Kwang Kim Yonsei University kbkim@yonsei.ac.kr

1. Foundations of Materials Science and Engineering Lecture Note 11 (Electrical Properties of Materials) June 3, 2013 Kwang Kim Yonsei University kbkim@yonsei.ac.kr 8 O 16.00 7 N 14.01 34 Se 78.96 53 I 126.9 39 Y 88.91

2. Electrical Properties 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?

3. 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.

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

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

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

7. Conductivity: Comparison

8. Example: Conductivity Problem What is the minimum diameter (D) of the wire so that V < 1.5 V? I = 2.5 A + - Cu wire V 100 m < 1.5 V 2.5 A 6.07 x 107 (Ohm-m)-1 Solve to get D > 1.87 mm

9. Electron Energy Band Structures

10. Band Structure • Valence band – (filled) highest occupied energy levels • Conduction band – (empty) lowest unoccupied energy levels Conduction band Valence band

11. Partially filled band Overlapping bands Energy Energy empty band empty GAP band partly filled filled band band filled states filled states filled filled band band Conduction & Electron Transport • Metals (Conductors): -- for metals empty energy states are adjacent to filled states. -- thermal energy excites electrons into empty higher energy states. -- two types of band structures for metals - partially filled band - empty band that overlaps filled band

12. • Semiconductors: -- narrow band gap (< 2 eV) -- more electrons excited across band gap empty empty Energy conduction conduction band band ? GAP filled valence band filled states filled band Energy Band Structures: Insulators & Semiconductors • Insulators: -- wide band gap (> 2 eV) -- few electrons excited across band gap Energy GAP filled valence band filled states filled band

13. Charge Carriers Two types of electronic charge carriers: Free Electron – negative charge – in conduction band Hole – positive charge – vacant electron state in the valence band

14. 6 r • Resistivity increases with: Cu + 3.32 at%Ni 5 Ohm-m) 4 -- temperature deformed Cu + 1.12 at%Ni Resistivity, -- wt% impurity 3 Cu + 1.12 at%Ni d -8 -- %CW 2 (10 i  = thermal “Pure” Cu 1 t + impurity 0 -200 -100 0 T (ºC) + deformation Metals: Resistivity vs. T, Impurities • Presence of imperfections increases resistivity -- grain boundaries -- dislocations -- impurity atoms -- vacancies These act to scatter electrons so that they take a less direct path.

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

16. • Concept of electrons and holes: valence electron hole electron hole Si atom electron pair creation pair migration - - + + no applied applied applied • Electrical Conductivity given by: # holes/m3 hole mobility electron mobility # electrons/m3 Conduction: Electron and Hole Migration electric field electric field electric field

17. Intrinsic Semiconductors: Conductivity vs. T • Data for Pure Silicon: -- s increases with T -- opposite to metals material Si Ge GaP CdS band gap (eV) 1.11 0.67 2.25 2.40

18. 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + • n-type Extrinsic: (n >> p) • p-type Extrinsic: (p >> n) 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + Phosphorus atom Boron atom hole conduction electron 5+ 3 + valence electron no applied no applied Si atom electric field electric field Intrinsic vs. Extrinsic Conduction • 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

19. Electrical Properties HOMO : Highest Occupied Molecular Orbital LUMO : Lowest Unoccupied Molecular Orbital

20. doped undoped 3 2 freeze-out extrinsic intrinsic concentration (1021/m3) Conduction electron 1 0 0 200 400 600 T (K) Extrinsic Semiconductors : Conductivity vs. T • Data for Doped Silicon: -- s increases doping -- reason: imperfection sites lower the activation energy to produce mobile electrons. • Comparison:intrinsic vs extrinsic conduction... -- extrinsic doping level: 1021/m3 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" EC EF EV

21. n-type Si

22. p-type Si

23. + - + - + + - - + - p-type - n-type + + + - + - - + - - + n-type - p-type + + - - + + - + - + - p-n Rectifying Junction • 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. p-type n-type -- 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.

24. Energy Band Bending

25. LED from p-n Rectifying Junction

26. Properties of Rectifying Junction

27. Junction Transistor

28. MOSFET Transistor Integrated Circuit Device Fig. 18.26, Callister & Rethwisch 8e. • MOSFET (metal oxide semiconductor field effect transistor) • 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

29. Electrical Properties of Ceramics • Basic properties of dielectric: • Dielectric constant:- Q = CV Q = Charge V = Voltage C = Capacitance C = ε0A/d ε0 = permeability of free space = 8.854 x 10-12 F/m • When the medium is not free space C = Kε0A/d Where K is dielectric constant of the material between the plates

30. Dielectric Strength and Loss Factor • Dielectric strength is measure of ability of material to hold energy at high voltage. • Defined as voltage gradient at which failure occurs. • Measured in volts/mil. • Dielectric loss factor: Current leads voltage by 90 degrees when a loss free dielectric is between plates of capacitor. • When real dielectric is used, current leads voltage by 900 – δ where δ is dielectric loss angle. • Dielectric loss factor = K tan δ measure of electric energy lost.

31. Ferroelectric Ceramics • Experience spontaneous polarization BaTiO3 -- ferroelectric below its Curie temperature (120ºC) If cooling takes place in electric field, dipoles align in the direction of the field.

32. Piezoelectric Materials Piezoelectricity – application of stress induces voltage – application of voltage induces dimensional change stress-free with applied stress Electric response Mechanical force