Electrical properties

Material Science 03

1. 1 ISSUES TO ADDRESS... • How are electrical conductance and resistance characterized ? • What are the physical phenomena that distinguish conductors, semiconductors, and insulators? • For metals, how is conductivity affected by imperfections, temperature, and deformation? • For semiconductors, how is conductivity affected by impurities (doping) and temperature? Electrical Properties of Materials • Dielectric Materials and their Application?

2. 2 • Scanning electron micrographs of an IC: Fig. (d) from Fig. 12.27(a), Callister & Rethwisch 3e. (Fig. 12.27 is courtesy Nick Gonzales, National Semiconductor Corp., West Jordan, UT.) • A dot map showing location of Si (a semiconductor): -- Si shows up as light regions. (b) View of an Integrated Circuit 0.5 mm (a) (d) 45 m m Al Si (doped) (d) • A dot map showing location of Al (a conductor): -- Al shows up as light regions. (c) Figs. (a), (b), (c) from Fig. 18.27, Callister & Rethwisch 8e.

3. 3 Electrical Conduction • Ohm's Law: V = I R voltage drop (volts = J/C) C = Coulomb resistance (Ohms) current (amps = C/s) • Conductivity, s • Resistivity, r : -- a material property that is independent of sample size and geometry surface area of current flow current flow path length J = σ ξ where ξ =  

4. 4 Electrical Properties Which will have the greater resistance? Analogous to flow of water in a pipe Resistance depends on sample geometry and size. D 2 D 2

5. 5 Definitions Further definitions J =   <= another way to state Ohm’s law J  current density   electric field potential = V /  Electron flux conductivity voltage gradient J =  ( V /  )

6. 6 • Room temperature values (Ohm-m) -1 = (  - m) -1 Selected values from Tables 18.1, 18.3, and 18.4, Callister & Rethwisch 8e. Conductivity: Comparison Silver 6.8 x 10 7 Copper 6.0 x 10 7 Iron 1.0 x 10 7 METALS Conductors Silicon 4 x 10 -4 Germanium 2 x 10 GaAs 10 -6 SEMICONDUCTORS Semiconductors Polystyrene <10 -14 Polyethylene 10 -15 -10 -17 Soda-lime glass 10 Concrete 10 -9 Aluminum oxide <10 -13 CERAMICS POLYMERS Insulators -10 -10 -11

7. 7 What should be the minimum diameter ( D ) of Cu wire so that V < 1.5 V? Example: Conductivity Problem Cu wire I = 2.5 A - + V Solve to get D > 1.87 mm < 1.5 V 2.5 A 6.07 x 10 7 (Ohm-m) -1 100 m

8. Electrical Resistivity Vs. Temperature Conductors, Semiconductors, Insulators Superconductors. 8

9. 9 Electrical Conductivity Vs. Temperature

10. 10 Electron Energy Band Structures

11. 11 Band Structure Representation Adapted from Fig. 18.3, Callister & Rethwisch 8e. a). The conventional representation of the electron energy band structure for a solid material at the equilibrium interatomic separation . b). Electron energy versus interatomic separation for an aggregate of atoms, illustrating how the energy band structure at the equilibrium separation in (a) is generated .

12. 12 Conduction & Electron Transport • Metals ( Conductors ): -- for metals empty energy states are adjacent to filled states at 0 K. -- two types of band structures for metals -- thermal energy excites electrons into empty higher energy states. - partially filled band such as Cu. - empty band that overlaps filled band such as Mg. filled band Energy partly filled band empty band GAP filled states Partially filled band Energy filled band filled band empty band filled states Overlapping bands E F E F is the energy of the highest filled state at 0 K .

13. 13 Energy Band Structures: Insulators & Semiconductors • Insulators: -- wide band gap (> 4 eV) -- few electrons excited across band gap Energy filled band filled valence band filled states GAP empty band conduction • Semiconductors: -- narrow band gap (< 4 eV) -- more electrons excited across band gap Energy filled band filled valence band filled states GAP ? empty band conduction

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15. Electrical Conductivity of Metals Room Temperature Electrical Conductivities for Nine Common Metals and Alloys 15

16. 16 Metals: Influence of Temperature and Impurities on Resistivity • Presence of imperfections increases resistivity -- grain boundaries -- dislocations -- impurity atoms -- vacancies These act to scatter electrons so that they take a less direct path. • Resistivity increases with:  = deformed Cu + 1.12 at%Ni T (ºC) -200 -100 1 2 3 4 5 6 Resistivity, r (10 -8 Ohm-m) Cu + 1.12 at%Ni “Pure” Cu  d -- % CW +  deformation  i -- wt% impurity +  impurity  t -- temperature  thermal Cu + 3.32 at%Ni

17. 17 Estimating Conductivity Adapted from Fig. 7.16(b), Callister & Rethwisch 8e. • Question: -- Estimate the electrical conductivity  of a Cu-Ni alloy that has a yield strength of 125 MPa . Yield strength (MPa) wt% Ni, (Concentration C ) 10 20 30 40 50 60 80 100 120 140 160 180 21 wt% Ni Adapted from Fig. 18.9, Callister & Rethwisch 8e. wt% Ni, (Concentration C ) Resistivity, r (10 -8 Ohm-m) 10 20 30 40 50 10 20 30 40 50 125 C Ni = 21 wt% Ni From step 1: 30

18. Charge Carriers in Insulators and Semiconductors Two types of electronic charge carriers: Free Electron – negative charge – in conduction band Hole – positive charge – vacant electron state in the valence band Adapted from Fig. 18.6(b), Callister & Rethwisch 8e. Move at different speeds - drift velocities, a few mm/s, (Classically), Move at - Fermi velocities ~ 10 6 m/s. ( Quantum Mechanically), These Charge Carriers;

19. 19 Intrinsic Semiconductors Pure material semiconductors: e.g., silicon & germanium Group IVA materials Compound semiconductors III-V compounds Example: GaAs & InSb II-VI compounds Example: CdS & ZnTe The wider the electronegativity difference between the elements the wider the energy gap.

20. 20 Intrinsic Semiconduction in Terms of Electron and Hole Migration Adapted from Fig. 18.11, Callister & Rethwisch 8e. electric field electric field electric field • Electrical Conductivity can be given by: # electrons/m 3 electron mobility # holes/m 3 hole mobility • Concept of electrons and holes: + - electron hole pair creation + - no applied applied valence electron Si atom applied electron hole pair migration [The electron mobility characterizes how quickly an electron can move through a metal or semiconductor, when pulled by an electric field].

21. 21 Number of Charge Carriers Intrinsic Conductivity For GaAs n i = 4.8 x 10 24 m -3 For Si n i = 1.3 x 10 16 m -3 Ex: GaAs for intrinsic semiconductor n = p = n i   = n i | e |( e +  h )

22. 22 Intrinsic Semiconductors: Conductivity vs T • Data for Pure Silicon : -- s increases with T -- opposite to metals Adapted from Fig. 18.16, Callister & Rethwisch 8e. material Si Ge GaP CdS band gap (eV) 1.11 0.67 2.25 2.40 Selected values from Table 18.3, Callister & Rethwisch 8e.

23. 23 Temperature variation of conductivity (Band gap determination)  = n|e | e + p|e | h Strong exponential dependence of carrier concentration in intrinsic semiconductors Temperature dependence of mobility's is weaker. n = p  A exp (- E g /2 kT )   C exp (- E g /2 kT )

24. 24 Temperature variation of conductivity (II) ln (n) = ln (p)  ln (A) - E g /2 kT n = p  A exp (- E g /2 kT )   C exp (- E g /2 kT ) Plotting log of  , p, or n vs. 1/T produces a straight line. Slope is E g /2k ; gives band gap energy. Plot of ln p vs. 1/T

25. 25 Temperature variation of Conductivity (III) Extrinsic semiconductors low T: all carriers due to extrinsic excitations mid T: most dopants ionized (saturation region) high T: intrinsic generation of carriers dominates

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27. 27 • Intrinsic : -- case for pure Si -- # electrons = # holes ( n = p ) • Extrinsic : -- electrical behavior is determined by presence of impurities that introduce excess electrons or holes -- n ≠ p Intrinsic vs Extrinsic Conduction 3 + • p -type Extrinsic: ( p >> n ) no applied electric field Boron atom 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + hole • n -type Extrinsic: ( n >> p ) no applied electric field 5+ 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + Phosphorus atom valence electron Si atom conduction electron Adapted from Figs. 18.12(a) & 18.14(a), Callister & Rethwisch 8e.

28. 28 Extrinsic Semiconductors: Conductivity vs. Temperature • Data for Doped Silicon : -- s increases with doping -- reason: imperfection sites lower the activation energy to produce mobile electrons. • Comparison: intrinsic vs extrinsic conduction... -- extrinsic doping level: 10 21 /m 3 of a n -type donor impurity (such as P). -- for T < 100 K: "freeze-out“, thermal energy insufficient to excite electrons. -- for 150 K < T < 450 K: "extrinsic" -- for T >> 450 K: "intrinsic" Adapted from Fig. 18.17, Callister & Rethwisch 8e. (Fig. 18.17 from S.M. Sze, Semiconductor Devices, Physics, and Technology , Bell Telephone Laboratories, Inc., 1985.) Conduction electron concentration (10 21 /m 3 ) T (K) 600 400 200 1 2 3 freeze-out extrinsic intrinsic doped undoped

29. Hall Effect Discovered in 1879 A.D. by Edwin Hall. The development of an electric field between the two faces of a current-carrying material whose faces are perpendicular to a magnetic field. Used to measure the type (p toward right and n toward left) of majority charge carriers in a material, Concentration, and Mobility of charge carriers Schematic demonstration of the Hall effect. Positive and/or negative charge carriers that are part of the I x current are deflected by the magnetic field B z and give rise to the Hall voltage V H =   =   Dependence of Hall coefficient, specimen thickness, and magnetic filed Hall coefficient for metals, For metals, electron mobility in terms of Hall coefficient and conductivity

30. Computation of Hall Voltage 30 The problem may be solved in two steps, calculation of Hall coefficient R H and then Hall voltage V H Now using the Equation for Hall voltage,

31. 31 • Allows flow of electrons in one direction only (e.g., useful to convert alternating current to direct current). • Processing: diffuse P into one side of a B-doped crystal. -- No applied potential: no net current flow. -- Forward bias: carriers flow through p -type and n -type regions; holes and electrons recombine at p - n junction; current flows. -- Reverse bias: carriers flow away from p - n junction; junction region depleted of carriers; little current flow. p - n Rectifying Junction + + + + + - - - - - p -type n -type + - + + + + + - - - - - p- type n -type Adapted from Fig. 18.21 Callister & Rethwisch 8e. + + + + + - - - - - p -type n -type - +

32. 32 Properties of Rectifying Junction Fig. 18.22, Callister & Rethwisch 8e. Fig. 18.23, Callister & Rethwisch 8e.

33. 33 Junction Transistor Fig. 18.24, Callister & Rethwisch 8e.

34. 34 Junction Transistor Emitter-base junction is forward biased, base-collector junction is reverse biased. Thus, the base of the PNP transistor must be negative with respect to the emitter, and the collector must be more negative than the base.

35. 35 PNP Forward-biased junction Forward biased emitter-base junction, positive terminal of battery repels emitter holes toward base, while negative terminal drives base electrons toward emitter

36. 36 PNP junction interaction In reverse-biased junction: negative voltage on collector and positive voltage on base blocks majority current carriers from crossing junction. Increasing forward-bias voltage of transistor reduces emitter-base junction barrier. This allows more carriers to reach the collector, causing an increase in current flow from emitter to collector and through external circuit.

37. 37 MOSFET transistor: two small islands of p-type semiconductor created within n-type silicon substrate. Islands connected by narrow p-type channel. Metal contacts are made to islands (source and drain), one more contact (gate) is separated from channel by a thin (< 10 nm) insulating oxide layer. Gate serves the function of the base in a junction transistor (electric field induced by gate controls current through the transistor) MOSFET (Metal-Oxide-Semiconductor Field Effect Transistor)

38. 38 MOSFET (Metal-Oxide-Semiconductor Field Effect Transistor) Voltage applied from source encourages carriers (holes in the case shown below) to flow from the source to the drain through the narrow channel. Width (and hence resistance) of channel is controlled by intermediate gate voltage. For example, if positive voltage is applied to the gate, most of the holes are repelled from the channel and conductivity is decreasing. Current flowing from the source to the drain is therefore modulated by the gate voltage (amplification and switching)

39. 39 MOSFET Transistor Integrated Circuit Device Integrated circuits - state of the art ca. 50 nm line width ~ 1,000,000,000 components on chip chips formed one layer at a time Fig. 18.26, Callister & Rethwisch 8e. MOSFET (metal oxide semiconductor field effect transistor)

40. 40 Transistors and microelectronic devices MOSFET dominates microelectronic industry (memories, microcomputers, amplifiers, etc.) Large Si single crystals are grown and purified. Thin circular wafers (“chips”) are cut from crystals Circuit elements are constructed by selective introduction of specific impurities (diffusion or ion implantation) A single 8” diameter wafer of silicon can contain as many as 10 10 - 10 11 transistors in total Cost to consumer ~ 0.00001c each.

41. Conduction in Polymers and Ionic Materials Ionic Materials The band gap is large and only very few electrons can be promoted to the conduction band by thermal fluctuations Cation and anion diffusion can be directed by the electric field and can contribute to total conductivity:  total =  electronic +  ionic High temperatures produce Frenkel and Schottky defects (vacancy) which result in higher ionic conductivity. 41 Polymers Polymers are typically good insulators but can be made to conduct by doping . A few polymers have very high electrical conductivity - about one quarter that of copper, or about twice that of copper per unit weight. where n I is the valence and D I , the diffusion coefficient of a particular ion A mobility μ I may be associated with each of the ionic species as follows:

42. Typical Room Temperature Electrical Conductivities for 13 Nonmetallic Materials 42

43. Dielectrics Capacitors and Optics

44. Dielectrics are the materials having permanent electric dipole moment. Dipole: A dipole is an entity in which equal positive and negative charges are separated by a small distance.. Dipole Moment (µ ele ): The product of magnitude of either of the charges and the separation distance b/w them is called Dipole Moment. It is directed from negative to positive charge. µ ele = q . d  Coul – m All dielectrics are electrical insulators and they are mainly used to store electrical energy. Examples: Mica, glass, plastic, water & polar molecules… d q -q Introduction

45. 45 Dielectric Materials Dielectric constant of vacuum is 1 and is close to 1 for air and many other gases. When piece of dielectric material is placed between two plates capacitance can increase significantly. C =  r  o A / L + _ Dielectric is an insulator in which electric dipoles are induced by electric field with  r = 81 for water, 20 for acetone, 12 for silicon, 3 for ice, etc. + _ + _ + _ Magnitude of electric dipole moment is p = q d d

46. 46 Capacitance Voltage V applied to parallel conducting plates  plates charged by +Q, –Q  electric field E develops between plates C depends on geometry of plates and material between plates C =  r  o A / L =  A / L + + + + + - - - - - - A is area of plates, L is distance between plates,  is permittivity of dielectric medium,  o is permittivity of vacuum (8.85x10 -12 F/m 2 ), and  r is relative permittivity (dielectric constant) of material ,  r =  /  o = C / C vac Ability to store charge  capacitance C = Q / V [Farads] Charge can remain even after voltage removed.

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48. 48 Dielectric Materials Dipole orientation along electric field in the capacitor causes charge redistribution. Surface nearest to the positive capacitor plate is negatively charged and vice versa . Dipole formation/alignment in electric field is called polarization  P = Q’/A Dipole alignment  extra charge Q’ on plates: Q t = |Q+Q’| now C = Q t / V Increased capacitance  r = C / C vac > 1 + + + + + + + + - - - - - - - - - - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + Q + Q’ -Q - Q’ region of no net charge net negative charge at the surface, Q’ net positive charge at the surface, Q’ = PA P

49. 49 Dielectric Materials Surface charge density (also called dielectric displacement ) is D = Q/A =  o ℰ + P and Polarization is responsible for the increase in charge density above that for vacuum Mechanisms: dipole formation/orientation electronic (induced) polarization: Electric field displaces negative electron “clouds” with respect to positive nucleus. Ionic materials (induced) polarization: Applied electric field displaces cations and anions in opposite directions molecular (orientation) polarization: Some materials possess permanent electric dipoles (e.g. H 2 O). In absence of electric field, dipoles are randomly oriented. Applying electric field aligns these dipoles, causing net (large) dipole moment P total = P e + P i + P o

50. 50 Types of Polarization, or Mechanisms of Polarization electronic polarization ionic polarization Molecular (orientation) polarization

51. Dielectric Strength 51 Breakdown : The maximum field to damage the dielectric medium, like high electric fields (>10 8 V/m) excite electrons to conduction band + accelerate them to high energies  they collide with and ionize other electrons Avalanche process (or electrical discharge). Field necessary is called dielectric strength or breakdown strength.

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53. Frequency Dependence of the Dielectric Constant 53

54. Frequency Relaxation; 54 Dipole orientation for one and reversed polarity of an alternating field =   A minimum time to reorientate the charge particles in the direction of the field. Variation of dielectric constant with frequency of an alternating electric field. Electronic, ionic and orientation polarization contributions to the dielectric constant are indicated.

55. Effect of temperature and Frequency on ε r

56. 56 Ferroelectric Ceramics Experience spontaneous polarization i.e. polarization in the absence of an electric field. Occurrence of permanent electric dipole moment (similar to ferromagnetic materials) Fig. 18.35, Callister & Rethwisch 8e. BaTiO 3 -- ferroelectric below its Curie temperature (120 ºC)

57. 57 Piezoelectric Materials stress-free with applied stress Adapted from Fig. 18.36, Callister & Rethwisch 8e. (Fig. 18.36) Piezoelectricity (Pressure electricity) – application of stress induces voltage (polarization) – application of voltage induces dimensional change Piezoelectric materials convert mechanical strain into electricity (microphones, strain gauges, sonar detectors). Piezoelectric materials include barium titanate BaTiO 3 , lead titanate (PbTiO 3 ), lead zirconate PbZrO 3 , potassium niobate (KNbO 3 ), quartz etc. https://upload.wikimedia.org/wikipedia/commons/c/c4/SchemaPiezo.gif

58. Piezo -electricity (Pressure Electricity)

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60. Piezoelectric Coefficient The rate of change of polarization with stress at constant field OR The rate of change of strain with electric field at constant stress. Unit: C/N or m/V Two types of stress: linear & shear (along each of 3 axis, so 6 possibilities occurs, Thus in general: (with i = 1,2,3; j = 1 .. 6) and where is the piezoelectric coefficient, S is strain, T is stress, and ‘E’ denotes the electric field strength.   60

61. Peizo -electric coefficients and Relative permittivity of some materials 61

62. 62 • Electrical conductivity and resistivity are: -- material parameters -- geometry independent • Conductors, semiconductors, and insulators... -- differ in range of conductivity values -- differ in availability of electron excitation states • For metals, resistivity is increased by -- increasing temperature -- addition of imperfections -- plastic deformation • For pure semiconductors, conductivity is increased by -- increasing temperature -- doping [e.g., adding B to Si ( p -type) or P to Si ( n -type)] • Other electrical characteristics -- ferroelectricity -- piezoelectricity Summary

63. 63 Summary: Make sure you understand language and concepts: Acceptor state Capacitance Conduction band Conductivity, electrical Dielectric constant Dielectric displacement Dielectric strength Diode Dipole, electric Donor state Doping Electrical resistance Electron energy band Energy band gap Extrinsic semiconductor Fermi energy Forward bias Free electron Hole Insulator Intrinsic semiconductor Ionic conduction Junction transistor Matthiessen’s rule Metal Mobility MOSFET Ohm’s law Permittivity Piezoelectric Polarization Polarization, electronic Polarization, ionic Polarization, orientation Rectifying junction Resistivity, electrical Reverse bias Semiconductor Valence band