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

1. Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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ELECTRONIC DEVICES and CIRCUITS
II B.TECH I SEMESTER-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: lendi_2008@yahoo.com website: www.lendi.org
EDC Textbook Prepared by
Mr. S S Kiran, Dr. M Rajanbabu and Dr. B Kiranmai
Electronic Devices and Circuits

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Subject Code Subject Name L T P C
R19ECE-PC2101 Electronic Devices and Circuits 3 0 0 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 knowledge about 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 the course, 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.NO Topic name Page No
1 Introduction about Course 3
2. Review of Semi Conductor Physics 3
3. Fermi Dirac Function 18
4. Continuity Equation 20
Junction Diode Characteristics, Special Semiconductor Diodes
S.No Topic Name Page No
1. Open Circuited P-N Junction 22
2. Biased P-N Junction, , P-N Junction Diode 26
3. Current Components in PN Junction Diode 30
4. Diode Equation 35
5. V-I Characteristics 36
6. Temperature Dependence on V-I Characteristics 38
7. Diode Resistance 39
8. Diode Capacitance 42
9. Energy Band Diagram of PN Junction Diode 43

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10. Zener Diode 46
11. Tunnel Diode 50
12. LED 54
Applications: 1. Detection signals in digital networks.
2. Lighting systems in various display boards
3. As switches in logic circuits
4. Diodes in Voltage Multiplier Circuits
5. Diodes in Reverse Current Protection based on their PIV.
6. Diodes in Voltage Spike Suppression
Introduction about Course:
Electron Definition:
An electron is a negatively charged subatomic particle. It can be either free or bound to the
nucleus of an atom as shown 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 1.60 X 10-19
C
(Coulombs) and 9.11 X 10-31
kg respectively.
Figure 0.0: Mechanics of Electron
Device Definition: A thing (System) is designed for a particular purpose, especially a piece of
Mechanical or Electrical or Electronic Equipment. This is taken input and gives output.
These Devices are generally categorized into various types like Electronic Devices, Electrical
Devices and Mechanical Devices shown in following figure 0.1
Figure 0.1: Different devices.

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Electronic Devices Definition: a device which is having electronic components for controlling
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 and produces desired electronic DC
output.
Figure 0.2a: Electronic Devices.
Circuit Definition:
A roughly circular line, route, or movement that starts and finishes at the same place, in general
way every 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 Circuits Notes Lendi Institute of Engineering and Technology
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Electronic Devices Definition: a device which is having electronic components for controlling
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 and produces desired electronic DC
output.
Figure 0.2a: Electronic Devices.
Circuit Definition:
A roughly circular line, route, or movement that starts and finishes at the same place, in general
way every 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 Circuits Notes Lendi Institute of Engineering and Technology
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Electronic Devices Definition: a device which is having electronic components for controlling
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 and produces desired electronic DC
output.
Figure 0.2a: Electronic Devices.
Circuit Definition:
A roughly circular line, route, or movement that starts and finishes at the same place, in general
way every 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 a conductor 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 applied electric 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 of Electronics
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 of Electronics:
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,
watching movies, 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
anytime from 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, and GaAs
The construction of every discrete (individual) solid-state (hard crystal structure)
electronic device or integrated circuit begins with a semiconductor material of the highest
quality.
Semiconductors are a special class of elements having conductivity between that of a good
conductor and that of an insulator.
In general, semiconductor materials fall into one of two classes: single-crystal and
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 atomic structures.
Figure 0.3: Atomic structure of (a) silicon; (b) germanium; and (c) gallium and arsenic.
As indicated in Fig. 0.3, silicon has 14 orbiting electrons 1s2 2s2 2p6 3s2 3p2, germanium has 32
electrons 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p2, gallium has 31 electrons, and arsenic has 33
orbiting electrons (the same arsenic that is a very poisonous chemical agent). For germanium and

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silicon there are four electrons in the outermost shell, which are referred to as valence electrons.
Gallium has three valence electrons and arsenic has five valence electrons. Atoms that have four
valence electrons are called tetravalent, those with three are called trivalent, and those with five
are called pentavalent. The term valence is used to indicate that the potential (ionization
potential) required to remove any one of these electrons from the atomic structure is significantly
lower than that required for any other electron in the structure.
Figure 0.4: Covalent banding of the silicon atom
In a pure silicon or germanium crystal the four valence electrons of one atom form a bonding
arrangement with four adjoining atoms, as shown in Fig. 0.4 .
The three semiconductors used most frequently in the construction of electronic devices are
Ge, Si, and GaAs.
Figure 0.5: 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 time the demand for
increased speed resulted in more funding for GaAs research, to the point that today it 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. Semi Conductors
3. Metals
Definition: A Very poor Conductor of electricity is called an Insulator: an excellent conductor
is a Metal and a substance whose conductivity lies between these extremes is a Semiconductor.
Table 1. Comparison table between Conductor Semiconductor and Insulator
# Characteristics Conductor or Metal Semi-Conductor Insulator
1 Conductivity High Moderate Low
2 Resistivity Low Moderate Very High
3 Forbidden Gap No forbidden gap Small forbidden gap Large forbidden gap
4 Conduction
Large number of
Electrons for Conduction
Very small number of
Electrons for Conduction
Moderate number of
Electrons for
Conduction
5 Conductivity value Very high 10-7mho/m
Between those of
conductors and insulators
i.e. 10-7 mho/m to 10-
13mho/m
Negligible like 10-
13mho/m
6 Resistivity value
Negligible; less than 10-
5 Ω-m
Between those of
conductors and insulators
i.e. 10-5 Ω-m to 105 Ω-m
Very high; more
than 105 Ω-m
7 Current flow Due to free electrons
Due to holes and free
electrons
Due to negligible free
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 of 6eV to 10eV
10 0 Kelvin Behavior
Acts like a
superconductor
Acts like an insulator Acts like an insulator
11 Formation
Formed by metallic
bonding
Formed by covalent
bonding
Formed by ionic
bonding

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12 Valence Electrons
One valence electron in
outermost shell
Four valence electron in
outermost shell
Eight valence electron in
outermost shell
13 Examples
Copper, Mercury,
Aluminum, Silver
Germanium, Silicon
Wood, Rubber, Mica,
Paper
Insulators:
Figure 0.6 Insulator Materials Using Plastic Rubber Material
Figure 0.7 Insulator Materials Using Ceramic Materials
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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12 Valence Electrons
One valence electron in
outermost shell
Four valence electron in
outermost shell
Eight valence electron in
outermost shell
13 Examples
Copper, Mercury,
Aluminum, Silver
Germanium, Silicon
Wood, Rubber, Mica,
Paper
Insulators:
Figure 0.6 Insulator Materials Using Plastic Rubber Material
Figure 0.7 Insulator Materials Using Ceramic Materials
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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12 Valence Electrons
One valence electron in
outermost shell
Four valence electron in
outermost shell
Eight valence electron in
outermost shell
13 Examples
Copper, Mercury,
Aluminum, Silver
Germanium, Silicon
Wood, Rubber, Mica,
Paper
Insulators:
Figure 0.6 Insulator Materials Using Plastic Rubber Material
Figure 0.7 Insulator Materials Using Ceramic Materials

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Figure 0.8 Different types of Insulating Materials
Metals (Conductors):
Figure 0.9 Different types of Metals
Figure 0.10 Copper Conductors
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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Figure 0.8 Different types of Insulating Materials
Metals (Conductors):
Figure 0.9 Different types of Metals
Figure 0.10 Copper Conductors
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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Figure 0.8 Different types of Insulating Materials
Metals (Conductors):
Figure 0.9 Different types of Metals
Figure 0.10 Copper Conductors

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Energy levels:
Within the atomic structure of each and every isolated atom there are specific energy
levels associated with each shell and orbiting electron, as shown in Fig. 1.1. The energy levels
associated with each shell will be different for 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 in the atomic
structure.
Note in Fig. 0.11 that 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
Figure 0.11 Energy Band Diagrams of Insulator, Semiconductor and Metal
A material may be placed in one of these three classes, depending upon its Energy-Band
Structure as shown in above figure.
Insulator:
The energy band structure is indicated schematically shown in figure 1.4a (Energy Gap is Eg =
6eV). The large forbidden band separates the filled valence region from the vacant conduction
band. Hence the electron cannot acquire sufficient applied energy so that conduction is not
possible i.e insulator. The number of free electrons in an insulator is very small, roughly around
107
electrons /m3

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Semiconductor:
A substance for which the width of the forbidden energy region is relatively small (Energy Gap
is 1 eV) is called Semiconductor. The number of free electrons in semiconductor lies between
107
electrons /m3
to 1028
electrons /m3
.
Metal (Conductor):
A solid which contains a partly filled band structure is called a metal. Under the influence of an
applied electric field the electrons may acquire additional energy and move into higher states.
Here there is energy gap between form valance bands to conduction band is overlapped each
other. The number of free electrons in an Metal is very high, roughly around 1028
electrons /m3

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Types of Semiconductors:
1) Intrinsic Semiconductor (Pure Semiconductor)
2) Extrinsic Semiconductor (Impure Semiconductor or Doped Semiconductor)
Intrinsic Semiconductor: A pure semiconductor is called intrinsic semiconductor, even at the
room temperature, some of the valence electrons may acquire sufficient energy 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 conduction in 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
Extrinsic material.
There are two extrinsic materials of immeasureable importance to semiconductor device
fabrication: n -type and p -type materials. Each is described in some detail in the following
subsections.
n -Type Material:
Both n -type and p -type materials are formed by adding a predetermined number of impurity
atoms to a silicon base. An n -type material is created by introducing impurity elements that have
five valence electrons ( Pentavalent), such as antimony , arsenic , and phosphorus. 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 antimony as the impurity in 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
unassociated with any particular covalent bond. This remaining electron, loosely bound to its
parent (antimony) atom, is relatively free to move within the newly formed n -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
The p -type material is formed by doping a pure germanium or silicon crystal with impurity
atoms having three valence electrons. The elements most frequently used for this purpose are
boron, gallium, and indium. Each is a member of a subset group of elements in the Periodic
Table of Elements referred to as Group III because each has three valence electrons. The effect
of one of these elements, boron, on a base of silicon is indicated in Fig. 0.15
Note that there is now an insufficient number of electrons to complete the covalent bonds of the
newly formed lattice. The resulting vacancy is called a hole and is represented by a small circle
or a plus sign, indicating the absence of a negative charge. Since the resulting vacancy will
readily accept a free electron

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Figure 0.15 Boron 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.
vd is the drift velocity for electrons so that Vd α E
Vd=µE
µ is the mobility constant unit is m2
/V-sec
# Si Ge GaAs InAs
mn (cm2
/Vs) 1400 3900 8500 30,000
mp (cm2
/Vs) 470 1900 400 500
Conductivity: The degree to which a specified material conducts 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)
σ is 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 field E is 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

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J = ρvu = E
Where σ =
J = σ E
σ is 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 conductor n is very large, approximately, 1028
electrons/m3
Semiconductor: The conductivity of a material is proportional to the concentration of free
electrons in a semiconductor lies between 107
electrons /m3
to 1028
electrons /m3
. Thus, a
semiconductor has conductivity much greater than that of an insulator but much smaller than 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 107
electrons/m3
.
Problem : A cylindrical shaped section of n-Type silicon has a 1 mm length and 0.1 mm2 cross
sectional area. Calculate its conductivity and resistance when free electron density of n= 8 X 1013
/ cm3
.
Solution :
Given Data :
l =1 mm= 0.1 cm and a = 0.1 mm2
= 10-3
cm2
n= 8 X 1013
/ cm3
.
Known Data :
ni = 1500 cm2
/ V.s and
µn = 1500 cm2
/ V.s

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µp = 500 cm2
/ V.s
Formula :
=(1.6 X 10-19
)[(1.5X 1010
X 1500) + (1.5X 1010
X 500)]
= 4.8X10-6
(Ω.cm)-1
R = 0.1/(4.8 X 10-6
(Ω.cm)-1
X 10-3
cm2
)
R = 20.8 ΩM
Summary:
Mobility: In some materials, ability to movement of electrons freely and easily with a drift
velocity due to the electric field is applied.
vd is the drift velocity for electrons so that Vd α E
Vd=µE
Conductivity: The degree to which a specified material conducts 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 = σ E
σ = (nµn+pµp)q
R=

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Fermi Dirac Function
Objectives
1. Fermi Dirac Distributed Function to be reviewed.
2. Necessity of Fermi Dirac Distribution Function to be reviewed
Figure 1.1 Internal Structure of a Typical Atom
Atoms constitute the building blocks of all materials in existence. In these atoms, there is a
central portion called nucleus shown in above figure. Which consists of protons and neutrons,
around which revolves the particles called electrons. Next, it is to be noted 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 electron as show in Figure
1.0 of a particular atom has its own dedicated path, called orbit, along which it circles around the
central nucleus as 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
of Fermi-Dirac distribution function, we are particularly interested in knowing the chance by
which we can find a fermion in a particular energy state of an atom. Here, by fermions, we mean
the electrons of an atom which are the particles with ½ spin, 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 electrons which 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 concentration of 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 × 10 JK
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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Fermi Dirac Function
Objectives
1. Fermi Dirac Distributed Function to be reviewed.
2. Necessity of Fermi Dirac Distribution Function to be reviewed
Figure 1.1 Internal Structure of a Typical Atom
Atoms constitute the building blocks of all materials in existence. In these atoms, there is a
central portion called nucleus shown in above figure. Which consists of protons and neutrons,
around which revolves the particles called electrons. Next, it is to be noted 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 electron as show in Figure
1.0 of a particular atom has its own dedicated path, called orbit, along which it circles around the
central nucleus as 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
of Fermi-Dirac distribution function, we are particularly interested in knowing the chance by
which we can find a fermion in a particular energy state of an atom. Here, by fermions, we mean
the electrons of an atom which are the particles with ½ spin, 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 electrons which 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 concentration of 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 × 10 JK
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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Fermi Dirac Function
Objectives
1. Fermi Dirac Distributed Function to be reviewed.
2. Necessity of Fermi Dirac Distribution Function to be reviewed
Figure 1.1 Internal Structure of a Typical Atom
Atoms constitute the building blocks of all materials in existence. In these atoms, there is a
central portion called nucleus shown in above figure. Which consists of protons and neutrons,
around which revolves the particles called electrons. Next, it is to be noted 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 electron as show in Figure
1.0 of a particular atom has its own dedicated path, called orbit, along which it circles around the
central nucleus as 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
of Fermi-Dirac distribution function, we are particularly interested in knowing the chance by
which we can find a fermion in a particular energy state of an atom. Here, by fermions, we mean
the electrons of an atom which are the particles with ½ spin, 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 electrons which 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 concentration of 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 × 10 JK

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is the Boltzmann constant
T is the absolute temperature
Ef is 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
Intrinsic semiconductors are the pure semiconductors which 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 Figure 1.2a.
Figure 1.2: Fermi levels of (a) Intrinsic Semiconductor (b) N-Type Semiconductor (c) P-Type
Semiconductor
Next, consider the case of an n-type semiconductor. 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 of p-type
semiconductors to be present near the valence band (Figure 1.2c). 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 Circuits Notes Lendi Institute of Engineering and Technology
19
is the Boltzmann constant
T is the absolute temperature
Ef is 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
Intrinsic semiconductors are the pure semiconductors which 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 Figure 1.2a.
Figure 1.2: Fermi levels of (a) Intrinsic Semiconductor (b) N-Type Semiconductor (c) P-Type
Semiconductor
Next, consider the case of an n-type semiconductor. 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 of p-type
semiconductors to be present near the valence band (Figure 1.2c). 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 Circuits Notes Lendi Institute of Engineering and Technology
19
is the Boltzmann constant
T is the absolute temperature
Ef is 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
Intrinsic semiconductors are the pure semiconductors which 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 Figure 1.2a.
Figure 1.2: Fermi levels of (a) Intrinsic Semiconductor (b) N-Type Semiconductor (c) P-Type
Semiconductor
Next, consider the case of an n-type semiconductor. 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 of p-type
semiconductors to be present near the valence band (Figure 1.2c). 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 Circuits Notes Lendi Institute of Engineering and Technology
20
Effect of temperature on Fermi-Dirac Distribution Function
Figure 1.3: 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 by electrons. Thus we have a step
function defining the Fermi-Dirac distribution function as shown by 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 Figure 1.3.
Continuity Equation:
Objectives:
Continuity Equation and Law of Junction to 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 with time 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 the excess density of electrons or holes in time
and space.
As shown following figure 1.4 consider 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 Ip and leaving at x+dx is Ip+ dIp which 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, dIp is the decrease in number of coulombs per second within
the volume.
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
20
Effect of temperature on Fermi-Dirac Distribution Function
Figure 1.3: 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 by electrons. Thus we have a step
function defining the Fermi-Dirac distribution function as shown by 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 Figure 1.3.
Continuity Equation:
Objectives:
Continuity Equation and Law of Junction to 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 with time 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 the excess density of electrons or holes in time
and space.
As shown following figure 1.4 consider 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 Ip and leaving at x+dx is Ip+ dIp which 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, dIp is the decrease in number of coulombs per second within
the volume.
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
20
Effect of temperature on Fermi-Dirac Distribution Function
Figure 1.3: 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 by electrons. Thus we have a step
function defining the Fermi-Dirac distribution function as shown by 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 Figure 1.3.
Continuity Equation:
Objectives:
Continuity Equation and Law of Junction to 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 with time 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 the excess density of electrons or holes in time
and space.
As shown following figure 1.4 consider 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 Ip and leaving at x+dx is Ip+ dIp which 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, dIp is the decrease in number of coulombs per second within
the volume.

21. Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
21
Figure 1.4: Relating to continuity equation
Since the magnitude of the carrier charges is q, then equals the decrease in 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 hole concentration per second, due to current Ip.
We know that there is an increase of holes per unit volume per second given by G = p0/τp due 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 derivates should 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 carrier holes. Here, partial derivatives
have been used since both p and Jp are 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 Circuits Notes Lendi Institute of Engineering and Technology
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=
−
−
1
Where J = -q +
Therefore, = − + D − μ
( )
Hall Effect
VH =
Theory of P-N Junction Diode:
PN Junction diode in Equilibrium with no applied Voltage (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. As shown 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 developed on 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 Circuits Notes Lendi Institute of Engineering and Technology
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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 the junction, as
shown in Fig. 1.5a . Note in Fig. 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 is called 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 1.5c Symbol of PN Junction Diode
Electronic Devices and Circuits Notes 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 the junction, as
shown in Fig. 1.5a . Note in Fig. 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 is called 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 1.5c Symbol of PN Junction Diode
Electronic Devices and Circuits Notes 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 the junction, as
shown in Fig. 1.5a . Note in Fig. 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 is called 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 1.5c Symbol of PN Junction Diode

24. Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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Figure 1.5d: Physical Representation of PN 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 away from 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 majority carriers 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= NA and to its right
it is n= ND.
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
24
Figure 1.5d: Physical Representation of PN 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 away from 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 majority carriers 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= NA and to its right
it is n= ND.
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
24
Figure 1.5d: Physical Representation of PN 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 away from 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 majority carriers 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= NA and to its right
it is n= ND.

25. Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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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-type semiconductor. 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 barrier as shown in Figure 1.8.
Electronic Devices and Circuits Notes 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-type semiconductor. 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 barrier as shown in Figure 1.8.
Electronic Devices and Circuits Notes 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-type semiconductor. 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 barrier as shown in Figure 1.8.

26. Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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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 the diffusion process has created a “built-in potential difference”
across the junction with an open-circuit (zero bias) potential of
= ln
.
Eo is the zero bias junction voltage, VT the thermal voltage of 26mV at room
temperature, ND and NA are the impurity concentrations and ni is 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 junction as shown in Figure 1.8 figure.
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 +
Biased P-N Junction
Forward-Bias Condition (VD> 0 V):
A forward-bias or “on” condition is established by applying the positive potential to the p -type
material and the negative potential to the n -type material as shown in Fig. 1.9. The application
of a forward-bias potential VD will “pressure” electrons in the n -type material and holes in the p
-type material to recombine with the ions near the boundary and reduce the width of the
depletion region as shown in Fig. 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 the p -type material to the n -type material (and of holes from the n –type
material to the p -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 Circuits Notes Lendi Institute of Engineering and Technology
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width of the depletion region has resulted in a heavy majority flow across the junction. An
electron of the n-type material now “sees” a reduced barrier at the junction due to the reduced
depletion region and a strong attraction for the positive potential applied to the p-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 of Fig. 1.16 Note that the
vertical scale of Fig. 1.16 is measured in milli amperes (although some semiconductor 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.
Figure 1.10: Forward biased P-N Junction with flow of charge carriers with resistor.
Figure 1.11: Circuit connection of Forward biased PN Diode
Reverse-Bias Condition (VD < 0 V):
If an external potential of V volts is applied across the p – n junction such that the positive
terminal is connected to the n -type material and the negative terminal is connected to the p -type
material as shown in Fig. 1.12 , the number of uncovered positive ions in the depletion region
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
27
width of the depletion region has resulted in a heavy majority flow across the junction. An
electron of the n-type material now “sees” a reduced barrier at the junction due to the reduced
depletion region and a strong attraction for the positive potential applied to the p-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 of Fig. 1.16 Note that the
vertical scale of Fig. 1.16 is measured in milli amperes (although some semiconductor 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.
Figure 1.10: Forward biased P-N Junction with flow of charge carriers with resistor.
Figure 1.11: Circuit connection of Forward biased PN Diode
Reverse-Bias Condition (VD < 0 V):
If an external potential of V volts is applied across the p – n junction such that the positive
terminal is connected to the n -type material and the negative terminal is connected to the p -type
material as shown in Fig. 1.12 , the number of uncovered positive ions in the depletion region
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
27
width of the depletion region has resulted in a heavy majority flow across the junction. An
electron of the n-type material now “sees” a reduced barrier at the junction due to the reduced
depletion region and a strong attraction for the positive potential applied to the p-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 of Fig. 1.16 Note that the
vertical scale of Fig. 1.16 is measured in milli amperes (although some semiconductor 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.
Figure 1.10: Forward biased P-N Junction with flow of charge carriers with resistor.
Figure 1.11: Circuit connection of Forward biased PN Diode
Reverse-Bias Condition (VD < 0 V):
If an external potential of V volts is applied across the p – n junction such that the positive
terminal is connected to the n -type material and the negative terminal is connected to the p -type
material as shown in Fig. 1.12 , the number of uncovered positive ions in the depletion region

28. Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
28
of the n-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 the p-type material. The net effect, therefore, is a widening 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 Circuits Notes Lendi Institute of Engineering and Technology
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of the n-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 the p-type material. The net effect, therefore, is a widening 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 Circuits Notes Lendi Institute of Engineering and Technology
28
of the n-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 the p-type material. The net effect, therefore, is a widening 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 Circuits Notes Lendi Institute of Engineering and Technology
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Figure: 1.14 Circuit Connection 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 minority carriers, however, entering the depletion region will not change,
resulting in minority-carrier flow vectors of the same magnitude indicated with 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 in µA and
nA, except for high-power devices. The term saturation comes from the fact that it reaches its
maximum level quickly and does not change significantly with increases in the reverse-bias
potential, as shown on the diode characteristics of Fig. 1.15 for VD<0V. The reverse-biased
conditions are depicted in Fig.1.13b for the diode symbol and P – N Junction. Note, in particular,
that the direction of IS is against the arrow of the symbol. Note also that the negative side of the
applied voltage is connected to the p -type material and the positive side to the n -type material,
the difference in underlined letters for each region revealing a 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 as Zener Diodes
This increase in level is due to a wide range of factors that include
Leakage currents, Generation of carriers in the depletion region and Temperature Sensitivity
whereas a 10°C increase in current will result in doubling of the actual reverse current of a diode
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
29
Figure: 1.14 Circuit Connection 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 minority carriers, however, entering the depletion region will not change,
resulting in minority-carrier flow vectors of the same magnitude indicated with 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 in µA and
nA, except for high-power devices. The term saturation comes from the fact that it reaches its
maximum level quickly and does not change significantly with increases in the reverse-bias
potential, as shown on the diode characteristics of Fig. 1.15 for VD<0V. The reverse-biased
conditions are depicted in Fig.1.13b for the diode symbol and P – N Junction. Note, in particular,
that the direction of IS is against the arrow of the symbol. Note also that the negative side of the
applied voltage is connected to the p -type material and the positive side to the n -type material,
the difference in underlined letters for each region revealing a 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 as Zener Diodes
This increase in level is due to a wide range of factors that include
Leakage currents, Generation of carriers in the depletion region and Temperature Sensitivity
whereas a 10°C increase in current will result in doubling of the actual reverse current of a diode
Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
29
Figure: 1.14 Circuit Connection 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 minority carriers, however, entering the depletion region will not change,
resulting in minority-carrier flow vectors of the same magnitude indicated with 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 in µA and
nA, except for high-power devices. The term saturation comes from the fact that it reaches its
maximum level quickly and does not change significantly with increases in the reverse-bias
potential, as shown on the diode characteristics of Fig. 1.15 for VD<0V. The reverse-biased
conditions are depicted in Fig.1.13b for the diode symbol and P – N Junction. Note, in particular,
that the direction of IS is against the arrow of the symbol. Note also that the negative side of the
applied voltage is connected to the p -type material and the positive side to the n -type material,
the difference in underlined letters for each region revealing a 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 as Zener Diodes
This increase in level is due to a wide range of factors that include
Leakage currents, Generation of carriers in the depletion region and Temperature Sensitivity
whereas a 10°C increase in current will result in doubling of the actual reverse current of a diode

30. Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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Current Components in PN junction Diode :
Drift current
The flow of charge carriers, which is due to the applied voltage or electric field is called 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, the free electrons move towards the positive
terminal of a battery and holes move towards the negative terminal of a battery.
Electrons are the negatively charged particles and holes are 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 the battery. But, due to continuous collision with the atoms they change the
direction of flow. Each time the electron strikes an atom it bounces back 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 Circuits Notes Lendi Institute of Engineering and Technology
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Current Components in PN junction Diode :
Drift current
The flow of charge carriers, which is due to the applied voltage or electric field is called 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, the free electrons move towards the positive
terminal of a battery and holes move towards the negative terminal of a battery.
Electrons are the negatively charged particles and holes are 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 the battery. But, due to continuous collision with the atoms they change the
direction of flow. Each time the electron strikes an atom it bounces back 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 Circuits Notes 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 applied voltage or electric field is called 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, the free electrons move towards the positive
terminal of a battery and holes move towards the negative terminal of a battery.
Electrons are the negatively charged particles and holes are 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 the battery. But, due to continuous collision with the atoms they change the
direction of flow. Each time the electron strikes an atom it bounces back 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 Circuits Notes Lendi Institute of Engineering and Technology
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µp = mobility of holes
E = applied electric field
The drift current density due to free electrons is given by
Jn = enµ n E
and the drift current density due to holes is given by
Jp = epµ p E
Where Jn = drift current density due to electrons
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
= enµ n E + epµ p E
J = e (nµ n + pµ p ) E
Diffusion current
The process by which, charge carriers (electrons or holes) in a semiconductor moves
from a 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 called lower 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 an n-type semiconductor that 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 Circuits Notes 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. In p-type semiconductor, the diffusion process
occurs in the similar manner.
Both drift and diffusion current occurs in semiconductor devices. Diffusion current occurs
without an external voltage or electric field applied. Diffusion current does not occur in a
conductor. The direction of diffusion current is same or opposite to that of the drift 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 concentration gradient 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 density due to electrons is given by
= +
Electronic Devices and Circuits Notes 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. In p-type semiconductor, the diffusion process
occurs in the similar manner.
Both drift and diffusion current occurs in semiconductor devices. Diffusion current occurs
without an external voltage or electric field applied. Diffusion current does not occur in a
conductor. The direction of diffusion current is same or opposite to that of the drift 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 concentration gradient 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 density due to electrons is given by
= +
Electronic Devices and Circuits Notes 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. In p-type semiconductor, the diffusion process
occurs in the similar manner.
Both drift and diffusion current occurs in semiconductor devices. Diffusion current occurs
without an external voltage or electric field applied. Diffusion current does not occur in a
conductor. The direction of diffusion current is same or opposite to that of the drift 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 concentration gradient 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 density due to electrons is given by
= +

33. Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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Where Dn is the diffusion coefficient of electrons
The diffusion current density due to holes is given by
= −
Where Dp is the diffusion coefficient of holes
The total current density due to electrons is the sum of drift and diffusion currents.
Jn = Drift current + Diffusion current
= nμ nE +
The total current density due to holes is the sum of drift and diffusion
currents.
Jp = Drift current + Diffusion current
= nμ nE −
The total current density due to electrons and holes is given by
J = Jn + Jp
The following figure shows a P-N Junction with a forward bias by an external voltage V as
shown in Figure 1.15a. Due to the applied voltage, there exists a potential gradient in P and N
materials.
Figure: 1.15a PN Diode by an external voltage V.
Now, the holes from P-region and the electrons from N-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 represent minority carriers. The minority carriers diffuse away from the
junction exponentially with distance as shown following Figure: 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 Circuits Notes Lendi Institute of Engineering and Technology
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Current Components:
Ipn(x) = hole current 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 Inn is given by Inn(x) = I - Ipn(x)
The majority (hole) current Ipp is 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 Circuits Notes 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 as Law of Junction. Here
V = applied voltage, and
VT= Volt equivalent of temperature = KT/q = T/ 11,600
Where k is Boltzmann Constant.
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 :
In solid-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- and reverse-bias
regions for exact demonstration.
= ( ŋ
⁄
− )
IS is the reverse saturation current
VD is the applied forward-bias voltage across the diode
ŋ is an ideality factor, which is a function of the operating conditions and physical construction;
it has a range between 1 and 2 depending on a wide variety of factors ( n =1 will be assumed
throughout this text unless otherwise noted).
The voltage VT is called the thermal voltage and is determined by
VT=
Where k is Boltzmann’s constant= 1.38 x 10-23
J/K
T K is the absolute temperature in kelvins = 273 + the temperature in o
C
q is the magnitude of electronic charge = 1.6 X10-19
c
Problem 1 At a temperature of 27°C (common temperature for components in an enclosed
operating system), determine the thermal voltage VT
Solution:
T = 273 + ° = 273 + 27 = 300
= =
1.38 ×
10
(300 )
1.6 × 10

36. Electronic Devices and Circuits Notes 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-I Characteristics:
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) with Is= 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 of VD the 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 format e x
appearing in Fig 1.16:
= ŋ
⁄
(VD positive)
Figure: 1.16a Silicon semiconductor Diode Characteristics

37. Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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Figure: 1.16b Silicon semiconductor Diode Characteristics with exponential representation
Figure: 1.16c Diode Characteristics in Forward Bias and Reverse Bias
Figure: 1.16d Comparison of Ge, Si, and GaAs commercial diodes.

38. Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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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 rise in 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 the K is the notation VK) of
the curve is about 0.3 V for Ge, 0.7 V for Si, and 1.2 V for GaAs as 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 Io in 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 Io for 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 Circuits Notes 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 Fig 1.16d:
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 on the 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 VD and
ID as shown in Fig. 1.18 and applying the following Equation:
=
The dc 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 resistance level.
Typically, the dc resistance of a diode in the active (most utilized) will range from about 10 Ω to
80Ω

40. Electronic Devices and Circuits Notes Lendi Institute of Engineering and Technology
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Figure 1.18a Determining the dc resistance of a diode at a particular operating point.
Problem 2 Determine the dc resistance levels for the diode of following figure. at
a. ID= 2 mA (low level)
b. I D=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
The dc resistance of a diode is independent of the shape of the characteristic in the region
surrounding the point of interest.

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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 in Fig.1.18b with no applied
varying signal, the point of operation would be the Q –point appearing on Fig. 1.18b, determined
by the applied dc levels. The designation Q-point is derived from the word quiescent, which
means “still or unvarying.”
Figure 1.18b Defining the Dynamic or ac resistance
A straight line drawn tangent to the curve through the Q -point as shown in Fig. 1.18c will
define a particular change in voltage and current that can be used to determine the ac or dynamic
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 the Q -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 Circuits Notes Lendi Institute of Engineering and Technology
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behavior of the system. The result is often a network that can be solved using traditional 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 basic resistor, as of any construction, 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 a role and 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 it can be considered infinite in magnitude, represented by an open circuit, and
ignored. At high frequencies, however, the level of XC can drop to the point where it will
introduce a low-reactance “shorting” path. If this shorting path is across the diode, it can
essentially keep the diode from affecting the response of the network.
In the p – n semiconductor diode, there are two capacitive effects to be considered. Both types of
capacitance are present in the forward- and reverse-bias regions, but one so outweighs the 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 by C = €A/d where € is the
permittivity of the dielectric (insulator) between the plates of area A separated by a distance d.
=
(0)
(1 + | ⁄ |)

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Figure 1.19 Transition and diffusion capacitance versus applied bias for a silicon diode.
=
Where τ is the minority carrier lifetime the time is world take for a minority carrier such as a
hole to recombine with an electron in the n -type material. However, increased levels of 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-bias region whereas
the diffusion capacitance is the predominant capacitive effect in the forward-bias region.
Energy Band Diagram of PN Junction Diode:
A p-n junction consists of two semiconductor regions with opposite doping type as shown in
Figure 4.2.1. The region on the left is p-type with an acceptor density Na, while the region on the
right is n-type with a donor density Nd. The dopants are assumed to be shallow, so that the
electron (Hole) density in the n-type (p-type) region is approximately equal to the donor
(Acceptor) density.
Figure 1.20: P-N Junction diode with density representation
Cross-section of a P-N Junction
We will assume, unless stated otherwise, that the doped regions are uniformly doped and that the
transition between the two regions is abrupt. We will refer to this structure as an abrupt p-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,