1. Lecture 1 - Review Kishore Acharya

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

3. 3 Electrical Conduction through a Conductor/Metal

4. 4 Simple transport equation Drude’s Method for conduction in Metals Mq (dv/dt) = q EMq 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  )/Mq m/sec where  is the mean time between collision Vd =  E Where mobility  = (q  ) / Mq m 2 /volt sec

5. 5 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  / 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  Conductivity and Resistivity T L W Vd

6. 6 Modern interpretation Mq must be replaced the effective mass Mq* and  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  depends upon lattice vibration and the concentration of defects and impurities that distorts the shape of the lattice. Thus   1/T and 1/Nimp where T is temperature and Nimp is the concentration of the impurities Effective Mass Concept Mq* = ħ 2 /(  2 E/  k 2 )

7. 7 Variation of carrier density with Temparature

8. 8 Variation of electron mobility with temperature and impurity concentration

9. 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. 10 Conductivity based Material classification Type Conductivity Range Carrier Concentration Band Gap (ev) Conductivity Variation Carrier Type Conductor/ Metal 10 6 mho  10 22 /cc 0Decreases as temperature is increased Electron Semi Conductor 10 -2 to 10 2 mho  10 10 /cc 0.7 to 1.6Increases with temperature. Electron and Holes Insulator  10 -6 mho  10 4 /cc  2.0 NA

11. 11 Properties of Semi Conductor Group IIGroup IIIGroup IVGroup VGroup VI B* CNO Al* Si P* S ZnGa* GeAs* Se Cd In Sn Sb* Te 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. 12 Energy Bands and Interatomic Spacing

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14. 14

15. 15 Derivation of Effective Mass E = p 2 /2Mq* p = momentum, E= Energy E = (ħk) 2 /2M*q since p = ħk where ħ=h/(2  ) or  E/  k = ħ 2 k/M*q or  2 E/  k 2 = ħ 2 /M*q or M*q = ħ 2 /  2 E/  k 2

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17. 17 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  m 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.

18. 18 Si 150A SiGe 400A Strained Si Typically 70% Si and 30% Ge Formation of Strained Si

19. 19 Mobility Enhancement

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21. 21 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  10 14 /cc

22. 22 Intrinsic Semiconductor n i = n = p = 10 10 /cc

23. 23 Impurities used for Semiconductor Doping

24. 24 N type Semiconductor P type Semiconductor Semiconductor Doping

25. 25 Increasing Carrier concentration by Doping np = n i 2 –n- elrctron concentration, p- hole concentration –n i = Intrinsic carrier concentration=10 10 /cc for silicon For N type semi conductor –n = Nd donor concentration [10 14 to 10 18 /cc] – majority carrier –p = n i 2 /Nd – minority carrier For P type semi conductor –p = Na acceptor concentration [10 14 to 10 18 /cc] – majority carrier –n = n i 2 /Na – minority carrier

26. 26 Practice Problem Given Nd = 10 16 /cc determine n and p for a N type semiconductor –n = Nd = 10 16 /cc – majority carrier –p = n i 2 /Nd = (10 10 ) 2 /10 16 = 10 4 /cc – minority carrier Given Na = 10 14 /cc determine n and p for a P type semiconductor –p = Na = 10 14 /cc – majority carrier –p = n i 2 /Nd = (10 10 ) 2 /10 14 = 10 6 /cc – minority carrier Note: As the concentration of majority carrier increases Concentration of minority carrier decreases