Results

equal to 3068 cells. By increasing the number of layers, like the previous case, the required area decreases from 361 cells with two tiers, to 144 cells with five layers. It means that by executing the algorithm the initial area can be reduced from the 88% to the 95%. Obviously, this big improvement is achieved with a price. The number of TSVs increase more respect to the B09 IC because now the total number of interconnections to manage are further. The ratio of #TSVs to the number of edges is greater for B09 than for B12. The initial Horizontal wirelength is equal to 117138µm with a maximum of 182µm. With two tiers their values become, respectively, 31820µm and 30µm for the Centroid strategy and 32490µm and 32µm for the Vertical strategy. A reduction not as drastic as that of B09 but still quite impressive. Also in this case, increasing the number of tiers lead to a lesser Horizontal wirelength, that remain always lower than the 2D initial value. For B12, the Vertical strategy lead all the time to a Horizontal wirelength greater than the one obtained with the Centroid strategy, while the Max wirelength still quite similar for both the approaches. The distribution of the wirelength, in this case, does not follow a decreasing trend when more than two layers are used.

Although the first tier remain the one characterized by a greater wirelength, due to the high number of connections, is possible to have lower levels characterized by a total length of the cables shorter than the higher ones.

The B14 IC is composed by 4088 nodes that create a network of 20240 edges.

Unlike the previous circuits B14 is more complex, and its initial area is equal to 23478 cells, almost eight times the initial size of B12. By increasing the number of tiers that are required for building the circuit, the size of the silicon area decrease.

With two layers the area needed is equal to 2304 cells (more than a tenth of the initial one), while with four layers the area assumes the value of 1156 cells. With a greater number of edges, the #TSVs value increase compared to the previous result.

Like the prior circuits, the value of the Horizontal wirelength decreases with the number of layers. The only difference is that the reduction brought about by adding each tier is greater than the previous cases. This is initially equal to 451096µm for Centroid strategy and 457126µm for Vertical strategy and drops respectively to 364216µm and 365602µm. This improvement derives from the fact that, in the presence of a large quantity of nodes, a high number of tiers does not affect

the dispersion in a heavy way as with the two previous circuits. In addition, the number of nodes that must be blocked due to connections with lower layers does not negatively affect the positioning of the others, because the area of the tiers is now larger and offers a greater quantity of positions. For this reason, even if the number of TSVs increase and affect in a negative way the total length of the interconnections, the reduction of the area involves a greater advantage and therefore the Horizontal wirelength improve. Having many Interconnections help also to understand the main difference between the Centroid and Vertical strategies. In all the B14 tests, the Vertical strategy leads to a greater Avg wirelength than the Centroid strategy, even if sometimes the Max wirelength has a opposite trend. It means that critical paths are managed better using the centroids coordinates. Like the B09 IC, the wirelength distribution on the different layer follow a decreasing behaviour with the increase of the number of tiers. Moreover, the maximum wirelength reach by a single layer is lower when many levels are used for the verticalization of the IC respect to cases with few tiers. The last and most complex IC tested is CNN which is constituted of 20362 nodes and 102126 edges. The number of TSVs is quite high and reach a maximum of 9424 with five tiers. Although the circuit is composed of a number of elements that is five times that of B14, its initial area is quite small, equal to 24576 cells. For this reason, it is possible to note that the Horizontal wirelength computed with a number of tiers higher than one is worse than that of the equivalent circuit in 2D. The Horizontal wirelength is initially equal to 2703646µm and become 4230306µm for the Centroid strategy and 4254206µm for the Vertical strategy, with two tiers. The small initial area results in a low wirelength which gets worse when the circuit is divided into several tiers because node that initially were close can be placed into different layer. By increasing the number of tiers, the Horizontal wirelength value decrease, thanks to more restricted area, reaching a minimum of 3237038µm with five layers. Although Horizontal wirelength worsens compared to the 2D circuit, its maximum value is mitigated, albeit slightly. Also in this case, the Centroid strategy achieves better average wirelength than the Vertical strategy. Like the B12 IC, in CNN IC is possible to find below tiers with a total wirelength lower than upper tiers.

B09ICResults CentroidStrategyVerticalStrategy TiersArea [cells]NodesEdgesTSVs[#]Vertical wirelength [µm]

Horizontal wirelength [µm]

Avgwire- length [µm]

Maxwire- length [µm]

Horizontal wirelength [µm]

Avgwire- length [µm]

Maxwire- length [µm] 122196486002387449.121312387449.12131 249964865050028346.861928226.8419 336964868080025006.791725106.8117 42596486104104021466.561622646.8014 Table5.2:ResultsobtainedbyrunningthealgorithmonB09IC B09ICTiers’HorizontalWire-length CentroidStrategyVerticalStrategy TiersTier1 [µm]Tier2 [µm]Tier3 [µm]Tier4 [µm]Tier1 [µm]Tier2 [µm]Tier3 [µm]Tier4 [µm] 12387400023874000 2231452000231051200 320763883602100374360 417602761046185627012810 Table5.3:Comparisonbetweenthewire-lengthsofthetiersusedonB09IC

B12ICResults CentroidStrategyVerticalStrategy TiersArea [cells]NodesEdgesTSVs[#]Vertical wirelength [µm]

Horizontal wirelength [µm]

Avgwire- length [µm]

Maxwire- length [µm]

Horizontal wirelength [µm]

Avgwire- length [µm]

Maxwire- length [µm] 1306862034240011713834.2118211713834.21182 236162034241311310318209.6830324909.8732 325662034242932930275408.9030278829.0028 419662034244464460251088.6425255688.7724 514462034245565560220048.0523231828.3925 Table5.4:ResultsobtainedbyrunningthealgorithmonB12IC B12ICTiers’HorizontalWire-length CentroidStrategyVerticalStrategy TiersTier1 [µm]Tier2 [µm]Tier3 [µm]Tier4 [µm]Tier5 [µm]Tier1 [µm]Tier2 [µm]Tier3 [µm]Tier4 [µm]Tier5 [µm] 111713800001171380000 218246135740001837614114000 3161048190324600160968462332400 4139364610527412880136445014552213880 51088637964368269026411142410447322854350 Table5.5:Comparisonbetweenthewire-lengthsofthetiersusedonB12IC

B14ICResults CentroidStrategyVerticalStrategy TiersArea [cells]NodesEdgesTSVs[#]Vertical wirelength [µm]

Horizontal wirelength [µm]

Avgwire- length [µm]

Maxwire- length [µm]

Horizontal wirelength [µm]

Avgwire- length [µm]

Maxwire- length [µm] 1234784088202400071675635.4131271675635.41312 2230440882024014881488045109623.0213045712623.32131 3152140882024026702670038859620.5211239588220.88109 4115640882024038113811036421619.8811436560219.95109 Table5.6:ResultsobtainedbyrunningthealgorithmonB14IC B14ICTiers’HorizontalWire-length CentroidStrategyVerticalStrategy TiersTier1 [µm]Tier2 [µm]Tier3 [µm]Tier4 [µm]Tier1 [µm]Tier2 [µm]Tier3 [µm]Tier4 [µm] 1716756000716756000 22968141542820029671616041000 3212148142516339320211568148048362660 417876810504868616117841784461073746605813724 Table5.7:Comparisonbetweenthewire-lengthsofthetiersusedonB14IC

CNNICResults CentroidStrategyVerticalStrategy TiersArea [cells]NodesEdgesTSVs[#]Vertical wirelength [µm]

Horizontal wirelength [µm]

Avgwire- length [µm]

Maxwire- length [µm]

Horizontal wirelength [µm]

Avgwire- length [µm]

Maxwire- length [µm] 1245762036210212600270364626.47355270364626.47355 21210020362102126274927490423030641.69239425420641.92247 3810020362102126491549150373927437.10255375597037.26255 4608420362102126781278120343888034.44223343993834.45248 5490020362102126942494240323703832.62212325717032.82207 Table5.8:ResultsobtainedbyrunningthealgorithmonCNNIC CNNICTiers’HorizontalWire-length CentroidStrategyVerticalStrategy TiersTier1 [µm]Tier2 [µm]Tier3 [µm]Tier4 [µm]Tier5 [µm]Tier1 [µm]Tier2 [µm]Tier3 [µm]Tier4 [µm]Tier5 [µm] 12703646000027036460000 22840830138947600028483601405846000 318952221137198706854001902098112957472429800 41429018797278909612302972014274487957649077943089320 512369845706766242926944341106521243762580010626716690200116482 Table5.9:Comparisonbetweenthewire-lengthsofthetiersusedonCNNIC

Chapter 6