MIT6_012s09_lec04

MIT6_012s09_lec04 - MIT OpenCourseWare http/ocw.mit.edu...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 6.012 Microelectronic Devices and Circuits Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Lecture 4 PN Junction and MOS Electrostatics(I) Semiconductor Electrostatics in Thermal Equilibrium Outline • Non-uniformly doped semiconductor in thermal equilibrium • Relationships between potential, φ (x) and equilibrium carrier concentrations, p o (x), n o (x) –Boltzmann relations & “60 mV Rule” • Quasi-neutral situation Reading Assignment: Howe and Sodini; Chapter 3, Sections 3.1-3.2 6.012 Spring 2009 Lecture 4 1 1. Non-uniformly doped semiconductor in thermal equilibrium Consider a piece of n-type Si in thermal equilibrium with non-uniform dopant distribution: n-type ⇒ lots of electrons, few holes ⇒ focus on electrons N d N d (x) x 6.012 Spring 2009 Lecture 4 2 What is the resulting electron concentration in thermal equilibrium? OPTION 1: electron concentration follows doping concentration EXACTLY ⇒ n o (x) = N d (x) Gradient of electron concentration ⇒ net electron diffusion ⇒ not in thermal equilibrium ! n o, N d n o (x)=N d (x)? N d (x) x 6.012 Spring 2009 Lecture 4 3 OPTION 2: electron concentration uniform in space n o (x) = n ave ≠ f(x) If N d (x) ≠ n o (x) ⇒ ρ (x) ≠ ⇒ electric field ⇒ net electron drift ⇒ not in thermal equilibrium!...
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This note was uploaded on 09/24/2010 for the course EE 6.012 taught by Professor Charlessodini during the Spring '08 term at MIT.

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MIT6_012s09_lec04 - MIT OpenCourseWare http/ocw.mit.edu...

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