Lecture 9ResistivityOhm’s LawSheet ResistanceUsing Sheet ResistanceIdealizationsIC CapacitorsMetal-Metal Capacitor LayoutCircuit ModelSurface Charge and Electric FieldR. T. HoweEECS 105 Fall 2001 Lecture 9Dept. of EECSUniversity of California at BerkeleyLecture 9• Last time:– Compensation– Drift current density• Today :– IC resistors– Metal-metal capacitors (start)R. T. HoweEECS 105 Fall 2001 Lecture 9Dept. of EECSUniversity of California at BerkeleyResistivityBulk silicon: uniform doping concentration, away from surfaces n-type example: in equilibrium, no=Nd. When we apply an electric field, n = Nd.ENqnEqJdnnnµµ==Resistivity ρn =R. T. HoweEECS 105 Fall 2001 Lecture 9Dept. of EECSUniversity of California at BerkeleyOhm’s Law• Current I in terms of Jn• Voltage V in terms of electric field– Result for RR. T. HoweEECS 105 Fall 2001 Lecture 9Dept. of EECSUniversity of California at BerkeleySheet Resistance• IC resistors have a specified thickness – not under the control of the circuit designer• Eliminate t by absorbing it into a new parameter: the sheet resistance===WLRWLtWtLRsqρρR. T. HoweEECS 105 Fall 2001 Lecture 9Dept. of EECSUniversity of California at BerkeleyUsing Sheet Resistance• Ion-implanted (or “diffused”) IC resistorR. T. HoweEECS 105 Fall 2001 Lecture 9Dept. of EECSUniversity of California at BerkeleyIdealizations• Why does current density Jn“turn”?• What is the thickness of the resistor?• What is the effect of the contact regions?R. T. HoweEECS 105 Fall 2001 Lecture 9Dept. of EECSUniversity of California at BerkeleyIC CapacitorsMetal layers separated by insulators Æ get intentional (or parasitic) capacitor dielectricMetal 2Metal 1ddtCε=R. T. HoweEECS 105 Fall 2001 Lecture 9Dept. of EECSUniversity of California at BerkeleyMetal-Metal Capacitor Layout A A’ A’A Overlap area A12 1 2R. T. HoweEECS 105 Fall 2001 Lecture 9Dept. of EECSUniversity of California at BerkeleyCircuit Model• Capacitance between metal 1 and metal 2:• Other capacitors: what is terminal 3?1212AtCdd=εR. T. HoweEECS 105 Fall 2001 Lecture 9Dept. of EECSUniversity of California at BerkeleySurface Charge and Electric Field x 0 td Q (C/cm2) + - V x td V
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