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Electrical Properties of Materials Conductivity, Bands & Bandgaps Objectives To understand: Electronic Conduction in materials Band Structure Conductivity Metals Semiconductors Ionic conduction in ceramics Dielectric Behavior Polarization Definitions Ohm’s Law V = iR V - Voltage, i - current, R -Resistance Units V - Volts i - amps (or W/A (Watts/amp) or J/C (Joules/Coulomb)) (or C/s (Coulombs/second) R - ohms () Definitions Consider current moving through a conductor with cross sectional area, A and a length, l Area R = V/i i Length Resistance 2 RA VA m = = = = m l il m Definitions Conductivity, : = 1/ (units: (-cm)-1 Conductivity is the “ease of conduction” Ranges over 27 orders of magnitude! Metals Semiconductors Insulators Conductivity 107 1/cm 10-6 - 104 1/cm 10-10 -10-20 1/cm 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+ 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 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 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 1S1 For many atoms 1S1 E 1S1 1S1 Energy Band 2s 1s interatomic separation A1 A2 3D 3D 4S 4S 3P 3P 3S 3S 2P 2S 1S Isolated Atom Energy Energy Banding 2P 2S 1S Bonded Atoms 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” Band Structure Valence Band Band which contains highest energy electron Conduction Band The next higher band empty empty Conduction Band Valence Band empty filled filled filled Metal Semiconductor Insulator 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 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 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 Temperature Dependence, Metals There are three contributions to t due to phonons (thermal) i due to impurities d due to deformation (not shown) = i + o+ d = i + o+ d Electrical Conductivity, Metals = conductivity = 1/ For charge transport to occur - must have: - something the carry the charge - the ability to move = nem Electrical Conductivity, Metals = nem = electrical conductivity n = number of concentration of charge carriers depends on band gap size and amount of thermal energy m = mobility measure of resistance to electron motion - related to scattering events - (e.g. defects, atomic vibrations) “highway analogy” Temperatures Dependence, Metals Metals, decreases with T (= nem) Two parameters in Ohm’s law may be T dependent: n and m Metals - number of electrons (in conduction band) does not vary with T. n = number of electrons per unit volume m102-103 cm2/Vsec n1022 cm-3 and 105-106 (ohm-cm)-1 All of the observed T dependence of in metals arises from m 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, 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 Thermal Stimulation E P exp kB T P = number of electrons promoted to conduction band Suppose the band gap is Eg = 1.0 eV T(°K) 0 100 200 300 400 kBT (eV) E/kBT 0 0.0086 0.0172 0.0258 0.0344 58 29 19.4 14.5 E exp k BT 0 -24 0.06x10 -12 0.25x10 -9 3.7 x10 -6 0.5x10 Stimulation of Electrons by Photons Eg •EEgg hn Photoconductivity E = hn = hc/lc l(m)n(sec -1) Conductivity is dependent on the intensity of the incident electromagnetic radiation Stimulation of Electrons by Photons Provided hn Eg (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) GaAs1.5 eV (Visible red) SiC 3.0 eV (Visible blue) 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 Conductivity of Intrinsic S.C. Intrinsic semiconductor pure material Band Gap Silicon - 1.1 eV Germanium - 0.7 eV For every electron, e, promoted to the conduction band, a hole, h, is left in the valence band (+ charge) Total conductivity = e + h = neme + nemh For intrinsic semiconductors: n = p & = ne(me + mh) 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. 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 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. QuickTime™ and a Graphics decompressor are needed to see this picture. QuickTime™ and a Graphics decompressor are needed to see this picture. Silicon n-type semiconductors: Si Si Si Si Bonding model description: Si Si Si Si Element with 5 bonding electrons. Only 4 electrons participate in bonding the extra ecan easily become a conduction electron Si P Si Si Si Si Si Si p-type semiconductors: Si Si Si Si Bonding model description: Si Si Si Si Element with 3 bonding electrons. Since 4 electrons participate in bonding and only 3 are available the left over “hole” can carry charge Si Si B Si Si Si Si Si 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 Group V elements Antimony Typical concentrations are ~ 10-6 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 Location of Impurity Energy Levels Typically, E ~ 1% Eg E Eg E Conductivity of Extrinsic S.C. There are three regimes of behavior: Excitation across band gap all impurities ionized impurity excitation Temperature It is possible that one or more regime will not be evident experimentally n-Type Semiconductors Band Model description: The dopant adds a donor state in the band gap Donor State Band Gap If there are many donors n>>p (many more electrons than holes) Electrons are majority carriers “n-type” - (negative) semiconductor = e + h = neme + nemh ≈ neu p-Type Semiconductors Band Model description: The dopant adds a acceptor state in the band gap Acceptor State Band Gap If there are many acceptors p>>n (many more electrons than holes) holes are majority carriers “p-type” - (negative) semiconductor = e + h = neme + nemh ≈ peu 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?