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Prediction and Comparison of High-Performance On ... - IEEE Xplore

Prediction and Comparison of High-Performance On ... - IEEE Xplore

ZHANG et al.: PREDICTION

ZHANG et al.: PREDICTION AND COMPARISON OF HIGH-PERFORMANCE ON-CHIP GLOBAL INTERCONNECTION 1157TABLE IIIDESIGN PARAMETERS FOR UE-TL/PE-TL SCHEMES (WIRE LENGTH =5mm)H = T = S =2W for T-lines used in UE-TL and PE-TL.Fig. 6. Wire configurations for on-chip T-line schemes. (a) Cross section ofsingle-ended stripline. (b) Cross section of differential stripline.TABLE IIPARAMETERS OF ON-CHIP GLOBAL T-LINE USED IN UT-TL/T-TL SCHEMESfindicates the corner frequency of RC and LC region.in Fig. 6. For single-ended scenarios, we insert power/ground(P/G) lines every three wires (shown in Fig. 6(a), following thetypical wiring and power arrangement for global wide data bus[16]) to provide current return paths in order to form well-controlledon-chip T-line structures. The adjacent orthogonal layerscould be replaced by the ground planes if performing 2-D capacitanceextraction. Considering orthogonal loading, the capacitanceobtained by a 2-D extraction is slightly overestimatedcompared with the 3-D value [17], but still acceptable with theassumption that on-chip loading density and lateral wire-to-wirecoupling are very high. 3 The dimensions of this single-endedT-line structure are listed in Table II, following the settings in[12]. Fat and unscaled wires implemented on the top-layer areutilized to reduce the resistive loss in this scenario, first proposedin [18], to alleviate the increasing RC delay of scaledon-chip wires. With the improvement of device speed, the transmission-lineeffect does kick in and cannot be neglected whilemodeling such fat global wires; on the other hand, it has beenverified by previous research works [6], [12], [17] that on-chipbus configuration comprising a low-impedance driver and uninterruptedfat wire outperforms repeated wire structures in highperformanceapplications (e.g., high-end processors [16]) due tothe T-line effect. As a result, we adopt the configuration comprisinga low-impedance driver and uninterrupted fat wire andassume the utilized wire geometry shown in Table II maintainsas technology scales. As shown in the last column of Table II,LC-mode behavior is dominant for this wire geometry, whichspeeds up the signal transmission through wave propagation.3 For the narrower lines traveling in the same layer, this is a reasonable approximation.As shown in [6], the impact of orthogonal layers on the capacitanceextraction depends on the wire geometries. When t=w ratio is large, couplingcapacitance changes a little with different orthogonal loading scenarios, also alleviatingthe internal reflection due to non-uniform capacitance distribution ofon-chip T-line in the practical cases.We also devise a similar coplanar configuration for differentialT-lines as shown in Fig. 6(b). Here, only one pair of wires isplaced in a P/G bay in order to reduce the crosstalk noise. Wiredimensions of such configuration are determined by the resistiveloss at given signal frequency, which is changing with the technology.Considering the differential T-line schemes discussedin this work, the overall signal bandwidth is limited by the SAin transceiver, as listed in Table III at each technology node.We derive the minimum wire widths of differential T-lines thatsatisfy the eye-opening constraint by binary search and SPICEsimulations, as shown in the third and forth row of Table III. 4 Bycomparison, it can be seen that equalization helps to improve thedata density by supporting narrower wires at the same bit rate.The modeling and simulation of on-chip T-lines generallyincorporates two steps. First, we extract the frequency-dependentRLGC parameters for the given wire structure usingfield solvers. For on-chip wires, since dielectric loss can beignored and wire capacitance is basically frequency independent,extraction is generally performed [6]. Thefrequency-dependent impedance extraction requires a groupof P/G wires located in a signal layer and sub-adjacent layers(parallel to the signal layer) to serve as return paths in orderto capture the wide-band characteristic of wire inductance[17]. As a result, parameter extraction can generate the tabularmodel or other kinds of SPICE-compatible macro-model. Inthe second step, SPICE simulations can be performed to studytransient characteristics and signal integrity. In this work, weevaluate performance metrics of all the T-line schemes based onthe tabular model generated by 2-D-extraction. Asa more practical modeling approach, a stable compact circuitmodel [19] synthesized from 2-D-extraction isused to study the signal integrity of global T-line schemes, asdiscussed in Section V.The previously discussed T-line structures can be implementedusing CMOS process. For single-ended schemes,T-lines are implemented on the top-layers of copper stackingwith well designed power/ground arrangement to control theT-line effect, as shown in the bus design for high-end processors[16]. Differential T-lines also have been implemented recentlyfor global clock distribution [20]. Similar configuration can beborrowed here to implement global differential data bus [21].There is no any further specific layout style required for suchT-line configuration, however, to improve the signal integrity(e.g., crosstalk), twisted structure might be used for the realchip designs [20], [22].4 The wire width values in this table are different from the previous work [11]because of the improved wire width optimization subroutine in this work. It isshown that narrower T-lines can be utilized to satisfy the eye-opening constraint,resulting in higher throughput density in the following results and also affectingother metrics.

1158 IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 19, NO. 7, JULY 2011TABLE IVMODELING PERFORMANCE METRICS (NORMALIZED DELAY, NORMALIZED ENERGY, NORMALIZED THROUGHPUT, AREA) OF SIX GLOBAL INTERCONNECTIONSTRUCTURES USING TECHNOLOGY-DEFINED PARAMETERSD. Performance AnalysisAn approximate high-level analysis is performed here toreveal how architecture-level performance metrics of differentglobal interconnects behave with technology scaling underthe min-d (minimum delay) objective. 5 As a result, we derivesimple linear models, which can be used for designers to approximatelyestimate the performance of different interconnectstructures at the early stage. In the following analysis, basictechnology-determined parameters, including supply voltage, dielectric constant , min-sized inverter FO4 delay ,aswell as the total wire length , are chosen to be the variablesto build such models.1) Latency: For the latency evaluation, we define the normalizeddelay aswhere the propagation delay includes both the wire delay andthe gate delay (repeaters and flip-flops in RC wires or transceiversin other T-line schemes).For R-RC structure, it can be shown that [4]with the assumption that the output resistance of a min-sizedinverter is roughly constant across different technologies, andFO4 delay reduces with the same scaling factor as the featuresize. For P-RC structure, additional delay is introduced by theinserted flip-flops and is linearly proportional to the pipeliningdepth and FO4 delay . For long global RC wires ( 5 mm)and advanced technologies (beyond 45 nm), the experimentalresults show that the maximum pipelining depth is chosen toreduce the overall energy over bandwidth ratio. Therefore, inour simple models, latency overhead of P-RC wire is assumedto be a linear function of FO4 delay only. 6For other T-line schemes, total latency can be expressed asthe sum of wire delay and transceiver delay. For LC-mode dominantT-lines, normalized wire delay is proportional to . Thetransceiver delay could be simply represented by the FO4 delaylinearly.Considering the total wire length in our delay models, thefinal results are shown in the second row of Table IV, where coefficientsand reflect the different process technologies.It can be seen that if item is dominant in the normalized5 P-RC scheme is optimized based on min-energy/bandwidth w/maximumpipelining depth constraint, as discussed in Section II-B.6 This assumption also holds for the following analysis of P-RC wire. Regardingthe performance analysis of ideal P-RC structure without maximumpipelining depth constraint, refer to Appendix A.(1)(2)delay expression for the R-RC and P-RC structures, the trend isan increase in the normalized delay of RC wires as technologyscales. The same table shows the opposite trend for the T-lineschemes, where normalized delay decreases with the reductionof dielectric constant and scaling of transistors.The most significant sources of error in our proposed delaymodel come from the simple modeling of transistor gate capacitanceand the approximation of the P-RC scheme in theshort wire-length range. As technology scales, the gate capacitanceper unit width actually reduces instead of being constant,7 resulting in the decreasing in (2), which partly cancelsout the RC-wire slowing caused by the wire scaling. Modelingerror of the P-RC scheme in the short wire-length range3mm is due to the neglect of optimal pipelining depthchanging in the delay model. As discussed in Appendix A, theoptimal pipelining depth in terms of lowest energy-bandwidthratio reduces as the wire length decreases, and is proportional tothe wire length. Therefore, for the cases with short wire length,the item in the delay model of P-RC structure approaches, causing relatively larger errors. This type of error source alsoapplies to energy and throughput modeling of P-RC structure,as shown below.Using the proposed delay models, the average percent errorfor RC wires is less than 15% and maximum percent error islimited by 30%. For other T-line schemes, maximum and averageerror are less than 13% and 5%, respectively.2) Energy per Bit: The normalized energy per bit is usedto evaluate the energy dissipation of global interconnect, whichis defined as follows:The bit rate for RC wires is assumed to be the inverse of propagationdelay over the total wire length for R-RC structure (notpipelined), or the inverse of delay between two flip-flops forP-RC structure (pipelined).As discussed in [4], the normalized energy per bit for R-RCstructure satisfies thatFor the P-RC structure, additional energy consumed by insertedflip-flops is represented by , which is approximately7 CMOS gate capacitance per unit width (C ) equals to L=t , where Lis the channel length, and t indicates the oxide thickness. For long channeldevices, L=t is roughly constant due to the same scaling factor along differentdimensions of transistor, whereas for short channel devices, oxide thicknesscannot scale as fast as transistor width and length due to leakage and processconsiderations. Therefore, gate capacitance per unit width decreases as technologyscales. In our study, C is 1.5 fF=m at 90 nm node and 0.8 fF=mat22 nm node.(3)(4)

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