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Unformatted text preview: CMOS VLSI For Computer Engineering Lecture 4 INTERCONNECT CMOS VLSI for Computer Engineering 1 Parts adapted from Lecture notes by Mary Jane Irwin www.cse.psu.edu/~cg477 , J. Rabaey et al. http://bwrc.eecs.berkeley.edu/IcBook and David Harris http://http://www3.hmc.edu/~harris/cmosvlsi/4e January 16, 2012 CMOS VLSI for Computer Engineering Interconnect Interconnect Delay has become a significant portion of the available clock period High frequency effects necessitates understanding of transmission line effects. Using lumped models versus distributed models can lead to over design if one is not careful Monday, August 20, 2007 Prof. Luke Theogarajan 2 CMOS VLSI for Computer Engineering Examples of Modern Day Interconnect Monday, August 20, 2007 Prof. Luke Theogarajan 3 CMOS VLSI for Computer Engineering Physical parameters of the wire: Capacitance Monday, August 20, 2007 Prof. Luke Theogarajan 4 Parallel plate model = di WL t di CMOS VLSI for Computer Engineering Permittivity of typical Dielectric Materials used Monday, August 20, 2007 Prof. Luke Theogarajan 5 Material di Free space 1 Teflon AF 2.1 Aromatic thermosets (SiLK) 2.6 2.8 Polyimides (organic) 3.1 3.4 Fluorosilicate glass (FSG) 3.2 4.0 Silicon dioxide 3.9 4.5 Glass epoxy (PCBs) 5 Silicon nitride 7.5 Alumina (package) 9.5 Silicon 11.7 CMOS VLSI for Computer Engineering Parallel plate model is not sufficient! Monday, August 20, 2007 Prof. Luke Theogarajan 6 Full analytical calculation for a rectangular conductor is difficult but we can make some useful approximations CMOS VLSI for Computer Engineering Contd Monday, August 20, 2007 Prof. Luke Theogarajan 7 We can approximate the rectangular conductor as a cylindrical one without too much error since for the fringing fields which are far way from the conductor the shape does not matter too much. CMOS VLSI for Computer Engineering How to calculate the capacitance? Assume a unit charge Q distributed uniformly over the length of the conductor. The E field can be calculated from Gauss law and the potential can be determined by integrating the field, from which we can derive the capacitance. A few examples will make this clear Monday, August 20, 2007 Prof. Luke Theogarajan 8 CMOS VLSI for Computer Engineering Examples Monday, August 20, 2007 Prof. Luke Theogarajan 9 2r 1 2r 2 E = Q 2 epr V = Q 2 per dr = Q 2 pe r 1 r 2 ln r 2 r 1 ae Q = 2 pe ln r 2 r 1 ae V C = dQ dV = 2 pe ln r 2 r 1 ae 2r t Coaxial Cable Wire Pair Just like coaxial cable but need to use superposition E = Q 2 pex V = Q 2 pex dx r t + Q 2 pex dx t r = Q ep ln t r ae C = dQ dV = pe ln t r ae CMOS VLSI for Computer Engineering What about a wire over a conductor?...
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 Fall '11
 LukeTheogarajan

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