Lecture 9: Interconnect
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1 Digital Integrated Circuits (83-313) Lecture 9: Interconnect Semester B, Lecturer: Dr. Adam Teman TAs: Itamar Levi, Robert Giterman 23 May 2017 Disclaimer: This course was prepared, in its entirety, by Adam Teman. Many materials were copied from sources freely available on the internet. When possible, these sources have been cited; however, some references may have been cited incorrectly or overlooked. If you feel that a picture, graph, or code example has been copied from you and either needs to be cited or removed, please feel free to adam.teman@biu.ac.il and I will address this as soon as possible.
2 2 Lecture Content
3 3 A First Glance at Interconnect
4 The Wire Transmitters Receivers schematic view physical realization All-inclusive model Capacitance-only 4
5 Impact of Interconnect Parasitics Interconnect parasitics affect all the metrics we care about Reliability Performance Power Consumption Cost Classes of parasitics Capacitive Resistive Inductive 5
6 6 Modern Interconnect
7 7 Capacitance
8 Capacitance of Wire Interconnect V DD V DD V in C gd12 M2 C db2 V out C g4 M4 V out2 M1 C db1 C w Interconnect C g3 M3 Fanout Simplified Model V in V out C L 8
9 Capacitance: The Parallel Plate Model How can we reduce this capacitance? L Current flow Typical numbers: Wire cap ~0.2 ff/um Gate cap ~2 ff/um Diffusion cap ~2 ff/um W Electrical-field lines H t di Dielectric Substrate c pp t di di WL 9
10 10 Permittivity
11 Fringing Capacitance H H (a) (a) W - H/2 W - H/2 + + w W H /2 11 (b) (b) W H 2 di 2 di CF mm cpp c fringe t log t H di di
12 Fringing versus Parallel Plate C fringe edge 0.05 ff m C C fringe PP L W L (from [Bakoglu89]) 12
13 Top Plate A simple model for deriving wire cap Wiring capacitances in 0.25μm af/µm 2 Bottom Plate C C W L wire parallel _ plate 2C L fringe af/µm fringing parallel 13
14 Impact of Interwire Capacitance 14 Stanford: EE311
15 Coupling Capacitance and Delay C C1 C C2 C L 15 C tot C L
16 Coupling Capacitance and Delay 0 1 C C1 1 C C2 C L 0 16 C C C C tot L C1 C 2
17 Coupling Capacitance and Delay C C1 C C2 C L 17 C C 2 C C tot L C1 C 2
18 Example Coupling Cap A pair of wires, each with a capacitance to ground of 5pF, have a 1pF coupling capacitance between them. A square pulse of 1.8V (relative to ground) is connected to one of the wires. How high will the noise pulse be on the other wire? 18
19 Example Coupling Cap Draw an Equivalent Circuit: V C 2 Vin Ccoupled 1.81p C C 1p 5p coupled 2 0.3V 19
20 Coupling Waveforms Simulated coupling for C agg =C victim 1.8 Aggressor Victim (undriven): 50% Victim (half size driver): 16% Victim (equal size driver): 8% Victim (double size driver): 4% t (ps)
21 21 Shielding
22 22 Feedthrough Cap
23 23 Measuring Capacitance
24 24 Resistance
25 Wire Resistance H H W L L R = L H W R = L H W Sheet Resistance R o R 1 R 2 o Metal Sheet Resistance Bulk resistivity (W*cm) Silver (Ag) 1.6 R W L A L H W R sq R 1 R 2 L, W R sq H Copper (Cu) 1.7 Gold (Au) 2.2 Aluminum (Al) 2.8 Tungsten (W) 5.3 Molybdenum (Mo)
26 Sheet Resistance Typical sheet resistances for 180nm process Layer Sheet Resistance (W/) N-Well/P-Well Diffusion (silicided) 3-10 Diffusion (no silicide) Polysilicon (silicided) 3-10 Polysilicon (no silicide) Metal Metal Silicides: WSi 2, TiSi 2, PtSi 2 and TaSi Conductivity: 8-10 times better than Poly 26 Metal Metal Metal Metal R 100 m W square
27 Contact Resistance Contact/Vias add extra resistance Similar to changing between roads on the way to a destination Contact resistance is generally 2-20 Ω Make contacts bigger BUT current crowds around the perimeter of a contact. There are also problems in deposition Contacts/Vias have a maximum practical size. Use multiple contacts But does this add overlap capacitance? 27
28 Dealing with Resistance Selective Technology Scaling Don t scale the H Use Better Interconnect Materials reduce average wire-length e.g. copper, silicides More Interconnect Layers reduce average wire-length Minimize Contact Resistance Use single layer routing When changing layers, use lots of contacts. 90nm Process 28
29 29 Interconnect Modeling
30 The Ideal Model In schematics, a wire has no parasitics: The wire is a single equipotential region. No effect on circuit behavior. Effective in first stages of design and for very short wires. 30
31 The Lumped Model R wire =1Ω V out Driver c wire R on =1kΩ-10kΩ R driver V out V in C lumped 31
32 The Distributed RC-line But actually, our wire is a distributed entity. We can find its behavior by breaking it up into small RC segments. I C V V V V rdx rdx dv cdx dt i1 i i i1 i rc V t i 2 V x i 2 lim dx0 f x dx f x dx f ' x rc L 2 2 t 0.38 pd RC 32 Quadratic dependence on wire length The lumped model is pessimistic
33 Step-response of RC wire Step-response of RC wire as a function of time and space 33
34 Elmore Delay Approximation Solving the diffusion equation for a given network is complex. Elmore proposed a reasonably accurate method to achieve an approximation of the dominate pole. 34 elmore R C R R C R R R C
35 Elmore Delay Approximation For a complex network use the following method: Find all the resistors on the path from in to out. For every capacitor: Find all the resistors on the path from the input to the capacitor. Multiply the capacitance by the resistors that are also on the path to out. The dominant pole is approximately the sum of all these time constants. 35
36 Simple Elmore Delay Example RC R R C R C elmore
37 General Elmore Delay Example RC RC R R C R R C R R R C elmore i i 37
38 Generalized Ladder Chain Lets apply the Elmore approximation for our original distributed wire. Divide the wire into N equal segments of dx=l/n length with capacitance cdx and resistance rdx. N L L L L c r 2 r.. Nr N N N N 2 L rc 2 rc.. Nrc N lim N D N N 2 rcl 2 2 rcl RC 2 2 2N 1 38
39 RC-Models Pie Model T-Model Pie-2 Model Pie-3 Model T-2 Model T-3 Model 39
40 Wire Delay Example Inverter driving a wire and a load cap. C W C C R C W 2 2 R R driver d inv ext inv w 40
41 A different look Again we ll look at our driver with a distributed wire. For the driver resistance, we can lump the output load as a capacitor. For the wire resistance, we will use the distributed time constant. For the load capacitance, we can lump the wire and driver resistance. C w R ff 0.2 μm W R C C 0.38R C 0.69 R R C D inv d W W W inv w L 41
42 Dealing with long wires Repeater Insertion 42
43 Dealing with long wires Buffer Tree Insertion 43
44 44 Wire Scaling
45 Wire Scaling We could try to scale interconnect at the same rate (S) as device dimensions. This makes sense for local wires that connect smaller devices/gates. But global interconnections, such as clock signals, buses, etc., won t scale in length. Length of global interconnect is proportional to die size or system complexity. Die Size has increased by 6% per year years) Devices have scaled, but complexity has grown! 45
46 46 Nature of Interconnect
47 Local Wire Scaling Looking at local interconnect: W, H, t, L all scale at 1/S C=LW/t1/S R=L/WH S RC=1 Reminder Full Scaling of Transistors R on =V DD /I on α 1 t pd =R on C g α 1/S So the delay of local interconnect stays constant. But the delay of local interconnect increases relative to transistors! 47
48 Local Wire Scaling Full Scaling What about fringe cap? H H/S 48 t C WL pp Cfringe L t R L t R C WH wire p,wire wire wire t/s C S C S pp R S t 1 1 fringe wire p,wire const
49 Local Wire Scaling - Constant Thickness Wire thickness (height) wasn t scaled! 49 H t C WL pp Cfringe L t R L t R C WH wire p,wire wire wire C S C S pp H t/s wire 1 1 fringe R const t S p,wire 1
50 Local Wire Scaling Interwire Capacitance Without scaling height, coupling gets much worse. Aspect ratio is limited and we eventually have to scale the height. Therefore, different metal layers have different heights. 50 C pp, side LH C D pp, side const
51 Global Wire Scaling Looking at global interconnect: W, H, t scale at 1/S L doesn t scale! C=LW/t1 R=L/WH S 2 RC=S 2!!! Long wire delay increases quadratically!! And if chip size grows, L actually increases!! 51
52 Global Wire Scaling Constant Thickness Leave thickness constant for global wires But wire delay still gets quadratically worse than gate delay H H t t/s 52 C WL pp Cfringe L t R L t R C WH wire p,wire wire wire C pp wire const C p,wire fringe R S t S const
53 Wire Scaling So whereas device speed increases with scaling: Local interconnect speed stays constant. Global interconnect delays increase quadratically. Therefore: Interconnect delay is often the limiting factor for speed. What can we do? Keep the wire thickness (H) fixed. This would provide 1/S for local wire delays and S for constant length global wires. But fringing capacitance increases, so this is optimistic. 53
54 Wire Scaling What is done today? Low resistance metals. Low-K insulation. Low metals (M1, M2) are used for local interconnect, so they are thin and dense. Higher metals are used for global routing, so they are thicker, wider and spaced farther apart. 54
55 Modern Interconnect Intel 45 nm Stack [Moon08] 55
56 Further Reading J. Rabaey, Digital Integrated Circuits 2003, Chapter 4 E. Alon, Berkeley EE-141, Lectures 15,16 (Fall 2009) B. Nicolic, Berkeley EE-241, Lecture 3 (Spring 2011) Stanford EE311 56
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