Electrical Properties of Materials I

1. Electrical Properties of MaterialsI

2. Microprocessor • Important Things in This Chapter: • Electrical conduction in metals • Effects of impurities • Effects of temperature • Energy band model • Semiconducting devices • Fabrication • Modern microelectronic circuitry

3. Metallic Bonding • Atoms in metals are closely packed in crystal structure. • Loosely bounded valence electrons are attracted towards nucleus of other atoms. • Electrons spread out among atoms forming electron clouds. • These free electrons are reason for electric conductivity and thermal conductivity • Since outer electrons are shared by many atoms, metallic bonds are Non-directional Positive Ion Valence electron charge cloud

4. Electric Conduction – Classical Model • Metallic bonds make free movement of valence electrons possible. • Outer valence electrons are completely free to move between positive ion cores. • Positive ion cores vibrate with greater amplitude with increasing temperature. • The motion of electrons are random and restricted in absence of electric field. • In presence of electric field, electrons attain directed drift velocity. 14-2

5. Electric Conduction – Classical Model

6. Ohm’s Law • Ohm’s law states that electric current flow I is directly proportional to the applied voltage V and inversely proportional to resistance of the wire. • Macroscopic Ohm’s law (dependent on the geometric shape of the electrical conductor): i = V/R where i = electric current (A) V = potential difference (V) R = resistance of wire (Ω) 14-3

7. Ohm’s Law • Electric resistivity ρ = RA/l where l = length of the conductor and A = Cross-sectional area of the conductor. • Electric Conductivity σ = 1/ ρ • Microscopic Ohm's law (independent of the shape of the electrical conductor): J = E/ ρ = i/A J= Current density (A/m2) E = electric field (V/m)

8. Example 1:

9. Example 2: • If a copper wire of commercial purity is to conduct 10A of current with a maximum voltage drop of 0.4V/m, what must be its minimum diameter? Given  (pure Cu)= 5.85107(.m)-1.

10. Solution 2:

11. Drift Velocity of Electrons • Electrons accelerate when electric field E is applied and collide with ion cores . • After collision, they accelerate again. • Electron velocity varies in a saw tooth manner. • Drift velocityvd = μE where μ = electron mobility m2/(V.s) • Direction of current flow is apposite to that of electron flow. 14-4

12. Drift Velocity of Electrons • The electron flow in a metal wire subjected to a potential difference dependent on the number of electron per unit volume, the electronic charge –e (-1.6010-19C), and the drift velocity of the electron, vd. • The rate of charge flow per unit area is –nevd. • Since current is considered positive charge flow, current density, J ,is given positive sign. • J=nevd

13. Electrical Resistivity • Electrical resistivity ρtotal = ρT + ρr • ρT = Thermal component : Elastic waves (phonons) generated due to vibration of electron core scatter electrons. • Resistivity increases with temperature. • Alloying increases resistivity. • ρr = Residual component : Due to structural imperfections like dislocations. • ρT = ρ0oC(1+αTT) ρ0oC = Resistivity at 00C αT = Coefficient of resistivity. T = Temperature of the metal Figure 13.7 14-5

14. Electrical Resistivity

15. Electrical Resistivity

16. Example 3:

17. Solution 3:

18. Energy Band Model of Electric Conduction • Valence electrons are delocalized, interact and interpenetrate each other. • Their sharp energy levels are broadened into energy bands. • Example:- Sodium has 1 valence electron (3S1). If there are N sodium atoms, there are N distinct 3S1 energy levels in 3S band. • Sodium is a good conductor since it has half filled outer orbital 14-6

19. Energy Band Model of Electric Conduction • Schematic energy band diagrams for several metallic conductors: • Sodium, 3s1: the 3s band is half filled since there is only one 3s1 electron. • Magnesium, 3s2: the 3s band is filled and overlaps the empty 3p band. • Aluminum, 3s23p1: the 3s band is filled and overlaps the partially filled 3p band.

20. Energy Band Model for Insulators • In insulators, electrons are tightly bound. • Large energy gap, Eg, separates lower filled valence band and upper empty conduction band. • To be available for conduction, the electron should jump the energy gap. 14-7

21. Conduction in Intrinsic Semiconductors • Semiconductors: Conductors between good conductors and insulators. • Intrinsic Semiconductors: Pure semiconductors and conductivity depends on inherent properties. • Example: Silicon and Germanium – each atom contributes 4 valence electrons for covalent bond. • Valence electrons are excited away from their bonding position when they are excited. • Moved electron leaves a hole behind. 14-8

22. Electrical Charge Transport in Pure Silicon • Both electrons and holes are charge carriers. • Hole is attracted to negative terminal, electron to positive terminal. • Valence electron ‘A’ is missing – Hole • Valence electron ‘B’ moves to that spot due to the electric field leaving behind a hole. • Movement of electrons is opposite to electric field. 14-9

23. Quantitative Relationship of Electrical Conduction in Intrinsic Semiconductor • J = nqvn* + pqvp* • Dividing by electric field E = J/σ • vn/E and vp/E are called electron and hole mobilitiesμn, μp, since they measure how fast the electrons and holes drift in an applied electric field. σ = nqμn+ pqμp n = p = ni Therefore σ = niq(μn+ μp) n = number of conduction electrons per unit volume. p = number of conduction holes per unit volume. q = absolute value of electron or hole charge = 1.6 x 10-19C vn, vp = drift velocities of electrons and holes. 14-10

24. Example 4: • What fraction of the conductivity in intrinsic silicon at room temperature is due to (a) electrons and (b) holes? Given μn=0.140, μp=0.038.

25. Solution 4: Let μn = μe, μp = μh

26. Effect of Temperature on Intrinsic Semiconductors • The conduction band is completely empty at 00K. • At higher temperatures, valence electrons are excited to conduction bands. • Conductivities increase with increasing temperature. ni= Concentrations of electrons having energy to enter conduction band. E= energy gap. Eav = average energy across gap. K = boltzmann's constant. T = temperature, K. σ0 = constant depending on the mobility. Since Since Or, 14-11

27. Effect of Temperature on Intrinsic Semiconductors

28. Example 5: Assume Eg=0.67eV, k=8.6210-5 eV/K.

29. Extrinsic Semiconductors • Extrinsic semiconductors have impurity atoms (100-1000 ppm) that have different valance characteristics. • n – type extrinsic semiconductors: Impurities donate electrons for conduction. • Example:- Group V A atoms ( P, As, Sb) added to silicon or Ge. 14-12

30. P-Type Extrinsic Semiconductors • Group III A atoms when added to silicon, a hole is created since one of the bonding electrons is missing. • When electric field is applied, electrons from the neighboring bond move to the hole. • Boron atom gets ionized and hole moves towards negative terminal. • B, Al, provide acceptor level energy and are hence called acceptor atoms. • Doping: Impurity atoms (dopants) are deposited into silicon by diffusion at 11000C. Figure 13.23 14-13

31. Effect of Doping on Carrier Concentration • The mass action law: np = ni2 where ni (constant) is intrinsic concentration of carriers in a semiconductor. • Since the semiconductor must be electrically neutral Na + n = Nd + p where Na and Nd are concentrations of negative donor and positive acceptors. • In a n-type semiconductor, Na = 0 and n>>p hence nn = Nd and pn = ni2/nn=ni2/Nd In a p-type semiconductor, Nd = 0 and p>>n np = ni2/pp = ni2/Na 14-14

32. Carrier Concentration • For Si at 300K, intrinsic carrier concentration, ni=1.5 x 1016 carier/m2 • For extrinsic silicon doped with arsenic nn = 1021 electrons/m3 pn = 2.25 x 1011 holes/m3 • As the concentration of impurities increase , mobility of carriers decrease. 14-15

33. Example 6: Assume ni(Si)=1.501010cm-3

34. Effect of Temperature on Electrical Conductivity • Electrical conductivity increases with temperature as more and more impurity atoms are ionized. • Exhaustion range: temperature at which donor atom becomes completely ionized . • Saturation range: Acceptor atoms become completely ionized. • Beyond these ranges, temperature does not change conductivity substantially. • Further increase in temperature results in intrinsic conduction becoming dominant and is called intrinsic range. 14-16

35. Effect of Temperature on Electrical Conductivity

36. Semiconductor Devices – pn Junction • pn junction if formed by doping a single crystal of silicon first by n-type and then by p type material. • Also produced by diffusion and impurities. • Majority carriers cross over the junction and recombine but the process stops later as electrons repelled by negative ions giving rise to depleted zones. • Under equilibrium conditions, there exists a barrier to majority carrier flow. Figure 13.30b 14-17

37. Reverse and Forward Biased pn Junction • Reverse biased: n-type is connected to the positive terminal and p-type to negative. • Majority carrier electrons and holes move away from junction and current does not flow. • Leakage current flows due to minority carriers. • Forward biased: n-type is connected to negative terminal and p-type to positive. • Majority carriers are repelled to the junction and recombine and the current flows. 14-18

38. Application of pn Junction Diode • Rectifier Diodes: Converts alternating voltage into direct voltage (rectification). • When AC signal is applied to diode, current flows only when p-region is positive and hence half way rectification is achieved. • Signal can be further smoothened by using electronics. Figure 13.34 14-19

39. Breakdown Diodes (Zener Diodes) • Zener diodes have small breakdown currents. • With application of breakdown voltage, in reverse bias, reverse current increases rapidly. • Electrons gain sufficient energy to knock more electrons from covalent bonds. • These are available for conduction in reverse bias. 14-20