Lecture21-MOS+Transitor+Quantitative+Id-Vd-Vg_posted_

Lecture21-MOS+Transitor+Quantitative+Id-Vd-Vg_posted_ - ECE...

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ECE 3040 - Dr. Ying Zhang Georgia Tech ECE 3040: Microelectronic Circuits Lecture 21 Reading: Pierret 17.1, 17.2, Jaeger 4.1-4.11, Notes
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ECE 3040 - Dr. Ying Zhang Georgia Tech Recapture MOS Capacitor Quantitative Solution Depletion: () width depletion the is W where W) x (0 for + = A A D qN N N n p q ρ The electric field in the depletion region: x W K qN x E o S A = ε ) ( The electrostatic potential in the depletion region: 2 2 x W K qN o S A = φ
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ECE 3040 - Dr. Ying Zhang Georgia Tech The depletion width, W S A o S qN K W φ ε 2 = The depletion width at the inversion-depletion transition, W T = = i A A o S F A o S T n N N q kT K qN K W ln 4 2 2 2 NOTE: To obtain the equations for n-type substrates, we simply repeat the above procedure replacing N A with -N D Recapture MOS Capacitor Quantitative Solution Depletion:
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ECE 3040 - Dr. Ying Zhang Georgia Tech () F S S o S A thickness oxide ox S S G K qN x K K V φ ε 2 0 for 2 + = Relates the applied gate voltage to the surface potential. Recapture MOS Capacitor Quantitative Solution Depletion: Inversion and Accumulation In inversion and accumulation , the vast majority of the gate voltage is dropped across the oxide In inversion, the depletion width remains ~ constant Thus, φ S can not be much less (greater) than 0 for p-type (n-type) Thus, φ S can not be much greater (less) than 2 φ F for p-type (n-type)
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ECE 3040 - Dr. Ying Zhang Georgia Tech ± Quantitative MOS Transistor Device Physics ± MOS Transistor Applications ± Deviation From Ideal ± Enhancement Mode Versus Depletion Mode Agenda
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ECE 3040 - Dr. Ying Zhang Georgia Tech MOS Transistor I-V Derivation With our expression relating the Gate voltage to the surface potential and the fact that φ S =2 φ 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 ε φ = = + = Where we have made use of the expression, o S S K ε=
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ECE 3040 - Dr. Ying Zhang 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) μ 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. Ying Zhang 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.
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Lecture21-MOS+Transitor+Quantitative+Id-Vd-Vg_posted_ - ECE...

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