Questions and Answers of Engineering Physics

1. What is Zener diode? Discuss Avalanche and Zener breakdown. (CU 2005,2010)

               A Zener diode is a PN junction device that is designed for operation in the reverse breakdown region. The voltage at which breakdown occurs under reverse bias is made to take place very sharply by proper doping.

            There are two kinds of reverse breakdown in a Zener diode.

      (i)Avalanche breakdown: The avalanche breakdown takes place at a sufficiently high reverse voltage. Zener diode with breakdown voltage of about 6V and above operates in the avalanche breakdown. In this breakdown the minority charge carries are accelerated by the bias applied and cross the depletion layer. These minority charge carries get enough kinetic energy to knock bound electrons of the covalent bond and as a result electron-hole pair is produced. These electrons will then collide with other atoms and increases the number of holes and electrons. Thus get an avalanche of charge carriers.

     (ii)Zener breakdown: Zener breakdown take place at breakdown is as follows. The diode is heavily dopped so that the depletion layer is very narrow. As a result a very high electric field exists across the depletion layer. (E=V/d). Near the Zener breakdown voltage the field is very intense enough to pull electrons from the covalent bond directly and create current.

      Uses Of Zener Diodes

       1. Used as a voltage regulator, 2.Used for providing a reference voltage, 3. Used as peak clipper, 4. For protecting meters form exceeds voltage, 5. Used in wave form generators.

2. How Zener diode act as a voltage regulator? (CU 2006)

      The circuit of a simple voltage regulator is shown in fig. The load R_L is connected in parallel with the reverse biased Zener diode. For limiting current a series resistor R is included.

       The manufactures usually supplies the value of breakdown voltage known as Zener voltage V_Z and the test current I_zr which is about 25% of the maximum current capability I_Z (max)of the diode. The input voltage V_in must be greater than V_Z. If I_L is the average load current, the total current through R,

        I=I_Z+I_L

      V_in=V_Z+RI=V_Z+R(I_Z+I_L)

                                    

       Let us examine the effects of change in output voltage and load current  separately. Suppose the input voltage  increases. Since the diode is operated in breakdown region, a slight increase in voltage in  causes slight increase in . The current through Zener diode increases by a large amount. This extra current passes through R and causes increases voltage drop in it. The increase in voltage drop in R is just sufficient to maintain an approximately constant output voltage . Similarly a decrease in  causes decrease in current through R and Zener diode. The change in  equals the change in voltage drops in R. So  is practically unaffected.

            Suppose  is unchanged, but I_L increases. The current through R and the voltage drop across it tend to increase. So tends to decrease. A slight decrease in potential difference across Zener diode causes large decrease in current through it. The decrease in current through Zener diode is just sufficient to keep the current through R practically unaltered. So  is practically unchanged. Similarly a decrease in load current through Zener diode and load are equal and opposite. So the total currents I is unaffected,. Since the voltage drop in R is unchanged the output voltage  does not change with change in load current.

3. Explain the construction and working of,

1.      LED

2.      Tunnel diode

3.      Varacter diode        (CU 2010)

      Light Emitting Diode (Led)

      It is a heavily doped p-n junction in which spontaneous emission takes place under forward bias. When the device is forward biased electrons from the n region and holes from p-region cross the junction and recombines. The electrons are in the conduction band and at higher energy state. The holes in the valence band are at lower sate. When these electrons recombine with holes the excess energy of the electrons is released in the form of heat and light.

      When the forward current is small the intensity of light emitted is small. If we increase the current the intensity of light increases and reaches a maximum value. Further increases in the current results in decreases of intensity of light.

The voltage- current characteristic of a diode is similar to that of ordinary diodes except in the knee voltage. It will be different for different colours.

      The frequency of emitted radiation depends on the band gap energy. Direct band gap semiconductors are used to make LEDs. The characteristics of such materials are the alignment of the bottom of conduction band with the top of valance band. GaAs and InP are the examples. The visible light LEDs must have a band gap between 1.8eV and 2.8eV. By doping we can modify the band gap.

      Different types of materials are used to emit different colours of light

            GaAs LEDs emit infrared radiations, using Gallium Arsenide phosphide-(GaAsP) on a Gallium Arsenide substrate visible red LEDs were produced.

      LED materials & White LEDs 

      The materials used to make different colour LEDs are the following

1.      Gallium phosphide GaP – Green color

2.      Indium gallium aluminum phosphide IGaAlP-red, orange, yellow and green

3.      Silicon carbide-blue

   White LEDs- using indium gallium nitride high intensity blue light can be produced. For making white LED GaNis coated with fluorescent phosphorus which absorbs blue light and re-emit white light.

      Properties

1.      The LEDs radiate very little heat.

2.      Fast on-off switching ability.

3.      Low operational voltage and less power.

4.      They do not contain mercury as in CF lamps.

5.      Small size and long life.

6.      Available in all Colours.

Applications

1.      Due to the lack of heat radiations LEDs are enormously used in stage decorations.

2.      It is  eco-friendly device. The amount of CO₂ produced by LEDs is comparatively smaller than incandescent bulbs.

3.      LEDs are suitable for backlighting in LCD televisions and laptops.

4.      In cameras and mobile phones LEDs are used for flash lamps.

5.      Used for indicator lamps and readout displays on devices. A common type of display used in calculators is seven segment display. Each segment in the display is a LED. By forward biasing the proper combination of segment any decimal digit can be formed. There are two types of connections, common anode and common cathode.

                                             

                                   

     6. used in optical communication system.

      Tunnel Diode

      Tunnel diode also known as Esaki diode was invented by the Japan scientist Esaki in 1958. It is a P-N junction diode in which the P and N regions are heavily doped than the ordinary diodes. (Concentration of impurity atoms 1000 times more). The depletion region is of the order of 10 nm. The Fermi level lies within the conduction band on n side and within the valence band on the p side. The energy levels of electrons within the conduction band on n side align with the levels of holes in the valence band on p side.

      The basic principle used in working is quantum mechanical tunneling.

       In classical mechanics the penetration of the particles through a potential barrier is not possible. But in quantum mechanics considering the wave nature of a practices there is a probability to penetrate through a potential barrier. This is the basic idea of quantum mechanical tunneling.

      First we connect the diode in forward bias. As the voltage is increased the filled electron energy levels in the conduction band on the n side becomes aligned with unfilled hole levels in the valence band on the p side of the junction. The depletion region is very thin junction. Then electron tunnel from n section to p section through the junction barrier producing a current from p to n diode behaves as a conductor.

      If the voltage is increased further the tunnel current increases and reaches a maximum value at a certain voltage. On increasing the voltage further the electrons states becomes more and more misaligned and the tunnel current begins to decreases and reaches a minimum value. This is called the negative resistance region where the Ohm’s law is violated.

      On increasing the voltage beyond this, the tunneling effect vanishes and the diode conducts as a forward biased pn junction.

      When a small reverse bias voltage is applied the position of the filled Levels in the valence band on p side will become more aligned with unfilled energy levels in the conduction band on n side. So the electrons tunnel through the junction barrier from p to n current flows from n to p.

      Symbol of tunnel diode

      The characteristics of tunnel diode are as shown in the diagram. The part OD represents the voltage-current relation under reverse bias. When the forward bias is increased the tunnel current increases and reaches a maximum at A. when the bias is increased beyond Va the current decrease and reaches a minimum value at B. The section AB is the negative resistance region. The diode begin to operate as a normal diode after the point B. The electrons travel by conduction across the junction and no more tunneling takes place.

      In figure 2 the dotted line represents the characteristics of the Zener diode. There is no negative region in Zener characteristics. Beyond the negative region the tunnel diode behaves like an ordinary diode. Tunnel diode conducts in the opposite direction even at small values of reverse bias where as Zener breakdown takes place at a certain reverse bias.

      Use

1.      A tunnel diode biased at the negative resistance region connected in series with the LCR tank circuit to produce sustained oscillation.

2.      Used in local oscillators for UHF Television tuners.

3.      For triggering circuits in oscilloscopes.

4.      Used in microwave amplifiers and pulse generating circuits.

5.      Since it is resistant to radiations it is used in space applications.

      Disadvantages:  Tunnel diode is a low power device, works at low current and low voltage.

      Varacter diode

      It is also called as variable capacitors diode. The capacitance of the space charge region of a pn junction varies with applied bias. This property is utilized in the action of a Varacter. It always

Operates in the reverse bias to ensure the capacitance maximum. Doping is done for maximum capacitance . The Varacter is similar to a parallel plate with the p and n section as parallel plates and the depletion layer as the dielectric. The capacitance of a parallel plate capacitors is

      Working- when the reverse bias voltage is increased the depletion layer widens so that the capacitance is decreased. On decreasing the reverse bias the width of depletion layer decreases and the capacitance of the Varacter increases. Thus we can control the capacitance of the diode by varying the bias voltage.

      Uses

1.      Conventional variable capacitor tuning can be easily replaced by using Varacter.

2.      One of the main advantage of a Varacter is that we can use dc voltages as bias for varying the capacitors. It is useful in simple remote control units.

3.      In a LC resonant circuit we can use Varacter as a capacitor and the frequency of oscillations can be varied by changing the reverse bias. This is the principle of tuning in electronic circuit and hence they are used in communication system.

4. Mention some Application of Semiconductors?

      These solid semiconductors have more advantage than vacuum tubes. They do not require any filament for operation. So they consume only a very small operating power and as a result a small amount of heat energy is produced. They are much smaller in size and easy to handle. They are very cheap and light. But their efficiency is higher. They are widely used in electronic circuits.

Used as p-n junction rectifier.

1.      Forward biasing and reverse biasing cases.

2.      Used as semiconductors transistors.

3.      Used to construct on-off switches.

4.      To amplify currents.

5.      For voltage regulations.

6.      To produce high oscillations in oscillators

7.      As light source in LED

8.      As solar cells.

4. What are Liquid Crystals? ( CU 2005,2011)

      Substances that have the properties between that of a liquid and that of a solid are called liquid crystals. The molecules moves as in a liquid and strongly interact to orient themselves as in solid. Many proteins, cell membranes and soap solutions exhibit this property.

           

      According to the orientation of the molecules liquid crystals are classified in to different types, nematic cell and twisted nematic cell. The most common type is nematic crystal in which the molecule tends to be almost parallel.

      Twisted nematic cell 

      If one of the plate is rotated through 90⁰ about an axis perpendicular to its surface the molecules in the crystal turn and as a result the molecules are aligned in vertical direction on one of the plate and gradually they are rotated layer to layer till they orient in horizontal direction on the other glass plate. The orientation is as show in the figure, When a beam of light polarized in the horizontal direction is passed through the crystal the plane of light will be twisted by 90⁰

5. Explain Construction of nematic cell and twisted nematic cell (CU 2005)

      It consists of a thin layer of liquid crystal placed in between two closely spaced flat glass plates. One surface of each of the glass plate coated with a thin layer of transparent conducting film of Indium Tin Oxide (ITO). Another coating of dielectric materials is also done on the film. The molecules of the crystal in contact with the glass plate have to be oriented in a direction parallel to the plate and parallel to each other. For this before keeping the liquid crystal in between the glass plates, the dielectric surface is rubbed unidirectional with a fine cloth. This will produce microgrooves on the glass plates and the molecules in contact with the surface algn in the direction of rubbing.

6. Explain Liquid Crystal Display?  (CU 2011)

      The twisted nematic crystal is placed between two crossed polarizers.  A mirror is kept near to a polarizer. Unpolarized light is passed through one of the polarizers and it becomes linearly polarized. This light enters in to the twisted nematic cell and the nematic cell rotates the plane of polarized light by 90⁰. Hence the light passes through the second polarizer and is reflected back by the mirror kept near to it. The light retraces back and comes out of the first polarizer. Thus we see a relatively a bright field of view. Now the cell is said to be in the grey state.

      When a voltage is applied across the conducting coatings of cell the molecules in the liquid crystals reorient themselves and its optical activity disappears. At this stage the polarized light passing through the liquid crystal experience no rotation and is incident on the second polarizer. Since the polarizers are in crossed position no light will be emitted from the second polarizer and the field of view is dark. The cell is in the dark state.

      So by applying a voltage to a nematic cell kept in between two crossed polarizers we can control intensity of light at the field of view.

      For displays the upper side of the conducting film is etched in to different characters forming segments. A voltage applied between any character segment and the lower conducting coating will disrupt  the LC molecules and the character on the upper plate will appear as darkened.

      In electronic devices, a liquid crystal display is a special thin flat panel made up of a very large number of pixels. Each pixel is filled with a liquid crystals.

7.  Explain solar cell and its working.

      Solar cell is an LED operating in the reverse method. A solar cell or photovollaic cell produces electric current form solar energy (Sun light). Sun light is absorbed at the p-n interface of a p-n junction. It excites electrons into the conduction band of n-type from the valence band of p-type. Hence sunlight produces electron-hole pairs. The electric field at the junction pulls the electron towards the n-region and holes towards the p-region. As a result a current flows from the p terminal to n terminal.

      The e.m.f of a silicon solar cell is about 6V and the current produced is very small.

      A solar cell of 4cm^2.  Area produces a p.d. of .5 volts and a current of 60 mA. Modern solar selenium cell converts 25% solar energy into electrical energy. Usually solar cells are grouped into

      module or panels like grouping of cells so that any desired voltage can be made available. Storage batteries arranged together with these solar cells store up the excess of energy during day time and it can be extracted at night.

      Here the semiconducting materials must be very thin so that it is transparent to sunlight. Usually this is achieved by depositing a thin layer of p type silicon on a wafer of n type silicon.

      By designing a diode with a very thin and transparent p-region light photons of proper frequency can reach the transition region. Each  photon carrier an energy E=h Joules. If the photon can break the covalent bonds and produce electron- hole pairs. The resulting carriers can produce a photocurrent.

       The minimum photon energy required to produce a current is given as

                                             

            Or the longest wavelength max=

                  the longest wavelength which can produce a photocurrent in silicon is 1.1  and for germanium it is 1.7μm.

             [Solar cells are employed for charging of battery in space equipments]

            Solar cells contain p-n junctions  located very close to semiconductors surface.

      Advantages and uses of solar cells

These solar cells are very simple and miniature in size. They are very cheap, light and convenient to handle. Solar cell is the only source of power in artificial satellites. Solar cells are employed to provide power in artificial satellites. Solar cells are widely used in so many appliances  like watches, calculators etc. they are used as electric power generators and the power thus generated is used in solar street lighting system, solar water pumps, solar driers etc. Using solar panels (solar panel is a group of solar cells) solar energy is used in solar cookers, solar lights and solar stills to produce distilled water. In remote area village can be electrified with the help of solar cells. Solar cells are used for providing electricity to light house situated in sea and of-shore drilling platforms.

Photo voltage system(PV) is used for the operation communication equipment in remote areas like forest, islands, deserts etc. PV system are used for railway signals, signal sights, alarm for fire, food etc. PV systems are used for recording of whether report in metrological stations. They are also used in mobile phones, telephones, calculators, remote radar, watches, toys etc.

8. Explain Bipolar junction Transistor (BJT)

A bipolar junction transistor consists of two p-n junction formed by sandwiching a layer of p-type or n-type semiconductor between two semiconductors of opposite type. The middle layer is called base. The other two semiconductors are called emitter and collector. The thickness is least for base and largest for collector. The emitter is heavily doped with impurity. The base is lightly doped and the collector is moderately doped.

There are two types of transistors, biz. n-p-n and p-n-p transistors. In an n-p-n transistor the base is of p-type semiconductor. The emitter and collector are of n-type. For a p-n-p transistor the base of n-type and emitter and collector are of p-type semiconductors.

The structure and symbols of the two types of transistor are shown. The three terminal for emitter, base and collector are marked as E.B and C respectively. The arrow marks on symbols represents the conventional direction of emitter current in a properly biased transistor.

Even though the current through the external circuit is due to the flow of electrons, the current inside any transistor is due to the flow of both free electrons and holes. So it is called a bipolar device. A device like field transistor (FET) in which a single type of charge carrier take part in conduction is said to be unipolar.

9. Explain how transistor acts as an amplifier?   (CU 2011)

The basic circuit of a transistor amplifier is shown in figure. The base emitter junction is forward biased using the source V_EE. The base collector junction is reverse –biased using V_Cc. R_L is the load resistance.

The signal to be amplifier is applied in series with V_EE. In the case of n-p-n transistor during negative half cycle of signals the potential difference between base and emitter becomes grater than V_EE. So more emitter current flows. Let ∆I_E .T be the increase in emitter current. Since the base current is negligibly small, the change in collector current ∆I_C is approximately Let ∆I_E. The potential difference across R_L changes by an amount R_L Let ∆I_c ≈ R_L∆I_E. During positive half-cycle of signal, the emitter and collector currents become smaller. The potential difference across R_L becomes lesser. If an alternating signals voltage is applied to the emitter, an amplified alternating output voltage is developed across R_L superposed on a d.c voltage. Thus a.c component of output can be separated from d.c using a capacitor. The ratio of the d.c component of output voltage gain A_v of the amplifier. Large voltage gain can be obtained by using a suitable large resistance as load.

10. Define transition temperature?

      Transition Temperature is that temperature at which resistivity of superconducting material to the component of input voltage is suddenly falls to zero and becomes a superconductor or it is that temperature at which a material changes from its is that temperature at which a material changes from its normal conducting state to superconducting state.

11. Explain Meissner effect?

       In 1993 Meissner and Ochenfeld studies the properties of materials like tin, lead etc., in the presence of magnetic field. They measured the magnetic flux density inside and outside the cylindrical specimens kept in the external magnetic field by varying temperature. It is found that all the magnetic lines have been expelled from the interior of the specimen when it is cooled below the transition temperature in a magnetic field. i,e superconducting materials become perfect diamagnets at the transition temperature. This property is known as the Meissner effect. This property of expulsion of magnetic flux density from the interior of superconducting materials during transition from normal state to superconducting state is called Meissner effect.

When a cylindrical specimen is placed in a magnetic field H, magnetic lines are passing through it as in fig (i). B is the Flux density inside the specimen

           Now flux density   B=μ₀(H+M)                                             (1)

        Where μ₀ permeability of free space and M is the intensity of magnetization induced in the specimen. When the specimen is cooled below the transition temperature, all the magnetic lines are cancelled from the specimen.

  Since B=0, μ ₀(H+M)=0                                                      (2)

         i.e H=-M                                                   (3)

Magnetic susceptibility M/H,    Ψ=-1                            (4)

  This is the maximum value of susceptibility for a diamagnets. Hence the superconductor becomes a perfect diamagnets at the transition temperature.

        When the superconductor is cooled in the magnetic field below the transition temperature, persistent current is produced on the surface of the material. When this current is circulating, it produces a magnetic field in a direction opposite to the applied field and cancels the applied fields. Thus the material behaves as a perfect diamagnet. Here superconductivity produces a new type of strong diamagnetism which oppose and repels the external magnetic field. This leads to levitation property.

      When the material is heated from a very low temperature to a temperature above the transition temperature, it loses the diamagnetic properties, magnetic lines of force begin to penetrate through the material and it returns to the normal sate from the superconductor’s state. Hence this process is reversible.

12. Mention the properties of superconductors. (CU 2009)

            1) Effect of magnetic field- Critical field Hc

       A metal exists in superconducting state only if its temperature and magnetic field are below certain critical values. Its super conducting property can be destroyed by increasing its temperature  as well as magnetic field strength.                                                                         

      Application of sufficiently strong magnetic field will destroy the super conducting property of a metal. The minimum strength of a magnetic field required to destroy the superconducting nature of a metal at a particular temperature is called critical field H_c. When the applied field is below Hc the material will be in the super conducting state and if it exceeds H_c, it gets converted into its normal sate. The variation of critical field H_c with temperature is represented by a parabolic curve as in

          It value is zero at Tc, and increases when temperature decreases. This variation is also represented by an equation

  Hc= H₀[1-(T/T c)²]

     Where H₀ IS the maximum critical field at absolute zero, H_c is the maximum critical field at a temperature T, and T_c is the transition temperature. It is also found that only a very small magnetic energy is needed to restore the normal state  compared to heat energy.

            2) Effect of current density – Critical current

               The magnetic field required to destroy the superconducting property of a material can be produced by applying electric current also. When a current is passed through a conductor, it produces a magnetic filed which changes it from superconducting state to normal sate. The minimum current that can be passed through a superconducting material without destroying its supercomputing property is called critical current I_c.

          The critical current I_c is given by                                                           

         I_c=     2π   r H_c

    Where r = radius of the cylindrical superconducting material and H_c is the critical field. Critical current density J_c is the minimum current density in superconducting materials below which the material remains in a superconducting state. If it exceeds this critical value, the material converts into its normal sate. This was discovered by Silsbee and hence it is called Silsbee effect.

         J_c= I_c/A where A is the area

            3) Isotope effect

        It is found the transition temperature varies with the isotopic mass. This variation of transition temperature with isotopic mass was discovered by Maxwell and Reynolds in 1950 and is called isotope effect.

                             T_c      ∝  where M is the mass of isotope

 

      Since ∝=1/2      T _c ∝     

i.e          T_cM^1/2= constant                                        (1)

      This relation suggests that superconductivity is due to electron - phonon interaction. Larger the isotopic mass, smaller the transition temperature. For example, in Hg, transition temperature decreases from 4. 185 to 4.146 when the isotopic mass increases from 199.5 to 203.4 a.m.u. Such results are obtained for lead and tin isotopes. It reveals that T_c  and H_o  are greater for lighter isotopes. Addition of neutrons to atoms and lattice plays an important role in superconductivity.

            4) Thermal properties

      The thermal properties like entropy, thermal conductivity, specific heat etc. of a metal are changing when the temperature is decreased below to transition temperature of superconducting material.

            a) Entropy effect

      Entropy measure the disorder of a system. Entropy decreases when a superconducting materials is cooled below the critical temperature. This decreases in entropy revels that the superconducting state is more ordered than the normal state.

i.e All the thermally excited electrons in the normal state are ordered in the superconducting state. This entropy difference is very small and it suggest that the rearrangement is relatively small when it changes into superconducting state.

      b) Thermal conductivity effect

      Thermal conductivity of a superconductors undergoes a continuous change between normal state and superconducting state. Thermal conductivity is lower in the superconducting state.

      It is found that specific heat of superconductor shows a sudden jump (increases) at the transition temperature. This reveals that there is an energy gap between the ground state and the lowest energy state.

            5) Persistent current

      When a superconducting ring is placed in a magnetic field, a current will be induced in it due to electromagnetic induction. Now when it is cooled in the magnetic field from a temperature above T_c it is found that this induced current persists in the ring for so many days or even years without any change. Such a current retaining in the superconductor is called persistent current.

            6) Effect of stress- mechanical effect

      Transition temperature T_c  and the critical field H_c  can be varied by the application of stress. When stress is applied, there is a small increase in volume and this raises T_c slightly.

            7) Effect of frequency

      When a high frequency a.c up to 10⁷ Hz is applied at a temperature less than T_c, resistance still remains as zero. But when it is further increased to 10¹⁰ Hz, some resistance will be developed in it. Thus there is a variation of superconducting state with the frequency variation.

      8) Effect of impurities

      Addition of impurities will affect the superconducting nature of the materials. It causes a change in T_c and H_c.

13. Explain AC Josehson and DC Josephson effect? (CU 2010,2008)

An insulating material of very small thickness is placed in between 2 pieces of super conducting materials. When a super current is allowed to flow, it passes across the insulator even without any potential difference. The arrangement of sandwich of superconductors & insulator is called Josephson junction weak link.

This flowing of superconductor is due to the tunneling of copper pairs of electrons through the insulator from one side to the other side. There are two types of Josephson Effect.

                                                                    insulator

 

The flowing of super current across a very thin insulator separated by two pieces of super conducting material even without any potential difference is called dc Josephson effect. When the distance between pieces is reduced to 2nm or Lnm; voltmeter suddenly shows zero voltage in indicating that a current is flowing across the insulating gap. This is dc Josephson Effect.

When a dc voltage is applied across the Josephson junction, high frequency electromagnetic radiations are produced from the insulating gap. When a dc voltage is applied alternating current is produced across the gap. This is ac Josephson Effect. It V is the pd across the gap, the energy of the cooper pairs of electrons.

            1) d.c. Josephson effect

      The flowing of super current across a very thin insulator separated by 2 pieces of superconducting materials even without any potential difference is called d.c Josephson effect.

      Josephson effect can be explained with the help of this experiment. A voltameter V is connected across the ends of a super conducting bar as in fig. Voltameter shows a drop in voltage as zero across the specimen. Now the specimen bar is cut into two pieces and separated through a distance of 1 cm. Now no current will flow across the bar and voltmeter equal indicates a voltage to the open circuit voltage of the cell. When the distance between pieces is reduced to 2 nm or 1 nm, voltameter suddenly shows zero pieces is indicating that a current is flowing across the insulating gap. This is d.c Josephson effect. Josephson showed that the d.c I_s flowing across the junction.

                                    I_s=I_c sin θ                    ⇢1

Where I_c is the critical current that the junction can support and θ is the phase difference of wave functions of Cooper pairs of electrons on both sides. I_c is depending on the thickness and width of the insulating gap.

      2) a.c. Josephson effect

      When a d.c voltage is applied across the Josephson junction, high frequency electromagnetic radiations are produced from the insulating gap. i.e when a d.c voltage is applied alternating current(a.c) is produced across the gap. This is a.c Josephson effect.

      If ‘V’ is the p.d across the gap, the energy of the Cooper pairs of electrons =2eV. (Cooper pair is a pair of electrons)

       But the energy of radiation = hv where v is the frequency and h is planck’s constant

                                          hv=2eV

                                          ∴ v=           

       The phase difference   θ=ω t=2π vt

      Josephson current      Is=Ic sin θ  

                                          Is=Ic sin         ⇢2

      This represent a.c

14. What is Flux quantization?

      Consider a supercurrent flowing through a superconducting ring of area A. As a result a magnetic flux ∅=B A is passing through the ring. By Faraday’s law, the rate of change of magnetic flux through the area is equal to the surface integral of the electric field E around the ring.      

       But here the electric field E is zero inside a superconductor. Hence the rate of change of magnetic flux  So magnetic flux is permanently trapped in the ring as in figure.

 In order to keep the phase of  Cooper pairs to be continuous, magnetic flux must be quantized.  By quantum theory magnetic flux must be an integral multiple of  where h is Planck’s constant and e is the charge of electron. (Since a cooper pair has a charge of 2e.)

  Magnetic flux∅=n

 i.e ∅=∅₀ where n is an integer= 1,2,3,4,⋯⋯and

    ∅₀=     

   ∅₀ is called quantum of magnetic flux or flux quantum. i.e total magnetic flux=n times flux   quantum.           

19. Explain SQUID?     (CU 2008)

         Superconducting Quantum Interference Device is a very sensitive instrument for measuring even small changes in magnetic flux. It is working on the principle of Josephson effect. Squid consists of superconducting ring with two side arms P and Q as in fig. X and Y are two very thin insulating junctions (Josephson junctions). Magnetic flux is applied in a direction in a direction perpendicular to it as shown

 Supercurrent flowing through P is branching into two and is passing through the insulating junctions X and Y. i.e Cooper pairs are tunneling through the junctions i.e The super currents emerging from the functions combines together at Q. This supercurrent changes periodically with the change in magnetic flux. The dependence of supercurrent with the magnetic field is similar to the interface pattern of light. Here this is due to the interference of wave functions of cooper pairs. Since the magnetic flux is quantized, current changes in a discontinuous manner. Even a very small change in magnetic field of 10^-21 T can be detected accurately.

Principle of SQUID

      The critical current I_c of the Josephson junction is made less than the critical current of superconducting part of squid. When I_c exceeds, the insulator returns to the normal state and magnetic flux begins to penetrate through it. But when the flux penetrates continuously, the critical current I_c again reduces, it becomes superconductor again eliminating the magnetic flux. Thus magnetic flux gets penetrated and eliminated alternately in a continuous manner and we get the interference pattern.

      Total current before crossing the junction

                                                      I₁=2l₀Sinδ₀                               (1)

Where δ₀ is the phase difference.

After crossing through the junction, total current

         I_T=2 l₀Sinδ₀    cos                                                     (2)

   Where ∅ is the magnetic flux. The current I_T varies with  This current is maximum when  where n=0,1,2,3,⋯⋯integers. It is maximum when

. This variation of supercurrent with magnetic flux is shown graphically.

Applications of squids

(1)   Squids are used as very sensitive magnetometer to measure even a minute change in magnetic field in the order of 10^-21T.

(2)   Used to detect small disturbance in the earth’s magnetic field. When a submarine or ship approaches a land, it produces its own magnetic disturbance with earths field. Hence the squid is used to measure minute changes of magnetic field and is used to detect the presence of ships, submarines, mines etc.

(3)   Heart, brain etc. Will generate very minute magnetic fields in the order of 10^-15 T. Squids have very high importance in the measurement of such weak magnetic pulses and in their pathological analysis.

(4)    Principle of squids is applied in MRI (Magnetic Resonance Imaging) for the investigation and diagnosis of various diseases.

(5)   It is used in neurophysics to investigate the changes in connection with the magnetic field produced by the neurons.

(6)   Used in the study of magnetic monopoles, gravitons etc.

(7)   Used to explore the oil deposits and other precious mineral deposits in different parts of the world.

(8)   To separate the paramagnetic impurities from the ores. Hence this helps in the manufacturing of fine potteries, glazed coatings, paintings etc.

(9)   An electronic counting circuit can be operated using this.

20. What are high temperature superconductors?

      The discovery a new type of superconductor is one of the most important scientific events in our country. Scientists made a lot of research works to produce superconductors with high T_c . in 1977 a high transition temperature 23 K was achieved using metallic compound of niobium and germanium. But in 1986 Bednorz and Muller discovered la- Ba-CuO system of ceramic superconductors with a T_c of 34 K for which they were awarded with Nobel prize. Such superconductors with high critical temperature are called High temperature superconductors. High Temperature Superconductors are ceramic superconductors with a high transition temperature greater than 40K.

      In low temperature superconductors, it is very difficult and expensive to maintain a low temperature for a long period. For example  it is very difficult to maintain the liquid helium temperature (4.2K) for a very long period. Nowadays it is possible to replace the expensive liquid he with cheaper and more efficient coolant liquid nitrogen. It is discovered that the transition temperature can be raised by microwave and laser radiations.

      In ceramic superconductors, the cell contains 1 atom of rare earth metal, 2 barium atoms, 3 copper atoms and 7 oxygen atoms. Since the numbers of atoms of metal are in the ratio 1:2:3, such ceramic superconductors are called 1-2-3 superconductors. A 1-2-3 superconductors is formed as layers of copper and oxygen sandwiched between the layer of other elements. Such 1-2-3 superconductors conducts electric current at its normal state by the hole conductivity of oxygen atoms. Oxygen atom captures electrons from the neighboring metal atoms and fills up its vac ancies. 1-2-3 superconductors is a complicated method and it is working at T_c of 90K.

      Copper oxide superconductors belong to another group of HTSC and are comprising of atoms of 5 elements. A transition temperature more than 120K was achieved and hence they can be used at liquid at liquid nitrogen temperature. It is discovered that lanthanum compounds can exhibit superconductivity at room temperature or even at higher temperature.

      High temperature superconductivity cannot be explained by BCS theory. But the Reasoning Valence Bond state Theory by P.W.Anderson and G. Bhaskaran explained the aspects of this theory.

21. Mention the applications of superconductivity? (CU 2011)

      Superconductivity developed a new method of energy production, energy saving and energy storage system. It has a wide range of applications

1) Superconductors are used to produce a very strong and powerful magnetic field in order of 20T at a low cost. This high magnetic field is used in so many devices.

(a) To bend and guide the charged particles in particle accelerators, cyclotrons etc.

(b) used for controlling and focusing high temperature plasma for the controlled nuclear fusion.       (c)  Used in magnetic levitation- maglev.

      The repulsion between the magnetic field in a solenoid and the magnetic field induced in a nearly superconducting track is used to levitate (raise) maglev coaches few cms above the track. Now such train can flow over the track minimum speed of 500km/h. Such levitation principle is used in the ship –drive system. This magnetic expulsion of superconductors is used for the magnetic propulsion of satellites into the orbit from the earth stations without the help of rocket.
(d) Superconducting magnets are used to produce very efficient ore separating machines.                                                            (e) Used for flux concentration, energy storage and magnetic shielding.

      Magnetic flux can be concentrated in a superconducting cylinder with the help of persistent current. This trapped magnetic field remains constant for a longer period along its bore. This trapped magnetic flux produces and stores up the energy inside the cylinder. If such a high cylinder is cooled in zero field, there is field free region in the bore. This is magnetic shielding.

2) Medical field

(a) MRI: the most important medical application of superconductivity is MRI. When magnetic field produced using the superconducting solenoid magnets is subjected to the body, hydrogen atoms are aligning in the direction of field. The atoms emit their characteristic signals in response to be the electromagnetic pulses. Analyzing these signals diagnosis can be made easier. MRI is free from harmful effects of other radiations like X-rays.

(b) Superconducting magnetic field is used to remove tumour cells from the healthy cells using high gradient magnetic separation method.

(c) A group of squid is used for the diagnosis of epilepsy. This technique is called  MEG (Mageto Ence Phalography). Sensing the electric and magnetic fields produced from the various parts of the brain, the exact epileptic center can be identified using MEG sensors.

(d) Superconducting susceptometer contains a superconducting magnet in a squid magnetometer. Using superconducting susceptometer the iron content in the body can be exactly estimated.

(e) Squids are used to measure minute magnetic fields produced from heart and brain very accurately and used for pathological analysis of their functions.

3) Electric energy and power transmission

      Another important application of superconductors is in the manufacture of electrical motors, generators and other machines using superconducting windings. The efficiency of such machines is higher. Since ferromagnetic iron core is not required, eddy current loss, hysteresis loss etc. are absent. As a result the size, weight and cost have reduced drastically. They are smaller, lighter, more efficient and they provide higher output. Superconducting homopolar machines generate very high electric current at a very low voltage. But such machines must be maintained at a very low temperature.0

      Electric power can be transmitted through superconducting cables without any transmission losses like I²R loss provided enough cooling in maintained throughout. If transformers use superconducting coils for windings, power losses can be eliminated. Portable type of powerful and transformers can be made.

4) Electronics and small devices

(a) Squid: Squid is very small and sensitive device based on Josephson principle. It is used as a magnetometer to measure a even a very feeble change in the magnetic field. Squid is used to explore the oil and mineral deposits from earth, to separate ores, to study the magnetic monopoles and gravitons, to detect the presence of mines and submarines and in the study of neurophysics.

(b) Josephson effect: Frictionless bearings, magnetically controlled superconducting switches called cryotron, superconductors fuses and breakers. Josephson voltage standards, superconducting transformers etc. are very sensitive and more efficient devices. HTSC cables are used for undersea communications.

5) Computers and information processing

      If superconducting wires are used, a large number of components and circuits can be set up within a very smaller area. This reduces size of components and other devices. Superconducting materials are used as efficient storage devices in computers. Supercomputers are built up with superconductors. The Josephson junctions can be operated within a very short time,(pico secs). This will increases the speed of computers.  

22. Explain superconductivity and distinguish between Type 1 and Type 2 superconductors      (CU 2011)                                  

     Superconductivity is an electrical resistance of exactly zero which occurs in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes in 1991. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon. It is also characterized by a phenomenon called the Meissner effect, the ejection of any sufficiently weak magnetic field from the interior of the superconductors as it transitions into the superconducting state.

     Type-I superconductors completely expel external magnetic fields if the strength of the applied field is sufficiently low. However at evaluated magnetic field, when the magnetic field energy becomes comparable with superconducting condensation energy, the superconductivity is destroyed.

 

A Type-II superconductor is a superconductor characteristics by its gradual transition from the superconducting to the normal state within an increasing magnetic field. Typically they super conduct at higher temperature and magnetic fields than   Type-I superconductors. This allows them to conduct higher currents and makes them useful for strong electromagnets

     A shape memory ally (SMA, smart metal, memory metal, memory alloy, muscle wire, smart alloy) is an alloy that “remembers” its original, cold- forged shape, and which return that shapes after being deformed by applying heat.                        

23. Explain the construction and working plane transmission grating. Light of wavelength 656 nm falls normally on a grating of width 2 cm. The first order is formed at 18”from normal. What is the total number of lines on the grating?           (KU MAY 2010,2007)

Plane Transmission Grating

A diffraction grating consists of a very large number of extremely narrow parallel slits separated by equal opaque spaces.

A plane transmission grating is made by ruling fine lines at equal distances on an optically plane glass plate with a diamond point. Gratings used in labs are not the actual ruled surfaces. They are only replicas. They are made as follows. A thin layer of gelatin solution is poured over the surface of a ruled grating and is allowed to harden. When stripped from the grating, the film retains an impression of the ruling of the original grating. These are attached to glass plates to act as grating.

The diffraction pattern is obtained due to light emerging from the small slits, as they satisfy conditions for maxima and minima.

        A plane diffraction grating is a plane glass plate containing a large number of equidistant parallel lines. The space between the lines acts as narrow slits through which light is transmitter XY separates a plane transmission grating placed r to the plane.

From ACK ; sinθ = AK/AC

Path difference ; AK = AC sinθ= (a+b) sinθ            à 1

    (a+b) sin θ = nλ                                           à 2

where n=0,1,2,3,… the two waves interference constructively.

If n=1, it is the first order principal maximum; if n =2, it is second order principal maximum.

If there are N lines/unit length of the grating

N(a+b) = 1 (unit length)

A+b=(1/N)

Substitute (a+b) in equation 2

(1/N) sinθ = nλ

Sinθ =Nnλ

Where θ is the angle at which the n^th order is formed. N is the number of lines, and it has to be determined. is wavelength.

θ=18”

  = 18/(60×60) degrees

  = 0.005

 =656×10^-9m

Sinθ=0.87

      Or, 0.87 =656×10^-9×N

      N=133

24. Explain BCS theory of superconductivity?        (KU MAY 2007)

      Ina superconductivity material a finite fraction of electrons is in real sense condensed into a super fluid (copper pairs). At low temperatures condensation is a acts as a super fluid. At critical temperatures super fluid tends to zero and the system undergoes a second order phase transition from super conductivity it normal state.

25. Explain Zener break down? (CU 2010)

A Zener diode is a PN junction device that is designed for operation in the reverse break down region. The diode is dopped so that the depletion layer is very narrow. As a result a very high electric field exists across the deflection layer. At Zener break down region, the electric field is more intense to pull the electron from the covalent bond directly & create current.

26. Explain how the Fermi level changes with the increasing amount of impurity in n-type and p-type semiconductor? (CU 2009,2010,2011)

Fermi energy is the highest energy of the electron in the valence band of a crystal in its ground state. It is also defined as the energy for which the probability [P(E)]

P(E) = N(E)/M(E) = 1/[e^(E-E_f⁾ +1]

Where N(E) is the density of electrons per unit energy & M(E) is the density of its quantum states per unit energy.

Fermi level is used as a reference level. For a semiconductor crystal when all the electron are paent in the valance band the probability will be maximum ie, [P(E) =1]. When the conduction band is vacant & the proabality of the conduction band will be zero [P(E)=0]. Therefore in between these two bands there will be another state ie, the Fermi level is in middle portion [P(E)= 1/2]

When donor impurities are added to the intrinsic semiconductor electrons are supplied and it becomes N type extrinsic semi conductor. Addition of these electrons creates new energy levels and as a result a new energy level. ED called donor level formed just below the conduction band.

When doner impurity is completely ionized, all the electrons try to occupy this donor level E_D. when we add a donor impurity like phosphorous, arsenic etc to an intrinsic semiconductor the Fermi level rises above the mean level and when we add an acceptor impurity like aluminum, boron etc. the Fermi leak falls below the mean level in forbidden energy gap.

In an extrinsic P-type semiconductor, the Fermi level is nearer to the valence band & in case of an extrinsic n type semiconductor, the Fermi level is nearer to the conduction band.

                         

In these diagrams E_F gives the Fermi level & E_C gives the Fermi level in the same semiconductor in the absence of impurity.

27. Distinguish between n type and p type semiconductor? (CU 2009)

N type semiconductor	P type semiconductor
It is an extrinsic semiconductor formed by doping fifth group elements of atoms.	It is an extrinsic semiconductor formed by doping third group elements of atoms.
Here impurity atoms are added supply additional electrons and are called donors	The impurity atoms are added to create holes and are called creaptors
Electrons are majority carriers & holes are minority carriers	Holes are majority carriers & electrons are majority carriers.
Fermi level is nearer to the conduction band	Fermi level is nearer to the valance band
The electron density is much greater than hole density	Hole density is much greater than electron density