Electrical Properties of Materials

1. Electrical Properties of Materials Conductivity, Bands & Bandgaps

2. Objectives To understand: • Electronic Conduction in materials • Band Structure • Conductivity • Metals • Semiconductors • Ionic conduction in ceramics • Dielectric Behavior • Polarization

3. Definitions Ohm’s Law • V = iR • V - Voltage, i - current, R -Resistance • Units • V - Volts • (or W/A (Watts/amp) or J/C (Joules/Coulomb)) • i - amps • (or C/s (Coulombs/second) • R - ohms ()

4. Area i Length Definitions Consider current moving through a conductor with cross sectional area, A and a length, l • Resistance R = V/i

5. Definitions • Conductivity,  : • Conductivity is the “ease of conduction” Ranges over 27 orders of magnitude!  = 1/ (units: (-cm)-1 Conductivity Metals 107 1/cm Semiconductors 10-6 - 104 1/cm Insulators 10-10 -10-20 1/cm

6. Definitions Charge carriers can be electrons or ions • Electronic conduction: • Flow of electrons, e and electron holes, h • Ionic conduction • Flow of charged ions, Ag+

7. Electronic Conduction • In each atom there are discrete energy levels occupied by electrons • Arranged into: • Shells K, L, M, N • Subshells s, p, d, f

8. In Solid Materials • Each atom has a discrete set of electronic energy levels in which its electrons reside. • As atoms approach each other and bond into a solid, the Pauli exclusion principle dictates that electron energy levels must split. • Each distinct atomic state splits into a series of closely spaced electron states - called an energy band

9. E 1S1 1S1 A1 A2 Electronic Conduction Pauli Exclusion Principle - no two electrons within a system may exist in the same “state” All energy levels (occupied or not) “split” as atoms approach each other For two atoms For many atoms 1S1 1S1

10. 3D 4S 3P 3S 2P Energy 2S 1S Isolated Atom Banding 3D 4S 3P 3S 2P Energy 2S 1S Bonded Atoms

11. Electronic Conduction Band Gap Equilibrium Separation Inter-atomic separation Once states are split into bands, electrons fill states starting with lowest energy band. Electrical properties depend on the arrangement of the outermost filled and unfilled electron bands. “boxes of marbles analogy”

12. empty filled Band Structure • Valence Band • Band which contains highest energy electron • Conduction Band • The next higher band Conduction Band empty empty Valence filled Band filled Metal Insulator Semiconductor

13. Band Structure • Fermi Energy, Ef • Energy corresponding to the highest filled state • Only electrons above the Fermi level can be affected by an electric field (free electrons) E Ef

14. Conduction in Metals- Band Model • For an electron to become free to conduct, it must be promoted into an empty available energy state • For metals, these empty states are adjacent to the filled states • Generally, energy supplied by an electric field is enough to stimulate electrons into an empty state

15. Resistivity,in Metals • Resistivity typically increases linearly with temperature: t = o + T • Phonons scatter electrons • Impurities tend to increase resistivity: • Impurities scatter electrons in metals • Plastic Deformation tends to raise resistivity • dislocations scatter electrons

16. Temperature Dependence, Metals There are three contributions to t due to phonons (thermal) i due to impurities d due to deformation (not shown) r = ri + ro+ rd r = ri + ro+ rd

17. Electrical Conductivity, Metals s = conductivity = 1/r • For charge transport to occur - must have: • - something the carry the charge • - the ability to move s = nem

18. Electrical Conductivity, Metals s = nem •  = electrical conductivity • n = number of concentration of charge carriers • depends on band gap size and amount of thermal energy •  = mobility • measure of resistance to electron motion - related to scattering events - (e.g. defects, atomic vibrations) “highway analogy”

19. Temperatures Dependence, Metals • Metals, decreases with T (= ne) • Two parameters in Ohm’s law may be T dependent: n and  • Metals - number of electrons (in conduction band) does not vary with T. • n = number of electrons per unit volume n1022 cm-3 and 102-103 cm2/Vsec 105-106 (ohm-cm)-1 All of the observed T dependence of  in metals arises from 

20. Semiconductors and Insulators • Electrons must be promoted across the energy gap to conduct • Electron must have energy: • e.g. heat or light absorptrion • If gap is very large (insulators) • no electrons get promoted • low electrical conductivity, 

21. Semiconductors • For conduction to occur, electrons must be promoted across the band gap Note - electrons cannot reside in gap Energy is usually supplied by heat or light

22. T ( ° K ) k T ( e V ) E / k T D B æ ö E B D ç ÷ exp - è ø k T B 0 0 ¥ 0 - 2 4 1 0 0 0 . 0 0 8 6 5 8 0 . 0 6 x 1 0 - 1 2 2 0 0 0 . 0 1 7 2 2 9 0 . 2 5 x 1 0 - 9 3 0 0 0 . 0 2 5 8 1 9 . 4 3 . 7 x 1 0 - 6 4 0 0 0 . 0 3 4 4 1 4 . 5 0 . 5 x 1 0 Thermal Stimulation P = number of electrons promoted to conduction band Suppose the band gap is Eg = 1.0 eV

23. Stimulation of Electrons by Photons Photoconductivity hn  Eg E = hn = hc/l, c = l(m)n(sec -1) Conductivity is dependent on the intensity of the incident electromagnetic radiation

24. Stimulation of Electrons by Photons hn  Eg Provided (If incident photons have lower energy, nothing happens when the semiconductor is exposed to light.) Band Gaps: Si - 1.1 eV (Infra red) Ge 0.7 eV (Infra red) GaAs 1.5 eV (Visible red) SiC 3.0 eV (Visible blue)

25. Intrinsic Semiconductors • Intrinsic Semiconductors • Once an electron has been excited to the conduction band, a “hole” is left behind in the valence band Since neither band is now completely full or empty, both electron and hole can migrate

26. Silicon - 1.1 eV Germanium - 0.7 eV Conductivity of Intrinsic S.C. • Intrinsic semiconductor • pure material • For every electron, e, promoted to the conduction band, a hole, h, is left in the valence band (+ charge) Total conductivity  = e + h = nee + neh For intrinsic semiconductors: n = p &  = ne(e + h)

27. Extrinsic Semiconductors • Extrinsic semiconductors • impurity atoms dictate the properties • Almost all commercial semiconductors are extrinsic • Impurity concentrations of 1 atom in 1012 is enough to make silicon extrinsic at room T! • Impurity atoms can create states that are in the bandgap.

28. Types of Extrinsic Semiconductors • In most cases, the doping of a semiconductor leads either to the creation of donor or acceptor levels • n-Type semiconductors • In these, the charge • carriers are negative • p-Type semiconductors • In these, the charge • carriers are positive

29. Silicon • Diamond cubic lattice • Each silicon atom has one s and 3p orbitals that hybridize into 4 sp3 tetrahedral orbitals • Silicon atom bond to each other covalently, each sharing 4 electrons with four, tetrahedrally coordinated nearest neighbors.

30. Si Si Si Si Si Si Si Si Si P Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si B Si Si Si Si Si Silicon n-type semiconductors: • Bonding model description: • Element with 5 bonding electrons. Only 4 electrons participate in bonding the extra e- can easily become a conduction electron p-type semiconductors: • Bonding model description: • Element with 3 bonding electrons. Since 4 electrons participate in bonding and only 3 are available the left over “hole” can carry charge

31. Doping Elements, n-Type • In order to get n-type semiconductors, we must add elements which donate electrons i.e. have 5 outer electrons. • Typical donor elements which are added to Si or Ge: • Phosphorus • Arsenic • Antimony • Typical concentrations are ~ 10-6 Group V elements

32. Doping Elements, p-type • To get p-type behavior, we must add acceptor elements i.e. have 3 outer electrons. • Typical acceptor elements are: • Boron • Aluminum • Gallium • Indium Group III elements

33.  E E g  E Location of Impurity Energy Levels • Typically, E ~ 1% Eg

34. Conductivity of Extrinsic S.C. • There are three regimes of behavior: It is possible that one or more regime will not be evident experimentally

35. n-Type Semiconductors • Band Model description: • The dopant adds a donor state in the band gap If there are many donors n>>p (many more electrons than holes) Donor State Band Gap Electrons are majority carriers “n-type” - (negative) semiconductor  = e + h = nee + neh s ≈ neu

36. p-Type Semiconductors • Band Model description: • The dopant adds a acceptor state in the band gap If there are many acceptors p>>n (many more electrons than holes) Band Gap Acceptor State holes are majority carriers “p-type” - (negative) semiconductor  = e + h = nee + neh s ≈ peu

37. III-V, IV-VI Type Semiconductors • Actually, Si and Ge are not the only usuable Semiconductors • Any two elements from groups III and Vor II and VI, as long as the average number of electrons = 4 and have sp3-like bonding, can act as semiconductors. • Example: Ga(III), As(V) GaAs Zn(II), Se(VI) ZnSe • Doping, of course, is accomplished by substitution, on either site, by a dopant with either extra or less electrons. In general, “metallic” dopants will substitute on the “metal” sites and “non-metallic” dopants will substitute on non-metal sites. For the case where the dopant is between the two elements in the compound, substitution can be amphoteric (i.e. on both sites) • Question: Give several p-type and n-type dopant for GaAs and ZnSe. What kind of dopant is Si in InP?