An Optimal Jumper An Optimal Jumper Insertion Algorithm for Antenna Insertion Algorithm for Antenna Avoidance/Fixing on General Routing Avoidance/Fixing on General Routing Trees with Obstacles Trees with Obstacles Bor- -Yiing Yiing Su and Su and Yao Yao- -Wen Wen Chang Chang Bor National Taiwan University Jiang Hu Hu Jiang Texas A&M University
Outline Outline � Introduction Introduction � � Problem Definition Problem Definition � � An Optimal Algorithm for Jumper Insertion An Optimal Algorithm for Jumper Insertion � � Complexity Analysis Complexity Analysis � � Experimental Results Experimental Results � � Conclusions Conclusions �
Antenna Effect Antenna Effect � The process antenna effect is a phenomenon of The process antenna effect is a phenomenon of � plasma- -induced induced gate oxide degradation gate oxide degradation caused caused plasma by charge accumulation charge accumulation on conductors. on conductors. by � During metallization, each time an additional During metallization, each time an additional � layer of interconnect is added. While the metal layer of interconnect is added. While the metal line is being manufactured, the floating floating line is being manufactured, the interconnect acts as a temporary acts as a temporary capacitor capacitor to to interconnect store charges induced from plasma etching. store charges induced from plasma etching. Metal 3 Metal 2 A two-pin net Metal 1 a b
Antenna Effect (cont’d) Antenna Effect (cont’d) � If the charged conductor is connected only to If the charged conductor is connected only to � the gate oxide gate oxide, Fowler , Fowler- -Nordheim Nordheim (F (F- -N) tunneling N) tunneling the current will discharge through the thin oxide current will discharge through the thin oxide and damage the gate. and damage the gate. – No harm to diffusion source (discharge No harm to diffusion source (discharge – Metal 3 through substrate) through substrate) Metal 2 Metal 1 A two-pin net a b Metal 3 Metal 2 Metal 1 Cross section view Poly a b terminalF-N tunneling source current
Solutions for Antenna Effect Solutions for Antenna Effect � Jumper Insertion Jumper Insertion � – Break the signal wires with antenna violations and Break the signal wires with antenna violations and – route them to the top- -most layer most layer route them to the top – Induce Induce vias vias – � Embedded Protection Diode Embedded Protection Diode � – Add a protection diode on every input port of a cell Add a protection diode on every input port of a cell – – May consume unnecessary areas May consume unnecessary areas – � Diode Insertion Diode Insertion � – Insert Insert “ “under under- -the the- -wire wire” ” diodes to fix the violation diodes to fix the violation – – Need extra silicon space to place the diodes Need extra silicon space to place the diodes –
Solutions for Antenna Effect Solutions for Antenna Effect � Jumper Insertion Jumper Insertion � – Break the signal wires with antenna violations and Break the signal wires with antenna violations and – route them to the highest layer route them to the highest layer – Induce Induce vias vias – � Embedded Protection Diode Embedded Protection Diode � – Add a protection diode on every input port of a cell Add a protection diode on every input port of a cell – – May consume unnecessary areas May consume unnecessary areas – � Diode Insertion Diode Insertion � – Insert Insert “ “under under- -the the- -wire wire” ” diodes to fix the violation diodes to fix the violation – – Need extra silicon space to place the diodes Need extra silicon space to place the diodes –
Jumper Insertion Jumper Insertion � Jumper insertion reduces the charge amount Jumper insertion reduces the charge amount � for violated nets during manufacturing for violated nets during manufacturing – Side effects Side effects: : Delay and congestion Delay and congestion – Metal 3 Metal 2 Metal 1 a b a b Jumper Metal 3 Metal 2 Metal 1 Poly a a b b A two-pin net A two-pin net with jumper insertion
Steiner Tree Steiner Tree � Steiner points are just wire junctions. They Steiner points are just wire junctions. They � cannot help discharge the wire. cannot help discharge the wire. � s s is a Steiner point. is a Steiner point. The charges accumulated The charges accumulated � on edges e(u e(u, s), , s), e(s e(s, v , v 1 ), and e(s e(s, v , v 2 ) will all will all on edges 1 ), and 2 ) cause antenna effect on the gate terminal u u . . cause antenna effect on the gate terminal v 1 gate terminal gate terminal u v 2 s
Routing Obstacles Routing Obstacles � Since a jumper routes a signal wire to the Since a jumper routes a signal wire to the � topmost layer, we must consider the routing topmost layer, we must consider the routing with obstacles obstacles in the in the active layers active layers, e.g., pre , e.g., pre- - with routed nets, power/ground nets, clock nets. routed nets, power/ground nets, clock nets. – Active layers: the layers from the current routing Active layers: the layers from the current routing – layer up to the topmost layer layer up to the topmost layer � Need to avoid obstacles when adding jumpers Need to avoid obstacles when adding jumpers � Invalid! Obstacle u 1 Jumper u 2
Previous Work Previous Work � Ho, Chang & Chen, ISPD Ho, Chang & Chen, ISPD- -04 04 � – Bottom Bottom- -up dynamic programming in up dynamic programming in loglinear loglinear time time – – Insert jumpers Insert jumpers right beside right beside nodes of a nodes of a spanning spanning tree tree – � Wu, Wu, Hu Hu & & Mahapatra Mahapatra, ISPD , ISPD- -05 05 � – Insert jumpers Insert jumpers at arbitrary positions at arbitrary positions of edges of a of edges of a – Steiner tree in linear time tree in linear time Steiner – Optimal Optimal only for some special tree topologies only for some special tree topologies – � Su and Chang, DAC Su and Chang, DAC- -05 05 � – Insert jumpers Insert jumpers at arbitrary positions at arbitrary positions of edges of a of edges of a – spanning tree in tree in loglinear loglinear time time spanning – Optimal for a Optimal for a spanning spanning tree with arbitrary topologies tree with arbitrary topologies –
Previous Work Previous Work Previous works are optimal only for restricted Previous works are optimal only for restricted cases & do not consider obstacles!! cases & do not consider obstacles!! ISPD- -04 04 DAC- -05 05 ISPD- -05 05 This ISPD DAC ISPD This work work Optimal for general for general N N N Yes Optimal N N N Yes routing tree? routing tree? Consider N N N Yes Consider N N N Yes obstacles? obstacles? Consider Steiner Steiner N N Yes Yes Consider N N Yes Yes trees? trees? Allow arbitrary arbitrary N N Yes Yes Yes Yes Yes Yes Allow insertion positions positions? ? insertion
Outline Outline � Introduction Introduction to Antenna Effect to Antenna Effect � � Problem Definition Problem Definition � � An Optimal Algorithm for Jumper Insertion An Optimal Algorithm for Jumper Insertion � � Complexity Analysis Complexity Analysis � � Experimental Results Experimental Results � � Conclusions Conclusions �
Problem Definition Problem Definition � Formulate the problem of jumper insertion on a Formulate the problem of jumper insertion on a � routing tree for antenna avoidance/fixing as a routing tree for antenna avoidance/fixing as a tree- -cutting problem cutting problem tree ∪ V G ∪ � T = T = ( ( V V G V N , E ): a Steiner tree ): a Steiner tree N , E � – Set Set V of nodes represents all gate terminals gate terminals V G G of nodes represents all – – Set Set V V N of nodes represents other nodes N of nodes represents other nodes – – Set Set E of edges denotes the wires wires connecting the connecting the E of edges denotes the – circuit terminals or junctions circuit terminals or junctions � D: D: set of set of obstacles obstacles in the active layers in the active layers � � Projection of the obstacles in Projection of the obstacles in D D defines the defines the � forbidden regions for jumper insertion for jumper insertion forbidden regions � F F: : set of the forbidden regions. set of the forbidden regions. � ∈ F); (u ∈ – f(u f(u) = 1 ) = 1 if node if node u u is in a forbidden region is in a forbidden region (u F); – f(u) = 0, ) = 0, otherwise otherwise f(u
Edge Weight Modeling Edge Weight Modeling � The The edge weight edge weight in a Steiner tree models the in a Steiner tree models the � strength of antenna effect caused by the strength of antenna effect caused by the corresponding wire. corresponding wire. � The edge weight can be The edge weight can be � – the the length length of the wire of the wire – – the the area area of the wire of the wire – – the the perimeter perimeter of the wire of the wire – – the the ratio ratio of antenna strength to gate size, or of antenna strength to gate size, or – – any other reasonable models. any other reasonable models. –
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