Chapter 2


A diode is a two terminal non linear device.A diode can be of two types namely vacuum diode and semiconductor diode.A vacuum diode is a two terminal non linear device which works on the principle of thermionic emission of electrons.On the other hand,the semiconductor dio de is a solid state device which works on the principle of chemical bonding and crystal theory.

Due to small size,fast response and low cost semiconductor diodes are the device of choice nowdays .Their counterpart vacuum diodes are getting extinct day by d ay.This is because vacuum diodes are slow,bulky and expensive.They require high power to operate and it takes heating time to start and operate.Their life time is relatively small.Also they require frequent replacement.On the other hand Semiconductor diodes have relativelty long lifetime and require very less power as compared to vacuum diode.At present except for few high power applications almost all of the two terminal non linear functions are carried out by Semiconductor diode s.So, in near future,it is certain that the use of vacuum diode will be completely discouraged .

In this chapter our concern is to study semiconductor diodes.Now onwards when we say diode we will mean semiconductor diode.The important analog functions that can be carried out by the diodes are clipping,clamping,rectification,switching etc.Before actually going into diode things we think that it will be appropriate to review some semiconductor terminologies.


Semiconductors are those materials whose electrical conductivity lies in between that of conductors and insulators.Their resistivity lies in the range from 10 -4Ωm to 0.5Ωm.

Following are the characterstics of semiconductors:

i.The resistivity of semiconductors is less than that of conductors and greater than tha t of insulators. ii.They have negative temperature coefficient of resistance .This means that their resistance is inversely proportional to temperature which of course means resistance decrease with increase in temperature and vice versa.

iii.When impurity is added, there is a significant change in the concentration of charge carriers. iv.Semiconductors are highly temperature dependent materials. Even a slight change in temperature can cause appreciable change in carrier concentration. At low temperature their behavior is similar to insulators and at high temperature their behavior is similar to conductors.

v.They have four valance electrons in their atoms. They lie in the group IV of modern periodic table. vi.Out of 1010 semiconductor atoms there is only one fr ee electron.


Energy Bands in Conductors,Semiconductors and Insulators:

We know that the conduction in conductor ,semiconductor and insulator is mainly due to electrons.Electrons are always in motion ,So they possess kinetic energy.And their energy can never have fixed value.This is because they can occupy different level of e nergy in an atom based on energy supplied to the atoms.So,we can describe the state of an electron with a range of energy rather than just a fixed value.

The different range of energy that an electron can occupy with in the atom are known as energy bands.Energy bands are used to describe the energy state of an electron but not it’s

position.Eg.The electrons in the valance shell of an atom have different energy.The range of energy that can be acquired by the electrons in the valance shell forms a valance band.

Similarly,the range of energy occupied by the electrons  taking part in conduction forms a conduction band and the range of energy which an electron cannot occupy forms a forbidden band/gap.

fig: Energy bands in insulator semiconductor and conductor

In case of conductors the valance band and conduction bands are overlapped and there is no forbidden gap .So,electrons are readily available for conduction.

In case of semiconductors the forbidden gap is 1.1eV for silicon,0.67eV for Germanium and 1.41eV for Gallium-Arsenide.Applying small electric field electrons can move from valance band to conduction band.

In case of insulators the forbidden gap is greater than 5 eV .A large electric field is required to move the electrons from the valance band to conduction band which is not feasible.

Bonding in semiconductors:

The bonding in semiconductors occurs by the formation of covalent bonds.Four electrons of o ne semiconductor atom pairs with four electrons from another semiconductor atom.

Hole current:

In a semiconductor,when energy is supplied to the atom the electrons moves from valance band to conduction band leaving a vacancy in the valance band known as hole.This hole physically doesnot have any charge but it has tendency to attract electron.So,it a cts like a positive charge but it is not a positive charge .The process of fusion of hole and electron is known as recombination.

In the figure below the electron from position L moves to conduction band leaving a hole.To occupy the vacancy ,the electron from position M moves to position L leaving behind another vacancy at position M.Again,the electron from position N occupy the vacancy at M leaving a vacant position which in turn attracts the electron f rom position S.This process goes on and on.

Here we see that ,there is a flow of hole in the valance band ,which constitutes hole current.It is similar to the flow of positive charge.In the conduction band the free electron is available for conduction.So, in semiconductors the total current is the sum of hole current and electron current.

∴I = Ie + Ih


I=total current

Ie=electron current Ih=hole current

Types of semiconductors:

a.intrinsic semiconductor:

Pure semiconductors are known as intrinsic semiconductors.Eg Pure Silicon,Germanium etc.

b.extrinsic semiconductor:

Impure semiconductors are known as extrinsic semiconductors.The process of mixing impurity to intrinsic semiconductor is known as doping which results to the formation of the extrinsic semiconductor.Generally for 108 semiconductor atoms 1 impurity atom is added.

There are two types of extrinsic semiconductors viz P-type and N-type. i.P-type semiconductor:

when the intrinsic semiconductor is dopped with the trivalent im purities like gallium,indium etc.the P-type extrinsic semiconductor is formed .In p-type extrinsic semiconductor four electrons from pure semiconductor atom has to pair with three electrons from impurity atom.Thus,three -three electrons from each atoms part take in paring and one electrons gets unpaired . So,there remains a vacancy

which is a hole.Hence,in a p-type materials there are large number of such holes.It is therefore the material is called P-type(or positive type , as holes are positive).

Sometimes due to the breakage of covalent bond in p -type material few thermal electrons are gener ted along with holes.These electrons are responsible for few leakage current and their number is very less than the number of holes.Hence,holes are present in excess and are called majority charge carriers and electrons are present in minimum and ar e called minority charge carriers .

ii.N-type semiconductor:

when the intrinsic semiconductor is doped with the pentavalent impurities l ike Arsenic,Antimony etc the N-type extrinsic semiconductor is formed .In N-type extrinsic semiconductor four electrons from pure semiconductor atom has to  pair with five    electrons from impurity atom.Thus,four -four electrons from each atoms part take in paring and one electrons gets surplus. So,there are large number of such surplus electrons .It is therefore the material is called N -type(or negative type).

Sometimes due to the breakage of covalent bond in N -type material few thermal holes are generated along with electrons.These holes are responsible for few leakage current and their number is very less than the no of electrons Hence,electrons are present in excess and are called majority charge carriers and holes are present in minimum and are called minority charge carriers .

Conductivity of a semiconductor:

From the knowledge of elementary physics ,we can write J=nevd, J=σE and vd=µE


J=current density n=no. of electrons vd=drift velocity

e=electronic charge=1.6*10 -19 C

σ=conductivity µ=mobility E=Electric field

When the electric field is applied to semiconductor holes drift in the direction of external applied electric field and electrons moves in the opposite direction of electric field.Hence ,total current will be in same direction.So,

J=neve+pevh Where,

n=no. of electrons e=electronic charge p=no. of holes

ve=drift velocity of electrons vh=drift velocity of holes


∴ σE=neve+pevh

or, σE=neµeE+peµhE (µe=mobility of electrons and µ h=mobility of holes)

∴ σ=(neµe+peµh)

This is the required expression for the conductivity of semiconductors.


When p-type semiconductor is suitably connected to the n -type semiconductor,the PN junction i s formed and the device is known as PN junction diode.The process of connecting p-type material and n-type material is done by fabrication.A PN junction can’t be formed by just connecting p -type material with n-type material.

When the P and N type materials are brought in contact , the free electrons from the N -type material diffuse into the P region to recombine with holes leaving behind the positive ions near the junction. Similarly, during the recombination of holes and electrons in P -region the negative ions are formed near the junction. These positive ions and negative ions fo rm a carrier depleted layer known as depletion layer. It is called so because the layer is composed of positive and negative ions wher e positive ions are depleted of negative carriers and negative ions are depleted of positive carriers.

After the depletion layer is formed the normal flow of the holes and electrons gets stopped.The depletion layer acts as a barrier .The potential difference across the depletion region is called as barrier potential or built in potential and it is denoted by V o.The expression for Vo is given by:

Due to the barrier potential there exist an electric field which acts as a barrier for flow of majority
charge carriers.

Symbol of PN Junction Diode:


The process of applying the dc voltage to the semiconductor diode(or any semiconductor device) is known as biasing.

Forward Biased PN Junction Diode:

When the positive terminal of the battery is connected to a P -type material and the negative terminal of the battery is connec ted to a N-type material then the diode is said to be forward biased. When the diode is forward biased the depletion layer continuously decrease and disappear. For the sake of simplicity in the figure shown below depletion layer is not drawn.

When the diode is forward biased ,the holes from P-type material gets repelled by the positive terminal of the battery and the electrons from N -type material get repelled by negative terminal of the battery.Thus,large number of holes and electrons recombi ne at the junction thereby permitting current to flow through the diode.

I-V Characterstics of forward Biased PN junction Diode:

Initially When the voltage across diode is zero no current flows through the diode.As the forward voltage increases and until it becomes equal to knee voltage(VK)the diode current remains zero.When the forward voltage (VF) becomes equal to knee voltage,the diode current starts increasing rapidly.

For Si diode,VK=0.7V For Ge diode,VK=0.3V

Reversed Biased PN Junction Diode

When the positive terminal of the battery is connected to N -type material and the negative terminal of the battery is connected to P -type material ,the diode is said to be reversed biased.When the

diode is reversed biased the width of the depletion layer increases.For the sake of simplicity the depletion layer is not shown in the figure below.

When the diode is reversed biased the holes from P-type material are attracted by the negative terminal of the battery and electrons from N -type material are attracted by th e positive terminal of the battery.Thus,the depletion layer is widened.Here diode acts as if it is an open circuit and it d oes conduct.However,few leakage current flows quantum mechanically.This current is known as reverse saturation current and is designated as IS. For each 10°c rise in temperature the reverse saturation current gets doubled.It is important to note that the leakage current is due to the minority charge carriers.

I-V characteristics of a Reversed biased diode:

When the reverse voltage is increased the reverse current I R increases gradually,when the reverse voltage attains certain value V B called Breakdown voltage,the reverse current increases rapidly and the breakdown occurs.Due to this breakdown the junction may be permanently damaged in ordinary(Rectifier)diodes.

Temperature Effects on I-V characterstics of Diode and The Diode equation:

The saturation current Is doubles for every 10°C rise in temperature as mentioned in the earlier section.

Modelling the semiconductor diode:

Modelling: The process of representing the semiconductor diode(or any other semiconductor device) by the basic electric filaments like resistor, inductor, capacitor and sources like voltage source, current source etc without the loss of its functional behavior is known as modeling.

Model: The circuitary representation of the diode(or any other semiconductor device) with the equivalent elements is known as the model of diode(or device model)

In our day to day life we have to frequently deal with two types of signals, DC signals and AC signal. In DC signal we generally require high voltage of the order of volts. So, DC signals are known as Large Signals.

In AC signal we require voltage of order mV so, AC signals are known as small signal.

It should be noted that the objective of modeling the non -linear device is to achieve linearity so that we can apply various circuit theory to obtain the parameters of the device.

DC or Large signal model of the diode:

In DC or large signal model we deal with the application of large signals to the diode circuit.

1. Ideal Diode and Ideal diode model:

An ideal diode is a diode such that ID=0 for VD<0

And ID>0 for VD>0

The above expression suggests us that the resistance of ideal diode is zero.

1. Piecewise linear model:


rD=Forward resistance VD=Diode Voltage drop

In piecewise linear model a diode is replaced by ideal diode with its voltage drop VD and internal resistance r D.So this model is also known as battery plus resistance model.

In this model,the exponential curve is approximated by two pieces of straight lines.So,this model is known as piecewise linear model.

1. Constant Voltage drop model:

In this model a diode is replaced by the constant diode voltage drop.In this model the diode resistance is assumed to be zero.Since the diode is replaced by a constant voltage drop,this model i s called constant voltage drop model.

Small Signal analysis of diode:

In the small signal model we study the applications of small signal or ac signals to the diode
circuit.Generally the signals with the amplitude around 10mV or less are known as small signals.

Fig:Graphical analysis of small signal model.Note that the signal used in the diode circuit is assumed
to have a triangular waveform.The current and Voltage swing occurs across the bias point whose
meaning will be apparent in the topic to come.In figure,vd(t) is the voltage signal and id(t) is the
current swing.Q is the bias point.

Note that here we have used dc voltage even in small signal analysis.This is done to ensure the diode

to be forward biased throughout the operation.
vd=voltage due to ac source
VD=voltage due to DC source
vD=Total voltage across diode
iD=Total current through diode
ID= current due to DC source
Id =current due to ac source
Then,applying the superposition theorem,

This is the required expression for the dynamic resistance or ac resistance of the diode.

Diode Load line:

The point of intersection of the load line and forward characterstics curve of the diode is
known as Q-point or quiescent point or operating point.It is after this point diode starts functioning.

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