6Worst Case Analysis Assumption The thin-oxide capacitance is voltage dependent.The worst case analysis uses CoxWL to compute its worst case value.
7Thin Oxide Capacitance:Cg CG=WLCox=WL(εox/tox)=WCgUnit of Cg: fF/μm[Worst Case Analysis]
8Cg tox L Cg 110 nm 5 1.61 fF/μm 7.5 nm 0.35 μm 1.65 fF/μm 2.2 nm Cg is approximately 1.61 fF/μm for the last 25 years.Exception: the 0.18 μm process, which has a Cg of 1.0 fF/ μm.[Worst Case Analysis]
10Components of Col Col=Cf+Cov Cf:fringing capacitance Cov: overlap capacitance
11Redefine CgFor 0.13 μm,Cg (due to tox alone): 1.6 fF/μm [Hodges, p.72]Col(due to Cov and Cf): 0.25 fF/ μm [Hodges, p.80]Redefine Cg [Hodges, p.259] asCg=CoxL+2ColCg =1.6 fF/μm fF/μm=2 fF/μmCg has been constant for over 20 yearsMultipy Cg by W to obtain the total capacitance due to tox, Cov and Cf[Worst Case Analysis][Worst Case Analysis]
12Gate Capacitance of an Inverter CG=Cg(Wn+Wp)CG=2fF/μm(Wn+Wp)[Worst Case Analysis]
13Input Capacitance of a 3-input NAND Gate 2W2W2W3W3W3WCG=Cg(Wn+Wp)=Cg(3W+2W)= Cg(5W)
14Fanout Gate capacitance of n Inverters Cfanout=2fF/μm[(Wn+Wp)1+(Wn+Wp)2…(Wn+Wp)n]For NANDs, NORs, apply theabove equation with appropiate widths.[Worst Case Analysis]
15Self-Capacitance Calculation Eliminate capacitors not connected to the outputAssume the transistors are either on (Saturation) or off (Cutoff).CGD is negligible in either saturation or cutoff.
16Calculation of Self-Capacitance of an Inverter Cself=CDBn+CDBP+2COL+2COLCDBn=CjnWnCDBp=CjpWpCOL=ColWCself=CjnWn+CjpWp+2Col(Wn+Wp)Assume Cjn=CjpCself=Ceff(Wn+Wp)For 0.13: Ceff=1 fF/μm [Hodges, p. 261]
17Self-Capacitance of a NOR Condition:A=0B=0→1CDB4, CSB3 do not need to be charged.→NOT THE WORST CASECDB3 is charged, while CDB1 and CDB2 are discharged.To avoid double counting, CDB1 and CDB2 will be called CDB12.
21Wire CapacitanceIgnore wire capacitance if the length of a wire is less than a few microns.Include wires longer than a few micronsCwire=CintLwireCint=0.2 fF/umFor very long wires use distributed model