Lecture25-MOSTransQuantitativeId-Vd-Vg

Lecture25-MOSTransQu - Lecture 25 MOSFET Basics(Understanding with Math Reading Pierret 17.1-17.2 and Jaeger 4.1-4.10 and Notes Georgia Tech ECE

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ECE 3040 - Dr. Alan Doolittle Georgia Tech Lecture 25 MOSFET Basics (Understanding with Math) Reading: Pierret 17.1-17.2 and Jaeger 4.1-4.10 and Notes
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ECE 3040 - Dr. Alan Doolittle Georgia Tech MOS Transistor I-V Derivation With our expression relating the Gate voltage to the surface potential and the fact that S =2 F we can determine the value of the threshold voltage  area unit per e capacitanc oxide the is where, devices) channel - p (for 2 2 2 devices) channel - n (for 2 2 2 ox ox ox F S D ox S F T F S A ox S F T x C qN C V qN C V Where we have made use of the use of the expression, o S S K 
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ECE 3040 - Dr. Alan Doolittle Georgia Tech MOS Transistor I-V Derivation Coordinate Definitions for our “NMOS” Transistor x=depth into the semiconductor from the oxide interface. y=length along the channel from the source contact z=width of the channel x c (y) = channel depth (varies along the length of the channel). n(x,y)= electron concentration at point (x,y) n (x,y)=the mobility of the carriers at point (x,y) Device width is Z Channel Length is L Assume a “Long Channel” device (for now do not worry about the channel length modulation effect)
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ECE 3040 - Dr. Alan Doolittle Georgia Tech MOS Transistor I-V Derivation Concept of Effective mobility The mobility of carriers near the interface is significantly lower than carriers in the semiconductor bulk due to interface scattering. Since the electron concentration also varies with position, the average mobility of electrons in the channel, known as the effective mobility, can be calculated by a weighted average,  ) ( 0 2 ) ( 0 ) ( 0 ) ( 0 ) , ( ) , ( ) ( / arg ) , ( ) ( , ) , ( ) , ( ) , ( y x x x n N n y x x x N y x x x y x x x n n c c c c dx y x n y x y Q q cm e ch dx y x n q y Q defining or dx y x n dx y x n y x Empirically  constants are , 1 and where V V o T GS o n
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ECE 3040 - Dr. Alan Doolittle Georgia Tech MOS Transistor I-V Derivation Drain Current-Voltage Relationship In the Linear Region, V GS >V T and 0<V DS <V dsat dy d n q nE q J J n qD nE q J n y n Ny N N n N Neglecting the diffusion current, and recognizing the current is only in the y-direction,
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ECE 3040 - Dr. Alan Doolittle Georgia Tech MOS Transistor I-V Derivation Drain Current-Voltage Relationship In the Linear Region, V GS >V T and 0<V DS <V dsat  DS DS DS c c V N n D V N n D V N n L y y D N n y x x x n y x x x Ny Ny D d Q L Z I d Q Z L I d Q Z dy I dy d Q Z dx y x n y x q dy d Z dx J Z dxdz J I 0 0 0 0 ) ( 0 ) ( 0 ) , ( ) , ( To find I D , we need an expression relating the electrostatic potential,  and Q N
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ECE 3040 - Dr. Alan Doolittle Georgia Tech MOS Transistor I-V Derivation “Capacitor-Like” Model for Q N Assumptions: •Neglect all but the mobile inversion charge (valid for deep inversion)
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This note was uploaded on 08/23/2011 for the course ECE 3040 taught by Professor Doolittle during the Spring '11 term at University of Florida.

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Lecture25-MOSTransQu - Lecture 25 MOSFET Basics(Understanding with Math Reading Pierret 17.1-17.2 and Jaeger 4.1-4.10 and Notes Georgia Tech ECE

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