Unit 4-Semeconductor Physics

8/13/2019 Unit 4-Semeconductor Physics

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Unit 4 - Semiconductor Physics

4.1Band Theory of solids (qualitative)Band theory, in solid-state physics, theoretical model describing the states ofelectrons,insolid materials,

that can have values ofenergy only within certain specific ranges. The behavior of anelectron in a solid (and

hence its energy) is related to the behavior of all other particles around it. This is in direct contrast to the

behavior of an electron in free space where it may have any specified energy. The ranges of allowed energies

of electrons in a solid are called allowed bands. Certain ranges of energies between two such allowed bands

are called forbidden bandsi.e., electrons within the solid may not possess these energies. The band theory

accounts for many of theelectrical andthermalproperties of solids and forms the basis of the technology of

solid-state electronics.

The band of energies permitted in a solid is related to the discrete allowed energiesthe energy levelsof

single, isolatedatoms.When the atoms are brought together to form a solid, these discrete energy levels

become perturbed through quantum mechanical effects, and the many electrons in the collection of

individual atoms occupy a band of levels in the solid called thevalence band.Empty states in each single

atom also broaden into a band of levels that is normally empty, called theconduction band.Just as electrons

at one energy level in an individual atom may transfer to another empty energy level, so electrons in the

solid may transfer from one energy level in a given band to another in the same band or in another band,often crossing an intervening gap of forbidden energies. Studies of such changes of energy in solids

interacting with photons of light, energetic electrons, X-rays, and the like confirm the general validity of the

band theory and provide detailed information about allowed and forbidden energies.

A variety of ranges of allowed and forbidden bands is found in pure elements, alloys, and compounds. Three

distinct groups are usually described: metals, insulators, and semiconductors. Inmetals,forbidden bands do

not occur in the energy range of the most energetic (outermost) electrons. Accordingly, metals are good

electrical conductors.Insulators have wide forbidden energy gaps that can be crossed only by an electronhaving an energy of several electron volts. Because electrons cannot move freely in the presence of an

applied voltage, insulators are poor conductors.Semiconductors have relatively narrow forbidden gaps

which can be crossed by an electron having an energy of roughly one electron voltand so are intermediate

conductors.
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4.2 Classification of Solids

There are several categories of classification used to group different kinds of solids. Some focus on the way

the solids are bonded together, others focus on the repeatability of the solid structure. We will try to clarify

these different categorizations with examples so that the student will be able to identify the category (ies)

where any given solid fits.

4.2.1 Classification based on the range of atom repeatability

Therepeatability of a solid refers to the ability to use atom arrangements in one location to predict atom

arrangements in other locations. In a perfectly repeatable structure, there exists a small set of atoms (called

the unit cell), whose positions can be used to predict atom positions in the whole solid structure by means of

repeating the unit cell positions according to the particular symmetry of the crystal itself. In solids that havelong-range repeatability, the atom positions be accurately described over an extended distance, using just the

unit cell structure. In solids that do not have long-range repeatability, the unit cell structure may at best give

us an idea of the kind of bonding involved in the solid but irregularity in the arrangements of the atoms will

quickly frustrate any attempt to predict atom positions any distance away from the "unit cell".

Crystalline Solidshave long-range repeatability. They contain atoms or molecules bonded together in a

regular pattern. A good example of these is quartz crystals (emperical formula: SiO2) where each silicon is

bonded to four oxygens, which in turn are bonded to two silicons in a continuous covalent network

extending in three dimensions. You can find these crystals in your quartz watch. The crystal vibrates at afixed frequency when electric charge is placed across certain directions. Your watch uses the vibrations to

keep time.

Amorphous solids(or glasses) have at best, short-range repeatability. They are made up of atoms or

molecules with little or no regular arrangement. Quartz that has been melted into liquid and cooled

(moderately) rapidly will form glass. Quartz glass is used for applications like windows on lasers, and fine

optics like Zeiss lenses. Many different solids can exist in both crystalline and amorphous forms.

For a particular solid (e.g., quartz), the glass and the crystal will have the same type of bonding, the same

emperical formula and some very similar physical properties. The glass and crystalline variances can alsohave some properties that are quite different. For example, quartz crystals do not transmit light equally in

all directions because of the crystallinity whereas the quartz glass will transmit light equally in all

directions. Quartz glass will not fracture the same way as quartz crystals.
http://www.chem.queensu.ca/people/faculty/mombourquette/firstyrchem/glossary.html#repeatabilityhttp://www.chem.queensu.ca/people/faculty/mombourquette/firstyrchem/glossary.html#repeatability


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Semi-crystallinesolids have medium-range repeatability, not true long-range repeatability but some

repeatability over the short range (i.e., not totally amorphous). Such semi-crystalline materials have

different properties from both glasses and crystals. Liquid crystals, for example, have medium range-

repeatability.

Fig.4.1: Types of solid based on range of atom repeatability

4.2.2 Classifications based on bond type.

Solids that are crystalline, semi-crystalline and amorphous can be made from all different types of atoms that

are bonded in different ways. Thus, another way to classify solids is to look at the type of bonds holding the

solid together. These different types of bond possibilities are listed here.

Molecular solidsconsist of molecules that are held together by week intermolecular forces. A prime

example of this is sulfur. Molecules of sulfur (S8) are held together by intermolecular forces far weaker than

the covalent bonds that keep the atoms within each molecule. This type of solid may not have a high

melting point; none are higher than 400C. Molecular solids may be fairly soft, i.e., they can be easily

distorted or warn away by physical force of some kind because of the relative weakness of the

intermolecular forces that are holding the solid together.

Covalent (network) solidsare made of atoms that are covalently bonded together to form one continuous

network of covalently bonded atoms. One could almost think of this type of solids as macroscopic

molecules (big enough to see). Diamonds are a prime example of such solids. This type of solid tends to

have a high melting point and are normally quite hard. For example, diamond melts at 3600C. Network

solids are not all crystalline. Quartz, mentioned above, is a network solid in crystalline and in amorphous

forms.


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Ionic solidscontain ions of opposite charge which hold together with electrostatic (Columbic)

interactions. A good example of this is sodium chloride (table salt). The crystal structure of NaCl is shown

on the right. The atoms of Na+ alternate with atoms of Cl- such that each positive ion has neighboring

negative ions and vice versa. Ionic solids tend to have a melting point that ranges from quite low to

moderately, depending on the strength of the ionic bond.

Metallic solidsare made up of metal atoms, whose loosely held outer electrons are somewhat free of their

positive cores and form a continuous dissociated sea of negative charge binding the positive cores

together. Metallic bonds are generally non-directional, which means the solid will hold together even if the

material is distorted significantly. Metals can be reshaped by striking (malleable) or drawn through small

openings (ductile) the way copper is formed into wires. Metals can have low melting points and also tend to

be soft. The crystal structure of copper is shown in the model on the right.

Fig.4.2: Types of solidbased on bond type.


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4.2.3 Classification based on the dimensionality of the solid

In Network solids, the atoms are all held together with covalent bonds such that there are no small

identifiable units (molecules or clusters) within the structure. The array of atoms extends

continuously throughout the whole solid. Network solids can form in different dimensionalities.

One dimensional networks(plastic), These tend to form very soft plastic or even waxy/tar-like

solids. One-dimensional solids generally do not form crystals by virtue of the easy entanglement of

the long "molecules", which makes long-range repeatability improbable. Some such molecules are

long enough theoretically to be measurable macroscopically individually by mass or size.

Two dimensional networks(graphite). These have planes of atoms that can easily slide over

each. For example, graphite is used as lubricant.

Three dimensional networks(diamond). These tend to be very strong and hard, and can have a

very high melting point. Ceramics used to line smelters and as a heat shield on spacecraft are three-

dimensional network solids.

Fig.4.3: Types of solid based on the dimensionality.


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4.3 Types of Materials and their Comparison

In electronic devices we mainly use 3 types of materials for manufacturing purposes.

Conductor Insulator SemiconductorConducting materialsare those materials in which electrons of the outermost shell are weakly

bonded with nucleus. Hence as force of attraction between nucleus and the outermost shell electrons

is weak, the outermost electrons become free and roam in the substrate of the material. These are

mostly those materials which have 1 or 2 or 3 electrons in the outer shell. E.g. Al, Mg, Cu.

Insulating materialsare those materials whose outermost electrons are tightly bonded with the

nucleus and hence at room temperature they dont get free. In this type of material, we usually have

more than 4 electrons in the outer most shell.

The bond strength between the nucleus and the outermost shell electrons increases with increase in

number of electrons in the outermost shell. Hence bond strength between nucleus and outermost

electron of atom with 1-outermost electron less than atom with 2-outermost electron and so on.

The order of bond strength between nucleus and outmost electron of an atom with number of

electrons in the outer shell vary as shown:

Semiconductor materials are those which lie in between conductors and insulators. These types of

materials have usually 4 electrons in the outer shell. Hence semiconducting materials are called

tetravalent. E.g. Si, Ge etc.

Although we have such type of materials also which act are semiconductor materials but are not

tetravalent. These materials are made by the combination of trivalent and pentavalent materials.

Some of materials of the above type are GaAs, GaAsP etc.


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4.4Concept of free electrons and HolesFree electrons

The electrons in the inner orbits (i.e. orbits close to the nucleus) of atomic structure of any atom aretightly bound to the nucleus.

The electrons in the orbits which are far away from the nucleus are quite loosely bound to the nucleusbut they are still attached to the parent atom.

The electrons in the last orbit are called valence electrons. Some of these valence electrons which are loosely attached to the nucleus of an atom can be easily

removed from the atom by application of external energy. Such electrons those are not attached to an

atom or ion or molecule but are free to move under the influence of an electric field are called free

electrons. Such free electrons take part in the current conduction through metal or semiconductor. Free

electron is denoted by filled circle () or minus (-) sign.

A holeis a charge carrier like the electron, except that it is oppositely charged. Remember that flow of

charges causes electric current, and electrons flow in the opposite direction of the current (from -ve to

+ve).

When an electron receives enough energy, due to increase in temperature it breaks a weak valence band

and enters a conduction band, thus creating a hole in the valence band.

Holes do not exist in real but is an abstraction (hypothetical idea) depicting the absence of an electron

caused due to its displacement. As another electron tries to occupy the place of the displaced electron it

leaves a new hole behind, thus giving the impression of a positive charge propagating in the opposite

direction (from +ve to -ve). Electrons and holes are created in "pairs".

A free electron exists in the conduction energy band because it has nowhere else to go. The valence

band is full. A hole exists in the valence band because there is not enough electrons to take up the space in

the valence band. As the electrons move in the valence band, holes are generated in their wake. This is hole

current and it is only in the valence band as in Fig4.4.


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Fig 4.4-1:Concept of free electrons and Holes

Fig 4.4-2:Concept of free electrons and Holes

4.5 Energy Band

The range of energies that an electron has in a solid is known as energy band.


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Important energy bands in solids

1. Valence band:The range of energies which the valence electrons have is known as valence band.Valence band has the electrons of highest energy. Thus valence electrons are found in valence band.

2. Conduction Band: The range of energies which the conduction electrons (free electrons) have isknown as the conduction band. Free electrons are found in conduction band.

3. Forbidden energy gap: The separation between the conduction band and the valence band on theenergy band diagram is known as the forbidden energy gap. The width of the forbidden energy gapshows the strength of bonding of the valence electrons with the atom. The greater the energy gap,

more tightly the valence electrons are bound to the nucleus. To push an electron from the valenceband to the conduction band (i.e. to make the valence electron free), external energy equal to theforbidden energy gap must be given otherwise electron will bounce back into the valence band (i.e

the valence electrons cannot jump across the band gap into the conduction band).

Fig.4.5: Energy Band


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Energy Band Diagrams

Fig. 4.6: Energy band diagram for: insulator, semiconductor and conductor.

4.6 Effect of temperature on the material

Insulators:With increase in temperature, the conducting property increases. So we call the semi-

conductor material have negative temperature coefficient i.e. with increase in temperature, resistance

decreases.


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Semiconductors: With increase in temperature, the conductivity of the semi-conductor material

increases. As with increase in temperature, outermost electrons acquire energy and hence by

acquiring energy, the outermost electrons leave the shell of the atom.

Hence with increase in temperature, number of carriers in the semiconductor material increases and

which leads to increase in conductivity of the material. So we call the semi-conductor material have

negative temperature coefficient i.e. with increase in temperature, resistance decreases.

Conductors: The outermost shell of conductors is mostly free at room temperature and hence due to

the fact that conducting materials leave the outermost electrons, the nucleus of the atom of

conducting material is more positive as it is a positive ion.

Cu Cu++ e

Hence taking out more electrons from the penultimate shell of the atom is very difficult and when

the temperature is increased, the energy supplied is not enough to take out more electrons but due to

the energy because of increase in temperature, the nucleus of the atoms start vibrating and hence

obstruct the flow of electrons already in the free space. So with increase in temperature, conductivity

of the conductors decreases and resistance increases. Hence we say conductors have positive

temperature coefficient.


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4.6.1 Effect of temperature on semiconductors

The electrical properties of a semiconductor change with temperature changes.

1. At absolute zeroAt absolute zero temperature (- 273.15 C or 0 K), semiconductor crystal behaves like a perfect

insulator.

In terms of energy band, the valence band is completely filled and the conduction band is completely

empty.

2. Above absolute zeroAs the temperature is increased, some of the valence electrons get energy and jump across the

forbidden energy gap into the conduction band and become free electrons. The empty states in thevalence band which are generated because of the movement of the valence electrons from the valence

band into the conduction band are called holes. Thus the holes can be found only in the valence band.

The free electrons in the conduction band and holes in the valence band take part in current

conduction and conduct a small current when connected to an external voltage source as shown in Fig

4.7 Moreover these free electrons and holes are in equal numbers.

In terms of energy band, the valence band is almost filled (i.e few holes or vacant states are there in

valence band) and the conduction band is almost empty (i.e. few electrons could found in conduction

band) as shown in Fig 4.7.

Fig4.7: stat of free electrons and holes at a temperature above zero


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4.7 Types of Semiconductors

Semiconductors are mainly classified into two categories: Intrinsic and Extrinsic.

4.7.1 Intrinsic Semiconductor

An intrinsic semiconductor material is chemically very pure and possesses poor conductivity. It has equal

numbers of negative carriers (electrons) and positive carriers (holes). A silicon crystal is different from an

insulator because at any temperature above absolute zero temperature, there is a finite probability that an

electron in the lattice will be knocked loose from its position, leaving behind an electron deficiency called a

"hole".

If a voltage is applied, then both the electron and the hole can contribute to a small current flow.

The conductivity of a semiconductor can be modeled in terms of the band theory of solids. The band

model of a semiconductor suggests that at ordinary temperatures there is a finite possibility that electrons

can reach the conduction band and contribute to electrical conduction.

The term intrinsic here distinguishes between the properties of pure "intrinsic" silicon and the dramatically

different properties of doped n-type or p-type semiconductors.

Fig.4.8: atomic structure of an intrinsic semiconductor


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4.7.2 Extrinsic Semiconductor

Whereas an extrinsic semiconductor is an improved intrinsic semiconductor with a small amount of

impurities added by a process, known as doping, which alters the electrical properties of the

semiconductor and improves its conductivity. Introducing impurities into the semiconductor

materials (doping process) can control their conductivity.

Depending on the type of impurity added, extrinsic semiconductors are classified into two types

of semiconductors:

a. The negative charge conductor (n-type) ; andb. The positive charge conductor (p-type).

4.8 Atomic Structure of Semiconductors

The most commonly used semiconductor material is Silicon. It has four valence electrons in its

outer most shell which it shares with its adjacent atoms in forming covalent bonds. The structure of

the bond between two silicon atoms is such that each atom shares one electron with its neighbor

making the bond very stable. As there are very few free electrons available to move from place to

place producing an electrical current, crystals of pure silicon (or germanium) are therefore good

insulators, or at the very least very high value resistors. Silicon atoms are arranged in a definite

symmetrical pattern making them a crystalline solid structure. A crystal of pure silicon (silicon

dioxide or glass) is generally said to be an intrinsic crystal.


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Fig.4.9: Atomic structure of semiconductor.

4.8.1 N-type SemiconductorIn order for our silicon crystal to conduct electricity, we need to introduce an impurity atom such as

Arsenic, Antimony or Phosphorus into the crystalline structure. These atoms have five outer electrons in

their outermost co-valent bond to share with other atoms and are commonly called "Pentavalent" impurities.

This allows four of the five electrons to bond with its neighboring silicon atoms leaving one "free electron"

to move about when an electrical voltage is applied (electron flow). As each impurity atom "donates" one

electron, pentavalent atoms are generally known as "Donors". Antimony(symbol Sb) is frequently used as

a pentavalent additive as it has 51 electrons arranged in 5 shells around the nucleus. The resulting

semiconductor material has an excess of current-carrying electrons, each with a negative charge, and is

therefore referred to as "N-type" material with the electrons called "Majority Carriers" and the resultant

holes "Minority Carriers".


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Fig.4.10: Structure of N-type semiconductor

4.8.2 P-Type SemiconductorIf we go the other way, and introduce a "Trivalent" (3-electron) impurity into the crystal structure, such

as Aluminum, Boron or Indium, only three valence electrons are available in the outermost covalent bond

meaning that the fourth bond cannot be formed. Therefore, a complete connection is not possible, giving the

semiconductor material an abundance of positively charged carriers known as "holes" in the structure of the

crystal. As there is a hole an adjoining free electron is attracted to it and will try to move into the hole to fill

it. However, the electron filling the hole leaves another hole behind it as it moves. This in turn attracts

another electron which in turn creates another hole behind, and so forth giving the appearance that the holes

are moving as a positive charge through the crystal structure (conventional current flow). As each impurity

atom generates a hole, trivalent impurities are generally known as "Acceptors" as they are continually

"accepting" extra electrons. Boron (symbol B) is frequently used as a trivalent additive as it has only 5

electrons arranged in 3 shells around the nucleus. Addition of Boron causes conduction to consist mainly of

positive charge carriers results in a "P-type" material and the positive holes are called "Majority Carriers"

while the free electrons are called "Minority Carriers".


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Fig.4.11: Structure of P-type semiconductor

Summary of the types of extrinsic semiconductor

N-type (e.g. add Antimony)

These are materials which have Pentavalent impurity atoms (Donors) added and conduct by "electron"

movement and are called, N-type Semiconductors.

In these types of materials are:

1. The Donors are positively charged.2. There are a large number of free electrons.3. A small number of holes in relation to the number of free electrons.4. Doping gives:

Positively charged donors. Negatively charged free electrons.

5. Supply of energy gives: Negatively charged free electrons. Positively charged holes.

P-type (e.g. add Boron)

These are materials which have Trivalent impurity atoms (Acceptors) added and conduct by "hole"movement and are called, P-type Semiconductors.


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In these types of materials are:

1. The Acceptors are negatively charged.2. There are a large number of holes.3. A small number of free electrons in relation to the number of holes.4. Doping gives:

Negatively charged acceptors. Positively charged holes.

5. Supply of energy gives: Positively charged holes. Negatively charged free electrons.

and both P and N-types as a whole, are electrically neutral.

4.9 The PN-junction Diode

Now its clear for ushow to make an N-typeSemiconductor material by doping it with Antimony and

also how to make a P-typeSemiconductor material by doping that with Boron. This is all well and good, but

these semiconductor N and P-type materials do very little on their own as they are electrically neutral, but

when we join (or fuse) together these two materials they behave in a very different way producing what is

generally known as a P-N Junction.

When the N and P-type semiconductor materials are first brought together some of the free

electrons move across the junction to fill up the holes in the P-type material producing negative ions, but

because the electrons have moved they leave behind positive ions on the negative N-side and the holes move

across the junction in the opposite direction into the region where there are large numbers of free electrons.

This movement of electrons and holes across the junction is known as diffusion. This process continues until

the number of electrons which have crossed the junction have a large enough electrical charge to repel or

prevent any more carriers from crossing the junction. Eventually a state of equilibrium (electrically neutralsituation) will occur producing a "Potential Barrier" zone around the area of the junction as the donor

atoms repel the holes and the acceptor atoms repel the electrons. Since no free charge carriers can rest in a

position where there is a potential barrier it is therefore "depleted" of any free mobile carriers, and this area

around the junction is now called the Depletion Layer.


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Fig.4.12: The PN-junction

As the N-type material has lost electrons and the P-type has lost holes, the N-type material has become

positive with respect to the P-type. The external voltage required to overcome this barrier potential that now

exists and allow electrons to move freely across the junction is very much dependent upon the type of

semiconductor material used and its actual temperature, and for Silicon this is about 0.6 - 0.7 volts and for

Germanium it 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.

The significance of this built-in potential is that it opposes both the flow of holes and electrons across

the junction and is why it is called the potential barrier. In practice, a PN-junctionis formed within a single

crystal of material rather than just simply joining or fusing together two separate pieces. Electrical contacts

are also fused onto either side of the crystal to enable an electrical connection to be made to an external

circuit.

Then the resulting device that has been made is called a PN-junction Diodeor a Semiconductor Diode.


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4.10 Diode

In electronics, a diodeis a two-terminal device (thermionic diodes may also have one or two

ancillary terminals for a heater).

Diodes have two active electrodes between which the signal of interest may flow, and most are used

for their unidirectional electric current property. The varicap diode is used as an electrically adjustable

capacitor.

The unidirectionality most diodes exhibit is sometimes generically called the rectifyingproperty. The

most common function of a diode is to allow an electric current in one direction (called theforward biased

condition) and to block the current in the opposite direction (the reverse biasedcondition). Thus, the diode

can be thought of as an electronic version of a check valve.

Real diodes do not display such a perfect on-off directionality but have a more complex non-linear

electrical characteristic, which depends on the particular type of diode technology. Diodes also have many

other functions in which they are not designed to operate in this on-off manner.

Early diodes included cats whisker crystals and vacuum tube devices (also called therm ionicvalves). Today the most common diodes are made from semiconductor materials such as silicon orgermanium.

Fig.4.13: Different types of diode.


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4.11 Forward Biased Junction Diode

When a diode is connected in a Forward Bias condition, a negative voltage is applied to the N-type material

and a positive voltage is applied to the P-type material. If this external voltage becomes greater than the

value of the potential barrier, approx. 0.7 volts for silicon and 0.3 volts for germanium, the potential barriers

opposition will be overcome and current will start to flow. This is because the negative voltage pushes or

repels electrons towards the junction giving them the energy to cross over and combine with the holes being

pushed in the opposite direction towards the junction by the positive voltage. This results in a characteristics

curve of zero current flowing up to this voltage point, called the "knee" on the static curves and then a high

current flow through the diode with little increase in the external voltage as shown below.

Forward Characteristics Curve for a Junction Diode

The application of a forward biasing voltage on the junction diode results in the depletion layer becoming

very thin and narrow which represents a low impedance path through the junction thereby allowing high

currents to flow. The point at which this sudden increase in current takes place is represented on the static I-

V characteristics curve above as the "knee" point.


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Forward Biased Junction Diode showing a Reduction in the Depletion Layer

Fig.4.14: Forward Biases

This condition represents the low resistance path through the PN junction allowing very large currents to

flow through the diode with only a small increase in bias voltage. The actual potential difference across the

junction or diode is kept constant by the action of the depletion layer at approximately 0.3v for germanium

and approximately 0.7v for silicon junction diodes. Since the diode can conduct "infinite" current above thisknee point as it effectively becomes a short circuit, therefore resistors are used in series with the diode to

limit its current flow. Exceeding its maximum forward current specification causes the device to dissipate

more power in the form of heat than it was designed for resulting in a very quick failure of the device.

4.12 Reverse Biased Junction Diode

When a diode is connected in a Reverse Bias condition, a positive voltage is applied to the N-type material

and a negative voltage is applied to the P-type material. The positive voltage applied to the N-type material

attracts electrons towards the positive electrode and away from the junction, while the holes in the P-type

end are also attracted away from the junction towards the negative electrode. The net result is that the


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depletion layer grows wider due to a lack of electrons and holes and presents a high impedance path, almost

an insulator. The result is that a high potential barrier is created thus preventing current from flowing

through the semiconductor material.

Reverse Biased Junction Diode showing an Increase in the Depletion Layer

Fig.4.15: Reverse Biases.

This condition represents a high resistance value to the PN junction and practically zero current flows

through the junction diode with an increase in bias voltage. However, a very small leakage current does flow

through the junction which can be measured in microamperes, (A). One final point, if the reverse bias

voltage Vr applied to the diode is increased to a sufficiently high enough value, it will cause the PN junction

to overheat and fail due to the avalanche effect around the junction. This may cause the diode to become

shorted and will result in the flow of maximum circuit current, and this shown as a step downward slope in

the reverse static characteristics curve below.


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Reverse Characteristics Curve for a Junction Diode

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.

4.13 Ideal Diode

When we talk about the ideal diode, the diode is a device which acts as a short circuit when forward biased

and acts as open circuit when reverse biased. Hence the behavior of ideal diode can be shown in Fig 4.16


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Fig.4.16:Ideal Diode behavior

In forward biased, current is zero till the point forward voltage is less than breakdown voltage and

after that diode offers no resistance while in the reverse biased, there is no current flow at all.

4.14 Volt-Ampere (V-I) Characteristics of a p-n junction diode

Volt-Ampere or V-I characteristics of a p-n junction is the curve between voltage applied across p-n junction

and the current flows through it under biased condition. Voltage is taken along the x-axis and diode current

along the y-axis.


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V-I Characteristicsof a Practical Diode

Fig 4.17: V-I Characteristics of a Practical Diode

4.15 Static and Dynamic Resistance

The Current-Voltage relationship of a diode is not constant (not a straight line) as in Fig 4.17 and hence the

resistance cannot be measured. Due to this non-linear nature of the curve, there exists a unique value of

resistance at every point of the curve which is called dynamic resistance (not static of constant resistance).

The dynamic resistance equals the change in voltage divided by the change in current, when the voltage is

changed by a small amount. In other words it is the slope of the graph of voltage against current. The

dynamic resistance is different at different current values.


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The static resistance, , of the diode is just the DC resistance we would calculate from measurementof the current through and voltage across it. This will vary depending on where we are on the I-V

characteristic.

The dynamic resistance, ,of the diode is its small signal AC resistance and also depends on the pointon the characteristic where it is measured. An expression for can be found by differentiating theapproximate diode equation for V 26mV with respect to V.

()

For V

26 mV, I in mA , T = 300K and assuming

.

Note that the diode quantities all depend on temperature.


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Exercises

1. What is an energy band?2. Explain valence band, conduction band and forbidden energy gap with the help of energy band

diagrams.3. Give the differences between conductors, insulators and semiconductors.4. Explain the covalent bonds in semiconductors.5. Explain the hole concept in a semiconductor material with the help of a diagram.6. What are intrinsic and extrinsic semiconductors?7. Explain an n-type semiconductor with the help of a diagram .8. Explain a p-type semiconductor with the help of a diagram9. What are the majority and minority carriers in an n-type semiconductor?10.What are the majority and minority carriers in a p-type semiconductor?11.What is a pn-junction? How is a depletion region formed in a pn-junction?12.Explain a forward biased pn-junction with the help of a diagram.13.Explain a reverse biased pn-junction with the help of a diagram.14.

Draw and explain the V-I characteristics of a pn-junction.

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Unit 4-Semeconductor Physics

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