L30 May 61 EE5342 – Semiconductor Device Modeling and Characterization Lecture 30 - Spring 2004 Professor Ronald L. Carter

L30 May 62 MOSFET circuit parameters

L30 May 63 Estimating LAMBDA

L30 May 64 SPICE mosfet Model Instance CARM*, Ch. 4, p. 290 L = Ch. L. [m] W = Ch. W. [m] AD = Drain A [m 2 ] AS = Source A[m 2 ] NRD, NRS = D and S diff in squares M = device multiplier

L30 May 65 SPICE mosfet model levels Level 1 is the Schichman-Hodges model Level 2 is a geometry-based, analytical model Level 3 is a semi-empirical, short- channel model Level 4 is the BSIM1 model Level 5 is the BSIM2 model, etc.

L30 May 66 SPICE Parameters Level (Static)

L30 May 67 SPICE Parameters Level (Static) * 0 = aluminum gate, 1 = silicon gate opposite substrate type, 2 = silicon gate same as substrate.

L30 May 68 SPICE Parameters Level (Q & N)

L30 May 69 Level 1 Static Const. For Device Equations Vfb = -TPG*EG/2 -Vt*ln(NSUB/ni) - q*NSS*TOX/eOx VTO = as given, or = Vfb + PHI + GAMMA*sqrt(PHI) KP = as given, or = UO*eOx/TOX CAPS are spice pars., technological constants are lower case

L30 May 610 Level 1 Static Const. For Device Equations  = KP*[W/(L-2*LD)] = 2*K, K not spice GAMMA = as given, or = TOX*sqrt(2*eSi*q*NSUB)/eOx 2*phiP = PHI = as given, or = 2*Vt*ln(NSUB/ni) I SD = as given, or = JS*AD I SS = as given, or = JS*AS

L30 May 611 Level 1 Static Device Equations vgs < VTH, ids = 0 VTH < vds + VTH < vgs, id = KP*[W/(L-2*LD)]*[vgs-VTH-vds/2] *vds*(1 + LAMBDA*vds) VTH < vgs < vds + VTH, id = KP/2*[W/(L-2*LD)]*(vgs - VTH)^2 *(1 + LAMBDA*vds)

L30 May 612 e - e - e - e - e n-channel enhancement MOSFET in ohmic region 0< V T < V G V B < 0 E Ox,x > 0 Acceptors Depl Reg V S = 0 0< V D < V DS,sat n+ p-substrate Channel e- channel ele + implant ion

L30 May 613 Subthreshold conduction Below O.S.I., when the total band-bending < 2|  p |, the weakly inverted channel conducts by diffusion like a BJT. Since V GS >V DS, and below OSI, then N a >n S >n D, and electr diffuse S --> D Electron concentration at Source Concentration gradient driving diffusion

L30 May 614 Subthreshold current data Figure 11.4* Figure 10.1**

L30 May 615 Mobility variation due to E depl Figures 11.7,8,9*

L30 May 616 Velocity saturation effects Figure 11.10*

L30 May 617 SPICE Parameters Level 2

L30 May 618 SPICE Parameters Level 2 & 3

L30 May 619 Level 2 Static Device Equations Accounts for variation of channel potential for 0 < y < L For vds < vds,sat = vgs - Vfb - PHI +  2 *[1-sqrt(1+2(vgs-Vfb-vbs)/  2 ] id,ohmic = [  /(1-LAMBDA*vds)] *[vgs - Vfb - PHI - vds/2]*vds -2  [vds+PHI-vbs) 1.5 -(PHI-vbs) 1.5 ]/3

L30 May 620 Level 2 Static Device Eqs. (cont.) For vds > vds,sat id = id,sat/(1-LAMBDA*vds) where id,sat = id,ohmic(vds,sat)

L30 May 621 Level 2 Static Device Eqs. (cont.) Mobility variation KP’ = KP*[(esi/eox)*UCRIT*TOX /(vgs-VTH-UTRA*vds)] UEXP This replaces KP in all other formulae.

L30 May 622 SPICE Parameters Level 3

L30 May 623 Project 3 Project 3 is posted on the web See /projects/5342Project3.pdf

L30 May 624 Project 2 Parameter Values Extracted IS " 891.8a" BF " " NF " " VAF " " IKF " 13.45m" ISE " 20.40f" NE " " BR " " NR " " VAR " " IKR " 2.000m" ISC " 537.6f" NC " " RB " 1.233K" IRB " 1.000u" RBM " " RE " " RC " " CJE " 2.344p" VJE " 762.0m" MJE " 344.9m" CJC " 1.234p" VJC " 570.8m" MJC " 347.6m" CJS " 100.4f" VJS " 566.0m" MJS " 267.0m"

L30 May 625 Project 2 Optimized Parameter Values IS " 890.9a" BF " " NF " " VAF " " IKF " 14.33m" ISE " 28.54f" NE " " BR " " NR " " VAR " " IKR " 6.470m" ISC " 537.6f" NC " " RB " 1.233K" IRB " 986.9n" RBM " " RE " " RC " " CJE " 2.344p" VJE " 762.0m" MJE " 344.9m" CJC " 1.234p" VJC " 570.8m" MJC " 347.6m" CJS " 100.4f" VJS " 566.0m" MJS " 267.0m"

L30 May 626 Project 2 Parameter Values Used for Data IS " 891.0a" BF " " NF " " VAF " " IKF " 14.91m" ISE " 28.86f" NE " " BR " " NR " " VAR " " IKR " 23.45m" ISC " 1.095p" NC " " RB " 1.234K" IRB " 987.0n" RBM " " RE " " RC " " CJE " 2.345p" VJE " 765.4m" MJE " 345.6m" CJC " 1.234p" VJC " 567.8m" MJC " 345.6m" CJS " 100.4f" VJS " 566.8m" MJS " 269.6m"

L30 May 627 References CARM = Circuit Analysis Reference Manual, MicroSim Corporation, Irvine, CA, M&A = Semiconductor Device Modeling with SPICE, 2nd ed., by Paolo Antognetti and Giuseppe Massobrio, McGraw-Hill, New York, M&K = Device Electronics for Integrated Circuits, 2nd ed., by Richard S. Muller and Theodore I. Kamins, John Wiley and Sons, New York, Semiconductor Physics and Devices, by Donald A. Neamen, Irwin, Chicago, 1997