Transcript ppt
ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 20: October 26, 2011 Driving Large Capacitive Loads 1 Penn ESE370 Fall2011 -- DeHon Today • How do we drive a large load? – Stages and buffer sizing – Minimum delay • Back to CMOS today 2 Penn ESE370 Fall2011 -- DeHon Message • To drive large loads – Scale buffers geometrically – Exponential scale up in buffer size • Scale factor: 3—4 typically – One origin of fanout 4 target • Drains contribute capacitance, too • Can formulate math to optimize 3 Penn ESE370 Fall2011 -- DeHon Start Cdiff=0 (same model we’ve been assuming) 4 Penn ESE370 Fall2011 -- DeHon One Stage • How size to minimize delay? 5 Penn ESE370 Fall2011 -- DeHon One Stage • Delay equation? R0 R0 2WN C0 Cload 2 WN 6 Penn ESE370 Fall2011 -- DeHon Minimize • Differentiate and set to zero. R0 R0WN C0 Cload WN R0 R0C0 2 Cload 0 WN • What’s WN? 7 Penn ESE370 Fall2011 -- DeHon Solving for size Cload WN C0 2 Cload WN C0 8 Penn ESE370 Fall2011 -- DeHon Concrete? • What is WN for Cload=4x104? 9 Penn ESE370 Fall2011 -- DeHon N-stage 10 Penn ESE370 Fall2011 -- DeHon N-stage Delay WN1 WN2 WN 3 R0 WNi WNi 1 2 ... ... Cload WN1 WN2 WNi 1 WNi 2 WNN 11 Penn ESE370 Fall2011 -- DeHon Size WNi to minimize delay • How minimize? WN1 WN 2 WN 3 R0 WNi WNi 1 2 ... ... Cload 2 WNN WN1 WN2 WNi 1 WNi 12 Penn ESE370 Fall2011 -- DeHon Size WNi to minimize delay • Take partial derivative wrt WNi WN1 WN 2 WN 3 R0 WNi WNi 1 2 ... ... Cload 2 WNN WN1 WN2 WNi 1 WNi 1 WNi 1 2 ... 0 0 0 ... WNi 1 0 0 WNi 13 Penn ESE370 Fall2011 -- DeHon Solving for WNi 1 WNi 1 2 ... 0 0 0 ... WNi 1 0 0 WNi WNi WNi 1 WNi 1 WNi WNi WNi 1 WNi 1 14 Penn ESE370 Fall2011 -- DeHon Delay WN1 WN 2 WN 3 R0 WNi WNi 1 2 ... ... Cload 2 WNN WN1 WN2 WNi 1 WNi WNi WNi 1 WNi 1 WNi 15 Penn ESE370 Fall2011 -- DeHon Stage Delay WN1 WN 2 WN 3 R0 WNi WNi 1 2 ... ... Cload 2 WNN WN1 WN2 WNi 1 WNi WN1 WNi WNi 1 Cload f 2 WNi 1 WNi WNN 2C0 f Penn ESE370 Fall2011 -- DeHon N 1 Cload 4C0 16 Stage Delay f N 1 Cload 4C0 Cload f N 1 4C0 17 Penn ESE370 Fall2011 -- DeHon Math Cload f N 1 4C0 C 1 C load load N 1 ln f ln ln 4C0 N 1 4C0 Penn ESE370 Fall2011 -- DeHon f e C lo a d 1 ln 4C 0 N 1 18 Total Delay WNi WNi 1 f WNi 1 WNi WN1 WN 2 WN 3 R0 WNi WNi 1 2 ... ... Cload 2 WNN WN1 WN2 WNi 1 WNi TotalDelay 2(N 1) f 19 Penn ESE370 Fall2011 -- DeHon Total Delay TotalDelay 2(N 1) f f e C lo a d 1 ln 4C 0 N 1 TotalDelay 2(N 1)e C load 1 ln 4C 0 N 1 20 Penn ESE370 Fall2011 -- DeHon How many stages? • How does this trend with N? TotalDelay 2(N 1)e C load 1 ln 4C 0 N 1 21 Penn ESE370 Fall2011 -- DeHon Plot Delay vs. N 450 400 350 300 250 Delay ( units) Series1 200 150 100 50 0 1 Penn ESE370 Fall2011 -- DeHon 2 3 N 4 5 6 7 8 9 10 11 12 22 Zoom Delay vs. N 100 90 80 70 Series1 60 50 40 30 1 2 3 4 5 6 7 8 9 10 11 12 23 Penn ESE370 Fall2011 -- DeHon Minimize TotalDelay 2(N 1)e 0e C load 1 ln 4C N 1 0 C load 1 ln 4C 0 N 1 2 lnC load 1 4C N 1 0 Cload 1 (N 1)ln e 4C0 N 1 24 Penn ESE370 Fall2011 -- DeHon Solve 0e C load 1 ln 4C 0 N 1 2 lnC load 1 4C 0 N 1 Cload 1 (N 1)ln e 4C0 N 1 Cload 1 0 1 ln 4C0 N 1 Cload N 1 ln 4C0 Penn ESE370 Fall2011 -- DeHon 25 Concrete • What is optimal N for Cload=4x104? Cload N 1 ln 4C0 26 Penn ESE370 Fall2011 -- DeHon Zoom Delay vs. N 100 90 80 70 Series1 60 50 40 30 1 2 3 4 5 6 7 8 9 10 11 12 27 Penn ESE370 Fall2011 -- DeHon Optimum Scale Up f e C lo a d 1 ln 4C 0 N 1 Cload N 1 ln 4C0 Penn ESE370 Fall2011 -- DeHon What is f? 28 Optimum Scale Up f e C lo a d 1 ln 4C 0 N 1 Cload N 1 ln 4C0 f e Penn ESE370 Fall2011 -- DeHon Deep result – take time to digest. 29 Delay at Optimum Cload N 1 ln 4C0 f e TotalDelay 2(N 1) f Cload TotalDelay 2e ln 4C0 30 Penn ESE370 Fall2011 -- DeHon Cdiff=gCgate 31 Penn ESE370 Fall2011 -- DeHon Day 11 Contact Capacitance • n+ contacts are formed by doping = diffusion • Depletion under contact – Contact-Body capacitance • Depletion around perimeter of contact – Also contact-Body capacitance 32 Penn ESE370 Fall2011 -- DeHon Day 11 Contact/Diffusion Capacitance • Cj – diffusion depletion • Cjsw – sidewall capacitance • LS – length of diffusion LS Cdiff C j LSW C jsw 2LS W 33 Penn ESE370 Fall2011 -- DeHon Day 11 Capacitance Roundup • • • • • CGS=CGCS+CO CGD=CGCD+CO CGB=CGCB CSB=Cdiff CDB=Cdiff 34 Penn ESE370 Fall2011 -- DeHon Impact on Capacitance 35 Penn ESE370 Fall2011 -- DeHon Contact/Diffusion Capacitance • Cj – diffusion depletion • Cjsw – sidewall capacitance • LS – length of diffusion Cdiff Cdiff 0W LS Cdiff C j LSW C jsw 2LS W 36 Penn ESE370 Fall2011 -- DeHon Diffusion Capacitance • What does this do to model? – Delay of middle stage? 37 Penn ESE370 Fall2011 -- DeHon Stage Delay R0 W 1 Cdiff 0 W 2 C0 W 1 Cdiff 0 gC0 R0 W 1 gC0 W 2 C0 W 1 Penn ESE370 Fall2011 -- DeHon 38 Stage Delay R0 W 1 gC0 W 2 C0 W 1 W 2 g W 1 39 Penn ESE370 Fall2011 -- DeHon N-stage Delay WN1 R0 WN1 WN2 WN2 WN 3 WNi WNi WNi 1 2g g g ... g ... Cload WNN 2 WN1 WN1 WN2 WN2 WNi 1 WNi WNi 40 Penn ESE370 Fall2011 -- DeHon N-stage Delay WN1 R WN1 WN2 WN2 WN 3 WNi WNi WNi 1 2g g g ... g ... 0 Cloa WNN 2 WN1 WN1 WN2 WN2 WNi 1 WNi WNi R0 WN1 WN2 WN 3 WNi WNi 1 2g N 1 ... ... Cload 2 WN1 WN2 WNi 1 WNi WNN 41 Penn ESE370 Fall2011 -- DeHon Impact on Min Wni ? • Partial Derivative unchanged R0 WN1 WN2 WN 3 WNi WNi 1 2g N 1 ... ... Cload WNN 2 WN1 WN2 WNi 1 WNi 42 Penn ESE370 Fall2011 -- DeHon Stage Delay: f unchanged (fixed N) WN1 WN 2 WN 3 R0 WNi WNi 1 2 ... ... Cload 2 WNN WN1 WN2 WNi 1 WNi WN1 WNi WNi 1 Cload f 2 WNi 1 WNi WNN 2C0 f Penn ESE370 Fall2011 -- DeHon N 1 Cload 4C0 43 Total Delay TotalDelay 2(N 1)( f g ) C load 1 ln 4C 0 N 1 2(N 1) g e Penn ESE370 Fall2011 -- DeHon 44 Impact of Gamma 450 400 350 300 Series1 250 Series2 Series3 200 Series4 150 100 50 g1.5 g1.0 g0.5 g0 0 1 2 3 4 5 6 7 8 9 10 11 12 45 Penn ESE370 Fall2011 -- DeHon Impact of Gamma 100 90 g1.5 80 Series1 Series2 70 Series3 Series4 60 50 g1.0 g0.5 g0 40 1 2 3 4 5 6 7 8 9 10 11 12 46 Penn ESE370 Fall2011 -- DeHon Minimize TotalDelay 2(N 1)e 0 g e C load 1 ln 4C N 1 0 C load 1 ln 4C 0 N 1 2 lnC load 1 4C N 1 0 Cload 1 (N 1)ln e 4C0 N 1 47 Penn ESE370 Fall2011 -- DeHon Solve 0 g e C load 1 ln 4C 0 N 1 2 lnC load 1 4C 0 N 1 Cload 1 (N 1)ln e 4C0 N 1 Cload 1 0 g f 1 ln 4C0 N 1 Cload 1 g f ln f 4C0 N 1 48 Penn ESE370 Fall2011 -- DeHon Solve Cload 1 g f ln f 4C0 N 1 C 1 g 1 ln load f 4C0 N 1 Cload 1 N 1 ln g 4C0 1 Penn ESE370 Fall2011 -- DeHon f 49 Optimum Scale Up f e C lo a d 1 ln 4C 0 N 1 Cload 1 N 1 ln g 4C0 1 Penn ESE370 Fall2011 -- DeHon f e 1 g f f 50 Optimal Staging g0 1g / f f e 51 Penn ESE370 Fall2011 -- DeHon F and gamma? • f=4 is optimal for what g? • f=3 is optimal for what g? 1g / f f e 52 Penn ESE370 Fall2011 -- DeHon Optimal Fanout • Clearer why we use f=4 as our benchmark? 53 Penn ESE370 Fall2011 -- DeHon Admin • Project – Should have baseline done – Have list of optimization ideas? 54 Penn ESE370 Fall2011 -- DeHon Idea • To drive large loads – Scale buffers geometrically – Exponential scale up in buffer size • Scale factor: 3—4 typically – One origin of fanout 4 target • Drains contribute capacitance, too • Can formulate math to optimize 55 Penn ESE370 Fall2011 -- DeHon