MIT6_012S09_lec04

# MIT6_012S09_lec04 - Lecture 4 PN Junction and MOS...

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Unformatted text preview: 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! Think about space charge density: ρ (x) ≈ q N d (x) − n o (x) [ ] n o, N d N d (x) x n o = f(x) ?...
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## This note was uploaded on 11/07/2011 for the course COMPUTERSC 6.012 taught by Professor Charlesg.sodini during the Spring '09 term at MIT.

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MIT6_012S09_lec04 - Lecture 4 PN Junction and MOS...

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