Polymer Physics Ph.D. Course

1. Behzad Pourabbas Sahand University of Technology Faculty of Polymer Engineering Polymer PhysicsPh.D. Course

2. Outlook • Conductivity Concept in Polymers • Electrically Conductive Polymers • Liquid Crystal Polymers • Electro Active Polymers and their Applications in Advanced Technologies

3. References • 2 CDs are available, • full of Ebooks and references,

4. Electrical Conductivity

5. Electrical Conductivity • Electrical conductivity of A MATTER is its ability to conduct electrons. • We can measure it by measuring Resistivity very easily by several methods, Using one OHM meter forexample. • There are more complicated and standard method to do this.

6. Electrical Conductivity • Range of Conductivity in Materials

7. Electrical Conductivity • Electrical Conductivity () may occur by Electrons or IONS. • What is the Charge of Carriers? How many Carriers? And with what speed (mobility)? • The ease with which the charged species will move under the influence of the applied electric field E and is usually expressed as a velocity per unit field (m2V-1s-1) • What happens in the absence of an electric field for the charge carriers?

8. Electrical Conductivity • There is a drift velocity: and an average for it: : time between scattering events + - - + + - - +

9. Electrical Conductivity • Mobile Species: • Electrons and Holes: (Electronic Conductors) • Electron is an Electron but (Negative Charge) • Hole is the empty place of a moved electron (Positively Charged). • Cations and Anions, (Ionic Conductors).

10. Electrical Conductivity • Theories of Conductions are aimed to explain how n and  depend on molecular structure, T and applied field. • In Polymers, the mobility depends on morphology as well. • There is a large range of mobity values for different materials. (The next Slide).

11. Electrical Conductivity • Mobility values for different materials

12. Electrical Conductivity • Conductivity in POLYMERS: • They are usually insulators if: • There is no charged species : (polymers are composed of covalent bonds) • Careful separation of any ionic species from for example: catalysts residues; Initiators, Ionic End groups, Oxidation Products. • Conversely, • One insulating polymer can made conductive by adding conductive fillers such as carbon black or metallic particles (Gold, Silver, Nickel,..) (Conductive Composites). • There are substantially conductive polymers as well!!!!!

13. ELECTRICAL CONDUCTIVITY • in order of conductivity: superconductors, conductors, semiconductors, insulators • conductors: material capable of carrying electric current, i.e. material which has “mobile charge carriers” (e.g. electrons, ions,..) e.g. metals, liquids with ions (water, molten ionic compounds), plasma • insulators: materials with no or very few free charge carriers; e.g. quartz, most covalent and ionic solids, plastics • semiconductors: materials with conductivity between that of conductors and insulators; e.g. germanium Ge, silicon Si, GaAs, GaP, InP • superconductors: certain materials have zero resistivity at very low temperature.

14. ELECTRICAL CONDUCTIVITY . • some representative resistivities (): • R = L/A, R = resistance, L = length, A = cross section area; resistivity at 20o Cresistivity in  mresistance(in )(L=1m, diam =1mm) • aluminum 2.8x10-8 3.6x10-2 • brass 8x10-8 10.1x10-2 • copper 1.7x10-8 2.2x10-2 • platinum 10x10-8 12.7x10-2 • silver 1.6x10-8 2.1x10-2 • carbon 3.5x10-5 44.5 • germanium 0.45 5.7x105 • silicon  640  6x108 • porcelain 1010 - 1012 1016 - 1018 • teflon 1014 1020 • blood 1.5 1.9x106 • fat 24 3x107

15. ENERGY BANDS IN SOLIDS: • In solid materials, electron energy levels form bands of allowed energies, separated by forbidden bands • valence band = outermost (highest) band filled with electrons (“filled” = all states occupied) • conduction band = next highest band to valence band (empty or partly filled) • “gap” = energy difference between valence and conduction bands, = width of the forbidden band • Note: • electrons in a completely filled band cannot move, since all states occupied (Pauli principle); only way to move would be to “jump” into next higher band - needs energy; • electrons in partly filled band can move, since there are free states to move to. • Classification of solids into three types, according to their band structure: • insulators: gap = forbidden region between highest filled band (valence band) and lowest empty or partly filled band (conduction band) is very wide, about 3 to 6 eV; • semiconductors: gap is small - about 0.1 to 1 eV; • conductors: valence band only partially filled, or (if it is filled), the next allowed empty band overlaps with it

16. Energy Band Structures Atoms form a solid  valence electrons interact two quantum mechanical effects. Heisenberg's uncertainty principle: constrain electrons to a small volume  raises their energy called promotion. Pauli exclusion principle limits the number of electrons with the same energy. Result: valence electrons form wide electron energy bands in a solid. Bands separated by gaps, where electrons cannot exist.

17. Band structure and conductivity • Fermi Energy (EF) - highest filled state at 0 K • Conduction band -partially filled or empty band • Valence band – highest partially or completely filled band Semiconductors and insulators, valence band is filled, and no more electrons can be added (Pauli's principle). Insulators > 2 eV

18. Band structure and conductivity

19. Intrinsic silicon: • DOPED SEMICONDUCTORS: • “doped semiconductor”: (also “impure”, “extrinsic”) = semiconductor with small admixture of trivalent or pentavalent atoms;

20. n-type material • donor (n-type) impurities: • dopant with 5 valence electrons (e.g. P, As, Sb) • 4 electrons used for covalent bonds with surrounding Si atoms, one electron “left over”; • left over electron is only loosely bound only small amount of energy needed to lift it into conduction band (0.05 eV in Si) •  “n-type semiconductor”, has conduction electrons, no holes (apart from the few intrinsic holes) • example: doping fraction of 10-8Sb in Si yields about 5x1016 conduction electrons per cubic centimeter at room temperature.

21. p-type material • acceptor (p-type) impurities: • dopant with 3 valence electrons (e.g. B, Al, Ga, In)  only 3 of the 4 covalent bonds filled  vacancy in the fourth covalent bond  hole • “p-type semiconductor”, has mobile holes, very few mobile electrons (only the intrinsic ones).

22. advantages of doped semiconductors: • Can “tune” conductivity by choice of doping fraction • can choose “majority carrier” (electron or hole) • can vary doping fraction and/or majority carrier within piece of semiconductor • can make “p-n junctions” (diodes) and “transistors”

23. DIODES AND TRANSISTORS • p-n JUNCTION: • p-n junction = semiconductor in which impurity changes abruptly from p-type to n-type ; • “diffusion” = movement due to difference in concentration, from higher to lower concentration; • in absence of electric field across the junction, holes “diffuse” towards and across boundary into n-type and capture electrons; • electrons diffuse across boundary, fall into holes (“recombination of majority carriers”);  formation of a “depletion region” (= region without free charge carriers) around the boundary; • charged ions are left behind (cannot move): • negative ions left on p-side  net negative charge on p-side of the junction; • positive ions left on n-side  net positive charge on n-side of the junction •  electric field across junction which prevents further diffusion.

24. DIODE • diode = “biased p-n junction”, i.e. p-n junction with voltage applied across it • “forward biased”: p-side more positive than n-side; • “reverse biased”: n-side more positive than p-side; • forward biased diode: • the direction of the electric field is from p-side towards n-side •  p-type charge carriers (positive holes) in p-side are pushed towards and across the p-n boundary, • n-type carriers (negative electrons) in n-side are pushed towards and across n-p boundary  current flows across p-n boundary

25. Forward biased pn-junction • Depletion region and potential barrier reduced

26. Reverse biased diode • reverse biased diode: applied voltage makes n-side more positive than p-side  electric field direction is from n-side towards p-side  pushes charge carriers away from the p-n boundary  depletion region widens, and no current flows • diode only conducts when positive voltage applied to p-side and negative voltage to n-side • diodes used in “rectifiers”, to convert ac voltage to dc.

27. Reverse biased diode • Depletion region becomes wider, barrier potential higher

28. Nobel Prize in 1956 • Shockley, Brattain and Bardeen start working with p- and n- type germanium and silicon semiconductors in 1946 • Bardeen and Brattain put together the first transistor in December 1947: • a point-contact transistor consisting of a single germanium crystal with a p- and an n- zone. Two wires made contact with the crystal near the junction between the two zones like the “whiskers” of a crystal-radio set.

29. Point-contact-transistor

30. TRANSISTORS • (bipolar) transistor = combination of two diodes that share middle portion, called “base” of transistor; other two sections: “emitter'' and “collector”; • usually, base is very thin and lightly doped. • two kinds of bipolar transistors: pnp and npn transistors • “pnp” means emitter is p-type, base is n-type, and collector is p-type material; • in “normal operation of pnp transistor, apply positive voltage to emitter, negative voltage to collector;

31. operation of pnp transistor: • if emitter-base junction is forward biased, “holes flow” from battery into emitter, move into base; • some holes annihilate with electrons in n-type base, but base thin and lightly doped  most holes make it through base into collector, • holes move through collector into negative terminal of battery; i.e. “collector current” flows whose size depends on how many holes have been captured by electrons in the base; • this depends on the number of n-type carriers in the base which can be controlled by the size of the current (the “base current”) that is allowed to flow from the base to the emitter; the base current is usually very small; small changes in the base current can cause a big difference in the collector current;

32. Transistor operation • transistor acts as amplifier of base current, since small changes in base current cause big changes in collector current. • transistor as switch: if voltage applied to base is such that emitter-base junction is reverse-biased, no current flows through transistor -- transistor is “off” • therefore, a transistor can be used as a voltage-controlled switch; computers use transistors in this way.

33. Field Effect Transistors • “field-effect transistor” (FET) • in a pnp FET, current flowing through a thin channel of n-type material is controlled by the voltage (electric field) applied to two pieces of p-type material on either side of the channel (current depends on electric field). • This is the kind of transistor most commonly used in computers.

34. FET Structure

35. Polymer Field Effect Transistor

36. Polymer FETs

37. Due to improvements in manufacturing, integrated circuits became smaller and smaller • Gordon Moore observed that “the number of transistors on a chip seems to double every year….” • Moore’s Law: the number of transistors on a chip seems to double every 18 months, while the price remains the same. • Grosch’s law for mainframes: every year, the power of computers doubles while the price is cut in half

38. Conduction Theories

39. Theories of Electronic ConductionBand structure: • Electronic conduction in organic molecular substance differs in several important ways from familiar metallic and inorganic semiconductors like silicone and germanium. • Even in idealized model, there are significant differences between inorganic and polymer conductors. • In polymers, the interaction between charge carriers is generally less well screened than in inorganic materials (Electron-electron and electron-hole interaction tend to localize electronic states to a much larger extend ) . • Resent studies of theses effects show that band structure may not be the best model even for ideal chains.

40. Theories of Electronic Conduction • Usual band structure formation in Crystalline inorganic and metallic substances:

41. Theories of Electronic ConductionPhotoconduction • Exposure of a semiconductor to light or other electromagnetic radiation may produce a temporary increase in the population of free charge carriers, and the resulting extra flow of current under influence of an applied electric fields is called photoconduction,

42. Theories of Electronic ConductionPhotoconuction • Interaction of light photons with semiconductors: • Adsorption of single photons to promote an electron to conduction band  Electron-hole pair formation  Absorption edge

43. Photoconduction • Recombination (Electron-hole): • If electron-hole pair have enough Energy grater than Coulomb interaction No recombination occurs. • If the electron –hole separation is such that Coulomb Interaction < kT, They are easily movable. • Coulomb Capture Radius: When Coulumb Interaction is equal to Thermal Energy (kT).

44. Photoconduction • Excitons: • If electron-hole pair can not escape their electrostatic attraction, this can lead to EXCITONS. • Excitons are mobile electronic States. • They can not transport charge by themselves but they can produce unbound charges

45. Photoconduction • Excitons: • Can collid to each other or other impurities: • Fusion; Collide to produce electron-hole pairs • Fission; Collide to defects, surface (NanoTechnology) and impurities to separate into charge carriers. • The surface effect ; Photoinjection of Carrieres is especially important in organic materials where direct charge carries is less probable.

46. Theories of Electronic ConductionHopping Conduction • Hopping condition makes charge transport possible where band conduction no longer occurs. • Just as carriers can be generates thermally by excitation of electrons across the band gap from the valance band to acceptor states or from donor to the conduction band – so it is also possible to move charges between localized states by thermal excitation.

47. Theories of Electronic ConductionHopping Conduction • Energy Barrier across the jump path.

48. Theories of Electronic ConductionHopping Conduction • An Electron may either hop over or tunnel through the barrier. • The relative importance of these two mechanisms depends on the shape of the barrier, the separation of the sites and the accessability of thermal energy.

49. Theories of Electronic ConductionHopping Conduction • both is also possible. • Temperature dependence of conduction is a good criteria for the mechanisms Identification. Electron needs enough energy Sepa ration must be short enough

50. Theories of Electronic ConductionHopping Conduction • As the disorder in the lattice increases both the energetic and spatial distribution of atoms (in amorphous material), the electronic energy states spread as a continuous tail into what is normally the forbidden energy zone, and the electrons in these states are localized.