MIT6_012s09_lec04

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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 .

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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?

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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) 0 electric field net electron drift not in thermal equilibrium!

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