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MIT6_012S09_lec03 - Lecture 3 Semiconductor Physics(II...

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Lecture 3 Semiconductor Physics (II) Carrier Transport Outline • Thermal Motion • Carrier Drift • Carrier Diffusion Reading Assignment: Howe and Sodini; Chapter 2, Sect. 2.4-2.6 6.012 Spring 2009 Lecture 3 1
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1. Thermal Motion Undergo collisions with vibrating Si atoms ( Brownian motion ) Electrostatically interact with each other and with ionized (charged) dopants In thermal equilibrium, carriers are not sitting still: Characteristic time constant of thermal motion: mean free time between collisions τ c collison time [ s ] In between collisions, carriers acquire high velocity: v th thermal velocity [ cms 1 ] …. but get nowhere! 6.012 Spring 2009 Lecture 3 2
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Characteristic length of thermal motion: λ ≡ mean free path [cm] λ = v th τ c Put numbers for Si at room temperature: τ c 10 13 s v th 10 7 cms 1 λ 0.01 μ m For reference, state-of-the-art production MOSFET: L g ≈ 0.1 µm Carriers undergo many collisions as they travel through devices 6.012 Spring 2009 Lecture 3 3
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2. Carrier Drift Apply electric field to semiconductor: E electric field [V cm -1 ] net force on carrier F = ±qE Between collisions, carriers accelerate in the direction of the electrostatic field: v ( t ) = a t = ± qE m n , p t E 6.012 Spring 2009 Lecture 3 4
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But there is (on the average) a collision every τ c and the velocity is randomized: The average net velocity in direction of the field: v = v d = ± qE 2 m n , p τ c = ± q τ c 2 m n , p E This is called drift velocity [cm s -1 ]
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