University oftokyo. LSI esign & ducation enter

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1 Analysis on An Interconnections in V Hi-Frequency Mido and Kunihiro Asada Tetsuhisa Electronic Engineering Dept. Considering Inductive Eects (V Design and E C (VDEC)), Mar. 9th, 999 Dept. E.E., Univ..

2 Contents Background and Target Physical model for skin eect Frequency characteristics considering eect skin Inductive eects on signal propagation Conclusions Dept. E.E., Univ..

3 (Speed improvement in Background system) V Importance Interconnection Increasing roadmap '97) (SIA frequency (V Chip) Operating Year [m] Tech. [GHz] Freq. Dept. E.E., Univ..

4 interconnections, High speed signal long propagation. RC model Distributed Distributed RLC model! Importance inductive eects Shrink to DSM region, Higher integration. (considering skin eect) Newer scaling method will be needed. Dept. E.E., Univ..

5 : depth from the surface, : resistivity conductor, : x permeability,! : angular frequency input signal. magnetic model for skin eect Physical model) (-D The diusion equation the magnetic eld, r 2 B Magnetic eld decreases from the surface conductor as, jb(x)j = jb 0 j exp(0x= s ) ; ( s = r 2=!) insulator B conductor B0 δ s e B0 x Dept. E.E., Univ..

6 Current Summation :I (!) = V W l T ef f T x e0 VW Z dx = s 0 model skin eect and current 2-D distribution T H l W Current Area C Wire δs Gnd Plane δs Eective thickness interconnection : T eff = maxft; s g VW = l l vut T ( 0 e0 s): 2! V :bias voltage, W :width, l :length Dept. E.E., Univ..

7 : Eective geometric distance R : Magnetic permeability eect estimation using split Skin model ber 2 L = µ l {log -} ( ) 2π R H/cm 2 M2= µ l {log -} ( ) 2π R H/cm l : length interconnection Dept. E.E., Univ..

8 cosh((s)) ended) (Open exp((s)) = (Matched termination) (s) = r (R + sl)sc characteristics Frequency skin eect considering (Transfer Function) G(s) = Expansion Fourier Output ) (Sum) ) input pulse Frequency dependence R and L.(skin eect) High speed input signal contains a lot higher components.! Inductive eects in- harmonics crease. Dept. E.E., Univ..

9 characteristics Frequency skin eect. considering e+4 00 Width=2µm R [Ω] (single interconnection)() R(-D model) [Ω] ωl [Ω] L [nh] e Width=6µm R [Ω] ωl [Ω] R(-D model) [Ω] L [nh] e-4 I Vin [Ω - ] 0.00 e-4 I Vin [Ω - ] e+06 e+08 e+0 e+2 Freq. [Hz] e+06 e+08 e+0 e+2 Freq. [Hz] (a) W=2m (b) W=6m Ideal ground model using mirror conductor Thickness :m,height from ground :m uniform current. R(D model): Resistance values horizontally Dept. E.E., Univ..

10 characteristics Frequency skin eect. considering e Width=32µm R [Ω] (single interconnection)(2) R(-D model) [Ω] ωl [Ω] Width=28µm R [Ω] R(-D model) [Ω] ωl [Ω] e-4 I Vin L [nh] [Ω - ] I Vin L [nh] [Ω - ] e+06 e+08 e+0 e+2 Freq. [Hz] e+06 e+08 e+0 e+2 Freq. [Hz] (a) W=22m (b) W=28m Ideal ground model using mirror conductor Thickness :m,height from ground :m uniform current. R(D model): Resistance values horizontally Dept. E.E., Univ..

11 L = L i (internal) + L e (external) { current) L i =0 Surface Increase R due to skin eect <<!L inductive eects Magnitude (summary) In interconnection m thickness, skin eect in over GHz operation. appears nnself-inductance becomes slightly lower in the where the skin eect appears area eect on signal propagation in interconnection Skin m thickness is negligible. Except RF resonator or so where the Q-factor becomes important. Dept. E.E., Univ..

12 distributed LCR Response with considering interconnection time input :20psec Rising :V Vdd Output [V] skin eect Distributed LCR model with skin effect Distributed LCR model w/o skin effect Time [psec] interconnection :32m Width termination (to avoid resonation) Matched Dept. E.E., Univ..

13 the digital response Comparison distributed LCR and distributed RC interconnections() Delay [psec] Delay [psec] 000 Width=4µm Input slope delay=20psec 000 Width=4µm Input slope delay=00psec LC RC model LCR model 2 RC 0. 0 Length [cm] LC RC model LCR model 2 RC 0. 0 Length [cm] W=4m W=4m Rising time input :20psec Rising time input :00psec Dierence grows larger in higher speed operation. Dept. E.E., Univ..

14 the digital response Comparison distributed LCR and distributed RC interconnections(2) Delay [psec] Delay [psec] 000 Width=4µm Input slope delay=20psec 000 Width=32µm Input slope delay=20psec LC RC model 0 LC RC model LCR model 2 RC 0. 0 Length [cm] LCR model 2 RC 0. 0 Length [cm] W=4m W=32m Rising time input :20psec Rising time input :20psec Dierence grows larger in wider interconnection Dept. E.E., Univ..

15 propagation delay on Comparison condition variation the the width interconnection and input Delay [psec] 000 slope. width=4µm input slope=20psec input slope=00psec width 4µm 4µm 32µm 32µm width=32µm input slope line width dominant factor input slope 20psec 00psec 20psec 00psec Length [cm] Rising time input l<2cm Width interconnection l>2cm dominant factor Dept. E.E., Univ..

16 response open ended Digital compared with interconnection [V] Input Output (open ended) Output (matched termination) Width=4µm Time [nsec] [V] Input Output (open ended) Output (matched termination) Width=32µm Time [nsec] matching termination Width :4m Width :32m between matched termination Comparison open ended and Rising time input :00psec, length :5mm is smaller in the narrower interconnections Ringing Dept. E.E., Univ..

17 Summary Frequency characteristics considering eect. skin the skin eect is not important in evaluating propagation delay V interconnections. { Except RF resonator. Inductance becomes very important in propagation delay V in- evaluating terconnections in over-ghz operation. Termination matching becomes important. Dept. E.E., Univ..