
/ cm
3
.
Solution :
Given Data :
l =1 mm= 0.1 cm and a = 0.1 mm
2
= 10
-3
cm
2
n= 8 X 10
13
/ cm
3
.
Known Data:
ni= 1500 cm
2
/ V.sand
µn= 1500 cm
2
/ V.s

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µp= 500 cm
2
/ V.s
Formula :
=(1.6 X 10
-19
)[(1.5X 10
10
X 1500) + (1.5X 10
10
X 500)]
= 4.8X10
-6
(Ω.cm)
-1
R = 0.1/(4.8 X 10
-6
(Ω.cm)
-1
X 10
-3
cm
2
)
R = 20.8ΩM
Summary:
Mobility: In some materials, ability to movement of electrons freely and easily with a drift
velocity due to the electric field is applied.
vdis the drift velocity for electrons so thatVdαE
Vd=µE
Conductivity:The degree to which a specified materialconducts electricity, calculated as the
ratio of the current density in the material to the electric field which causes the flow of current
and it is property of a material.
J=σE
σ = (nµn+pµp)q
R=

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Fermi Dirac Function
Objectives
1.Fermi DiracDistributed Function to be reviewed.
2.Necessity of Fermi Dirac Distribution Function to be reviewed
Figure 1.1Internal Structure of a Typical Atom
Atomsconstitute the building blocks of all materials in existence. In these atoms, there is a
central portion called nucleusshown in above figure. Which consists of protons and neutrons,
around which revolves the particles called electrons. Next, it is to benoted that all the electrons
constituting the considered material do not revolve along the same path. However this even does
not mean that their revolutionary paths can be random. That is, each electronas show in Figure
1.0of a particular atom has its own dedicated path, called orbit, along which it circles around the
central nucleusas shown in Figure 1.1. It is these orbits which are referred to as energy levels of
an atom.
Fermi Dirac Distribution Function:
Distribution functions are nothing but the probability density functions used to describe the
probability with which a particular particle can occupy a particular energy level. When we speak
ofFermi-Diracdistributionfunction, we are particularly interested in knowing the chance by
which we canfind a fermion in a particular energy state of an atom. Here, by fermions, we mean
the electrons of anatomwhich are the particles with ½spin, bound to Pauli Exclusion Principle.
Necessity of Fermi Dirac Distribution Function
In fields like electronics, one particular factor which is of prime importance is the conductivity of
materials. This characteristic of the material is brought about the number of electrons which are
free within the material to conduct electricity.
As per energy band theory, these are the number of electronswhich constitute the conduction
band of the material considered.Thus in order to have an idea over the conduction mechanism, it
is necessary to know the concentrationof the carriers in the conduction band.
Fermi Dirac Distribution Expression
Mathematically the probability of finding an electron in the energy state E at the temperature T is
expressed as
()= . . . . . . . .(1)
Where,
K= 1.38 ×10JK
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Fermi Dirac Function
Objectives
1.Fermi DiracDistributed Function to be reviewed.
2.Necessity of Fermi Dirac Distribution Function to be reviewed
Figure 1.1Internal Structure of a Typical Atom
Atomsconstitute the building blocks of all materials in existence. In these atoms, there is a
central portion called nucleusshown in above figure. Which consists of protons and neutrons,
around which revolves the particles called electrons. Next, it is to benoted that all the electrons
constituting the considered material do not revolve along the same path. However this even does
not mean that their revolutionary paths can be random. That is, each electronas show in Figure
1.0of a particular atom has its own dedicated path, called orbit, along which it circles around the
central nucleusas shown in Figure 1.1. It is these orbits which are referred to as energy levels of
an atom.
Fermi Dirac Distribution Function:
Distribution functions are nothing but the probability density functions used to describe the
probability with which a particular particle can occupy a particular energy level. When we speak
ofFermi-Diracdistributionfunction, we are particularly interested in knowing the chance by
which we canfind a fermion in a particular energy state of an atom. Here, by fermions, we mean
the electrons of anatomwhich are the particles with ½spin, bound to Pauli Exclusion Principle.
Necessity of Fermi Dirac Distribution Function
In fields like electronics, one particular factor which is of prime importance is the conductivity of
materials. This characteristic of the material is brought about the number of electrons which are
free within the material to conduct electricity.
As per energy band theory, these are the number of electronswhich constitute the conduction
band of the material considered.Thus in order to have an idea over the conduction mechanism, it
is necessary to know the concentrationof the carriers in the conduction band.
Fermi Dirac Distribution Expression
Mathematically the probability of finding an electron in the energy state E at the temperature T is
expressed as
()= . . . . . . . .(1)
Where,
K= 1.38 ×10JK
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Fermi Dirac Function
Objectives
1.Fermi DiracDistributed Function to be reviewed.
2.Necessity of Fermi Dirac Distribution Function to be reviewed
Figure 1.1Internal Structure of a Typical Atom
Atomsconstitute the building blocks of all materials in existence. In these atoms, there is a
central portion called nucleusshown in above figure. Which consists of protons and neutrons,
around which revolves the particles called electrons. Next, it is to benoted that all the electrons
constituting the considered material do not revolve along the same path. However this even does
not mean that their revolutionary paths can be random. That is, each electronas show in Figure
1.0of a particular atom has its own dedicated path, called orbit, along which it circles around the
central nucleusas shown in Figure 1.1. It is these orbits which are referred to as energy levels of
an atom.
Fermi Dirac Distribution Function:
Distribution functions are nothing but the probability density functions used to describe the
probability with which a particular particle can occupy a particular energy level. When we speak
ofFermi-Diracdistributionfunction, we are particularly interested in knowing the chance by
which we canfind a fermion in a particular energy state of an atom. Here, by fermions, we mean
the electrons of anatomwhich are the particles with ½spin, bound to Pauli Exclusion Principle.
Necessity of Fermi Dirac Distribution Function
In fields like electronics, one particular factor which is of prime importance is the conductivity of
materials. This characteristic of the material is brought about the number of electrons which are
free within the material to conduct electricity.
As per energy band theory, these are the number of electronswhich constitute the conduction
band of the material considered.Thus in order to have an idea over the conduction mechanism, it
is necessary to know the concentrationof the carriers in the conduction band.
Fermi Dirac Distribution Expression
Mathematically the probability of finding an electron in the energy state E at the temperature T is
expressed as
()= . . . . . . . .(1)
Where,
K= 1.38 ×10JK

19. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
19
is the Boltzmann constant
T is the absolute temperature
Efis the Fermi level or the Fermi energy
Now, let us try to understand the meaning of Fermi level. In order to accomplish this, put
in equation (1).
By doing so, we get,
f(E)=
1
1+e
=
1
1+e
= =
This means the Fermi level is the level at which one can expect the electron to be present exactly
50% of the time.
Fermi Level in Semiconductors
Intrinsicsemiconductorsare the puresemiconductorswhich have no impurities in them.
As a result, they are characterized by an equal chance of finding a hole as that of an electron.
This inturn implies that they have the Fermi-level exactly in between the conduction and the
valence bands as shown by Figure1.2a.
Figure1.2:Fermi levels of (a) Intrinsic Semiconductor (b) N-Type Semiconductor (c) P-Type
Semiconductor
Next, consider the case of ann-typesemiconductor. Here, one can expect more number of
electrons to be present in comparison to the holes. This means that there is a greater chance of
finding an electron near to the conduction band than that of finding a hole in the valence band.
Thus, these materials have their Fermi-level located nearer to conduction band as shown by
Figure1.2b
Following on the same grounds, one can expect the Fermi-level in the case ofp-type
semiconductorsto be present near the valence band (Figure1.2c). This is because, these
materials lack electrons i.e. they have more number of holes which makes the probability of
finding a hole in the valence band more in comparison to that of finding an electron in the
conduction band.
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
19
is the Boltzmann constant
T is the absolute temperature
Efis the Fermi level or the Fermi energy
Now, let us try to understand the meaning of Fermi level. In order to accomplish this, put
in equation (1).
By doing so, we get,
f(E)=
1
1+e
=
1
1+e
= =
This means the Fermi level is the level at which one can expect the electron to be present exactly
50% of the time.
Fermi Level in Semiconductors
Intrinsicsemiconductorsare the puresemiconductorswhich have no impurities in them.
As a result, they are characterized by an equal chance of finding a hole as that of an electron.
This inturn implies that they have the Fermi-level exactly in between the conduction and the
valence bands as shown by Figure1.2a.
Figure1.2:Fermi levels of (a) Intrinsic Semiconductor (b) N-Type Semiconductor (c) P-Type
Semiconductor
Next, consider the case of ann-typesemiconductor. Here, one can expect more number of
electrons to be present in comparison to the holes. This means that there is a greater chance of
finding an electron near to the conduction band than that of finding a hole in the valence band.
Thus, these materials have their Fermi-level located nearer to conduction band as shown by
Figure1.2b
Following on the same grounds, one can expect the Fermi-level in the case ofp-type
semiconductorsto be present near the valence band (Figure1.2c). This is because, these
materials lack electrons i.e. they have more number of holes which makes the probability of
finding a hole in the valence band more in comparison to that of finding an electron in the
conduction band.
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
19
is the Boltzmann constant
T is the absolute temperature
Efis the Fermi level or the Fermi energy
Now, let us try to understand the meaning of Fermi level. In order to accomplish this, put
in equation (1).
By doing so, we get,
f(E)=
1
1+e
=
1
1+e
= =
This means the Fermi level is the level at which one can expect the electron to be present exactly
50% of the time.
Fermi Level in Semiconductors
Intrinsicsemiconductorsare the puresemiconductorswhich have no impurities in them.
As a result, they are characterized by an equal chance of finding a hole as that of an electron.
This inturn implies that they have the Fermi-level exactly in between the conduction and the
valence bands as shown by Figure1.2a.
Figure1.2:Fermi levels of (a) Intrinsic Semiconductor (b) N-Type Semiconductor (c) P-Type
Semiconductor
Next, consider the case of ann-typesemiconductor. Here, one can expect more number of
electrons to be present in comparison to the holes. This means that there is a greater chance of
finding an electron near to the conduction band than that of finding a hole in the valence band.
Thus, these materials have their Fermi-level located nearer to conduction band as shown by
Figure1.2b
Following on the same grounds, one can expect the Fermi-level in the case ofp-type
semiconductorsto be present near the valence band (Figure1.2c). This is because, these
materials lack electrons i.e. they have more number of holes which makes the probability of
finding a hole in the valence band more in comparison to that of finding an electron in the
conduction band.

20. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
20
Effect of temperature on Fermi-Dirac Distribution Function
Figure1.3: Fermi-Dirac Distribution Function at Different Temperatures
At T = 0 K, the electrons will have low energy and thus occupy lower energy states. The highest
energy state among these occupied states is referred to as Fermi-level. This in turn means that no
energy states which lie above the Fermi-level are occupied byelectrons. Thus we have a step
function defining theFermi-Diracdistributionfunctionas shownby the black curve in Figure
1.3.However as the temperature increases, the electrons gain more and more energy due to
which they can even rise to the conduction band. Thus at higher temperatures, one cannot clearly
distinguish between the occupied and the unoccupied states as indicated by the blue and the red
curves shown in Figure1.3.
Continuity Equation:
Objectives:
Continuity Equation and Law of Junctionto be reviewed
The fundamental law governing the flow of charge is called the Continuity Equation. The
continuity equation as applied to semiconductor described how the carrier concentration equation
in a given elemental volume of the crystal varies withtime and distance. The variation in density
is attributable two basic causes.
i) The rate of generation and loss by recombination of carriers within the element
ii)Drift of carriers into or out of the element.
The continuity equations enable us to calculate theexcess density of electrons or holes in time
and space.
As shown following figure1.4consider an infinitesimal N-Type semiconductor bar of volume of
area A and length dx and the average minority carrier (hole) concentration p, which is very small
compared with the density of majority carriers. At time t, if minority carriers (holes) are injected,
the minority current entering the volume at x is Ipand leaving at x+dx is Ip+ dIpwhich is
predominantly due to diffusion. The minority carrier concentration injected into one end of the
semiconductor bar decreases exponentially, with distance into the specimen, as a result of
diffusion and recombination, Here, dIpis the decrease in number of coulombs per second within
the volume.
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
20
Effect of temperature on Fermi-Dirac Distribution Function
Figure1.3: Fermi-Dirac Distribution Function at Different Temperatures
At T = 0 K, the electrons will have low energy and thus occupy lower energy states. The highest
energy state among these occupied states is referred to as Fermi-level. This in turn means that no
energy states which lie above the Fermi-level are occupied byelectrons. Thus we have a step
function defining theFermi-Diracdistributionfunctionas shownby the black curve in Figure
1.3.However as the temperature increases, the electrons gain more and more energy due to
which they can even rise to the conduction band. Thus at higher temperatures, one cannot clearly
distinguish between the occupied and the unoccupied states as indicated by the blue and the red
curves shown in Figure1.3.
Continuity Equation:
Objectives:
Continuity Equation and Law of Junctionto be reviewed
The fundamental law governing the flow of charge is called the Continuity Equation. The
continuity equation as applied to semiconductor described how the carrier concentration equation
in a given elemental volume of the crystal varies withtime and distance. The variation in density
is attributable two basic causes.
i) The rate of generation and loss by recombination of carriers within the element
ii)Drift of carriers into or out of the element.
The continuity equations enable us to calculate theexcess density of electrons or holes in time
and space.
As shown following figure1.4consider an infinitesimal N-Type semiconductor bar of volume of
area A and length dx and the average minority carrier (hole) concentration p, which is very small
compared with the density of majority carriers. At time t, if minority carriers (holes) are injected,
the minority current entering the volume at x is Ipand leaving at x+dx is Ip+ dIpwhich is
predominantly due to diffusion. The minority carrier concentration injected into one end of the
semiconductor bar decreases exponentially, with distance into the specimen, as a result of
diffusion and recombination, Here, dIpis the decrease in number of coulombs per second within
the volume.
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
20
Effect of temperature on Fermi-Dirac Distribution Function
Figure1.3: Fermi-Dirac Distribution Function at Different Temperatures
At T = 0 K, the electrons will have low energy and thus occupy lower energy states. The highest
energy state among these occupied states is referred to as Fermi-level. This in turn means that no
energy states which lie above the Fermi-level are occupied byelectrons. Thus we have a step
function defining theFermi-Diracdistributionfunctionas shownby the black curve in Figure
1.3.However as the temperature increases, the electrons gain more and more energy due to
which they can even rise to the conduction band. Thus at higher temperatures, one cannot clearly
distinguish between the occupied and the unoccupied states as indicated by the blue and the red
curves shown in Figure1.3.
Continuity Equation:
Objectives:
Continuity Equation and Law of Junctionto be reviewed
The fundamental law governing the flow of charge is called the Continuity Equation. The
continuity equation as applied to semiconductor described how the carrier concentration equation
in a given elemental volume of the crystal varies withtime and distance. The variation in density
is attributable two basic causes.
i) The rate of generation and loss by recombination of carriers within the element
ii)Drift of carriers into or out of the element.
The continuity equations enable us to calculate theexcess density of electrons or holes in time
and space.
As shown following figure1.4consider an infinitesimal N-Type semiconductor bar of volume of
area A and length dx and the average minority carrier (hole) concentration p, which is very small
compared with the density of majority carriers. At time t, if minority carriers (holes) are injected,
the minority current entering the volume at x is Ipand leaving at x+dx is Ip+ dIpwhich is
predominantly due to diffusion. The minority carrier concentration injected into one end of the
semiconductor bar decreases exponentially, with distance into the specimen, as a result of
diffusion and recombination, Here, dIpis the decrease in number of coulombs per second within
the volume.

21. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
21
Figure1.4: Relating to continuity equation
Since the magnitude of the carrier charges is q, thenequals the decreasein the number of
holes per second within the elemental volume A∝x. As the current density
J=
We have
I
q
.
dI
dx
=
I
q
.
dI
dx
Decrease in holeconcentration per second, due to current Ip.
We know that there is an increase of holes per unit volume per second given by G = p0/τpdue to
recombination but charge can neither be created nor destroyed. Hence, increase in holes per unit
volume per second,dp/dt, must equal the algebraic sum of all the increase in hole concentration.
Thus,
∂P
∂t
=−
P−P
−
1
Where J=-q+
Therefore, =− +D −μ
()
Partial derivatesshould be used and modified as,
=− +D −μ
()
This is the Continuity equation or equation of Conservation of charge for holes stating the
condition of dynamic equilibrium for the density of mobile carrierholes. Here, partial derivatives
have been used since both p and Jpare functions of both t and x.
Similarly, the continuity equation for electrons states the condition of dynamic
equilibrium for the density of mobile carrier electrons and is given by

22. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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=
−
−
1
Where J=-q +
Therefore,=− +D −μ
()
Hall Effect
VH=
Theory ofP-N Junction Diode:
PN Junction diode in Equilibrium with no appliedVoltage (can be treated as Open
Circuited PN Junction)
In a piece of sc, if one half is doped by p type impurity and the other half is doped by n type
impurity, a PN junction is formed. The plane dividing the two halves or zones is called PN
junction. Asshown in the fig the n type material has high concentration of free electrons, while p
type material has high concentration of holes. Therefore at the junction there is a tendency of
free electrons to diffuse over to the P side and the holes to the N side.This process is called
diffusion. As the free electrons move across the junction from N type to P type, the donor atoms
become positively charged. Hence a positive charge is built on the N-side of the junction. The
free electrons that cross the junction uncover the negative acceptor ions by filing the holes.
Therefore a negative charge is developedon the p–side of the junction.This net negative charge
on the p side prevents further diffusion of electrons into the p side. Similarly the net positive
charge on the N side repels the hole crossing from p side to N side. Thus a barrier sis set up near
the junction which prevents the further movement of charge carriers i.e. electrons and holes. As a
consequence of induced electric field across the depletion layer, an electrostatic potential

23. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
23
difference is established between P and N regions, which are called the potential barrier, junction
barrier, diffusion potential or contact potential, Vo. The magnitude of the contact potential Vo
varies with doping levels and temperature. Vo is 0.3V for Ge and 0.72 V for Si.
No Applied Bias (V=0 V)
At the instant the two materials are “joined” the electrons and the holes in the region of the
junction will combine, resulting in a lack of free carriers in the region near thejunction, as
shown in Fig. 1.5a . Note inFig. 1.5a that the only particles displayed in this region are the
positive and the negative ions remaining once the free carriers have been absorbed.
This region of uncovered positive and negative ions iscalled the depletion region due to the
“depletion” of free carriers in the region.
Figure 1.5a:No bias Semi Conductor Diode
Figure 1.5b:No bias Semi Conductor Diode without ions
Figure 1.5cSymbol of PN Junction Diode
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
23
difference is established between P and N regions, which are called the potential barrier, junction
barrier, diffusion potential or contact potential, Vo. The magnitude of the contact potential Vo
varies with doping levels and temperature. Vo is 0.3V for Ge and 0.72 V for Si.
No Applied Bias (V=0 V)
At the instant the two materials are “joined” the electrons and the holes in the region of the
junction will combine, resulting in a lack of free carriers in the region near thejunction, as
shown in Fig. 1.5a . Note inFig. 1.5a that the only particles displayed in this region are the
positive and the negative ions remaining once the free carriers have been absorbed.
This region of uncovered positive and negative ions iscalled the depletion region due to the
“depletion” of free carriers in the region.
Figure 1.5a:No bias Semi Conductor Diode
Figure 1.5b:No bias Semi Conductor Diode without ions
Figure 1.5cSymbol of PN Junction Diode
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
23
difference is established between P and N regions, which are called the potential barrier, junction
barrier, diffusion potential or contact potential, Vo. The magnitude of the contact potential Vo
varies with doping levels and temperature. Vo is 0.3V for Ge and 0.72 V for Si.
No Applied Bias (V=0 V)
At the instant the two materials are “joined” the electrons and the holes in the region of the
junction will combine, resulting in a lack of free carriers in the region near thejunction, as
shown in Fig. 1.5a . Note inFig. 1.5a that the only particles displayed in this region are the
positive and the negative ions remaining once the free carriers have been absorbed.
This region of uncovered positive and negative ions iscalled the depletion region due to the
“depletion” of free carriers in the region.
Figure 1.5a:No bias Semi Conductor Diode
Figure 1.5b:No bias Semi Conductor Diode without ions
Figure 1.5cSymbol of PN Junction Diode

24. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Figure 1.5d:Physical Representation ofPN Junction Diode
The electrostatic field across the junction caused by the positively charged N-Type region tends
to drive the holes away from the junction and negatively charged p type regions tend to drive the
electrons awayfrom the junction. The majority holes diffusing out of the P region leave behind
negatively charged acceptor atoms bound to the lattice, thus exposing a negatives pace charge in
a previously neutral region. Similarly electrons diffusing from the N region expose positively
ionized donor atoms and a double space charge builds up at the junction as shown in the fig. 1.7a
Figure 1.7a:Diffusion of holes and electrons in P-N Diode
It is noticed that the space charge layers are of opposite sign to the majoritycarriers diffusing
into them, which tends to reduce the diffusion rate. Thus the double space of the layer causes an
electric field to be set up across the junction directed from N to P regions, which is in such a
direction to inhibit the diffusion of majority electrons and holes as illustrated in fig 1.7b. The
shape of the charge density, ρ, depends upon how diode id doped. Thus the junction region is
depleted of mobile charge carriers. Hence it is called depletion layer, space region, and transition
region. The depletion region is of the order of 0.5µm thick. There are no mobile carriers in this
narrow depletion region. Hence no current flows across the junction and the system is in
equilibrium. To the left of this depletion layer, the carrier concentration is p= NAand to its right
it is n= ND.
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
24
Figure 1.5d:Physical Representation ofPN Junction Diode
The electrostatic field across the junction caused by the positively charged N-Type region tends
to drive the holes away from the junction and negatively charged p type regions tend to drive the
electrons awayfrom the junction. The majority holes diffusing out of the P region leave behind
negatively charged acceptor atoms bound to the lattice, thus exposing a negatives pace charge in
a previously neutral region. Similarly electrons diffusing from the N region expose positively
ionized donor atoms and a double space charge builds up at the junction as shown in the fig. 1.7a
Figure 1.7a:Diffusion of holes and electrons in P-N Diode
It is noticed that the space charge layers are of opposite sign to the majoritycarriers diffusing
into them, which tends to reduce the diffusion rate. Thus the double space of the layer causes an
electric field to be set up across the junction directed from N to P regions, which is in such a
direction to inhibit the diffusion of majority electrons and holes as illustrated in fig 1.7b. The
shape of the charge density, ρ, depends upon how diode id doped. Thus the junction region is
depleted of mobile charge carriers. Hence it is called depletion layer, space region, and transition
region. The depletion region is of the order of 0.5µm thick. There are no mobile carriers in this
narrow depletion region. Hence no current flows across the junction and the system is in
equilibrium. To the left of this depletion layer, the carrier concentration is p= NAand to its right
it is n= ND.
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
24
Figure 1.5d:Physical Representation ofPN Junction Diode
The electrostatic field across the junction caused by the positively charged N-Type region tends
to drive the holes away from the junction and negatively charged p type regions tend to drive the
electrons awayfrom the junction. The majority holes diffusing out of the P region leave behind
negatively charged acceptor atoms bound to the lattice, thus exposing a negatives pace charge in
a previously neutral region. Similarly electrons diffusing from the N region expose positively
ionized donor atoms and a double space charge builds up at the junction as shown in the fig. 1.7a
Figure 1.7a:Diffusion of holes and electrons in P-N Diode
It is noticed that the space charge layers are of opposite sign to the majoritycarriers diffusing
into them, which tends to reduce the diffusion rate. Thus the double space of the layer causes an
electric field to be set up across the junction directed from N to P regions, which is in such a
direction to inhibit the diffusion of majority electrons and holes as illustrated in fig 1.7b. The
shape of the charge density, ρ, depends upon how diode id doped. Thus the junction region is
depleted of mobile charge carriers. Hence it is called depletion layer, space region, and transition
region. The depletion region is of the order of 0.5µm thick. There are no mobile carriers in this
narrow depletion region. Hence no current flows across the junction and the system is in
equilibrium. To the left of this depletion layer, the carrier concentration is p= NAand to its right
it is n= ND.

25. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
25
Figure 1.7b:Diffusion of holes and electrons in P-N Diode
Barrier voltage
Positive charge present at n-side and negative charge present at p-side of p-n junction acts as
barrier between p-type and n-typesemiconductor.Thus, a barrier is build near the junction which
prevents the further movement of electrons and holes.
Figure 1.8:Indicates barrier potential and depletion width
The negative charge formed at the p-side of the p-n junction is called negative barrier voltage
while the positive charge formed at the n-side of the p-n junction is called positive barrier
voltage. The total charge formed at the p-n junction is called barrier voltage, barrier potential or
junction barrieras shown in Figure 1.8.
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
25
Figure 1.7b:Diffusion of holes and electrons in P-N Diode
Barrier voltage
Positive charge present at n-side and negative charge present at p-side of p-n junction acts as
barrier between p-type and n-typesemiconductor.Thus, a barrier is build near the junction which
prevents the further movement of electrons and holes.
Figure 1.8:Indicates barrier potential and depletion width
The negative charge formed at the p-side of the p-n junction is called negative barrier voltage
while the positive charge formed at the n-side of the p-n junction is called positive barrier
voltage. The total charge formed at the p-n junction is called barrier voltage, barrier potential or
junction barrieras shown in Figure 1.8.
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
25
Figure 1.7b:Diffusion of holes and electrons in P-N Diode
Barrier voltage
Positive charge present at n-side and negative charge present at p-side of p-n junction acts as
barrier between p-type and n-typesemiconductor.Thus, a barrier is build near the junction which
prevents the further movement of electrons and holes.
Figure 1.8:Indicates barrier potential and depletion width
The negative charge formed at the p-side of the p-n junction is called negative barrier voltage
while the positive charge formed at the n-side of the p-n junction is called positive barrier
voltage. The total charge formed at the p-n junction is called barrier voltage, barrier potential or
junction barrieras shown in Figure 1.8.

26. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
26
The size of the barrier voltage at the p-n junction is depends on, the amount of doping, junction
temperature and type of material used. The barrier voltage for silicon diode is 0.7 volts and for
germanium is 0.3 volts.
This electric field created by thediffusion process has created a “built-in potential difference”
across the junction with an open-circuit (zero bias) potential of
=ln
.
Eois the zero bias junction voltage,VTthe thermal voltage of 26mV at room
temperature,NDandNAare the impurity concentrations andniis the intrinsic concentration.
Typically at room temperature the voltage across the depletion layer for silicon is about 0.6–0.7
volts and for germanium is about 0.3–0.35 volts. This potential barrier will always exist even if
the device is not connected to any external power source, as seen in diodes.
Depletion Width:
Let us consider the width of the depletion region in the junctionas shown inFigure 1.8figure.
The region contains space charge due to the fact that, donors on the N-Side and acceptors on the
P-Side have lost their accompanying electrons and holes. Hence electric field is established
which turns causes a difference in potential is built up across the junction.Hence space charge
finally described as an alloy junction, the depletion width W is proportional to (VO)
1/2
=
2 +
BiasedP-N Junction
Forward-Bias Condition (VD>0 V):
Aforward-biasor “on” condition is established by applying the positive potential to thep-type
material and the negative potential to then-type material as shown in Fig. 1.9. The application
of a forward-bias potentialVDwill “pressure” electrons in then-typematerial and holes in thep
-type material to recombine with the ions near the boundary and reduce the width of the
depletion region as shown inFig. 1.9a . The resulting minority-carrier flow
Figure 1.9: Forward-biased P-N junction: (a) internal distribution of charge under forward-bias
conditions; (b) forward-bias polarity and direction of resulting current.
of electrons from thep-type material to then-type material (and of holes from then–type
material to thep-type material) has not changed in magnitude (since the conduction level is
controlled primarily by the limited number of impurities in the material), but the reduction in the

27. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
27
width of the depletion region has resulted in a heavymajority flow across the junction. An
electron of then-type material now “sees” a reduced barrier at the junction due to thereduced
depletion region and a strong attraction for the positive potential applied to thep-type material.
As the applied bias increases in magnitude, the depletion region will continue to decrease in
width until a flood of electrons can pass through the junction, resulting in an exponential rise in
current as shown in the forward-bias region of the characteristics ofFig. 1.16Note that the
vertical scale ofFig. 1.16is measured in milliamperes (although somesemiconductor diodes
have a vertical scale measured in amperes), and the horizontal scale in the forward-bias region
has a maximum of 1 V. Typically, therefore, the voltage across a forward-biased diode will be
less than 1 V. Note also how quickly the current rises beyond the knee of the curve.
Figure1.10:Forward biased P-N Junction with flow of charge carrierswithresistor.
Figure 1.11:Circuit connection ofForward biasedPN Diode
Reverse-Bias Condition (VD<0 V):
If an external potential ofVvolts is applied across thep–njunction such that the positive
terminal is connected to then-type material and the negative terminal is connected to thep-type
material as shown inFig. 1.12, the number of uncovered positive ions in the depletion region
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
27
width of the depletion region has resulted in a heavymajority flow across the junction. An
electron of then-type material now “sees” a reduced barrier at the junction due to thereduced
depletion region and a strong attraction for the positive potential applied to thep-type material.
As the applied bias increases in magnitude, the depletion region will continue to decrease in
width until a flood of electrons can pass through the junction, resulting in an exponential rise in
current as shown in the forward-bias region of the characteristics ofFig. 1.16Note that the
vertical scale ofFig. 1.16is measured in milliamperes (although somesemiconductor diodes
have a vertical scale measured in amperes), and the horizontal scale in the forward-bias region
has a maximum of 1 V. Typically, therefore, the voltage across a forward-biased diode will be
less than 1 V. Note also how quickly the current rises beyond the knee of the curve.
Figure1.10:Forward biased P-N Junction with flow of charge carrierswithresistor.
Figure 1.11:Circuit connection ofForward biasedPN Diode
Reverse-Bias Condition (VD<0 V):
If an external potential ofVvolts is applied across thep–njunction such that the positive
terminal is connected to then-type material and the negative terminal is connected to thep-type
material as shown inFig. 1.12, the number of uncovered positive ions in the depletion region
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
27
width of the depletion region has resulted in a heavymajority flow across the junction. An
electron of then-type material now “sees” a reduced barrier at the junction due to thereduced
depletion region and a strong attraction for the positive potential applied to thep-type material.
As the applied bias increases in magnitude, the depletion region will continue to decrease in
width until a flood of electrons can pass through the junction, resulting in an exponential rise in
current as shown in the forward-bias region of the characteristics ofFig. 1.16Note that the
vertical scale ofFig. 1.16is measured in milliamperes (although somesemiconductor diodes
have a vertical scale measured in amperes), and the horizontal scale in the forward-bias region
has a maximum of 1 V. Typically, therefore, the voltage across a forward-biased diode will be
less than 1 V. Note also how quickly the current rises beyond the knee of the curve.
Figure1.10:Forward biased P-N Junction with flow of charge carrierswithresistor.
Figure 1.11:Circuit connection ofForward biasedPN Diode
Reverse-Bias Condition (VD<0 V):
If an external potential ofVvolts is applied across thep–njunction such that the positive
terminal is connected to then-type material and the negative terminal is connected to thep-type
material as shown inFig. 1.12, the number of uncovered positive ions in the depletion region

28. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
28
of then-type material will increase due to the large number of free electrons drawn to the
positive potential of the applied voltage. For similar reasons, the number of uncovered negative
ions will increase in thep-type material. The net effect, therefore, is awidening of the depletion
region.
Figure 1.12:Reverse-biased P-N Junction: (a) internal distribution of charge under reverse-bias
conditions; (b) reverse-bias polarity and direction of reverse saturation current.
Figure 1.13:Reverse-biased P-N Junction with resistor
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
28
of then-type material will increase due to the large number of free electrons drawn to the
positive potential of the applied voltage. For similar reasons, the number of uncovered negative
ions will increase in thep-type material. The net effect, therefore, is awidening of the depletion
region.
Figure 1.12:Reverse-biased P-N Junction: (a) internal distribution of charge under reverse-bias
conditions; (b) reverse-bias polarity and direction of reverse saturation current.
Figure 1.13:Reverse-biased P-N Junction with resistor
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
28
of then-type material will increase due to the large number of free electrons drawn to the
positive potential of the applied voltage. For similar reasons, the number of uncovered negative
ions will increase in thep-type material. The net effect, therefore, is awidening of the depletion
region.
Figure 1.12:Reverse-biased P-N Junction: (a) internal distribution of charge under reverse-bias
conditions; (b) reverse-bias polarity and direction of reverse saturation current.
Figure 1.13:Reverse-biased P-N Junction with resistor

29. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
29
Figure: 1.14 CircuitConnection of Reverse biased PN Diode
This widening of the depletion region will establish too great a barrier for the majority carriers to
overcome, effectively reducing the majority carrier flow to zero, as shown in Fig. 1.12a .
The number of minoritycarriers, however, entering the depletion region will not change,
resulting in minority-carrier flow vectors of the same magnitude indicatedwith no applied
voltage.
The current that exists under reverse-bias conditions is called the reverse saturation
current and is represented by Is
The reverse saturation current is seldom more than a few microamperes and typically inµA and
nA, except for high-power devices. The termsaturationcomes from the fact that it reaches its
maximum level quickly and does notchange significantly with increases in the reverse-bias
potential, as shownon the diode characteristics of Fig.1.15 forVD<0V.The reverse-biased
conditions are depicted inFig.1.13b for the diode symbol andP–NJunction. Note, in particular,
that the direction ofISis against the arrow of the symbol. Note also that thenegative side ofthe
appliedvoltage is connected to thep-type material and thepositive side to then-type material,
the difference in underlined letters for each region revealinga reverse-bias condition.
Sometimes this avalanche effect has practical applications in voltage stabilizing circuits where a
series limiting resistor is used with the diode to limit this reverse breakdown current to a preset
maximum value thereby producing a fixed voltage output across the diode. These types of diodes
are commonly known asZener Diodes
This increase in level is due to a wide range of factors that include
Leakage currents,Generation of carriers in the depletion regionandTemperature Sensitivity
whereas a 10°C increase in current will result in doubling of the actual reverse current of a diode
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
29
Figure: 1.14 CircuitConnection of Reverse biased PN Diode
This widening of the depletion region will establish too great a barrier for the majority carriers to
overcome, effectively reducing the majority carrier flow to zero, as shown in Fig. 1.12a .
The number of minoritycarriers, however, entering the depletion region will not change,
resulting in minority-carrier flow vectors of the same magnitude indicatedwith no applied
voltage.
The current that exists under reverse-bias conditions is called the reverse saturation
current and is represented by Is
The reverse saturation current is seldom more than a few microamperes and typically inµA and
nA, except for high-power devices. The termsaturationcomes from the fact that it reaches its
maximum level quickly and does notchange significantly with increases in the reverse-bias
potential, as shownon the diode characteristics of Fig.1.15 forVD<0V.The reverse-biased
conditions are depicted inFig.1.13b for the diode symbol andP–NJunction. Note, in particular,
that the direction ofISis against the arrow of the symbol. Note also that thenegative side ofthe
appliedvoltage is connected to thep-type material and thepositive side to then-type material,
the difference in underlined letters for each region revealinga reverse-bias condition.
Sometimes this avalanche effect has practical applications in voltage stabilizing circuits where a
series limiting resistor is used with the diode to limit this reverse breakdown current to a preset
maximum value thereby producing a fixed voltage output across the diode. These types of diodes
are commonly known asZener Diodes
This increase in level is due to a wide range of factors that include
Leakage currents,Generation of carriers in the depletion regionandTemperature Sensitivity
whereas a 10°C increase in current will result in doubling of the actual reverse current of a diode
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
29
Figure: 1.14 CircuitConnection of Reverse biased PN Diode
This widening of the depletion region will establish too great a barrier for the majority carriers to
overcome, effectively reducing the majority carrier flow to zero, as shown in Fig. 1.12a .
The number of minoritycarriers, however, entering the depletion region will not change,
resulting in minority-carrier flow vectors of the same magnitude indicatedwith no applied
voltage.
The current that exists under reverse-bias conditions is called the reverse saturation
current and is represented by Is
The reverse saturation current is seldom more than a few microamperes and typically inµA and
nA, except for high-power devices. The termsaturationcomes from the fact that it reaches its
maximum level quickly and does notchange significantly with increases in the reverse-bias
potential, as shownon the diode characteristics of Fig.1.15 forVD<0V.The reverse-biased
conditions are depicted inFig.1.13b for the diode symbol andP–NJunction. Note, in particular,
that the direction ofISis against the arrow of the symbol. Note also that thenegative side ofthe
appliedvoltage is connected to thep-type material and thepositive side to then-type material,
the difference in underlined letters for each region revealinga reverse-bias condition.
Sometimes this avalanche effect has practical applications in voltage stabilizing circuits where a
series limiting resistor is used with the diode to limit this reverse breakdown current to a preset
maximum value thereby producing a fixed voltage output across the diode. These types of diodes
are commonly known asZener Diodes
This increase in level is due to a wide range of factors that include
Leakage currents,Generation of carriers in the depletion regionandTemperature Sensitivity
whereas a 10°C increase in current will result in doubling of the actual reverse current of a diode

30. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
30
Current Components in PN junction Diode:
Drift current
The flow of charge carriers, which is due to the appliedvoltageor electric field iscalled drift
current.In a semiconductor, there are two types of charge carriers, they are electrons and holes.
When the voltage is applied to a semiconductor, thefree electronsmove towards the positive
terminal of a battery and holes move towards the negative terminal of a battery.
Electrons are the negatively charged particles andholesare the positively charged
particles. As we already discussed that like charges repel each other and unlike charges attract
each other. Hence, the electrons (negatively charged particle) are attracted towards the positive
terminal of a battery and holes (positively charged particle) are attracted towards the negative
terminal.
In a semiconductor, the electrons always try to move in a straight line towards the
positive terminal of thebattery. But, due to continuous collision with theatomsthey change the
direction of flow. Each time the electron strikes an atom it bouncesback in a random direction.
The applied voltage does not stop the collision and random motion of electrons, but it causes the
electrons to drift towards the positive terminal.
The average velocity that an electron or hole achieved due to the applied voltage or
electric field is called drift velocity.
The drift velocity of electrons is given by
Vn= µnE
The drift velocity of holes is given by
Vp= µpE
Where vn= drift velocity of electrons
vp= drift velocity of holes
µn= mobility of electrons
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
30
Current Components in PN junction Diode:
Drift current
The flow of charge carriers, which is due to the appliedvoltageor electric field iscalled drift
current.In a semiconductor, there are two types of charge carriers, they are electrons and holes.
When the voltage is applied to a semiconductor, thefree electronsmove towards the positive
terminal of a battery and holes move towards the negative terminal of a battery.
Electrons are the negatively charged particles andholesare the positively charged
particles. As we already discussed that like charges repel each other and unlike charges attract
each other. Hence, the electrons (negatively charged particle) are attracted towards the positive
terminal of a battery and holes (positively charged particle) are attracted towards the negative
terminal.
In a semiconductor, the electrons always try to move in a straight line towards the
positive terminal of thebattery. But, due to continuous collision with theatomsthey change the
direction of flow. Each time the electron strikes an atom it bouncesback in a random direction.
The applied voltage does not stop the collision and random motion of electrons, but it causes the
electrons to drift towards the positive terminal.
The average velocity that an electron or hole achieved due to the applied voltage or
electric field is called drift velocity.
The drift velocity of electrons is given by
Vn= µnE
The drift velocity of holes is given by
Vp= µpE
Where vn= drift velocity of electrons
vp= drift velocity of holes
µn= mobility of electrons
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
30
Current Components in PN junction Diode:
Drift current
The flow of charge carriers, which is due to the appliedvoltageor electric field iscalled drift
current.In a semiconductor, there are two types of charge carriers, they are electrons and holes.
When the voltage is applied to a semiconductor, thefree electronsmove towards the positive
terminal of a battery and holes move towards the negative terminal of a battery.
Electrons are the negatively charged particles andholesare the positively charged
particles. As we already discussed that like charges repel each other and unlike charges attract
each other. Hence, the electrons (negatively charged particle) are attracted towards the positive
terminal of a battery and holes (positively charged particle) are attracted towards the negative
terminal.
In a semiconductor, the electrons always try to move in a straight line towards the
positive terminal of thebattery. But, due to continuous collision with theatomsthey change the
direction of flow. Each time the electron strikes an atom it bouncesback in a random direction.
The applied voltage does not stop the collision and random motion of electrons, but it causes the
electrons to drift towards the positive terminal.
The average velocity that an electron or hole achieved due to the applied voltage or
electric field is called drift velocity.
The drift velocity of electrons is given by
Vn= µnE
The drift velocity of holes is given by
Vp= µpE
Where vn= drift velocity of electrons
vp= drift velocity of holes
µn= mobility of electrons

31. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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µp= mobility of holes
E = applied electric field
The drift current density dueto free electrons is given by
Jn=enµnE
and the drift current density due to holes is given by
Jp=epµpE
Where Jn= drift current density due toelectrons
Jp= drift current density due to holes
e= charge of an electron =1.602× 10
-19
Coulombs (C).
n = number of electrons
p = number of holes
Then the total drift current density is
J =Jn+Jp
=enµnE+epµpE
J =e(nµn+pµp) E
Diffusion current
The process by which, charge carriers (electrons orholes) in a semiconductor moves
froma region of higher concentration to a region of lower concentration is called diffusion.
The region in which more number of electrons is present is called higher concentration region
and the region in which less number of electrons is present is calledlower concentration region.
Current produced due to motion of charge carriers from a region of higher concentration to a
region of lower concentration is called diffusion current. Diffusion process occurs in a
semiconductor that is non-uniformly doped.
Consider ann-type semiconductorthat is non-uniformly doped as shown in below figure. Due to
the non-uniform doping, more number of electrons is present at left side whereas lesser number
of electrons is present at right side of the semiconductor material. The number of electrons
present at left side of semiconductor material is more. So, these electrons will experience a
repulsive force from each other.

32. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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The electrons present at left side of the semiconductor material will moves to right
side,to reach the uniform concentration of electrons. Thus, the semiconductor material achieves
equal concentration of electrons.Electrons that move from left side to right side will constitute
current. This current is called diffusion current. Inp-type semiconductor, the diffusion process
occurs in the similar manner.
Bothdriftand diffusion current occurs insemiconductor devices. Diffusion current occurs
without an externalvoltageor electric field applied.Diffusion current does not occur in a
conductor. The direction of diffusion current is same or opposite to that of thedrift current.
Concentration gradient
The diffusion current density is directly proportional to the concentration gradient. Concentration
gradient is the difference in concentration of electrons or holes in a given area. If the
concentration gradient is high, then the diffusion current density is also high. Similarly, if the
concentration gradient is low, then the diffusion current density is also low.
The concentration gradient for n-type semiconductor is given by
The concentrationgradient for p-type semiconductor is given by
Where
Jn=diffusion current density due to electrons
Jp= diffusion current density due to holes
Diffusion current density
The diffusion current densitydue to electrons is given by
=+
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
32
The electrons present at left side of the semiconductor material will moves to right
side,to reach the uniform concentration of electrons. Thus, the semiconductor material achieves
equal concentration of electrons.Electrons that move from left side to right side will constitute
current. This current is called diffusion current. Inp-type semiconductor, the diffusion process
occurs in the similar manner.
Bothdriftand diffusion current occurs insemiconductor devices. Diffusion current occurs
without an externalvoltageor electric field applied.Diffusion current does not occur in a
conductor. The direction of diffusion current is same or opposite to that of thedrift current.
Concentration gradient
The diffusion current density is directly proportional to the concentration gradient. Concentration
gradient is the difference in concentration of electrons or holes in a given area. If the
concentration gradient is high, then the diffusion current density is also high. Similarly, if the
concentration gradient is low, then the diffusion current density is also low.
The concentration gradient for n-type semiconductor is given by
The concentrationgradient for p-type semiconductor is given by
Where
Jn=diffusion current density due to electrons
Jp= diffusion current density due to holes
Diffusion current density
The diffusion current densitydue to electrons is given by
=+
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
32
The electrons present at left side of the semiconductor material will moves to right
side,to reach the uniform concentration of electrons. Thus, the semiconductor material achieves
equal concentration of electrons.Electrons that move from left side to right side will constitute
current. This current is called diffusion current. Inp-type semiconductor, the diffusion process
occurs in the similar manner.
Bothdriftand diffusion current occurs insemiconductor devices. Diffusion current occurs
without an externalvoltageor electric field applied.Diffusion current does not occur in a
conductor. The direction of diffusion current is same or opposite to that of thedrift current.
Concentration gradient
The diffusion current density is directly proportional to the concentration gradient. Concentration
gradient is the difference in concentration of electrons or holes in a given area. If the
concentration gradient is high, then the diffusion current density is also high. Similarly, if the
concentration gradient is low, then the diffusion current density is also low.
The concentration gradient for n-type semiconductor is given by
The concentrationgradient for p-type semiconductor is given by
Where
Jn=diffusion current density due to electrons
Jp= diffusion current density due to holes
Diffusion current density
The diffusion current densitydue to electrons is given by
=+

33. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Where Dnis the diffusion coefficient of electrons
The diffusion current density due to holes is given by
=−
Where Dpis the diffusion coefficient of holes
The total current densitydue to electrons is the sum of drift and diffusion currents.
Jn= Drift current + Diffusion current
=nμnE+
The total current density due to holes is the sum of drift and diffusion
currents.
Jp= Drift current + Diffusion current
=nμnE−
The total current density due to electrons and holes is given by
J = Jn+ Jp
The following figure shows a P-N Junction with aforward bias by an external voltage Vas
shown in Figure 1.15a. Due to the applied voltage, there exists a potential gradient in P and N
materials.
Figure: 1.15aPN Diode by an external voltage V.
Now, the holes from P-region and the electrons fromN-region drift towards the junction.The
holes drifted from P-region towards the junction enter the N-region where they represent
minority carriers.Similarly, the electrons drifted from N-region towards the junction enter the P-
region where they representminority carriers.The minority carriers diffuse away from the
junction exponentially with distance as shown followingFigure: 1.15b.
Figure: 1.15b Current components in forward-biased unsymmetrical junction.
Their concentration reduces steadily because of recombination with electrons and holes
respectively. We know that diffusion current of minority carriers is proportional to the
concentration gradient and hence this must also vary exponentially with distance.

34. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Current Components:
Ipn(x) = holecurrent in N material.
Ipn(0) = hole current at junction (x=0)
Inp(x) = electron current in P material.
Inp(0) = electron current at junction (x=0)
(The first letter refers to the type of the carrier and the second to the type of material)
At junction (x=0), the electrons crossing from right to left constitute a current in the same
direction as hole crossing from left to right.
Thus the total current I at junction is given by
I = Ipn(0) + Inp(0)
The majority (electron) current Innis given by Inn(x) = I-Ipn(x)
The majority (hole) current Ippis given by Ipp(x) = I–Inp(x)
Quantitative Theory of PN Diode currents
By using Quantitative theory to derive the expression for the total current as a function of the
applied voltage. When a P-N diode is forward biased, then the holes are injected from P-Side
into the N-Material. As shown in following figure the several components of hole concentration
in N-side of a forward biased diode. It is obvius from the figure the hole concentration decreases
exponentially with distance.
Figure: 1.15c Graph between Concentration and Distance
i) The hole concentration in N material is given by
()= +́(0)
Where pn0= Thermal equilibrium concentration
Lp= diffusion length of holes in N-material
X = distance from the junction where concentration is considered.
́(0)=(0)−
ii) we know that diffusion hole current in N-side is given by
I()=
́(0)
L
At junction i.e.,x= 0
I()=
́(0)
L

35. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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iii) Using Boltzmann relationship of Kinetic theory of gases, it can be established that
(0)=
This is known asLaw of Junction. Here
V = applied voltage, and
VT= Volt equivalent of temperature = KT/q = T/ 11,600
Where k is BoltzmannConstant.
Total Diode Current
The total diode current I at x = 0 is given by
I = Ipn(0) + Inp(0),
Ipn(0) = current caused by holes entering N–region
Inp(0) = current caused by electrons entering P–region
= −1,
=
(0)
L
+
(0)
L
Diode Equation:
Insolid-state physics that the general characteristics of a semiconductor diode can be defined by
the following equation, referred to as Shockley’s equation, for the forward-andreverse-bias
regions for exact demonstration.
=(
ŋ⁄
−)
ISis the reverse saturation current
VDis the applied forward-bias voltage across the diode
ŋis an ideality factor, which is a function of the operating conditions and physicalconstruction;
it has a range between 1 and 2 depending on a wide variety offactors (n=1 will be assumed
throughout this text unless otherwise noted).
The voltage VTis called thethermal voltageand is determined by
VT=
Wherekis Boltzmann’s constant= 1.38 x 10
-23
J/K
TKis the absolute temperature in kelvins = 273 + the temperature in
o
C
q is the magnitude of electronic charge = 1.6 X10
-19
c
Problem 1At a temperature of 27°C (common temperature for components in anenclosed
operating system), determine the thermal voltageVT
Solution:
T=273+°=273+27=300
= =
1.38×
10
(300)
1.6×10

36. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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= 25.875mV≅26Mv
The thermal voltage will become an important parameter in the analysis to follow in this chapter
and a number of those to follow.
V-ICharacteristics:
Initially, Eq. (1.2) with all its defined quantities may appear somewhat complex. However, it will
not be used extensively in the analysis to follow. It is simply important at this point
to understand the source of the diode characteristics and which factors affect its shape. A plot of
Eq. (1.2) withIs=10 pA is provided in Fig. 1.15 as the dashed line. If we expand Eq. (1.2)
into the following form, the contributing component for each region of Fig. 1.15 can be
described with increased clarity:
=
ŋ⁄
−
For positive values ofVDthe first term of the above equation will grow very quickly and totally
overpower the effect of the second term. The result is the following equation, which only has
positive values and takes on the exponential formate
x
appearing in Fig 1.16:
=
ŋ⁄
(VDpositive)
Figure: 1.16aSilicon semiconductorDiodeCharacteristics

37. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Figure: 1.16bSilicon semiconductor Diode Characteristics with exponential representation
Figure: 1.16c Diode Characteristics in Forward Bias and Reverse Bias
Figure: 1.16dComparison of Ge, Si, and GaAs commercial diodes.

38. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
38
Simply plots the actual response of commercially available units. The total reverse current is
shown and not simply the reverse saturation current. It is immediately obvious that the point of
vertical risein the characteristics is different for each material, although the general shape of
each characteristic is quite similar. Germanium is closest to the vertical axis and GaAs is the
most distant. As noted on the curves, the center of the knee (hence theKis the notationVK) of
the curve is about 0.3 V for Ge, 0.7 V for Si, and 1.2 V for GaAsas shown in Figure 1.16d
Temperature Dependence on V-I Characteristics:
Temperature can have a marked effect on the characteristics of a semiconductor diode, as
demonstrated by the characteristics of a silicon diode shown in Fig.1.17. An increase from room
temperature (20°C) to 100°C (the boiling point of water) results in a drop of 80(2.5 mV) = 200
mV, or 0.2 V, which is significant on a graph scaled in tenths of volts. A decrease in temperature
has the reverse effect, as also shown in the figure:In the reverse-bias region the reverse current
of a silicon diode doubles for every 10°C rise in temperature.
Figure: 1.17 Variation in Si diode characteristics with temperature change.
It is not uncommon for a germanium diode with an Ioin the order of 1 or 2 A at 25°C to have a
leakage current of 100 A-0.1 mA at a temperature of 100°C. Typical values of Io for silicon are
much lower than that of germanium for similar power and current levels. The result is that even
at high temperatures the levels of Iofor silicon diodes do not reach the same high levels
obtained. For germanium—a very important reason that silicon devices enjoy a significantly
higher level of development and utilization in design. Fundamentally, the open-circuit equivalent
in the reverse bias region is better realized at any temperature with silicon than with germanium.
The increasing levels of I with temperature account for the lower levels of threshold voltage, as
shown in Fig. 1.11. Simply increase the level of Io in and not rise in diode current. Of course, the
level of TK also will be increase, but the increasing level of Io will overpower the smaller

39. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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percent change in TK. As the temperature increases the forward characteristics are actually
becoming more “ideal,”
Problem:
Using the curves of Fig1.16d:
a. Determine the voltage across each diode at a current of 1 mA.
b. Repeat for a current of 4 mA.
c. Repeat for a current of 30 mA.
d. Determine the average value of the diode voltage for the range of currents listed above.
Diode resistance:
DC or Static Resistance
The application of a dc voltage to a circuit containing a semiconductor diode will result in an
operating point onthe characteristic curve that will not change with time. The resistance of the
diode at the operating point can be found simply by finding the corresponding levels of VDand
IDas shown in Fig. 1.18and applying the following Equation:
=
Thedc resistance levels at the knee and below will be greater than the resistance levels obtained
for the vertical rise section of the characteristics. The resistance levels in the reverse-bias region
will naturally be quite high. Since ohmmeters typically employ a relatively constant-current
source, the resistance determined will be at a preset current level (typically, a few milliamperes).
In general, therefore, the higher the current through a diode, the lower is the dc resistancelevel.
Typically, the dcresistance of a diode in the active (most utilized) will range from about10Ω to
80Ω

40. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Figure 1.18aDetermining the dc resistance of a diode at a particular operating point.
Problem 2Determine the dc resistance levels for the diode offollowing figure. at
a.ID=2 mA (low level)
b.ID=20 mA (high level)
c.VD=10 V (reverse-biased)
a.At= 2 mA,=0.5 V (from the curve) and
==
0.5
2
=
b.At= 20 mA,=0.8 V (from the curve)
==
0.8
20
=
c.At=-10V,=-=-1(from the curve) and
== =M
Clearly supporting some of the earlier comments regarding the dc resistance levels of a diode
AC or Dynamic Resistance
Thedc resistance of a diode is independent of the shape of the characteristic in the region
surrounding the point of interest.

41. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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If a sinusoidal rather than a dc input is applied, the situation will change completely.The varying
input will move the instantaneous operating point up and down a region of the characteristics and
thus defines a specific change in current and voltage as shown inFig.1.18bwith no applied
varying signal, thepoint of operation would be theQ–point appearing on Fig. 1.18b, determined
by the applied dc levels. The designationQ-pointis derived from the wordquiescent, which
means “still or unvarying.”
Figure 1.18bDefining theDynamic or ac resistance
A straight line drawn tangent to the curve through theQ-point as shown inFig.1.18cwill
define a particular change in voltage and current that can be used to determine theacordynamic
resistance for this region of the diode characteristics. An effort should be made to keep the
change in voltage and current as small as possible and equidistant to either side of theQ-point.
In equation form
=
∆
∆
where Δ signifies a finite change in the quantity
Figure 1.18c Determining the ac resistance at a Q–point.
Diode Equivalent Circuits (Add on Course)
An equivalent circuit is a combination of elements properly chosen to best represent the actual
terminal characteristics of a device or system in a particular operating region.
In other words, once the equivalent circuit is defined, the device symbol can be removed from a
schematic and the equivalent circuit inserted in its place without severely affecting the actual

42. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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behavior of the system. The result is often a network that can be solved usingtraditional circuit
analysis techniques.
Diode capacitance:
Transition and Diffusion Capacitance
Every electronic or electrical device is frequency sensitive.
That is, the terminal characteristics of any device will change with frequency. Even the
resistance of a basicresistor, as of anyconstruction, will be sensitive to the applied frequency.At
low to mid-frequencies most resistors can be considered fixed in value. However,as we
approach high frequencies, stray capacitive and inductive effects start to play aroleand will
affect the total impedance level of the element.
For the diode it is the stray capacitance levels that have the greatest effect. At low frequencies
and relatively small levels of capacitance the reactance of a capacitor, determined by XC= 1/2πfc
is usually so high itcan be considered infinite in magnitude, represented byan open circuit, and
ignored. At high frequencies, however, the level ofXCcan drop to thepoint where it will
introduce a low-reactance “shorting” path. If this shorting path is acrossthe diode, it can
essentially keep the diode from affecting the response of the network.
In thep–nsemiconductor diode, there are two capacitive effects to be considered. Bothtypes of
capacitance are present in the forward-and reverse-bias regions, but one so outweighsthe other
in each region that we consider the effects of only one in each region.Recall that the basic
equation for the capacitance of a parallel-plate capacitor is defined byC =€A/d where €is the
permittivity of the dielectric (insulator) between the plates of areaAseparated by a distanced.
=
(0)
(1+|⁄|)

43. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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Figure 1.19 Transition and diffusion capacitance versus applied bias for a silicon diode.
=
Where τis the minority carrier lifetimethe time isworld take for a minority carrier suchas a
hole to recombine with an electron inthe n-type material. However, increased levelsof current
result in a reduced level of associated resistance (to be demonstrated shortly),and the resulting
time constant(τ =RC), which is very important in high-speed applications,does not become
excessive. In general, therefore,
The transition capacitance is the predominant capacitive effect in the reverse-biasregion whereas
the diffusion capacitance is the predominantcapacitive effect in theforward-bias region.
Energy Band Diagram of PNJunction Diode:
A p-n junction consists of two semiconductor regions with opposite doping type as shown in
Figure4.2.1. The region on the left isp-type with an acceptor densityNa, while the region on the
right isn-type with a donor densityNd. The dopants are assumed to be shallow, so that the
electron (Hole) density in then-type (p-type) region is approximately equal to the donor
(Acceptor) density.
Figure 1.20:P-N Junction diode with densityrepresentation
Cross-section of aP-N Junction
We will assume, unless stated otherwise, that the doped regions areuniformlydoped and that the
transition between the two regions is abrupt. We will refer to this structureas anabruptp-n
junction.Frequently we will deal with p-n junctions in which one side is distinctly higher-doped
than the other. We will find that in such a case only the low-doped region needs to be considered,

44. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
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since it primarily determines the device characteristics. We will refer to such a structure as aone-
sidedabrupt p-n junction.
The junction is biased with a voltageVaas shown in Figure1.21 (a).We will call the junction
forward-biased if a positive voltage is applied to thep-doped region andreversed-biased if a
negative voltage is applied to thep-doped region. The contact to thep-type region is also called
the anode, while the contact to then-type region is called the cathode, in reference to
theanionsor positive carriers andcationsornegative carriers in each of these regions.
Flatband diagram
Figure1.21Energy band diagram of a p-n junction (a) before and (b) after merging the n-type
and p-type regions
Note that this does not automatically align the Fermi energies,EF,nandEF,p.Also, note that this
flatband diagram is not an equilibrium diagram since both electrons and holes can lower their
energy by crossing the junction. A motion of electrons and holes is therefore expected before
thermal equilibrium is obtained. The diagram shown in Figure1.21(b) is called a flatband
diagram. This name refers to the horizontal band edges. It also implies that there is no field and
no net charge in the semiconductor.
ThermalEquilibrium
To reach thermal equilibrium, electrons/holes close tothe metallurgical junction diffuse across
the junction into thep-type/n-type region where hardly any electrons/holes are present. This
process leaves the ionized donors (acceptors) behind, creating a region around the junction,
which is depleted of mobilecarriers. We call this region the depletion region, extending fromx=
-xptox=xn. The charge due to the ionized donors and acceptors causes an electric field, which
in turn causes a drift of carriers in the opposite direction. The diffusion of carriers continues until
the drift current balances the diffusion current, thereby reaching thermal equilibrium as indicated
by a constant Fermi energy. This situation is shown in Figure4.2.3

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Figure1.22aEnergy band diagram of a p-n junction in thermalequilibrium
Figure1.22bEnergyBand Structure
While in thermal equilibrium no external voltage is applied between then-type andp-type
material, there is an internal potential,fi, which is caused by the workfunction difference
between then-type andp-type semiconductors. This potential equals thebuilt-inpotential, which
will be further discussed in the next section.
The built-in potential
The built-in potential in a semiconductor equals the potential across the depletion region in
thermal equilibrium. Since thermal equilibrium implies that the Fermi energy is constant

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throughout the p-n diode, the built-in potential equals the difference between the Fermi
energies,EFnandEFp, divided by the electronic charge. It also equals the sum of the bulk
potentials of each region,fnandfp, since the bulk potential quantifies the distance between the
Fermi energy and the intrinsic energy. This yields the following expression for the built-in
potential.
∅=
Forward and reverse bias
We now consider a p-n diode with an applied bias voltage,Va. A forward bias corresponds to
applying a positive voltage to the anode (thep-typeregion) relative to the cathode (then-type
region). A reverse bias corresponds to a negative voltage applied to the cathode. Both bias modes
are illustrated withFigure1.23. The applied voltage is proportional to the difference between the
Fermi energy in then-type andp-type quasi-neutral regions.
As a negative voltage is applied, the potential across the semiconductor increases and so does the
depletion layer width. As a positive voltage is applied, the potential across the semiconductor
decreases andwith it the depletion layer width. The total potential across the semiconductor
equals the built-in potential minus the applied voltage.
∅=∅−
Figure1.23Energy band diagram of a p-n junction under reverse and forward bias
Zener Diode and itsCharacteristics
Introduction:
A Zener Diode is a highly doped PN junction, which is specially designed to operate in reverse
direction.Generally Zener Diode acting as voltage regulator used in power supply sections for
maintaining constant voltage.The zener diodeas shown in figure 1.24a,b,cis specially designed
for optimizing the breakdown region.

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Figure1.24aZener diode circuitconnectionsin bread board.
Then take Digital Multimeteras shown in 1.24b, verify and check the voltage across the zener
Diode, it is displays breakdown voltage.
Figure1.24bZener diodetestingusing Mulitmeter
ThisDiodecan be used in all power supply sections interface with mother boards like TV,
Washing Machine, ATM Machine and Electronic Panel Boardsas shown in figure 1.24c.
Figure 1.24cZener diode used power supply boards
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Figure1.24aZener diode circuitconnectionsin bread board.
Then take Digital Multimeteras shown in 1.24b, verify and check the voltage across the zener
Diode, it is displays breakdown voltage.
Figure1.24bZener diodetestingusing Mulitmeter
ThisDiodecan be used in all power supply sections interface with mother boards like TV,
Washing Machine, ATM Machine and Electronic Panel Boardsas shown in figure 1.24c.
Figure 1.24cZener diode used power supply boards
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Figure1.24aZener diode circuitconnectionsin bread board.
Then take Digital Multimeteras shown in 1.24b, verify and check the voltage across the zener
Diode, it is displays breakdown voltage.
Figure1.24bZener diodetestingusing Mulitmeter
ThisDiodecan be used in all power supply sections interface with mother boards like TV,
Washing Machine, ATM Machine and Electronic Panel Boardsas shown in figure 1.24c.
Figure 1.24cZener diode used power supply boards

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Figure 1.24dHeavily doped Zener diode
The symbolic representationas shown in figure 1.24eof ZenerDiodeis similar to the P–N
junction, but with bend edges on the vertical bar.
Figure 1.24e Symbol of Zener diode
Operation:
ZenerDiodes acts like normal p-n junctionDiodes under forward biased condition.When
forward biased voltage is applied to the zenerDiodeit allows electric current in forward
direction like a normalDiodeas shown in Figure 1.25a.
Figure 1.25aForwardbiasCharacteristics of silicon diodeand Zener diode
But, the uniqueness lies in the fact is that it also operates in reverse break down region.
Breakdown in zenerDiode:
There are two types of reverse breakdown regions in a zenerDiode.
zener breakdown and
Avalanche break down
Zener break down:
When reverse biased voltage applied to theDiodeis increased, the narrow depletion region
generates strongelectric field.When the voltage reaches close to zener voltageas shown in
Figure 1.25b(less than 6V for zener break down). This electric field in the depletion region is
strong enough to pull electrons from their valence band. The valence electrons which gains
sufficient energy from the strong electric field of depletion region will breaks bonding with the
parent atom. Thevalance electronswhich break bonding with parent atom will become free
electrons.

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This free electroncarries electric current from one place to another place. At zener breakdown
region, a small increase in voltage will rapidly increases the electric current.
Figure 1.25b Reverse bias connection in Zener Diode with Zener breakdown Characteristics
Avalanche breakdown:
The avalanche breakdown occurs in both normalDiodes and zenerDiodes at high reverse
voltage. When high reverse voltageis applied, thefree electrons(minority carriers) gains large
amount ofenergyand accelerated to greater velocities.
Figure 1.25c Reverse bias connection in Zener Diode with Avalanche breakdown Characteristics
The free electrons moving at highspeed will collides with theatomsand knock off more
electrons. These electrons are again accelerated and collide with other atoms. Because of this
continuous collision with the atoms, a large number of free electrons are generated. As a result,
electriccurrent in theDiodeincreases rapidly. This sudden increase in electric current may
permanently destroys the normalDiode. However, avalancheDiodes may not be destroyed
because they are carefully designed to operate in avalanche breakdown region.Avalanche
breakdown occurs in zenerDiodes with zener voltage (Vz) greater than 6Vas shown in Figure
1.25c.
V-I Characteristics:
This curve shows that the ZenerDiode, when connected in forwarding bias, behaves like an
ordinaryDiode.when the reverse voltage applies across itis less than 6v, the zener break down
occurs in theDiode.When it rises beyond 6V the Avalanche break down occursas shown in
Figure 1.25d.
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This free electroncarries electric current from one place to another place. At zener breakdown
region, a small increase in voltage will rapidly increases the electric current.
Figure 1.25b Reverse bias connection in Zener Diode with Zener breakdown Characteristics
Avalanche breakdown:
The avalanche breakdown occurs in both normalDiodes and zenerDiodes at high reverse
voltage. When high reverse voltageis applied, thefree electrons(minority carriers) gains large
amount ofenergyand accelerated to greater velocities.
Figure 1.25c Reverse bias connection in Zener Diode with Avalanche breakdown Characteristics
The free electrons moving at highspeed will collides with theatomsand knock off more
electrons. These electrons are again accelerated and collide with other atoms. Because of this
continuous collision with the atoms, a large number of free electrons are generated. As a result,
electriccurrent in theDiodeincreases rapidly. This sudden increase in electric current may
permanently destroys the normalDiode. However, avalancheDiodes may not be destroyed
because they are carefully designed to operate in avalanche breakdown region.Avalanche
breakdown occurs in zenerDiodes with zener voltage (Vz) greater than 6Vas shown in Figure
1.25c.
V-I Characteristics:
This curve shows that the ZenerDiode, when connected in forwarding bias, behaves like an
ordinaryDiode.when the reverse voltage applies across itis less than 6v, the zener break down
occurs in theDiode.When it rises beyond 6V the Avalanche break down occursas shown in
Figure 1.25d.
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This free electroncarries electric current from one place to another place. At zener breakdown
region, a small increase in voltage will rapidly increases the electric current.
Figure 1.25b Reverse bias connection in Zener Diode with Zener breakdown Characteristics
Avalanche breakdown:
The avalanche breakdown occurs in both normalDiodes and zenerDiodes at high reverse
voltage. When high reverse voltageis applied, thefree electrons(minority carriers) gains large
amount ofenergyand accelerated to greater velocities.
Figure 1.25c Reverse bias connection in Zener Diode with Avalanche breakdown Characteristics
The free electrons moving at highspeed will collides with theatomsand knock off more
electrons. These electrons are again accelerated and collide with other atoms. Because of this
continuous collision with the atoms, a large number of free electrons are generated. As a result,
electriccurrent in theDiodeincreases rapidly. This sudden increase in electric current may
permanently destroys the normalDiode. However, avalancheDiodes may not be destroyed
because they are carefully designed to operate in avalanche breakdown region.Avalanche
breakdown occurs in zenerDiodes with zener voltage (Vz) greater than 6Vas shown in Figure
1.25c.
V-I Characteristics:
This curve shows that the ZenerDiode, when connected in forwarding bias, behaves like an
ordinaryDiode.when the reverse voltage applies across itis less than 6v, the zener break down
occurs in theDiode.When it rises beyond 6V the Avalanche break down occursas shown in
Figure 1.25d.

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Figure 1.25d zener diode Characteristics
Applications of ZenerDiode:
1. ZenerDiodeas a voltage
In a DC circuit, ZenerDiodecan be used as a voltage regulator or to provide voltage reference.
The main use of zenerDiodelies in the fact that the voltage across a ZenerDioderemains
constant for a larger change in current. This makes it possible to use a ZenerDiodeas a constant
voltage device or a voltage regulator.
In anypowersupplycircuit, a regulator is used to provide a constant output (load) voltage
irrespective of variation in input voltage or variation in load current. The variation in input
voltage is called line regulation, whereas the variation in load current is called load regulation.
Figure 1.26a Circuit diagram of Zener diode as a voltage regulator
2. ZenerDiodeas a voltage reference
In power supplies and many other circuits, ZenerDiodefinds its application as a constant voltage
provider or a voltage reference.The only conditions are that the input voltage should be greater
than zener voltage and the series resistor should have a minimum value such that the maximum
current flows through the device.
Figure 1.26b Circuit diagram of Zener diode as a voltage reference
3. ZenerDiodeas a voltage clamper

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In a circuit involving AC input source, different from the normalPNDiodeclampingcircuit, a
ZenerDiodecan also be used. TheDiodecan be used to limit the peak of the output voltage to
zener voltage at one side and to about 0V at other side of the sinusoidal waveform.
Figure 1.26c Circuit diagram of Zener diode as a voltageclamper
In the above circuit, during positive half cycle, once the input voltage is such that the zener
Diodeis reverse biased, the output voltage is constant for a certain amount of time till the voltage
starts decreasing.
Now during the negative half cycle, the zenerDiodeis in forward biased connection. As the
negative voltage increases till forward threshold voltage, theDiodestarts conducting and the
negative side of the output voltage is limited to the threshold voltage.
Note that to get an outputvoltage in positive range only, use two oppositely biased ZenerDiodes
in series.
Working Applications of ZenerDiode
With growing popularity of smart phones,androidbasedprojectsare being preferred these days.
These projects involve use ofBluetoothtechnologybased device. These Bluetooth devices
require about 3V voltage for operation. In such cases, a zenerDiodeis used to provide a 3V
reference to the Bluetooth device.
Advantages of zener diode
Power dissipation capacity is very high
High accuracy
Small size
Low cost
Tunnel Diodes:
Tunnel diode definition
A Tunnel diode is a heavily dopedp-n junction diodein which the electric current decreases as
thevoltageincreases.
In tunnel diode, electric current is caused by “Tunneling”. The tunneldiode is used as a very fast
switching device in computers. It is also used in high-frequency oscillators and amplifiers.
The tunnel diode was first introduced by Leo Esaki in 1958. Its characteristics, shown inFigure
1.27, are different from any diodediscussed thus far in that it has a negative-resistance region. In
this region, an increase in terminal voltage results in a reduction in diode current.

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Figure 1.27 Tunnel diode characteristics
The tunnel diode is fabricated by doping the semiconductor materials that will form thep–n
junction at a level 100 to several thousand times that of a typical semiconductor diode. This
results in a greatly reduced depletion region, of the order of magnitude of 10
-6
cm, or typically
about 1/100the width of this region for a typical semiconductor diode. It is this thin depletion
region, through which many carriers can “tunnel” rather than attempt to surmount, at low
forward-bias potentials that accounts for the peak in the curve ofFigure 1.27For comparison
purposes, a typical semiconductor diode characteristic is superimposed on the tunnel-diode
characteristic ofFigure 1.27.This reduced depletion region results in carriers “punching
through” at velocities that far exceed those available withconventional diodes. The tunnel diode
can therefore be used in high-speed applications such as in computers, where switching times in
the order of nanoseconds or picoseconds are desirable.Recall fromSection 1.15 that an
increase in the doping levelreduces the Zener potential. Note the effect of a very high doping
level on this region inFigure 1.27. The semiconductormaterials most frequently used in the
manufacture of tunnel diodes are germanium and gallium arsenide. The ratioIP>Ivis very
important for computer applications. For germanium, it is typically 10:1, and for gallium
arsenide, it is closer to 20:1.The peak currentIPof a tunnel diode can vary from a few
microamperes to severalhundred amperes. The peak voltage, however, is limited toabout 600
mV. For this reason,a simple VOM with an internal dc battery potential of1.5 V can severely
damage a tunneldiode if applied improperly.The tunnel-diode equivalent circuit in the negative-
resistance region is provided inFigure 1.28, with thesymbols most frequently employed for
tunnel diodes. The values forthe parameters are typical for today’s commercial units.
The inductorLsis due mainlyto the terminal leads. The resistorRis due to the leads, the
ohmic contact at the lead–semiconductor junction, and the semiconductor materials themselves.
The capacitance is the junction diffusion capacitance, and theRSis the negative resistance of the
region. Thenegative resistance finds application in oscillators to be described later.

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Figure 1.28 Tunnel diode (a) equivalent (b) symbols.
InFigure 1.28, the chosen supply voltage and load resistance define a load line that intersects the
tunnel diode characteristics at three points. Keep in mind that the load line is determined solely
bythe network and the characteristics of the device. The intersections ataandbare referred to
asstableoperating points, due to the positive-resistance characteristic.
That is, at either of these operating points, a slight disturbance in the network will not set the
network into oscillations or result in a significant change in the location of theQ-point. For
instance, if the defined operating point is atb,a slight increase in supply voltageEwill move the
operating point up the curve since the voltage across the diode will increase. Once the
disturbance has passed, the voltage across the diode and the associated diode current will return
to the levels defined by theQ-point atb.The operating point defined bycis anunstableone
because a slightFigure 1.29change in the voltage across or current through the diode will result
in theQ-pointas shown inmoving to eitheraorb.For instance, the slightest increase inEwill
cause the voltage across the tunnel diode to increase above its level atc.In this region, however,
an increase inVTwill cause a decrease inITand a further increase inVT
Figure 1.29 Tunne diode and resulting load line.
Tunnel Diode Energy Band Diagram:

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Figure 1.30 Energy level diagrams of tunnel diode
Figure1.30(a)shows energy level diagrams of the tunnel diode for three interesting bias levels.
The shaded area show the energy states occupied by electrons in the valence band, whereas the
cross hatched regions represent energy states are occupied by electrons eitherside of the
junctions are shown by dotted lines. When the bias is zero, these linear are at the same height.
Unless energy is imparted to the electrons from external source, the energy possessed by the
electrons on the N-Side of the junction isinsufficientpermit over the junction barrier to reach the
P-Side. However,quantummechanics show that there is finite probability for the electrons to
tunnel though the junction to reach the other side, provided there are allowed empty energy states
in the P-sideof the junction at the same energy level. Hence, the forward current is Zero.
When a small forward bias is applied to the junction, the energy level of the P-side is lower as
compared with the N-Side. As shown in fig.Figure 1.30(b), electrons in the conduction band of
the N-side see empty energy level on the P-side. Hence, tunneling from N-side to P-side takes
place. Tunneling is otherdirections arenot possible because the valence band electrons on the P-

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side are now opposite to theforbiddenenergygapon the N-side. The energy band diagram
shown inFigure 1.30(b)is for the peak of the diode characteristics.
When theforwardbias is raised beyond this point tunneling will decrease as shown inFigure
1.30(c). The energy of the P-Side is now depressed further, with the result that fewer conduction
band electrons on the N-Side are opposite to the unoccupied P-side energy levels. As the bias is
raised, forward current drops. This corresponds to the negative resistance region of the diode
characteristics. As forward bias is raised still further, tunneling stops altogether and it behaves as
normal P-N Junction diode.
Advantages of tunnel diodes
Long life
High-speed operation
Low noise
Low power consumption
Disadvantages of tunnel diodes
Tunnel diodes cannotbe fabricated in large numbers
Being a two terminal device, the input and output are not isolated from one another.
Applications of tunnel diodes
Tunnel diodes are used as logic memory storage devices.
Tunnel diodes are used in relaxation oscillator circuits.
Tunnel diode is used as an ultra high-speed switch.
Tunnel diodes are used in FM receivers.
LED:
Before going into how LED works, let’s first take a brief look at light self. Since ancient times
man has obtained light from various sources likesunrays, candles and lamps.
In 1879, Thomas Edison invented the incandescent light bulb. In the light bulb, an electric
current is passed through a filament inside the bulb.
Unlike the light bulb in which electrical energy first converts into heat energy,the electrical
energy can also be directly converted into light energy.
Light is a type ofenergythat can be released by anatom. Light is made up of many small
particles called photons.Photons have energy and momentum but no mass.
Light Emitting Diodes(LEDs)as shown inFigure 1.31aare the most widely used semiconductor
diodes among all the different types of semiconductor diodes available today. Light Emitting
Diodes emit either visible light or invisible infrared light when forward biased. The LEDs which
emit invisible infrared light are used for remote controls.
A light Emitting Diode (LED) is an optical semiconductor device that emits light whenvoltageis
applied. In other words, LED is an optical semiconductor device that converts electrical energy
into light energy.
Figure 1.31a:Different colors of LEDs

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When Light Emitting Diode (LED) is forward biased,free electronsin the conduction band
recombines with theholesin the valence band and releases energy in the form of light.
The process of emitting light in response to thestrongelectric fieldorflow of electric currentis
calledelectroluminescence.
A normalp-n junction diodeallows electric current only in one direction. It allows electric
current when forward biased and does not allow electric current when reverse biased. Thus,
normal p-n junction diode operates only in forward bias condition.Like the normal p-n junction
diodes, LEDs also operates only in forward bias condition. To create an LED, the n-type material
should be connected to the negative terminal of thebattery and p-type material should be
connected to the positive terminal of the battery. In other words, the n-type material should be
negatively charged and the p-type material should be positively charged.The construction of
LED is similar to the normalp-n junction diode except that gallium, phosphorus and arsenic
materials are used for construction instead of silicon or germanium materials.
In normal p-n junction diodes, silicon is most widely used because it is less sensitive to the
temperature. Also,it allows electric current efficiently without any damage. In some cases,
germanium is used for constructing diodes.However, silicon or germanium diodes do not emit
energy in the form of light. Instead, they emit energy in the form of heat. Thus, siliconor
germanium is not used for constructing LEDs.
Layers of LED
A Light Emitting Diode (LED) consists of three layers:p-type semiconductor,n-type
semiconductorand depletion layer. The p-type semiconductor and the n-type semiconductor are
separated by adepletion regionor depletion layer.
P-type semiconductor
When trivalent impurities are added to the intrinsic or pure semiconductor, a p-type
semiconductor is formed.In p-type semiconductor, holes are the majority charge carriers and
free electrons arethe minority charge carriers. Thus, holes carry most of the electric current in p-
type semiconductor.
N-type semiconductor
When pentavalent impurities are added to the intrinsic semiconductor, an n-type semiconductor
is formed.In n-type semiconductor, free electrons are the majority charge carriers and holes are
the minority charge carriers. Thus, free electrons carry most of the electric current in n-type
semiconductor.
Depletion layer or region
Depletion region is a region present between the p-type andn-type semiconductor where no
mobile charge carriers (free electrons and holes) are present. This region acts as barrier to the
electric current. It opposes flow of electrons from n-type semiconductor and flow of holes from
p-type semiconductor.
To overcome the barrier of depletion layer, we need to apply voltage which is greater than the
barrier potential of depletion layer.If the applied voltage is greater than the barrier potential of
the depletion layer, the electric current starts flowing.
LightEmitting Diode (LED) working:

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Light Emitting Diode (LED) works only in forward bias condition. When Light Emitting Diode
(LED) is forward biased, the free electrons from n-side and the holes from p-side are pushed
towards the junctionas shown inFigure 1.31b.
When free electrons reach the junction or depletion region, some of the free electrons recombine
with the holes in the positive ions. We know that positive ions have less number of electrons than
protons. Therefore, they are ready to accept electrons.Thus, free electrons recombine with holes
in the depletion region. In the similar way, holes from p-side recombine with electrons in the
depletion region.
Figure 1.31b:Biasing of LED
Because of the recombination of free electrons and holes in thedepletion region, thewidth of
depletion regiondecreases. As a result, more charge carriers will cross thep-n junction.
Some of the charge carriers from p-side and n-side will cross the p-n junction before they
recombine in the depletion region. For example, some free electrons from n-type semiconductor
cross the p-n junction and recombines with holes in p-type semiconductor. In the similar way,
holes from p-type semiconductor cross the p-n junction and recombines with free electrons in the
n-type semiconductor.
Thus, recombination takes place in depletion region as well as in p-type and n-type
semiconductor.The free electrons in the conduction band releases energy in the form of light
before they recombine with holes in the valence band.In silicon and germanium diodes, most of
the energy is released in the form of heat and emitted light is too small.However, in materials
like gallium arsenide and gallium phosphide the emitted photons have sufficient energy to
produce intense visible light.
Operation ofLED
When external voltage is applied to thevalence electrons, they gain sufficient energy andbreak
the bonding with the parent atom. The valenceelectrons which breakbonding with the parent
atom are called free electrons.When the valence electron left the parent atom, they leave an
empty space in the valence shell at which valence electron left. This empty space in the valence

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shell is called a hole.The energy level of all the valence electrons is almost same. Grouping the
range of energy levels of all the valence electrons is called valence band.In the similar way,
energy level of all the free electrons is almost same. Grouping the range of energy levels of all
the free electrons is called conduction band.
The energy level of free electrons in the conduction band is high compared to the energy level of
valence electrons or holes in the valence band. Therefore, free electrons in the conduction band
need to lose energy in order to recombine with the holes in the valence band.
The free electrons in theconduction band do not stay for long period. After a short period, the
free electrons lose energy in the form of light and recombine with the holes in the valence band.
Each recombination of charge carrier will emit some light energy.
Figure 1.31c:Process of light emission in LED
The energy lose of free electrons or the intensity of emitted light is depends on the forbidden gap
or energy gap between conduction band and valence band.The semiconductor device with large
forbidden gapas shown inFigure 1.31cemits high intensity light whereas the semiconductor
device with small forbidden gap emits low intensity light.In other words, the brightness of the
emitted light is depends on the material used for constructing LED and forward current flow
through the LED.
In normal silicon diodes, the energy gap between conduction band and valence band is less.
Hence, the electrons fall only a short distance. As a result, low energy photons are released.
These low energy photons have low frequency which is invisible to human eye.In LEDs, the
energy gap between conduction band and valence band is very large so the free electrons in
LEDs have greater energy than the free electrons in silicon diodes. Hence, the free electrons fall
to a large distance. As a result, high energy photons are released. These high energy photons
have high frequency which is visible to human eye.
The efficiency of generation of light in LED increases with increase in injected current and with
a decrease in temperature.In light emittingdiodes, light is produced due to recombination
process. Recombination of charge carriers takes place only under forward bias condition. Hence,
LEDs operate only in forward bias condition.When light emitting diode is reverse biased, the
free electrons (majority carriers) from n-side and holes (majority carriers) from p-side moves
away from the junction. As a result, the width of depletion region increases and no

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recombination of charge carriers occur. Thus, no light is produced.If the reverse bias voltage
applied to the LED is highly increased, the device may also be damaged.All diodes emit photons
or light but not all diodes emit visible light. The material in an LED is selected in such a way that
the wavelength of the released photons falls within the visible portion of the light spectrum.
Light emitting diodes can be switched ON and OFF at a very fast speed of 1 ns.
Light emitting diode (LED) symbol
The symbol of LED is similar to the normal p-n junction diode except that it contains arrows
pointing awayfrom the diode indicating that light is being emitted by the diode.
Figure 1.31d: Symbol of LED
LEDs are available in different colors. The most common colors of LEDs are orange, yellow,
green and red.The schematic symbol of LED does not represent thecolor of light. The schematic
symbolas shown in Figure 1.31dis same for all colors of LEDs. Hence, it is not possible to
identify the color of LED by seeing its symbol.
LEDConstruction
One of the methods used to construct LED is to deposit three semiconductor layers on the
substrate. The three semiconductor layers deposited on the substrate are n-type semiconductor, p-
type semiconductor and active region. Active region is present in between the n-type and p-type
semiconductor layers.
Figure 1.31e:Construction of LED
When LED is forward biased, free electrons from n-type semiconductor and holes from p-type
semiconductor are pushed towards the active region.When free electrons from n-side and holes
from p-side recombine with the opposite charge carriers (free electrons with holes or holes with
free electrons) in active region, an invisible or visible light is emitted.In LED, most of the
charge carriers recombine at active region. Therefore, most of the light is emitted by the active
region. The active region is also called as depletion regionas shown inFigure 1.31e.
Biasing of LED
The safe forward voltage ratings of most LEDs is from 1V to 3 V and forward current ratings is
from 200 mA to 100 mA.If the voltage applied to LED is in between 1V to 3V, LED works

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perfectly because the current flowas shown inFigure 1.31ffor the applied voltage is in the
operating range. However, if the voltage applied to LED is increased to a value greater than 3
volts. The depletion region in the LED breaks down and the electric current suddenly rises. This
sudden rise in current may destroy the device.
To avoid this we need to place aresistor(Rs) in series with the LED. The resistor (Rs) must be
placed in between voltage source (Vs) and LED.
Figure 1.31f:Currentflow in LED circuit.
The resistor placed between LED and voltage source is called current limiting resistor. This
resistor restricts extra current which may destroy the LED. Thus, current limiting resistor
protects LED from damage.
The current flowing through the LED is mathematically written as
I
Where
IF=Forward current
VS=Source voltage or supply voltage
VD=Voltage drop across LED
RS=Resistor or current limiting resistor
Voltage drop is the amount of voltage wasted to overcome the depletion region barrier (which
leads to electric current flow).
Thevoltage drop of LED is 2 to 3V whereas silicon or germanium diode is 0.3 or 0.7 V.
Therefore, to operate LED we need to apply greater voltage than silicon or germanium diodes.
Light emitting diodes consume more energy than silicon or germanium diodes to operate.
Output characteristics of LED
The amount of output light emitted by the LED is directly proportional to the amount of forward
current flowing through the LED. More the forward current, the greater is the emitted output
light. The graph of forward current vs output light is shown in the figure.

61. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
61
Figure 1.31g: Characteristics of LED
The material used for constructing LED determines its color. In other words, the wavelength or
color of the emitted light depends on the forbidden gap or energy gap of thematerial.Different
colors of LEDs Forward voltage values are mentioned in following table2.
Table2: Typical values of LEDs
Different materials emit different colors of light.
Gallium arsenide LEDs emit red and infrared light.
Gallium nitride LEDsemit bright blue light.
Yttrium aluminium garnet LEDs emit white light.
Gallium phosphide LEDs emit red, yellow and green light.
Aluminium gallium nitride LEDs emit ultraviolet light.
Aluminum gallium phosphide LEDs emit green light.
Advantages of LED
1.Thebrightness of light emitted by LED is depends on the current flowing through the
LED. Hence, the brightness of LED can be easily controlled by varying the current. This
makes possible to operate LED displays under different ambient lighting conditions.
2.Light emitting diodes consume low energy.
3.LEDs are very cheap and readily available.
4.LEDs are light in weight.
5.Smaller size.
6.LEDs have longer lifetime.
7.LEDsoperates very fast. They can be turned on and off in very less time.
8.LEDs do not contain toxicmaterial like mercury which is used in fluorescent lamps.
9.LEDs can emit different colors of light.
Disadvantages of LED
1.LEDs need more power to operate than normal p-n junction diodes.
2.Luminous efficiency of LEDs is low.
Applications of LED
The various applications of LEDs are as follows
1.Burglar alarms systems
2.Calculators
3.Picture phones
4.Traffic signals
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
61
Figure 1.31g: Characteristics of LED
The material used for constructing LED determines its color. In other words, the wavelength or
color of the emitted light depends on the forbidden gap or energy gap of thematerial.Different
colors of LEDs Forward voltage values are mentioned in following table2.
Table2: Typical values of LEDs
Different materials emit different colors of light.
Gallium arsenide LEDs emit red and infrared light.
Gallium nitride LEDsemit bright blue light.
Yttrium aluminium garnet LEDs emit white light.
Gallium phosphide LEDs emit red, yellow and green light.
Aluminium gallium nitride LEDs emit ultraviolet light.
Aluminum gallium phosphide LEDs emit green light.
Advantages of LED
1.Thebrightness of light emitted by LED is depends on the current flowing through the
LED. Hence, the brightness of LED can be easily controlled by varying the current. This
makes possible to operate LED displays under different ambient lighting conditions.
2.Light emitting diodes consume low energy.
3.LEDs are very cheap and readily available.
4.LEDs are light in weight.
5.Smaller size.
6.LEDs have longer lifetime.
7.LEDsoperates very fast. They can be turned on and off in very less time.
8.LEDs do not contain toxicmaterial like mercury which is used in fluorescent lamps.
9.LEDs can emit different colors of light.
Disadvantages of LED
1.LEDs need more power to operate than normal p-n junction diodes.
2.Luminous efficiency of LEDs is low.
Applications of LED
The various applications of LEDs are as follows
1.Burglar alarms systems
2.Calculators
3.Picture phones
4.Traffic signals
Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
61
Figure 1.31g: Characteristics of LED
The material used for constructing LED determines its color. In other words, the wavelength or
color of the emitted light depends on the forbidden gap or energy gap of thematerial.Different
colors of LEDs Forward voltage values are mentioned in following table2.
Table2: Typical values of LEDs
Different materials emit different colors of light.
Gallium arsenide LEDs emit red and infrared light.
Gallium nitride LEDsemit bright blue light.
Yttrium aluminium garnet LEDs emit white light.
Gallium phosphide LEDs emit red, yellow and green light.
Aluminium gallium nitride LEDs emit ultraviolet light.
Aluminum gallium phosphide LEDs emit green light.
Advantages of LED
1.Thebrightness of light emitted by LED is depends on the current flowing through the
LED. Hence, the brightness of LED can be easily controlled by varying the current. This
makes possible to operate LED displays under different ambient lighting conditions.
2.Light emitting diodes consume low energy.
3.LEDs are very cheap and readily available.
4.LEDs are light in weight.
5.Smaller size.
6.LEDs have longer lifetime.
7.LEDsoperates very fast. They can be turned on and off in very less time.
8.LEDs do not contain toxicmaterial like mercury which is used in fluorescent lamps.
9.LEDs can emit different colors of light.
Disadvantages of LED
1.LEDs need more power to operate than normal p-n junction diodes.
2.Luminous efficiency of LEDs is low.
Applications of LED
The various applications of LEDs are as follows
1.Burglar alarms systems
2.Calculators
3.Picture phones
4.Traffic signals

62. Electronic Devices and CircuitsNotes Lendi Institute of Engineering and Technology
62
5.Digital computers
6.Multimeters
7.Microprocessors
8.Digital watches
9.Automotive heat lamps
10.Camera flashes
11.Aviation lighting