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These PowerPoint color diagrams can only be used by instructors if the 3rd Edition has been adopted for his/her course. Permission is given to individuals who have purchased a copy of the third edition with CD-ROM Electronic Materials and Devices to use these slides in seminar, symposium and conference presentations provided that the book title, author and © McGraw-Hill are displayed under each diagram. Metal interconnects are used in microelectronics to wire the devices within the chip, the intergraded circuit. Multilevel interconnects are used for implementing the necessary interconnections. |SOURCE: Dr. Don Scansen, Semiconductor Insights, Kanata, Ontario, Canada Drift of electrons in a conductor in the presence of an applied electric field. Electrons drift with an average velocity vdx in the xdirection.(Ex is the electric field.) Fig 2.26 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Ex u x + Vibrating Cu ions V (b) (a) (a) A conduction electron in the electron gas moves about randomly in a metal (with a mean speed u) being frequently and randomly scattered by by thermal vibrations of the atoms. In the absence of an applied field there is no net drift in any direction. (b) In the presence of an applied field, Ex, there is a net drift along the x-direction. This net drift along the force of the field is superimposed on the random motion of the electron. After many scattering events the electron has been displaced by a net distance, x, from its initial position toward the positive terminal Fig 2.2 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Velocity gained along x Present time vx 1-u x1 Last collision Electron 1 t1 vx 2-u x2 Free time time t Electron 2 t2 t time v x3-u x3 Electron 3 t3 time t Velocity gained in the x-direction at time t from the electric field (Ex) for three electrons. There will be N electrons to consider in the metal. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Electric field E s1 x 1 Collision uy1 Start 0 Collision p t2 t1 ux1 3 t3 Finish 2 4 s = x Distance drifted in total time t The motion of a single electron in the presence of an electric field E. During a time interval ti, the electron traverses a distance si along x. After p collisions, it has drifted a distance s = x. Fig 2.4 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) S = a2 =u a u Electron Scattering of an electron from the thermal vibrations of the atoms. The electron travels a mean distance = u between collisions. Since the scattering cross sectional area is S, in the volume S there must be at least one scatterer, Ns(Su) = 1. Fig 2.5 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Strained region by impurity exerts a scattering force F = - d (PE) /dx I Two different types of scattering processes involving scattering from impurities alone and thermal vibrations alone. Fig 2.6 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Silicon electron mobility 1 t 1 m = = 1 + 1 t lattice t impurity 1 ml + 1 mi W.F. Beadle, et. al.,”Quick reference manual for semiconductor engineers,” Wiley, NY, 1985. Diffusivity (cm2/s) Mobility (cm2/V-s) 2000 Inconel-825 NiCr Heating Wire 1000 Iron Tungsten Resistivity (n m) Monel-400 T Tin 100 Platinum Copper Nickel Silver 10 100 1000 10000 Temperature (K) The resistivity of various metals as a function of temperature above 0 °C. Tin melts at 505 K whereas nickel and iron go through a magnetic to non-magnetic (Curie) transformations at about 627 K and 1043 K respectively. The theoretical behavior ( ~ T) is shown for reference. [Data selectively extracted from various sources including sections in Metals Handbook, 10th Edition, Volumes 2 and 3 (ASM, Metals Park, Ohio, 1991)] Fig 2.7 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)