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MIT6_012F09_lec11 - 6.012 Microelectronic Devices and...

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6.012 - Microelectronic Devices and Circuits Lecture 11 - MOSFETs II; Large Signal Models - Outline Announcements On Stellar - 2 write-ups on MOSFET models The Gradual Channel Approximation (review and more) MOSFET model: 0 K (v GS K (v GS with K (W/L) µ e gradual channel approximation (Example: n-MOS) for (v GS – V T )/ α 0 v DS (cutoff) i D – V T ) 2 /2 α for 0 (v GS – V T )/ α v DS (saturation) – V T α v DS /2)v DS for 0 v DS (v GS – V T )/ α (linear) C ox * , V T = V FB – 2 φ p-Si + [2 ε Si qN A (|2 φ p-Si | – v BS )] 1/2 /C ox * and α = 1 + [( ε Si qN A /2(|2 φ p-Si | – v BS )] 1/2 /C ox (frequently α 1) Refined device models for transistors (MOS and BJT) Other flavors of MOSFETS: p-channel, depletion mode The Early Effect: 1. Base-width modulation in BJTs: w B (v CE ) 2. Channel-length modulation in MOSFETs: L(v DS ) Charge stores: 1. Junction diodes 2. BJTs 3. MOSFETs Extrinsic parasitics: Lead resistances, capacitances, and inductances Clif Fonstad, 3/18/08 Lecture 11 - Slide 1
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An n-channel MOSFET showing gradual channel axes 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 Extent into plane = W Gradual Channel Approximation: - A one-dimensional electrostatics problem in the x direction is solved to find the channel charge, q N * (y); this charge depends on v GS , v CS (y) and v BS . - A one-dimensional drift problem in the y direction then gives the channel current, i D , as a function of v GS , v DS , and v BS . Clif Fonstad, 3/18/08 Lecture 11 - Slide 2
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Gradual Channel Approximation i-v Modeling (n-channel MOS used as the example) The Gradual Channel Approximation is the approach typically used to model the drain current in field effect transistors.* It assumes that the drain current, i D , consists entirely of carriers flowing in the channel of the device, and is thus proportional to the sheet density of carriers at any point and their net average velocity. It is not a function of y, but its components in general are: i D = " W # " q # n ch * ( y ) # s ey ( y ) In this expression, W is the width of the device, -q is the charge on each electron, n* ch (y) is sheet electron concentra- tion in the channel (i.e. electrons/cm 2 ) at y, and s ey (y) is the net electron velocity in the y-direction. If the electric field is not too large, s ey (y) = - µ e E y (y) , and i D = " W # q # n ch * ( y ) # μ e E y ( y ) = W # q # n ch * ( y ) # μ e dv CS ( y ) dy Cont. * Junction FETs (JFETs), MEtal Semiconductor FETs (MESFETs 1 ), and Heterojunction FETs Clif Fonstad, 3/18/08 (HJFETs 2 ), as well as Metal Oxide Semiconductor FETs (MOSFETs). Lecture 11 - Slide 3 1. Also called Shottky Barrrier FETs (SBFETs). 2. Includes HEMTs, TEGFETs, MODFETs, SDFETs, HFETs, PHEMTs, MHEMTs, etc.
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i D = W " q " n ch * ( y ) " μ e dv CS ( y ) dy GCA i-v Modeling, cont. 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 We have: To eliminate the derivative from this equation we integrate both sides with respect to y from the source (y = 0) to the drain (y = L). This corresponds to integrating the right hand side with respect to v CS from 0 to v DS , because v CS (0) = 0 to v CS (L) = v DS : i D 0 L " dy = W # μ e # q # n ch * ( y ) dv CS ( y ) dy 0 L " dy = W # μ e # q # n ch * ( v CS ) 0 v DS " dv CS
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