Part A 1. What are the source of resistance in metals? The resistance in metals is due to (i) Impurities present in the metals (ii) Temperature of the metal (iii) Number of free electrons 2. Define Fermi function and give its importance? Fermi function F(E) represents the probability of an electron occupying a given energy state. To find out the energy states actually occupied by the free electron at any temperature (T) 3. Mention the demerits of classical free electron theory? (Or) Give the draw backs of Classical Free Electron theory of metals. (i) It is a macroscopic theory (ii) Classical theory states that all free electrons will absorb energy, but Quantum theory states that only few electrons will absorb energy. (iii) This theory cannot explain the Compton, Photo-electric effect, Paramagnetism, ferromagnetnism, etc. (iv) The theoretical and experimental values of specific heat and electronic specific heat is not matched. (v) By classical theory K/T= constant for all temperatures but by Quantum theory K/T constant for all temperatures. (vi) The Lorentz number by classical theory does not have good agreement with the experimental value and is rectified by quantum theory 4. Calculate the Fermi energy of copper at 0°K if the concentration of electron is 8.5×1028m-3. 5. Define Density of energy states? Density of states Z(E)dE is defined as the number of available electron states per unit volume in an energy interval(dE). (Z(E)dE)=(The number of available electron states)/(unit volume) 6. What is Fermi energy level? It is the highest reference energy level of a particle at absolute zero. It is the state at which the probability of electron occupation is 50% at any temperature. 7.Define mobility of electrons? Mobility of an electron is defined as the velocity acquired by the electron per unit electric field (E) applied. μ=v/E 8. State Widemann-Franz law. The ratio between the thermal conductivity and electrical conductivity of a metal is directly proportional to the absolute temperature of the metal. K/ T K/=LT 9. What is Fermi Dirac distribution function? Fermi function F(E) represents the probability of an electron occupying a given energy state. F(E)=1/(1+e^(((E-E_F))⁄(K_B T)) ) 10.Define the terms (a) relaxation time and (b) mobility. Relaxation time(): It is the time taken by the free electron to reach its equilibrium position from its disturbed position, in the presence of applied field. τ=l/v_d Mobility(): Mobility is defined as the drift velocity acquired by the free electron per unit electric field (E) applied to it. μ=v_d/E 11. What is work function? The amount of kinetic energy required at absolute zero temperature to move an electronfrom the outer orbit at absolute zero temperature is called work function 12. Define the terms ‘mean free path’ and ‘mean collision time’ Collision time(c): It is the average time taken by a free electron between two successive collision.τ_c=λ/v Where is the mean free path. Mean free path(): The average distance travelled between two successive collision is called mean free path . λ=(c ) ̅τ_c Where ( c ) ̅ is the root mean square the velocity of the electron 13. Why J = E/ is called microscopic form of Ohm’s law? According to classical free electron theory current density J = E Where is the electrical conductivity Since conductivity =1/ Resistivity() E = J For a conductor of length ‘l’ and area of cross section ‘A’ Resistance =l/A Voltage V = Iρl/A 14. Evaluate the value of Fermi distribution function for an energy kT above the Fermi energy. The Fermi function varies withrespect to the temperature as shown in fig. Here ar 0K all the energy states belowE_(F_o ) are filles and all those above it are empty. Now when the temperature is increased, the electron takes an energy KBT and hence the Fermi function falls to zero. 15. What do you mean by carrier concentration in metals? Let N(E) dE represents the number of field energy states between states between the interval of energy dE. Normally all the energy states will not be filled. The probability of filling of electrons in a given energy state is given by Fermi function F(E). N(E)dE = Z(E)dE.F(E) (7) Substituting equation (6) in equation (7), we get Number of filled energy states per unit volume N(E)dE= π/2 [8m/h^2 ]^(3⁄2) 〖 E〗^(1⁄2) dE.F(E) (8) N(E) is known as carrier distribution function (or) Carrier concentration in metals 17. What is the Fermi energy? It is the maximum energy of the quantum state corresponding to Fermi energy level at absolute zero. It is the state at which the probability of electron occupation is 50% at any temperature. 18.What is mean by a free electron? 19. List out the three main theories developed for metals. Classical free electron theory: It is a macroscopic theory, proposed by Drude and Lorentz in 1900. This theory explains the free electrons in lattice and it obeys the laws of classical mechanics. Quantum free electron theory: It is a microscopic theory, proposed by Summerfield in 1928. This theory is explained with the concept that the electron moves on a constant potential and it obeys the Quantum laws. Brillouin Zone theory (or) Band theory: This theory is proposed by Bloch in 1928. It is explained with the concept that the electron moves in a periodic potential. This theory also explains the mechanism of semi conductivity, based on the bands and hence called band theory. 20. Give the postulates of free electron theory. In the absence of electric field (i)The free electron in the metals moves freely in the boundaries of the metal, similar to the gas molecules moving in a vessel. Fig 1.1 The free electrons move randomly in all directions. The free electron collides with each other and also with the lattice Elastically, without any loss in the energy. In the presence of electric field The free electron moves in the direction opposite to that of the field direction as shown in fig. 1.2 Fig1.2 Since the electrons are assumed to be a perfect gas they obey classical kinetic theory of gases and the electron velocities in the metal obey the Maxwell-Boltzmann statistics. 21. What are the success of classical free electron theory. (i) It verifies Ohms law (ii) It explains the electrical and thermal conductivity of metals (ii) It is used to derive Wiedemenn-Franz law (iv) The optical properties of metals can be explained using this theory Part B 1. State and prove the Wiedemann-Franz Law. 2. Deduce a mathematical expression for electrical conductivity of a conducting material and hence obtain Wiedemann-Franz Law. 3. Drive an expression for electrical conductivity in a material in terms of mobility of electrons. How does the conductivity vary with temperature? 4.(i) On the basis of free electron theory derive an expression for the electrical conductivity. (ii) What are the sources of resistance in metals? 5. What are the main sources of electrical resistance in metals? Discuss the effect of impurity and temperature on the electrical resistivity of metals. 6. Define Fermi energy. Obtain a general expression for the Fermi energy of electrons in solids at zero degree Kelvin. Show that at the same temperature, the average energy of the electron I s (3/5)th the of the Fermi energy. 7.Disscuss qualitatively how band theory of solids leads to the classification of solids into conductors, semiconductor and insulators. 8. (i) Define Fermi energy. (ii) Explain Fermi Dirac distribution for electrons in a metal. 9. Derive an expression for the density of states and based on that calculate the carrier concentration in metals. 10. Derive an expression for the density of energy states and carrier concentration in a solid material (Metal) by using the Fermi distribution function. UNIT 2 Part A 1. State the properties of a semiconductor. 1. The resistivity of semiconductors lies between conducting and insulating materials. (i.e.,) 10-4 to 0.5 ohm-metre. 2. At 0 K they behave as insulators. 3. When the temperature is raised or when impurities are added, their conductivity increases. Ρ α 1/T (This is converse compared to usual conductors for which ρ α T) 4. They have negative temperature co-efficient of resistance. 5. In semiconductor both the electron and holes are charge carriers and will take part in conduction 2. What are elemental semiconductors and compound semiconductors? Elemental semiconductor Semiconductor elements of fourth group, which are doped with pentavalent or trivent impurities, in order to get n-type or p-type semiconductors, are called elemental semiconductor Compound semiconductors Semiconductors formed by combining fifth and third group or sixth and second group elements are called Compound semiconductor 3. Compare elemental and compound semiconductor. (or) What are the differences between indirect band gap semiconductor and direct band gap semiconductor. S.No Elemental semiconductor (or) Indirect band gap semiconductor Compound semiconductor (or) Direct band gap semiconductor 1 They are made of single element. Eg:Ge, Si, etc. They are made of compounds. Eg: GaA, GaP, CdS, MgO etc., 2 They are called as indirect band gap semiconductors They are called as direct band gap semiconductors. 3 Here heat is produced due to recombination Here the photons are emitted during recombination 4 Life time of charge carriers is more due to indirect recombination Life time of charge carriers is less due to direct recombination 5 Current amplification is more Current amplification is less 6 They are used for the manufacture of diodes and transistors., etc They are used for making LED’s Laser diodes, IC’s etc. 4. What is meant by intrinsic semiconductor and extrinsic semiconductor? (or) What are the differences between intrinsic and extrinsic semiconductor. S.No Intrinsic semiconductor Extrinsic semiconductor 1 Semiconductor in a pure form is called intrinsic semiconductor Semiconductor which are doped with impurity is called extrinsic semiconductor 2 Here the charge carriers are produced only due to thermal agitation Here the charge carriers are produced due to impurities and may also be produced due to thermal agitation 3 They have low electrical conductivity They have high electrical conductivity 4 They have low operating temperature They have high operating temperature 5 At 0K, the Fermi level exactly lies between conduction band and valence band. Eg: Si, Ge, etc. At 0K, Fermi level lies closer to conduction band in ‘n’ type semiconductor and lies near valence band in ‘p’ type semiconductor. Eg: Si and Ge doped with Al, In, P, As ect. 5. Give the expression for Fermi energy of an intrinsic semiconductor and extrinsic semiconductors at 0K. Fermi energy level is the energy level which distinguishes the filled and empty states (or) it is the maximum energy level upto which the electrons are filled At 0K (i) The Fermi energy of an intrinsic semiconductor is E_F=(〖(E〗_c+E_v))/2 i.e., the Fermi energy level exactly lies between the lowest energy level of conduction band and highest energy level of valence band. (ii) The Fermi energy of ‘n’-type semiconductor is a E_F=(〖(E〗_c+E_d))/2 i.e., the Fermi energy level lies exactly between minimum energy level of conduction band and donor energy level. (iii) The Fermi energy of a ‘p’-type semiconductor is E_F=(〖(E〗_v+E_a))/2 i.e., the Fermi energy level lies exactly between the acceptor energy level and maximum energy level of valence band. 6. What are the applications of Hall effect? (i) It is used to determine whether the material is p-type or n-type semiconductor. (i.e.,) If RH is negative then the material is n-type. It the RH is positive then the material is p-type. (ii) It is used to find the carrier concentration n_e=-(1/(eR_H )) and n_h=(1/(eR_H )). (iii) It is used to find the mobility of charge carriersμ_(e ),μ_h. (iv) It is used to determine the sign of the current carrying charges. (v) It is used to design magnetic flux meters and multipliers on the bases of Hall voltage. (vi) It is used to find the power flow in an electromagnetic wave. 7. Mention any four advantage of semiconducting materials. (i) It can behave as insulators at 0K and as conductors at high temperature (ii) It possess some properties of both conductors and insulators. (iii) On doping we can produce both n and p-type semiconductors with charge carriers of electrons and holes respectively. (iv) If possess many applications in electrons field such as manufacturing of diodes, transistors, LED’s, ICs etc., 8. What is mean by Hall effect, Hall voltage? And Hall coefficient? Hall effect: When a conductor (metal or 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 the magnetic field. This phenomenon is known as Hall effect . Hall voltage: The generated voltage is called Hall voltage Hall coefficient: Hall field per unit current density per unit magnetic induction is called Hall coefficient 9.Compare n-type and p-type semiconductors. Part B 1. Discuss with necessary theory the variation of Fermi level with temperature in an n-type semiconductor. 2. (i) Explain direct and indirect band gap semiconductors. (ii) Derive an expression for the number density of holes in an intrinsic semiconductor. 3. (i) Explain with a neat sketch the intrinsic and extrinsic semiconducting materials. (ii) Differentiate the elemental and compound semiconductors. 4.(i)Explain with a sketch the variation of Fermi level and carrier concentration with temperature in the case of P and n-type semiconductors for high and low doping levels. (ii) What is Hall effect? Give some of its applications. 5. What is Hall effect? Show that for a p-type semiconductor the Hall Coefficient RH is given by –I/e. Describe an experimental setup to measure the Hall voltage. 6. Derive an expression for the density of holes and electrons in valence band and conduction band in the case of P- type and N-type semiconductors respectively 7. What is Hall Effect? Derive expression for Hall Co-efficient. Describe an experimental setup for the measurement of the same. 8. what is Hall effect? Obtain an expression for the Hall coefficient for a p- type semiconductor. Describe an experiment setup for the measurement of Hall voltage. 9. Derive expressions for carrier concentration and Fermi energy in a n-type semiconductor. Explain the variation of Fermi level with temperature and donar impurity concentration.
Posted on: Fri, 14 Jun 2013 06:34:43 +0000
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