Electrical behavior Topic 3 Reading assignment Chung Multifunctional cementbased Materials Ch 2 Askeland and Phule The Science and Engineering of Materials 4th Ed Chapter 18 Supplementary reading Shackelford Materials Science for Engineers 6th Ed Ch 15 2003 Brooks Cole a division of Thomson Learning Inc Thomson Learning is a trademark used herein under license Figure 18 2 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 2003 Brooks Cole a division of Thomson Learning Inc Thomson Learning is a trademark used herein under license Mean free path The average distance that electrons can move without being scattered by other atoms Current I charge time 1 ampere 1 coulomb sec Current density I J A Current density The current flowing through per unit crosssectional area Electrical resistance R R A 1 A where is the electrical conductivity R V I I A A V V I J V Electric field The voltage gradient or volts per unit length dV dx V Electric field E V dV dx dV dx J E E Drift velocity v E v E where is the mobility Drift velocity The average rate at which electrons or other charge carriers move through a material under the influence of an electric or magnetic field Mobility The ease with which a charge carrier moves through a material Current density The current flowing through per unit cross sectional area Electric field The voltage gradient or volts per unit length Drift velocity The average rate at which electrons or other charge carriers move through a material under the influence of an electric or magnetic field Mobility The ease with which a charge carrier moves through a material Dielectric constant The ratio of the permittivity of a material to the permittivity of a vacuum thus describing the relative ability of a material to polarize and store a charge the same as relative permittivity I qnvA I qnvA J qnv A A J qnv E E v E qn Flux J n Dn dn dx Current density Jn q J n dn Jn q D n dx q D n dn dx Flux J p Dp dp dx Current density dp dp Jp q J p q D p q Dp dx dx Einstein relationship Dn n Dp p kT q Energy levels of an isolated atom 2003 Brooks Cole a division of Thomson Learning Inc Thomson Learning is a trademark used herein under license Energy bands of solid sodium 2003 Brooks Cole a division of Thomson Learning Inc Thomson Learning is a trademark used herein under license 2003 Brooks Cole a division of Thomson Learning Inc Thomson Learning is a trademark used herein under license Energy bands of an insulator Valence band The energy levels filled by electrons in their lowest energy states Conduction band The unfilled energy levels into which electrons can be excited to provide conductivity Energy gap Bandgap The energy between the top of the valence band and the bottom of the conduction band that a charge carrier must obtain before it can transfer a charge 2003 Brooks Cole a division of Thomson Learning Inc Thomson Learning is a trademark used herein under license 2003 Brooks Cole a division of Thomson Learning Inc Thomson Learning is a trademark used herein under license Holes are in the valence band Conduction electrons are in the conduction band Holes Unfilled energy levels in the valence band Because electrons move to fill these holes the holes move and produce a current Radiative recombination Recombination of holes and electrons that leads to emission of light this occurs in direct bandgap materials Electrical conduction through a composite material consisting of three components 1 2 and 3 that are in a parallel configuration 123 V I Resistance due to component i R i i Ai Current through component i Ii VA i i Total current through the composite I I1 I 2 I 3 V A1 A2 A3 1 2 3 Total resistance R A1 A 2 A 3 Total current I V A1 A2 V R V A 1 A 2 A 3 A3 V A1 A 2 A 3 1 2 3 A1 A2 1 1 1 1 A1 A 2 A 3 2 A1 A 2 A 3 A3 1 3 A1 A 2 A 3 1 1 f1 f2 1 2 Rule of Mixtures 1 f3 3 Electrical conduction through a composite material consisting of three components 1 2 and 3 that are in a series configuration 1 2 3 V Area A I Vi IR i I i Li A Total voltage drop I V 1 L1 A 2L2 3L3 Total resistance R L L 1 2 L 3 A Total voltage drop V IR I L 1 L L 2 A 3 Total voltage drop I V 1 L1 A V IR I L 1 2L2 L 2 A 3L3 L 3 I 1L1 2 L 2 A I L 1 3L3 L L 2 A 3 L L L 2 2 3 3 1 1 L1 L 2 L 3 1 f 1 2 f 2 3 f 3 Rule of Mixtures Conduction through a composite material with an insulating matrix and short conductive fibers 2003 Brooks Cole a division of Thomson Learning Inc Thomson Learning is a trademark used herein under license Percolation threshold Minimum volume fraction of conductive fibers or particles for adjacent fibers or particles to touch each other and form a continuous conductive path Conduction through an interface Contact resistance Rc Rc 1 A c A where c is the contact resistivity Energy bands of an intrinsic semiconductor Without thermal excitation With thermal excitation Intrinsic silicon Without thermal excitation With thermal excitation Electrical conductivity of a semiconductor q n n q p p where q magnitude of the charge of an electron n number of conduction electrons per unit volume p number of holes per unit volume n mobility of conduction electrons and p mobility of conduction holes For an intrinsic semiconductor n p q n n p Current density due to both an electric field and a concentration gradient qn E qD dn Jn n n dx qp E qD dp Jp p p dx J Jn Jp Intrinsic semiconductor A semiconductor in which properties are controlled by the element or compound that makes the semiconductor and not by dopants or impurities Extrinsic semiconductor A semiconductor prepared by adding dopants which determine the number and type of charge carriers Doping Deliberate addition of controlled amounts of other elements to increase the number of charge carriers in a semiconductor Extrinsic semiconductor doped with an electron donor Without thermal excitation With thermal excitation 2003 Brooks Cole a division of Thomson Learning Inc Thomson Learning is a trademark used herein under license Energy bands Intrinsic semiconductor Extrinsic semiconductor doped with an electron donor …