Berkeley ELENG 105 - Lecture Notes (11 pages)

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Lecture Notes



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Lecture Notes

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Pages:
11
School:
University of California, Berkeley
Course:
Eleng 105 - Microelectronic Devices and Circuits
Microelectronic Devices and Circuits Documents

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EECS 105 Spring 2005 Lecture 3 R T Howe Lecture 3 Last time Drift current density Ohm s and resistivity and IC resistors Today Applied electrostatics Gauss s Law boundary conditions IC capacitors metal metal and pn junction Dept of EECS University of California Berkeley EECS 105 Spring 2005 Lecture 3 R T Howe Electrostatics a Tool for Device Modeling Physics approach vector calculus highly symmetrical problems E E 2 Dept of EECS University of California Berkeley EECS 105 Spring 2005 Lecture 3 R T Howe One Dimensional Electrostatics Gauss s Law d E dx Potential Def d E dx Poisson s Eqn Dept of EECS 2 d d d dx 2 dx dx University of California Berkeley EECS 105 Spring 2005 Lecture 3 R T Howe Boundary Conditions x 1 2 x 0 x 0 x 0 1 E x 0 Q 2 E x 0 Q is a surface charge C cm2 located at x 0 Dept of EECS University of California Berkeley EECS 105 Spring 2005 Lecture 3 R T Howe Silicon Silicon Dioxide Interface 1 3 2 E x common materials 1 silicon s 11 7 o 2 1 2 silicon dioxide SiO2 ox 3 9 o 0 Dept of EECS x University of California Berkeley EECS 105 Spring 2005 Lecture 3 R T Howe Getting Past the Math Electric field vector points from positive to negative charge Electric field points downhill on a plot of potential Electric field is confined to a narrow charged region in which the positive charge is balanced by an equal and opposite negative charge Boundary conditions on potential or electric field can patch together solutions from regions of differing material properties Gauss s law in integral form relates the electric field at the edges of a region to the charge inside Often the field on one side is known to be zero e g because it s on the outside of the charged region which allows the electric field at an interface to be solved for directly Dept of EECS University of California Berkeley EECS 105 Spring 2005 Lecture 3 R T Howe IC Capacitors Metal layers separated by insulators get intentional or parasitic capacitor Metal 2 Metal 1 C Dept of EECS dielectric d td



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