ISPD 2000, San DiegoApr 10, Requirements for Models of Achievable Routing Andrew B. Kahng, UCLA Stefanus Mantik, UCLA Dirk Stroobandt, Ghent Univ. Supported by Cadence Design Systems, Inc. and the MARCO Gigascale Silicon Research Center
ISPD 2000, San DiegoApr 10, Outline Models of achievable routing Review of existing models Validation of models through experiments! Experimental analysis of assumptions Future model requirements Conclusions
ISPD 2000, San DiegoApr 10, –wirelength estimation models (Donath, …) –actual placement information Models of achievable routing Required versus available resources
ISPD 2000, San DiegoApr 10, Models of achievable routing Required versus available resources limited by routing efficiency factor r
ISPD 2000, San DiegoApr 10, Models of achievable routing Required versus available resources limited by power/ground (signal net fraction s i )
ISPD 2000, San DiegoApr 10, Models of achievable routing Required versus available resources limited by via impact factor v i (ripple effect) utilization factor U i (available / supplied area)
ISPD 2000, San DiegoApr 10, Use of achievable routing models Optimizing interconnect process parameters for future designs (number of layers, wire width and pitch per layer,...) With given layer characteristics: predict the number of layers needed If number of layers fixed: oracle “(not) routable!” (SUSPENS, GENESYS, RIPE, BACPAC, GTX) Supplying objectives that guide layout tools to promising solutions (wire planning)
ISPD 2000, San DiegoApr 10, Validation is key Models must be accurate, must support empirical verification and calibration No existing model is validated with real place-and-route data Our work concentrates on validation: –understanding reasons for validation gap –processes for model validation –improvements needed in future models
ISPD 2000, San DiegoApr 10, Review of existing models Sai-Halasz [Proc. IEEE, 1995] –power/ground: s i 20% –routing efficiency: r = 40% –via impact: each layer blocks 15% on layers below with same pitch –model is widely used –model is rather pessimistic
ISPD 2000, San DiegoApr 10, Review of existing models (cont.) Chong and Brayton [SLIP, 1999] –layer assignment model layer pairs form tiers (H and V) wires are routed on 1 tier shorter wires on lower tiers –available resources model constant routing efficiency for all layers: r = 65% via impact factor v i based on actual via area –each wire uses 2 via stacks (block wires on lower layers) –total number of wires per layer (thus vias) defined by layer assignment model H H V V } } tier
ISPD 2000, San DiegoApr 10, Review of existing models (cont.) Chen et al. [private communication, 1999] –layer assignment model similar to Chong’s –available resources model constant routing efficiency (40% < r < 66%) via impact model –terminal vias and turn vias –each wire uses 2 via stacks –number of terminal vias defined by layer assignment model –sparse via model = Chong –dense via model: give up 1 track every X tracks –results in via impact proportional to sqrt(Chong’s impact factor) H H V V } } tier tracks
ISPD 2000, San DiegoApr 10, Model validation Models can be validated only by testing against comparable experimental results –none of reviewed models was validated –even simple comparison: huge differences Via fill rate (%) Utilization factor/layer (%) Sai-Halasz (M4) Sai-Halasz (M1) Chong Chen Sai-Halasz (M3) Sai-Halasz (M2)
ISPD 2000, San DiegoApr 10, Model validation (cont.) Experimental validation –Typical industry standard-cell block design cells, 1999, 5 layers Cadence placement and gridded routing tools same pitch (1 m) for all layers via size.62 m all pins for cells are on M1 Experimental validation –ensure congested design Via fill rate (%) Utilization factor (%) Sai-Halasz (M4) Sai-Halasz (M1) Chong Chen Sai-Halasz (M3) Sai-Halasz (M2) Exp M Exp M4 Exp M3
ISPD 2000, San DiegoApr 10, Model validation (cont.) Experimental validation –adding virtual vias on M3 and M4 (effect of wires on virtual upper layers) Exp M4 Exp M3 Via fill rate (%) Utilization factor (%) Sai-Halasz (M4) Sai-Halasz (M1) Chong Chen Sai-Halasz (M3) Sai-Halasz (M2) Exp M
ISPD 2000, San DiegoApr 10, Model validation (cont.) Predictions for future designs –number of layers >>, die size >> –via impact severely underestimated –predicted limits on number of layers too high Via fill rate (%) Utilization factor (%) Chong Chen M4 M
ISPD 2000, San DiegoApr 10, Model validation (cont.) Predictions for future designs LayerChongChenExperiment M M M M4000 Total Layers needed224 Number of terminal vias
ISPD 2000, San DiegoApr 10, Outline Models of achievable routing Review of existing models Validation of models through experiments! Experimental analysis of assumptions Future model requirements Conclusions
ISPD 2000, San DiegoApr 10, Routing efficiency Constant over all layers? Via fill rate (%) Utilization factor (%) Chong Chen M4 M
ISPD 2000, San DiegoApr 10, Routing efficiency Are we measuring routing efficiency or inefficiency? –thought experiment given placement of given netlist route with very good router, measure U i route again with very bad router, measure U i –which one has better routing efficiency? –which one has higher utilization factor? –Give credit for completing nets, not for using metal (use Steiner length instead of actual length for U i )!
ISPD 2000, San DiegoApr 10, Layer assignment assumptions shorter wires on lower tiers / wires on 1 tier Actual Length (%) Actual Number of Layers Steiner Length ( m)
ISPD 2000, San DiegoApr 10, Real Wiring Effects Cascade/ripple effect Effect of vias depends on wire length Proposal: l+1 intersections
ISPD 2000, San DiegoApr 10, Real Wiring Effects (cont.) A simple proposal –probability wire is not blocked: –via impact factor: Via fill rate (%) Utilization factor (%) Chong Chen M4 M Model M3Model M4
ISPD 2000, San DiegoApr 10, Conclusion Better/more accurate models needed –understanding routing efficiency –layer assignment model allows >1 tier/wire –via impact based on real wiring effects wirelength on layer is important cascade/ripple effect Experimental verification of models a must! There is a lot of work yet to be done
ISPD 2000, San DiegoApr 10, Constant via impact factor Utilization factor constant? LayerSai-HalaszU i /U i+1 M1/M M2/M M3/M M3/M4 Utilization factor ratio Via fill rate (%)