*UNIT-5SemiconductorsSuperconductivity

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*APPLIED PHYSICS CODE : 07A1BS05 I B.TECH CSE, IT, ECE & EEE UNIT-5 : CHAPTER:1 NO. OF SLIDES :20

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*UNIT INDEX

S.No.ModuleLectureNo. PPT Slide No.1Introduction L1-24-82Extrinsic semiconductorsL39-163.EINSTEIN EQUATIONL4-517-20

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*Lecture-1Solids are classified as metals, semiconductors and insulators.Solids with either overlapping valence band and conduction band or partially filled valence bands are metals.Solids with finite forbidden gap in the range 1-3ev are semi conductors.Insulators have much larger band gap.

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*Germanium and silicon are important semiconductors which are widely used in the manufacturing of diodes and transistors.Germanium and silicon are tetravalent atoms i.e they have four valence electrons. Since all the four valence electrons are covalently bound to the four neighboring atoms the crystal acts as a perfect insulator at 0k.

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*Germanium and silicon are pure semiconductors with no impurities. At room temperature the thermal enrgy is sufficient to break covalent bonds. When a covalent bond is broken a free electron-hole pair is generated.Conductivity increases with temperature as more and more electrons cross over the small energy gap.

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*Lecture-2In an intrinsic semiconductor, the Fermi energy level is at the middle of valence and conduction bands.If Ev and Ec are the energy levels respectively at the top of the valance band and bottom of conduction band, the enerrgygap Eg is given by Eg =Ec-EvAnd EF=(Ec+Ev)/2

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*The density of electrons is given by

n= 2(2me*kT/h2)3/2 exp[ (EF-Ec)/kT]The density of holes is given by

p = 2(2mh*kT/h2)3/2 exp[ (Ev-EF)/kT]

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*Extrinsic semiconductorsA semiconducting material in which the charge carriers originate from impurity atoms added to the material is called impurity semiconductor or extrinsic semiconductor.The addition of impurity increases the carrier concentration and hence the conductivity of the conductor.

Lecture-3

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*N-type semiconductorThere are two types of impurities possible namely pentavalent and trivalent.If a pentavalent atom is doped to the tetravalent host crystal, four of the five valence electrons of the impurity atom form covalent bonds with four neighboring host atoms and one electron is left unpaired.

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*Antimony, phosphorous, arsenic etc., are examples of pentavalent elements. When they are added to Si or Ge as impurities, they are called donors as they donate free electrons.The semiconductor prepared in this way will have more electrons than holes.Since the excess free charge is negative, these are named as N-type semiconductors.

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*At 0k

EF =(Ed+Ec)/2 i.e. at 0k Fermi level lies exactly at the middle of the donor level Ed and the bottom of the conduction band Ec.The density of electrons in the conduction band is given by

n = 2(2me*kT/h2)3/4 exp[ (Ed-Ec)/kT]

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*P-type semiconductorIf a trivalent atom is doped into the trivalent host crystal, its three valence electrons fill only three of the four covalent bonds of the host atoms and one vacancy exists in the fourth bond.Thus in this case one extra hole per doped atoms is formed.The examples of trivalent atoms are boron, gallium, indium etc.

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*When they are added to Si or Ge as impurities, they are called acceptors as they readily accept electrons due to the presence of the hole.Since the holes behave like positive charges, the acceptors are called P-type impurities and these impure semiconductors are called P-type semiconductors.

Lecture-3

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At 0k EF =(Ev+Ea)/2 i.e. Fermi level lies exactly at the middle of the acceptor level and the top of the valence band.Density of holes in valence band is given by

p = 2(2mh*kT/h2)3/4 exp[ (Ev-Ea)/kT]

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* For a semiconducting material the electrical conductivity is given by

= (nee + peh)Since n=p=ni = (e + h) 2e (2kT/h2)3/2 (me*mh*)3/4 exp(-Eg/2kT)

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*EINSTEIN EQUATIONThe relation between diffusion coefficient and mobility of a charge carrier is termed Einstein equation. Dn = ekT/e (For electrons)Dp = fkT/e (For holes)

Lecture-4

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* HALL EFFECTWhen a piece of semiconductor carrying a current is placed in a transverse magnetic field, an electric field is produced inside the conductor in a direction normal to both the current and magnetic field. This phenomenon is known as the Hall effect and the generated voltage is known as Hall voltage.

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*Lecture-5The Hall coefficient

RH = -1/ne (for n-type semiconductors) = 1/pe (for p-type semiconductors)

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*Mean life time is the time taken for the injected concentration to fall to 1/e of its initial value.Minority carrier life time can be defined as the time taken for the excess charge carriers to reduce to 1/e times its initial value, once the source generating these excess charge carriers is cut off.

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**UNIT INDEX

S.No.ModuleLectureNo. PPT Slide No.1properties of superconductors. L7-83-112Types of superconductors L9-1012-283.DC & AC Josephson effectL11-1229-334.ApplicationsL1334-37

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**APPLIED PHYSICS CODE : 07A1BS05 I B.TECH CSE, IT, ECE & EEE UNIT-5: CHAPTER-2 NO. OF SLIDES :37

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**SUPERCONDUCTIVITY.Superconductivity is a phenomenon occurring in certain materials at extremely low temperatures, characterized by almost zero electrical resistance and the exclusion of the interior magnetic field (the Meissner effect).

Lecture-7

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Superconductivity occurs in a wide variety of materials, including simple elements like tin and aluminium, various metallic alloys and some heavily-doped semiconductors. Superconductivity does not occur in noble metals like gold and silver, nor in most ferromagnetic metals.

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TcO ResistivityTEMP(K)Impure PureResistance of superconducter suddenly drops to zero

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**Critical temperatureThe temperature at which the transition from normal state to superconducting state takes place on cooling in the absence of magnetic field is called the critical temperature or the transition temperature

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**A magnet levitating above a high-temperature superconductor, cooled with liquid nitrogen. Persistent electric current flows on the surface of the superconductor, acting to exclude the magnetic field of the magnet (the Meissner effect). This current effectively forms an electromagnet that repels the magnet.

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**Lecture-8 Persistent current

The electrical current in a superconducter,in superconducting state remains for a long time .This current remains for very long period without attenuation.The time taken by the super current to reduce 1/e times of its initial value is more than

1,00,000 years. This current is called called persistent current.

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**Effect of magnetic field.By applying magnetic field of sufficient strength, superconductivity of material can be destroyed.The minimum magnetic field strength required to destroy superconductivity of substance,below Tc is called critical magnetic field (Hc) at that temperature.Hc = Ho [1-(T/Tc)2].

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**Meissner effect.

T > Tc

T

**Meissner Effect

High Tc Superconductor and High Energy Permanent Magnet

Magnets in repulsive mode for levitationLevitation Experiments

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**Types of Superconductors.Depending on the way of transition from superconducting state to normal state by the application of magnetic field, superconductors are classified into Type-I superconductors and Type-II superconductors.

Lecture-1Lecture-9

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**TYPE-I SUPERCONDUCTORS

Superconductors exhibiting complete Meissner effect (perfect diamagnetism) are called Type-I Superconductors. They are also known as soft Superconductors.

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**Transition between normal and superconducting states is sharp and well defined.There is only one value of critical magnetic field Hc.

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**Critical temperatures are low. Hence these are not commercially useful but are useful to understand the exciting phenomenon of superconductivity.Type-I Superconductors are mostly of pure specimens.Examples: Pure specimens of Al, Zn, Hg and Sn.

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SUPER CONDUCTING STATE NORMAL STATE.HcM OTYPE-I SUPERCONDUCTERSRELATION BETWEEN MAGNETIZATION AND APPLIED MAGNETIC FIELD FOR TYPE-I SUPER CONDUCTERS.

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**TYPE-II SUPERCONDUCTERSThey are developed from alloys, compounds, ceramics, transition metals etc.For any Type2 material, two critical values of applied magnetic field Hc1 and Hc2 can be identified. In between, there is a thermodynamic critical magnetic field Hc corresponding to that of type1 materials.

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**The material behaves as a perfect superconductor in the range 0

SUPERCONDUCTIONG STATE.MIXED STATE (OR) VORTEX STATENORMALSTATE.Hc1Hc2OMHTYPE-II SUPERCONDUCTERS.Variation of Magnetization with applied magnetic field for Type II superconducters.

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**Super electronsAccording to London brothers, a superconductor is composed of two distinct type of electrons, i.e., normal electrons and super electrons. super electrons experience no scattering.

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**Penetration depthAccording to London equations, the magnetic flux does not drop to zero suddenly at the surface of Type-I superconductors, but decreases exponentially. The depth from the surface at which the magnetic flux density falls to 1/e of its initial value at the surface is called penetration depth.

Lecture-10

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**BCS theoryAccording to BCS theory, superelectrons are responsible for the superconductivity. They exist as Cooper pairs. They form a bound single system. Their motions are correlated.

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MetalMetalInsulaterVIQuantum TunnelingLecture-1

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MetalSuper conducterInsulaterVIQuantum Tunneling

Vc

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EfEfInsulaterEE1METALSuper ConducterAvailable States.

QUANTUM TUNNELINGLecture-1

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**Cooper Pairs

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**Flux quantizationThe magnetic flux enclosed by a ring is quantized. This concept is known as flux quantization.

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**Josephson effectWhen a thin insulating layer is sandwiched between a metal and a superconductor or two superconductors, electrons can tunnel through the junction. Their wave functions on both sides are highly correlated. This is known as Josephson effect.

Lecture-11

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**d.c. Josephson effectA d.c. current flows across the junction of two superconductors separated by a thin insulating layer in the absence of any external electric or magnetic field.

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**a.c.Josephson effectWhen d.c. voltage applied across the junction of the two superconductors separated by a thin insulating layer then microwaves are emitted.

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**Applications of Josephson effectJosephson effect is used to generate microwaves with frequency W = 2eVo/A.C. Josephson effect is used to define standard volt

Lecture-12

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**Applications of Josephson effectA.C. Josephson effect is used to measure very low temperatures based on the variation of frequency of the emitted radiation with temperatureA Josephson junction is used for switching of signals from one circuit to another. The switching time is of the order of 1ps and hence very useful in high speed computers.

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**Applications of Superconductors

1.It is a basis of new generation of energy saving power system. Superconducting generators are smaller in size and less in weight compare with conventional generators. These generators consume very low energy, hence more energy will be saved.2.All electric power companies are looking forward to the superconducting transmission system that would save most of the energy now being lastLecture-13

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**from conventional power lines in the form of useless radiation and heat.

.3.In japan, Superconducting magnets have been used to levitate an experimental train above its track and can drive it at a great speed of 500 Km/h with minimum expenditure of energy. A similar magnetic propulsion system may be used to launch satellites into orbits directly from the earth without the use of rockets.

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**4.High efficiency ore-separating machines are built using Super-conducting magnets, which are also used to separate tumour cells from healthy cell by High Gradient Magnetic separation method.

5.Superconducting materials can be used as a memory or storage device in computers, since the current in it can flow without any change in its value with time.

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**6.Using Superconducting elements one can build up an extremely fast and large-scale computer in a compact size. The power consumed by this computer will be less than 0.5 watt. 7. The Josephon devices are used to produce microwaves, which are made up of superconductors.

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