This document provides an overview of diodes, including: 1. It discusses different types of materials like conductors, semiconductors, and insulators based on their resistivity. Semiconductors have resistivities between conductors and insulators. 2. It explains current flow in metals and semiconductors. In metals, loosely bound electrons flow under an applied electric field. In intrinsic semiconductors, electrons can gain enough energy to reach the conduction band, leaving holes. 3. A PN junction is formed when a P-type and N-type semiconductor are joined. A depletion region and built-in electric field are created at the junction, forming a diode that allows

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Pilani Campus
CHAPTER 6
DIODES
Vikas Kalwani
EEE Department
BITS Pilani, Pilani

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INTRODUCTION
This chapter deals with
 Types of Materials
 Current flow in a Metal
 Semiconductors
 Intrinsic (pure) (undoped)
 Extrinsic (doped) (impurity added to enhance the conductivity of Intrinsic)
 Non Uniform Doping Case
 PN Junction Diode
 An Ideal PN Junction Diode
 Zener Diodes

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TYPES OF MATERIALS
Any material can be classified as Conductor, Insulator or a Semiconductor based on
it’s ability to conduct electricity or resist electricity (in terms of resistivity)
 Conductors – Usually metals with high conductivities and less resistivity. Resistivity of
a conductor is of an order of 10-7 to 10-8 Ω − 𝑚
 Semiconductors − Resistivities of the order of 10-3 to 103 Ω − 𝑚
 Insulators − Mostly Non Metals with Resistivities of the order of 104 to 1014 Ω − 𝑚
 Copper is an Excellent conductor
 Silver is even better but it is costly to be used domestically
 Many High voltage lines are made of Aluminium having a central core made of steel to
support the structure

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COMMON RESISTIVITY VALUES

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CURRENT FLOW IN A METAL
 A metal consists of atoms with loosely bound electrons such that they get drifted by
the electric field that is applied across its ends and produce current
 Because of the thermal energy, the electrons are in a random motion in all directions,
and thus their average velocity is 0 hence no current when no Electric field is applied
 Mean Free Path − When no electric field is applied, the motion of electrons is random
and they collide with the heavy ions. The velocity of the electron changes. The average
distance travelled by the electron between 2 collisions is the mean free path of the
electron
 When Electric Field (Voltage V) is applied across the metal, the electrons move under
the drift of the field with a drift velocity given by
𝒗 𝒅 = 𝝁𝑬Drift Velocity
Mobility of electron
Electric Field

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CURRENT FLOW IN A METAL
L
A
 Consider a metallic conductor of length L and area of cross
section A and let a voltage V be applied across it.
 Let T be the time taken by an electron to move from the left to
the right through a length L. If be the drift velocity, then
𝑻 =
𝑳
𝒗 𝒅
=
𝑳
𝝁𝑬
𝑣 𝑑
 Let there be N number of electrons drifting from left to right so the total current is −
𝒊 =
𝑵𝒒
𝑻
=
𝑵𝒒𝝁𝑬
𝑳
𝑱 =
𝒊
𝑨
=
𝑵𝒒𝝁𝑬
𝑳𝑨
Current Density
𝒏 =
𝑵
𝑳𝑨
Free electron concentration
Number of free electrons in
this volume
𝑱 = 𝝈𝑬 where 𝜎 is the conductivity of the conductor given by 𝝈 = 𝒏𝒒𝝁

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TEMPERATURE COEFFICIENT OF RESISTIVITY
𝜌 = 1
𝜎 Resistivity is inversely proportional to conductivity
 Charge Density = 𝑛𝑞
 The resistivity of a material is a property of a material and varies with temperature as −
𝜌 = 𝜌0 1 + 𝛼 𝑇 − 𝑇0
 The current in a metal is given by –
 Resistance of a material (R) −
𝑅 = 𝜌𝐿/𝐴
 Temperature in Kelvin = Temperature in Degree Celsius + 273
Temperature coefficient of resistivity
𝑖 = 𝐽𝐴 = 𝜎𝐸𝐴 =
𝐸𝐴
𝜌
=
𝑉𝐴
𝜌𝐿
=
𝑉
𝑅
 Conductivity 𝜎 is proportional to 𝑛
 Good conductor like copper has 𝑛 = 1028 free electrons per cubic meter
 Insulators have 𝑛 = 107 Si – n=1.5x1016 /m3 and Ge - n=2.5x1013 /m3

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CONCEPT OF ENERGY BAND GAP
 For every material there exists 2 Energy bands – 1. Conduction Band (at a higher
Energy Level) and 2. Valence Band (at a lower Energy Level)
 Presence of an electron in the conduction band and a hole in the valence band
makes the material conductive
 The electrons are very tightly bounded in an insulator and require large energies to
reach the conduction band and start conducting

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INTRINSIC SEMICONDUCTOR
 An intrinsic SC has a crystal lattice structure as shown
 An atom has 4 valence electrons and all the atoms
achieve a stable noble gas configuration by sharing of
electrons or COVALENT BONDING
 Since all the electrons are tightly bound to the
nucleus at 0 K, an Intrinsic SC behaves like an
INSULATOR at 0 K.
 At room temperature, some of the electrons gain
enough energy reaching the conduction band leaving
a hole in the valence band. The electron and the hole
both contribute to the current equally

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INTRINSIC SEMICONDUCTOR
HOLE – It does not
exist in reality. It is
the absence of a –ve
charge practically
 If we supply 1.1 eV of Energy to an Electron of Silicon, the
Electron will reach the conduction band and start conducting.
This Energy value is called the BANDGAP
 This means that the covalent bond breaks when the electron
gains sufficient Energy releasing an electron and a hole

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INTRINSIC SEMICONDUCTOR
 1 electron volt – 1.602 x 10 -19 Joules
 At Room temperature, the Energy required to form an electron-hole pair is 1.1 eV for
Silicon and 0.72 eV for Germanium
 At room temperature, the electron and the hole densities are equal i.e. n=p=ni (Intrinsic
Concentration)
 Hole Current – Flow of +ve charge
 Recombination – When an electron and a hole combine, energy is released in released
in the form of heat or light. This is called Recombination
 Due to thermal Energy, new electron hole pairs are generated and old ones getting
recombined
 The current density in an intrinsic SC is given by
𝐽 = 𝑛𝑞𝜇 𝑛 + 𝑝𝑞𝜇 𝑝 𝐸
Bipolar Device – 2 types
of current carriers

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EFFFECT OF INCREASING THE
TEMPERATURE ON CONDUCTIVITY
 For a metal, the conductivity reduces as the atoms gain
high energy and vibrate more providing a more resistive
path to the flow of electrons
 For an Intrinsic SC, as the temperature is increased,
more and more number of covalent bonds get broken
and there is an increase in the current
 For an Insulator, almost no change in the conductivities

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EXTRINSIC SEMICONDUCTOR (doped)
 Doping – The process of adding impurities in controlled amounts to a pure SC is Doping
 Group III and V Elements are used as impurity
Pentavalent Impurity
 When a Group V element is added in minute
amounts to a Pure Silicon crystal, the result is an
increase in conductivity of the Si sample
 Group V element’s atoms replace the Si atoms in the
crystal structure
 4 electrons of Si are bonded to 4 electrons of the
impurity atom leaving behind an electron per
impurity atom for conduction purposes
 Electrons are majority carriers and current is
dominated by them
 Since the impurity donates an
electron for conduction, we call the
impurity a DONOR

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EXTRINSIC SEMICONDUCTOR (doped)
Trivalent Impurity
 When group III elements are doped, each impurity
atom produces an extra hole that is willing to accept
an electron
 We call the impurity atom the ACCEPTOR or the p-type
 Current is dominated by holes in p type SC

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MASS ACTION LAW
This law states that “Regardless of the amount of doping for a SC under thermal
equilibrium, 𝒏𝒑 = 𝒏𝒊 𝟐 “
As a semiconductor is electrically neutral,
𝑁 𝐷 + 𝑝 = 𝑁𝐴 + 𝑛
For n-type For p-type
1. n ≈ 𝑁 𝐷
2. Minority carrier concentration (p)
𝑝 ≈
𝒏𝒊
𝟐
𝑁 𝐷
3. Conductivity
1. p ≈ 𝑁 𝐴
2. Minority carrier concentration (p)
n≈
𝒏𝒊
𝟐
𝑁 𝐴
3. Conductivity𝜎 = 𝑛𝑞𝜇 𝑛 𝜎 = 𝑝𝑞𝜇 𝑝

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GRADED SEMICONDUCTORS
 Diffusion – The movement of charge from its higher concentration to its lower
concentration is diffusion
 Diffusion can lead to current flow and is due to concentration gradient
 Concentration of holes or electrons depends on the distance x 𝑑𝑝/𝑑𝑥
 Net motion of the holes is in the direction of decreasing hole concentration

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GRADED SEMICONDUCTORS
 Flux Density
∅ 𝑛 = 𝐷𝑛
𝑑𝑛
𝑑𝑥
∅ 𝑝 = −𝐷 𝑝
𝑑𝑝
𝑑𝑥
 Diffusion Current Density
𝐽 𝑛 = 𝑞𝐷𝑛
𝑑𝑛
𝑑𝑥
𝐽 𝑝 = −𝑞𝐷𝑝
𝑑𝑝
𝑑𝑥
Diffusion Constant

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GRADED SEMICONDUCTORS
Einstein’s Equation
𝑉 𝑇 =
𝐷 𝑛
𝜇 𝑛
=
𝐷 𝑝
𝜇 𝑝
=
𝑘𝑇
𝑞
=
𝑇
11600
Boltzmann constant
1.38x10-23 J/K
Consider a SC with hole and electron concentrations p and n.
If an Electric Field E is present across its ends then the total current density is given by -
For HOLES
For ELECTRONS
𝐽 𝑝 = 𝑝𝜇 𝑝 𝑞𝐸 − 𝑞𝐷𝑝
𝑑𝑝
𝑑𝑥
𝐽 𝑛 = 𝑛𝜇 𝑛 𝑞𝐸 + 𝑞𝐷𝑛
𝑑𝑛
𝑑𝑥

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PN JUNCTION
 Consider a P type SC that is doped
with N type SC on it’s other side
 As a result of concentration Gradient,
Diffusion current starts to flow
 The majority carriers at the P side
(holes) rush towards the N side
 The majority carriers at the N side
(electrons) rush towards the P side
 Both these carriers recombine at the
junction
 On recombination, there is a region
devoid of charge carriers known as
depletion region

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PN JUNCTION

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PN JUNCTION DIODE
 After diffusion, the ions get exposed and there is an Electric Field setup from the
N to the P side.
 The built in Electric Field helps the minority carriers to cross the junction but does
not allow the majority carriers to cross the junction
 Thus, a barrier potential is setup between the two regions
 The barrier potential of a pn junction cannot cause an external current. If external
connections are made, the contacts negate the barrier potential
 The depletion width is of the order of 5 × 10
− 7 𝑚
 If we connect metal contacts to a PN Junction, we get a Junction diode

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BIASING OF A JUNCTION DIODE
FORWARD BIAS REVERSE BIAS
P side connected to +ve terminal and N
side connected to -ve terminal of the
Battery
P side connected to -ve terminal and N
side connected to +ve terminal of the
Battery

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BIASING OF A JUNCTION DIODE
FORWARD BIAS REVERSE BIAS

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BIASING OF A JUNCTION DIODE
FORWARD BIAS REVERSE BIAS
Ideal Diode behaves as a Short
Circuit with no cut-in voltage or no
barrier when forward biased
Ideal Diode behaves as an Open
Circuit when reverse biased

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BIASING OF A JUNCTION DIODE
FORWARD BIAS REVERSE BIAS
VD ID
VD
ID
Reverse Saturation current
𝐼 𝐷 = 𝐼𝑆(𝑒
𝑉 𝐷
𝜂𝑉𝑇 − 1)

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DIODE CHARACTERISTICS
Current in the forward
direction flows only
when the external
voltage is greater than
the barrier potential

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LEAKAGE CURRENT
 The current that is due to thermally generated electrons and holes is called as leakage
current
 When a diode is reverse biased, the majority carriers cannot cross the junction because of
increased potential but the thermally generated minority carriers can cross the junction
 Leakage current doubles with every 10° rise in Temperature
 It is in micro-amperes
 Less for Si (nanoamps) than Ge (microamps)
𝐼1 = 𝐼0(2
𝑇1
−𝑇0
10 )
 By reducing the voltage appropriately, we can compensate for the increase in Temperature
 A constant current can be maintained if the voltage is decreased by 2.5 mV for each degree
rise in temperature

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DIODE LOAD LINE
VOLTAGE ACROSS THE DIODE
Q
VQ
IQ
𝐼 𝐷 = 𝐼𝑆(𝑒
𝑉 𝐷
𝜂𝑉𝑇 − 1)
R
VDD
𝐼 𝐷 =
−𝑉𝐷
𝑅
+
𝑉 𝐷𝐷
𝑅

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IDEAL DIODE
Forward Bias –
Short Circuit –
Switch ON
Reverse Bias –
Open Circuit –
Switch OFF

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APPLICATIONS OF DIODE
 Rectification
For one half cycle of AC
voltage the diode will be
conducting when the
instantaneous value
across the diode will be
greater than built in
potential. For the other
half cycle, the diode is
reverse biased and is not
conducting.
We can have Full wave rectifiers too that is nothing but 2
half wave rectifiers working turn by turn when their cycle is
conducting
HALF WAVE
RECTIFIER
FULL WAVE
RECTIFIER

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APPLICATIONS OF DIODE
 Clipper Circuits
Clippers are used to
change the waveform
by clipping it. Clippers
are of 2 types –
positive and negative.
We can have a
combination of both
the clippers in 1 circuit
as shown
Double Diode Clipper
Series Negative Clipper

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APPLICATIONS OF DIODE
 Application to
Digital Logic
Circuits
Diodes can be used
to make logic gates
as shown