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Electron Mobility ELECTRONIC MATERIALS Electronic Materials Superconductors Conductors Semi-Conductors Dielectrics Type I Linear Elemental Insulators Dielectrics Hg, MgB2 Ag, Au, Cu, Hg, W Si, Ge, a-Sn, C Porcelain, glasses, Al2O3 Type II Non-Linear Compound Linear YBCO,BSCCO ZnO, diodes GaAs, AlAs Al2O3, SiO2, ZrO2 Organic NonLinear BaTiO3, PZT Inorganic ITO,YSZ, BaTiO3 Electrical Properties Objectives To understand: Electronic Conduction in materials Band Structure Conductivity Metals Semiconductors Ionic conduction in ceramics Dielectric Behavior Polarization Important Terms Acceptor: element introduced to semiconductor to generate free hole (by “accepting” electron from semiconductor atom and “releasing” hole at the same time); acceptor atom must have one valence electron less than semiconductor; boron (B) is the most common acceptor in silicon technology; alternatives include indium and gallium. Donor: element introduced to semiconductor to generate free electron (by “donating” a electron to semiconductor); must have one more valence electron than semiconductor; common donors in Si: P, As, Sb and in GaAs: S, Se, Sn. Dopant: element introduced to semiconductor to establish either p-type (acceptor) or n-type (donor) conductivity Electron: negatively charged particle in an atom; carrier of smallest (elemental) charge of 1.6x10- 19C; carrier of negative charge in semiconductors Hole: positive charge carrier in a semiconductors which materially does not exits; lack of electron moving in the direction opposite to that of electron and carrying a positive charge; features higher effective mass than electron, hence, lower mobility. Fermi level: energy level in solids at which the Fermi-Dirac distribution function is equal to 0.5. Fermi-Dirac distribution function: formula describing the probability of a state being occupied by an electron depending on the state's energy level. Semiconductor: solid-state material in which, in contrast to metals and insulators: (i) electrical conductivity can be controlled by orders of magnitude by adding very small amounts of alien elements known as dopants, (ii) electrical conductivity can be controlled not only by negatively charged electrons, but also by positively charged holes and (iii) electrical conductivity is sensitive to temperature, illumination, and magnetic fields; these properties result from the fact that, due to the nature of interatomic bonds (mostly covalent), in semiconductors, in contrast to metals but similarly to insulators, the valence band and the conduction band are separated by the energy gap; in semiconductors, however, width of the energy gap rarely exceeds about 3.5 eV while in insulators energy gap is typically wider that about 5 eV; semiconductor properties are displayed by the elements from the IVth group of periodic table: carbon, (C) in the form of diamond, silicon (Si), germanium (Ge) and tin (Sn); numerous compound semiconductors can be formed by combining elements from IVth group, e.g. SiGe and SiC, as well as from groups III and V,e.g. GaAs, InP, or GaN, and groups II and Vi, e.g. CdTe, ZnS, etc. Furthermore, select organic materials display semiconductor properties. Semiconductor Diode: two-terminal device in which current is a very strong function of the direction of applied voltage; large current is allowed to flow under forward voltage bias while almost no current will flow under the reverse voltage bias, hence, displays rectifying characteristics; typically implemented by p-n junction. Intrinsic semiconductor: semiconductor materials in which free electrons and holes result only from band-to band generation, and hence, feature the same concentration; undoped; does not display neither n- or p-type conductivity. Extrinsic semiconductor: doped semiconductor featuring either p- or n-type conductivity. Scattering: process responsible for electron in a certain state defined by its crystal momentum suddenly moving into a different state; fundamental effect defining electron transport in semiconductor. Drift velocity: velocity of carriers under electric field; as opposed to carriers in free space carriers in a semiconductor are not "infinitely" accelerated by the electric field due to scattering - thus they reach a finite velocity regardless of the period of time over which the field is acting; at a given electric field drift velocity is determined the carrier mobility. Electron mobility: measure of electron scattering in semiconductor; proportionality factor between electron drift velocity and electric field as well as carrier concentration and conductivity of semiconductor; unit cm2/V s; the same way as effective mass of an electron, electron mobility is different for different semiconductors; electron mobility at 300 K for three key semiconductors: Si - 1500 cm2/V s, GaAs -7500 cm2/V s, 6H-SiC -400 cm2/V s; higher mobility makes semiconductor better suited for high speed applications. Hall Effect: magnetic field applied to semiconductor through which current is flowing causes generation of electric field perpendicular to the direction of current flow and the magnetic field; used to derive some electrical properties of semiconductor. Band gap: energy band separating conduction and valence bands in the solid; no electron energy levels are allowed in the forbidden band; no energy gap in metals in which case conduction and valence bands overlap; solids featuring energy gap are defined as either semiconductors or insulators based on the width of energy gap; values of Eg (at 300K) for common semiconductors: InSb - 0.17 eV, Ge - 0.67 eV, Si - 1.12 eV, GaAs - 1.43 eV GaP - 2.26 eV, 6H-SiC - 2.9 eV, GaN - 3.5 eV, and insulators Ta2O5 - 4.2 eV , TiO2 -5 eV, Si3N4 - 5.1, Al2O3 ~5 eV, SiO2 -8.0. Dielectric: a solid displaying insulating properties (energy gap wider than 4 eV); upper most energy band is completely empty, hence, extremely low conductivity; characteristics of material are independent of the applied voltage. Lithography: process used to transfer pattern from the mask/reticle to the layer of resist deposited on the surface of the wafer; kind of lithography depends on the wavelength of radiation used to expose resist: photolithography (or optical lithography) uses UV radiation, X-ray lithography uses X-ray, e- beam lithography uses electron bean, ion beam lithography uses ion beam. Electron beam (e-beam) lithography, EBL: lithography technique using focused beam of electrons to expose the resist; no mask is used as pattern is "written" directly into the resist by very fast scanning of electron beam; pattern transfer resolution below 0.1 µm is possible. Transistor: three-terminal semiconductor device in which input signal (voltage or current depending on the type of transistor) controls output current, the most important semiconductor device; performs switching and amplifying functions; early on replaced bulky and inefficient vacuum triode in electronic circuits; invention of transistor (Schockley, Brattain and Bardeen) triggered electronic revolution after the World Word II; can operate as a discrete device or a building cell of integrated circuits; numerous kinds of transistors can be distinguished based on their design and principles of operation; two major types: field-effect (unipolar) transistor and bipolar transistor. 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 – amperes (or C/s - Coulombs/second) R - ohms (Ω) The resistance is influenced by specimen configuration Consider current moving through a conductor R = V/I with cross sectional area, A and a length, L Area (A) Resistivity (ρ) and Conductivity (σ) I Geometrically independent forms of Ohm’s Law Length (L) Probe Conductivity Measurements L R = Rsample + Rcontact A R = V/I RA Ωm − 2 ρ= = = Ωm − L m V It can give erroneous values if I contact resistance, Rcontact, is not Voltmeter negligible with respect to R L sample A I = V1/R1 I Rsample = V2/I V2 R = (V R )/V sample 2 1 1 R1 Current Source ρ = Rsample (A/L) Eliminates contact resistance V1 Voltmeter 1 Conductivity (σ) σ ()−Ω= m −1 Conductivity is the “ease of conduction” ρ Ranges over 27 orders of magnitude! Metals 107 (Ω.cm)-1 Semiconductors 10-6 -104 (Ω.cm)-1 Insulators 10-10 -10-20 (Ω.cm)-1 ResistivitiesResistivities ofof RealReal MaterialsMaterials Compound Resistivity Compound Resistivity (Ω-cm) (Ω-cm) Ca 3.9 × 10-6 Si ~ 0.1 Ti 42 × 10-6 Ge ~ 0.05 Mn 185 × 10-6 ReO3 36 × 10-6 Zn 5.9 × 10-6 Fe3O4 52 × 10-6 Cu 1.7 × 10-6 TiO2 9 × 104 Ag 1.6 × 10-6 ZrO2 1 × 109 Pb 21 × 10-6 Al2O3 1 × 1019 (a) Charge carriers, such as electrons, are deflected by atoms or defects and take an irregular path through a conductor. The average rate at which the carriers move is the drift velocity (v). (b) Valence electrons in the metallic bond move easily. (c) Covalent bonds must be broken in semiconductors and insulators for an electron to be able to move. (d) Entire ions must diffuse to carry charge in many ionically bonded materials. • Electronic conduction: – Flow of electrons, e- and electron holes, h+ • Ionic conduction – Flow of charged ions, Ag+ Electrical Conductivity in Metals If the nuclei are arranged in a perfectly ordered lattice then there should be no resistance to oppose the flow of current. Also, an increase in temperature causes an increase in the thermal population of the higher levels and it should increase the electrical conductivity. BUT, thermal vibrations of the nuclei increase electrical resistance so conductivity actually decreases with temperature. Movement of an electron through (a) a perfect crystal, (b) a crystal heated to a high temperature, and (c) a crystal containing atomic level defects. Scattering of the electrons reduces the mobility and conductivity. The effect of temperature on the electrical resistivity of a metal with a perfect crystal structure. The slope of the curve is the temperature resistivity coefficient. For most metals, resistivity increases approx. linearly with temperature. ρ=ρ o []1 +αTT()− o ρ is the resistivity at temperature T (measured in Celsius).
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