Assumptions of classical free electron model

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1 Module 2 Electrical Conductivity in metals & Semiconductor 1) Drift Velocity :- The Velocity attain by an Electron in the Presence of applied electronic filed is Known as drift Velocity. 2) Mean free Path:- The av9 distance travelled by an & b/w two successive collision is known as mean free path. 3) Mean collision Time :- The av9 time taken by an & b/w two successive collision is known as mean collision time 4) Relaxation Time :- it is the time taken by an electron to reduce its av9 velocity times from the point where the field is switched off Assumptions of classical free electron model 1) There exists a large no of free electron inside the metal they are having 3-D Freedom. 2) The free electron situation is equated to gaseous molecules in the container & then theory of gaseous molecules in the container & then theory of gaseous molecule is then theory of gaseous molecule is extended to free electron. 3) The energy of an electron at a given temperature is t= 3 2 KT 4) The force of attraction or repulsion b/w like charge & unlike charge is ignored 5) The field due to positive ionic core is considered to be smaller hence neglected. 6) The electrical conductivity in a metal is a consequence of drift velocity in presence of applied electric field Failures of classical foes electron 1) Specific head :- The molar specific head of a gas at constant volume is cv= 2 2 RT but experimentally it was found that the specific head of a metal by its conduction e was CV=10-4 RT which shows dependence on temperature which is contra vary to the theory. 2) The temperature dependent electrical conductivity of a metal experimentally was found that Expt σ T The theoretical was found that

2 Theort σ T 3) Dependence of electrical conductivity on electron concentration. 4) σ = ne2 T m n- electron concentration. Cu 8.2x10 28 e/m 3 A X10 28 e/m 3 A 1 > CU classical theory σ Cu A 1 experimentally Quantum free electron model 1) The energy of an electron is quantized 2) No two electrons can occupy the same energy is opposite 3) The distribution of electron in each energy level obeys Pauli s exclusion principle 4) The distribution of electron in various energy level follows Fermi-Dirac statistics 5) The attraction or repulsion b/w the electron is ignored Fermi energy levels :- Fermi energy :- Fermi on s :- Fermi factor :- The highest energy level where the last electron accumulated & that energy level is known as Fermi-energy level. The energy possessed by Fermi energy is called Fermi energy. The electrons which are present the Fermi energy level The Fermi factor is the probability of occupation of a given energy state for a material in thermal equilibrium ( ) = e ( f) / KT 1) Probability of occupation for < f

3 f( ) = ( f) / KT e + f( ) = 1 e + = O+ f( ) = means the energy level is certainly < f applies to all the below energy level T=O All the energy level below the Fermi level are occupied 2) Probability of occupation for > f at T=O When T=O & > f f( )= f( ) = 1 e + = f( )= o for > f t T=O all the energy level above termi level are unoccupied 3) Probability of occupation at ordinary temp At ordinary temp through the value of probability remains for 6 < < f & starts decreasing term as the values of become closer to f f( )= f( ) ( f) KT e + ( )= f( ) = + = 2 The Fermi energy is the most probable Density states :- It is the no of available states per unit energy range centered at a given energy 6 in the valence band of a material of unit volume The possible energy valves for free electrons correspond to vacant energy level adjacent to the filled energy levels band let the material be unit volume let the energy band be spread in a energy interval between. Consider an infinite smelly small interment de at an arbitrary energy value e in the band

4 Since d is en infinitesimally small increment in 6 we can assume that g(.) remains constant b/w 6 & + d. then the no of energy levels in the range 6 & 6 + ( 6+d ) is attain by evaluation of g ( ) d G( )d = [ 2 2πm 3/2 ] 1/2 d As per the above eking it is clearage that no of emerge states h 3 in an energy de is energy interval de is proportion to 6. A plot of g (E) Versus e is shown into the shape of the curve is parabola. Terumi Dirac statistics Under thermal equilibrium the free electron acquire energy belying a statistical rule known as Fermi Dirac statistics Fermi Dirac statistic is applicable to the assembly of particles which abbeys Pauli s exclusion? Panicle of must also be identical particles of spin these condition they electrons satisfy these condition they abbey Fermi Dirac statistics With the knowledge of f ( ) one can proceed to study the no density of electron states as function of energy in the permitted range of energy values cause called terms Dirac (statistics) distribution Critical Filed Superconducting material looses its resistivity at temp to and becomes a superconductor but at this stage if is subjected to a magnetic field, it become a normal conductor again then if needs to cool the material to still lower temp for it to recover its super condition property. however it possible to turn a superconductor into a normal a conductor by subjecting it a sufficiently strong magnetic field at a temp T< tc

5 Express s for electrical Conductivity based on quantum free electron theory We have K= 2π λ λ = h p K= 2π h J=ne v P= hk 2π Mv=hk ne h M J= ne h M ee h TE ee h TE V= hk M J= ne2 ETF M V = h K J ε J= σ J= ne 2 TF = σ = ne2 λf m M M Vt ±=e = m a m dv dt = e D (hk) m h (hk) m Dv= e m dt = e m dt = e m dt dk = e h dk K(t)-k(0)= ee h Tf K = e h Tf

6 Conductivity in Intrinsic Semi conduction Drift velocity Vd =μ e 1 The current density due to electrons is given by J= n e μ e 2 y for holes H=n h μ h 3 W.K.T J= σ σ = J ε The conductivity of electron J σ e= ε = n eμ e σ e= = n eμe y total current in semiconductor is due to electrons & holes. I =I e + I h I= I e + I h A A J = J e + J h J=n e μ e +n h μ n J J= (n e μ e + n h μ n ) E = (n eμ e + n h μ n )

7 σ Total= n e μ e + n h μ n σ Total= ni(μ e + n h n e = n h = ni Laws of mass Action We have electrons & holes concentration equation n e = 4 2 h 3 t f t (πme kt) 3/2 g e KT n h= 4 2 h 3 n e n h= 32 h 6 ( πkt) 3 (me mh ) 3/2 e g/kt The above equation shows that the product (πmh kt) 3/2 e t/kt n e n h does not depend on t but remains constant at a given temperature n e n h = a consatant The above equation is called as law of mass action This Law says that for a given semiconductor material their extrinsic / Intrinsic, the product of e carrier concentration remains a constant at a given temperature even if the doping is varied. Super Conductivity Super Conductivity is the phenomenon conserved in some metals & materials the electrical resistivity of pelre mercury drop at about k is the state called super conducting state the material is called super conductor.the temp at which material losses it s resistivity is called critical temp Temperature dependence of resistivity in super conducting material the electrical conductivity of metal varies with temperature the electrical resistance of metal to the flow of current is due to scattering of conduction electrons by lattice vibrations when the temperature increases the amplitude of lattice vibration also increases so resistance also increases.

8 Material below critical temperature changes to super conductor & material above critical temperature behave normal speed Important properties of superconductor 1) Zero Resistivity & the magnetic flux pert rates 2) Persistent current thought the body. the 3) Meissonier effect resistance changes from zero to a value as applicable to a normal 4) Isotonic effect Conductor the critical field value for type I superconductor 5) Critical field are found to be very low. Type I The material which complete messier effect and have well defined critical field these are perfect diamagnetic in superconducting State & posses Ve magnetic moment. The material remain in superconducting when the field is less than the critical fiel.it expels the magnetic lines of force From the body of matter immediately after He then the material transits to normal State & the flux penetrates the material The dependence of magnetic Moment on H for type I superconductor as shown in fig. As soon as the applied Field H exceeds H C the entire material becomes normal by loosing it s diamagnetic property As the magnetic Field increases (-m ) also increases as till the magnetic Field (H) reaches He Beyond Hc material moves to normal state having temp less than critical temp (T<Tc) critical magnetic field is too small,low & sharp that can take the material to normal state suddenly. Application 1) It is used in squid It measures the magnetic field penetrated by single electron. SQUID Superconducting quantum Interference Device

9 Type 2 nd These material have two critical field Hc1 & HC2 For the Field less than HC1 it Expels magnetic field Completely & there is no flux penetration It becomes perfected diamagnetic & material is in superconducting state the field is increased more than Ha Hc1 the material Posses both like normal &Super Conducting State called mixed State later after expanding beyond HC2 it Behaves as a Normal State. From the graph O Hc1 Superconducting State Hc1-Hc2 Mixed State Beyond Hc2 Normal State. Application :- It is used in vehicles running at high Speed

Model Question Paper ENGINEERING PHYSICS (14PHY12/14PHY22) Note: Answer any FIVE full questions, choosing one full question from each module.

Model Question Paper ENGINEERING PHYSICS (14PHY1/14PHY) Time: 3 hrs. Max. Marks: 100 Note: Answer any FIVE full questions, choosing one full question from each module. MODULE 1 1) a. Explain in brief Compton