Chapter 18 Electrical properties

1. Chapter 18 Electrical properties • Electrical conduction • How many moveable electrons are there in a material (carrier density)? • How easily do they move (mobility) ? • Semiconductivity • Electrons and holes • Intrinsic and extrinsic carriers • Semiconductor devices: p-n junctions and transistors • Conduction in polymers and ionic materials • Dielectric behavior Optional reading: 18.14, 18.21, 18.24, 18.26

2. Electrical Properties of Metals Electrical potential, V --> Current, I [volts, J/C] [amperes, C/s] Ohm's law: I = V/R R is the electrical resistance[ohms, ]

3. R due to intrinsic resistivity  [-m] + geometry (length l, area A through which the current passes) R = l/A In most materials (e.g. metals), the current is carried by electrons (electronic conduction). In ionic crystals, the charge carriers are ions (ionic conduction).

4. Electrical Properties of Metals Electrical conductivity (ability to conduct)  = 1/ Electric field intensity: E = V/l Ohm's law can be rewritten in terms of the current density J = I/A J =  E

5. Electrical conductivity varies between different materials by over 27 orders of magnitude, the greatest variation of any physical property  (.cm)-1 Metals:  > 105 (.m)-1 Semiconductors: 10-6 <  < 105 (.m)-1 Insulators:  < 10-6 (.m)-1

6. Energy Band Structures (I) 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.

7. Energy Band Structures 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). > 2 eV insulator semiconductor Electrical conduction --> electrons gain energy in an electric field. Not possible in these materials: forbidden band gap

8. Probability an electron reaches the conduction band is ~exp(-Eg/2kT) Eg is band gap • Probability < 10-24 no electrons in the conduction band in a solid of 1 cm3 • Requires Eg/2kT > 55 At room temperature, 2kT = 0.05 eV  Eg > 2.8 eV an insulator

9. Energy Band Structures and Conductivity (semiconductors and insulators) • Semiconductors and insulators: electrons must jump across band gap into conduction band to find conducting states above Ef • Energy needed  heat or radiation • Difference: semiconductors electrons reach conduction band at room temperature: not in insulators • Electron promoted to conduction band leaves a hole (positive charge) in the valence band it also participates in conduction.

10. Energy Band Structures and Conductivity (metals) Metals: highest occupied band is partially filled or bands overlap Conduction occursby promoting electrons into conducting states: start right above Fermi level. Energy provided by an electric field is sufficient to excite many electrons into conducting states. Cu Mg

11. Energy Band Structures and Bonding (metals, semiconductors, insulators) • Metals: valence electrons form an “electron gas” • Insulators: valence electrons tightly bound to (or shared with) the individual atoms: ionic + covalent • Semiconductors: mostly covalent bonding

12. Energy Band Structures and Conductivity Metals Semiconductors and Insulators

13. Electron Mobility • Force on electron is -eE, e = charge • No obstacles  electron speeds up in an electric field. Vacuum (TV tube) or perfect crystal • Real solid: electrons scattered by collisions with imperfections and thermal vibrations  friction  resistance  net drift velocity of electrons vd = eE E e– electron mobility [m2/V-s]. 1 / Friction Transfers part of energy supplied by electric field into lattice as heat. Electric heater Scattering events Net electron motion

14. Electron Mobility • Electrical conductivity proportional to number of free electrons per unit volume, Ne, and electron mobility, e  = Nee e Nmetal >> Nsemi metal >> semi metal < semi

15. Conductivity / Resistivity of Metals Total resistivity tot (Matthiessen rule) total = thermal+impurity+deformation Increases with T, with deformation, and with alloying.

16. Conductivity / Resistivity of Metals • Influence of temperature: • Increasing thermal vibrations and density of vacancies • T = o + aT • Impurities: • Solid solution • I = Aci(1-ci) • ci is impurity concentration • Two-phase alloy ( and  phases): • i = V + V  • Plastic deformation:

17. Materials of Choice for Metal Conductors • Silver: One of best for electrical conduction but high cost • Copper: inexpensive, abundant, high , but soft • Cu-Be alloy: Precipitation hardening, solid solution alloying, cold working decrease conductivity. • Aluminum: low weight, more resistant to corrosion but half as good as Cu • Nickel-chromium alloy: low  (high R), resistant to high temperature oxidation Heating elements

18. Semiconductivity Intrinsic semiconductors: conductivity defined by electronic structure of pure material Extrinsic semiconductors - electrical conductivity is defined by impurity atoms

19. Intrinsic semiconductors (I) Number of electrons in conduction band Ne n = C T3/2 exp(-Eg/2kT) Eg is band gap Conduction band Conducting Electrons Eg Holes (positive charge carriers Valence band T = 0 K T = 300 K Electron promoted into the conduction band  hole (positive charge) in valence band. In electric field, electrons and holes move in opposite direction and participate in conduction. Si (Eg = 1.1 eV) one out of every 1013 atoms contributes an electron to conduction band at room T.

20. Intrinsic semiconductors (II)  = n|e|e + p|e|h p, hole concentration, h hole mobility n, electron concentration, e, mobility e > h and n = p   = n|e|(e +h) = p|e|(e +h) n (and p) increase exponentially with T e andh decrease about linearly with T  Conductivity of intrinsic semiconductors increases with temperature (different from metals!)

21. Intrinsic semiconductors (III)

22. Extrinsic semiconductors  defined by impurity atoms Si extrinsic at room T if impurity concentration is one atom per 1012 (remember estimate of number of electrons promoted to conduction band at 300 K) Different concentrations of p and n p-type if p > n and n-type if n > p. Doping (addition of a small concentration of impurity atoms) Methods: diffusion or ion implantation.

23. n-type extrinsic semiconductors (I) Excess electron carriers produced by substitutional impurities: more valence electrons per atom than semiconductor matrix Example: phosphorus with 5 valence electrons is an electron donor in Si which has 4 electrons that bond. Fifth outer electron of P is weakly bound in donor state (~0.01 eV); easily promoted to conduction band. P is a donor impurity. Elements in columns V and VI of periodic table are donors for semiconductors in column IV, Si or Ge

24. n-type extrinsic semiconductors (II) Hole in donor state is far from the valence band and is immobile Conduction occurs mainly by the donated electrons (n-type). ND ~ n  ~ n|e|e ~ ND |e|e

25. p-type extrinsic semiconductors (I) Excess holes: substitutional impurities that have fewer valence electrons per atom than matrix Bond with neighbor is incomplete: a hole weakly bound to the impurity atom. Elements in columns III of periodic table (B, Al, Ga) are donors for semiconductors in column IV, Si and Ge. Impurities are called acceptors, NA = NBoron ~p

26. p-type extrinsic semiconductors (II) Energy state corresponding to hole (acceptor state) is close to top of valence band Electron easily hops from valence band to complete the bond leaving a hole behind. Conduction occurs mainly by the holes (p-type)  ~ p|e|p ~ NA |e|p