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Lecture 1 - Review

Lecture 1 - Review. Kishore Acharya. Agenda. Transport Equation (Conduction through Metal) Material Classification based upon Conductivity Properties of Semi Conductor. Electrical Conduction through a Conductor/Metal. Simple transport equation Drude’s Method for conduction in Metals

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Lecture 1 - Review

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  1. Lecture 1 - Review Kishore Acharya

  2. Agenda • Transport Equation (Conduction through Metal) • Material Classification based upon Conductivity • Properties of Semi Conductor

  3. Electrical Conduction through a Conductor/Metal

  4. Simple transport equation Drude’s Method for conduction in Metals Mq (dv/dt) = q E Mq is the mass of the charge q, E is the electric field v = (q E t)/Mq + c At the instant of collision t=0 and v =0 Velocity change in between collision v = (q E t)/Mq The average velocity between collision is called drift velocity (Vd) Vd = (q E t)/Mq m/sec where t is the mean time between collision Vd =  EWhere mobility  = (q t) / Mq m2/volt sec

  5. Conductivity and Resistivity Vd W T L Electric current I is the amount of charge crossing area A = WT in a second Total Charge Q = nqAVd contained within the Parallalopiped P will cross the marked area A in 1 sec. Where n is the number of particle with vharge q per unit volume. Therefore, I = nqAVd or J = I/A = nqVd = nq (q t / Mq) E Noting that J =  E from the theory of Electro magnetic field theory it is seen that the conductivity  = nq and the resistivity  = 1/(nq m)

  6. Effective Mass Concept Modern interpretation Mq must be replaced the effective mass Mq* and t is calculated based upon Quantum Mechanics Mq* is based upon the curvature of the energy band and is therefore depends upon the crystal structure of the material. Since Mq* is smaller for Ge, GaAs than Si the drift velocity Vd is higher for Ge and GaAs than Si The collision of the conductive particle is with the lattice and therefore t depends upon lattice vibration and the concentration of defects and impurities that distorts the shape of the lattice. Thus t 1/T and 1/Nimp where T is temperature and Nimp is the concentration of the impurities Mq* = ħ2/(2E/k2)

  7. Variation of carrier density with Temparature

  8. Variation of electron mobility with temperature and impurity concentration

  9. A Note on Device Performance Specification • Since mobility decreases with increased temperature • Since drift velocity decreases as the electric field decreases • Device speed is stipulated at a temperature of 120 C and 4.5 Volts

  10. Type Conductivity Range Carrier Concentration Band Gap (ev) Conductivity Variation Carrier Type Conductor/ Metal 106 mho 1022 /cc 0 Decreases as temperature is increased Electron Semi Conductor 10-2 to 102mho 1010 /cc 0.7 to 1.6 Increases with temperature. Electron and Holes Insulator 10-6 mho 104 /cc  2.0 NA NA Conductivity based Material classification

  11. Group II Group III Group IV Group V Group VI B* C N O Al* Si P* S Zn Ga* Ge As* Se Cd In Sn Sb* Te Properties of Semi Conductor Elemental Semi Conductor: Si, Ge (elements from Group IV) Alloy Semi Conductor: InP, GaAs, ZnS, CdS, CdTe * Elements used for Doping intrinsic semi conductor

  12. Energy Bands and Interatomic Spacing

  13. Derivation of Effective Mass • E = p2/2Mq* p = momentum, E= Energy E = (ħk)2/2M*q since p = ħk where ħ=h/(2) or E/k = ħ2k/M*q or 2E/k2 = ħ2/M*q or M*q = ħ2/ 2E/k2

  14. A note regarding Effective mass Effective mass depends on curvature of the E-k curve a fundamental property of the material based upon atomic spacing and crystal structure. In 0.09 mm Silicon technology the curvature is manipulated by stressing the silicon. The stressed silicon has flatter curvature than standard silicon. The flatter curvature lowers the effective mass in stressed silicon resulting in higher speed device.

  15. Formation of Strained Si Strained Si Si 150A SiGe 400A Typically 70% Si and 30% Ge

  16. Mobility Enhancement

  17. Building Devices • Insulator cannot be used for building devices • Not enough charge carriers • Conductors/ Metals cannot be used for building devices • No internal field for carrier flow control • Semiconductors can be used for building devices • Supports internal field for carrier flow control • Carrier concentration must be increased to  1014/cc

  18. Intrinsic Semiconductor ni = n = p = 1010/cc

  19. Impurities used for Semiconductor Doping

  20. Semiconductor Doping P type Semiconductor N type Semiconductor

  21. Increasing Carrier concentration by Doping • np = ni2 • n- elrctron concentration, p- hole concentration • ni = Intrinsic carrier concentration=1010/cc for silicon • For N type semi conductor • n = Nd donor concentration [1014 to 1018 /cc] – majority carrier • p = ni2 /Nd – minority carrier • For P type semi conductor • p = Na acceptor concentration [1014 to 1018 /cc] – majority carrier • n = ni2 /Na – minority carrier

  22. Practice Problem • Given Nd = 1016/cc determine n and p for a N type semiconductor • n = Nd = 1016/cc – majority carrier • p = ni2 /Nd = (1010)2/1016 = 104/cc – minority carrier • Given Na = 1014/cc determine n and p for a P type semiconductor • p = Na = 1014/cc – majority carrier • p = ni2 /Nd = (1010)2/1014 = 106/cc – minority carrier Note: As the concentration of majority carrier increases Concentration of minority carrier decreases

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