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# lec12 - 6.012 Electronic Devices and Circuits Lecture 12...

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6.012 - Electronic Devices and Circuits Lecture 12 - MOSFET Basics - Outline Announcements On web site - 2 write-ups on MOSFET models Review - MOS Capacitor (n-MOS example) Flat-band voltage : V FB v GB such that f (0) = f p-Si ; V FB = f p-Si f m Threshold voltage: V T v GC such that f (0) = – f p-Si ; V T (v BC ) = V FB – 2 f p-Si + [2 e Si qN A (|2 f p-Si | – v BC )] 1/2 /C ox * (v GC at threshold) Inversion layer sheet charge density: q N * = – C ox * [v GC – V T (v BC )] The MOSFET - qualitative explanation Definition of structure: cross-section (Example: n-channel MOSFET) Gate action (creating a channel) and channel current (drift) Quantitative modeling - the Gradual-Channel Approximation The gate and substrate currents: i G (v GS , v DS ,v BS ), i B (v GS , v DS ,v BS ) The drain current: i D (v GS , v DS ,v BS ) 1. the in-plane problem (relating voltage drop along channel to channel charge) 2. the normal problem (relating gate voltage to channel charge) 3. the full drain current expression (quadratic approximation) Characteristics and regions of operation V T V FB 0 v GC Depletion Inversion Accumulation v BC < 0 p-Si n+ B C G SiO 2 + v GC v BC + Clif Fonstad, 10/03 Lecture 12 - Slide 1

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An n-channel MOSFET capacitor Reviewing the results of Lecture 11 Clif Fonstad, 10/03 Lecture 12 - Slide 2 V T V FB 0 v GC Depletion Inversion Accumulation v BC < 0 p-Si n+ B C G SiO 2 + v GC v BC + Flat - band voltage : V FB v GB at which f (0) = f p - Si V FB = f p - Si - f m Threshold voltage : V T v GC at which f (0) = - f p - Si + v BC V T ( v BC ) = V FB - 2 f p - Si + 1 C ox * 2 e Si qN A 2 f p - Si - v BC [ ] { } 1/ 2 Inversion layer sheet charge density: q N * = - C ox * v GC - V T ( v BC ) [ ] Accumulation layer sheet charge density: q P * = - C ox * v GB - V FB ) [ ]
An n-channel MOSFET p-Si B G + v GS n+ D n+ S v DS v BS + i G i B i D Clif Fonstad, 10/03 Lecture 12 - Slide 3

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An n-channel MOSFET showing gradual channel axes Extent into plane = W p-Si B G + v GS n+ D n+ S v DS v BS + i G i B i D L 0 y x 0 Clif Fonstad, 10/03 Lecture 12 - Slide 4
Gradual Channel Approximation i-v Modeling (n-channel MOS used as the example) Restrict voltage ranges: v BS 0, v DS 0, so i G (v GS , v DS ,v BS ) 0, i B (v GS , v DS ,v BS ) 0 The issue is the drain current (and only when v GS > V T , otherwise i D = 0): The in-plane problem:

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lec12 - 6.012 Electronic Devices and Circuits Lecture 12...

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