6 Worst Case Analysis Assumption The thin-oxide capacitance is voltage dependent.The worst case analysis uses CoxWL to compute its worst case value.
7 Thin Oxide Capacitance:Cg CG=WLCox=WL(εox/tox)=WCgUnit of Cg: fF/μm[Worst Case Analysis]
8 Cg 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]
10 Components of Col Col=Cf+Cov Cf:fringing capacitance Cov: overlap capacitance
11 Redefine 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]
12 Gate Capacitance of an Inverter CG=Cg(Wn+Wp)CG=2fF/μm(Wn+Wp)[Worst Case Analysis]
13 Input Capacitance of a 3-input NAND Gate 2W2W2W3W3W3WCG=Cg(Wn+Wp)=Cg(3W+2W)= Cg(5W)
14 Fanout 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]
15 Self-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.
16 Calculation 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]
17 Self-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.
21 Wire 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
22 Example 6.4Capacitance Calculation for Inverter