this invention concerns timing closure in integrated circuit design . timing closure means that the circuit of the integrated circuit preforms its intended function in a timely manner to feed other subsequent functions . a technique called variation comprehension in layout optimization is often used for effective timing closure and to reduce signoff - timer to layout iterations . a typical prior art technique uses flat derate based closure which employs very pessimistic assumptions for safety . these pessimistic assumptions result in increased area and power requirements than are necessary . these pessimistic assumptions may result in some designs that cannot be closed . this means that the designed circuit cannot be assured of operating correctly at the intended speed . thus it is not practical to derive a single flat derate covering whole library the prior art includes the following techniques to attempt to solve this problem . the first such technique is custom cell based derates ( csd ). in custom cell based derates a design depth and index into an advanced on chip variation ( aocv ) table is selected for the cell to determine a derate number . this derate number is used as derate for the cell throughout optimization cycle . the second technique is instance based derates ( isd ). instance based derates generates instance based derates depending on the level in which the instance get used in violating timing path . both methods gives a constant derate to a cell which may be pesimistic / optimistic based on the path depth . there are the following techniques for a current semiconductor processing technology . a flat derate is feasible . a particular semiconductor processing technology may need very high flat derates because the variability is high . with flat derate timing closure is difficult with flat margins as worst case derate is very high . the combination of csd / isd ( described above ) needs static timing analysis ( sta ) tool intervention to generate margins . this generally produces high run times in generating margins post route . this is not a global solution because different blocks need different derate based on depth profile . this technique provides poor correlation to gba timer numbers because cell derate is a function of path depth . the gba aocv technique is very pessimistic because short paths can bias the derates heavily . post - route closure is difficult . this technique does provide very good coverage . this invention attempts to reduce pessimism in gba aocv while maintaining coverage . this invention is a gradient aocv flow . this invention creates design dependent aocv tables using standard aocv information from the cell library . a new aocv table is created using the probability of a short path failing setup is very low if layout is optimized within a tight slew and cap envelop . this invention determines that there is generally no need to have derates for shallow depth in aocv table for setup analysis . short paths do not fail setup if optimized inside tight electrical limits . the same is true for short paths for hold . the invention alters the aocv tables so that the gba analysis is not very different from the pba signoff sta analysis . the place and route tools see the right problems when using this invention and resulting in a significant jump in productivity . for the example circuit illustrated in fig2 , the prior art gba path delay is : design analysis shows that the median path depth in a current example design is 6 . this example of the invention changes the aocv tables such that d1 = d2 = d3 = d5 = d5 = d6 . this invention creates a k level gradient aocv by replacing derate values for all levels less than k with the level k derate value . this reduces pessimism from short paths and enables different levels of pessimism with multiple tables . fig5 illustrates the gradient aocv table of this invention . in the inventive table illustrated in fig5 , each to depth 201 to 203 . . . 211 to 212 . . . 220 is matched with a corresponding derate value . in fig2 however depths 201 to 203 . . . ( depths & lt ; k ) have the same derate value 241 as for depth k 211 . other depths 212 . . . 220 are matched with corresponding unique derate values 242 . . . 250 . a preferred embodiment of this invention uses a k cutoff depth of 30 for standard cells and of 50 for clock tree synthesis ( cts ) cells . which is unchanged from the prior art value in this example . fig6 illustrates a first example of flow 600 of this invention . block 601 performs an non - aocv trial implementation with flat detates . block 602 is an early static timing analysis ( sta ). block 603 identifies critical and non - critical paths and builds design critical path profiles . as shown in fig6 , blocks 601 , 602 and 603 constitute design exploration phase 610 . block 604 generates the custom aocv depth table of this invention based upon the design critical path depth profiles according to block 603 . block 605 integrates into the place and route ( pnr ) flows the timing driven optimization using the custom aocv tables . block 606 tunes the custom aocv table for multiple stages of the place and route ( pnr ) flow . blocks 605 and 606 constitutr implementation phase 620 . this invention generates a custom aocv table for use with gba timing analysis in the implementation tools ( pnr ). this invention modifies the existing signoff aocv tables based on design critical path learning . this invention is not a signoff closure scheme using place and route tools and gba analysis . this invention is unique from other schemes such as flat global derates , sta based timing optimization loops and the like . the productivity gain of this invention is seen as gba timing analysis in timing driven place and route flows will see similar critical paths as the pba sta engines in terms of derates and hence the pppa optimization goals will be real and not overtly pessimistic . this invention minimizes over optimization and hence results in power and area savings . this invention is based on design learning which is usually done in the early part of design exploration . tedious repetitions and iterations with sta are avoided . this invention thus saves time . this invention does not preclude sta - to - pnr timing analysis correlation tuning methods such as flat margins , endpoint margins , additional uncertainty , wire delay multipliers and the like . this invention is not restricted to a method for extracting design specific minimum depth limits . the minimum depth levels of this invention may be different for each standard cell , family of standard cells and the like . this invention poses no restrictions on the design critical path driven selection of minimum depth levels . multiple statistical methods , such as mean path depth , median of the critical path distribution and the like , may be used with this invention . fig7 illustrates the details of a flow 700 used in this invention . flow 700 employs learning through the trial explorations integrated in terms of disconnect margins and multiple threshold - clipped custom aocv table usage . this flow begins with placement optimization of cells at aocv25 in block 701 . this block uses an aocv table modified according to this invention with a value k equal to 25 . this value of k is an example only . flow 700 next performs a post placement optimization of cells at aocv25 in block 702 . the flow then performs clock tree synthesis to generate the circuit clock tree in block 703 . next is post clock tree synthesis optimization at aocv30 in block 704 . this block uses an aocv table modified according to this invention with a value k equal to 30 in this example . the flow next performs routing at aocv25 in block 705 . the flow fixes violations at aocv30 with margin according to timer correlation of 70 ps in block 706 . lastly , the flow 700 completes by signing - off sta driven last mile timing closure in block 707 . using a derate table with k depth and not just one derate value per standard cell gives the following benefits . the sign - off aocv tables have different derates for different cell famillies . this invention doesn &# 39 ; t mix them up and introduce pessimism / optimism in timing analysis . because the gradient aocv tables of this invention are monotonically decreasing , for paths that are deeper than the trim threshold k , the place and route tool can use the lower derates available in the signoff aocv tables . this improves power - leakage and area performance . the isd / csd approach of the prior art makes a single cut on derate graph . this brings in pessimism in analysis as even deeper paths gets same derate . in the gradient aocv of this invention the place and route ( pnr ) tool still sees the graph beyond the cut point . this enables accurate delay estimation . the gradient aocv table is created as follows . the level to be used to cut the aocv graph for cells in library is derived from design depth analysis . this depth is chosen to cover 95 % of violating endpoints . input / outputs ( ios ) are handled via extra uncertainty on virtual clocks . this invention may include separate derate tables for clock and data . separate tables are advantageous because launch and capture depths are very different . one example used a launch depth of 30 and a capture depth of 11 in the separate gradient aocv tables . the gradient aocv flow advantage of this invention has these advantages . this invention does not require signoff tool intervention to derive the derates . this invention covers a larger part of aocv derate range reducing optimism in the prior art csd / isd technique . this invention reduces gba aocv pessimism by hiding low depth derates from the aocv table . this invention enables near pba aocv timing closure with gba aocv timer . this invention has no nworst limitations , gba aocv is guaranteed to cover pba aocv assuming full timer correlation between implementation and signoff timers . this invention provides detter crosstalk comprehension compared to margin flow . with this invention tables can be used along with any optimization tool supporting gba aocv timer updates . the tables of this invention can be user right from placement stage providing maximum pppa improvement . this invention enables the entire flow to be automated using custom scripts . this invention was applied to an example design having a cell count of 700 k with a power density of 300 mw / mm 2 . this example design has a utilization of 77 % with flat derates and of 73 % with this invention . table 2 shows a comparison of this invention and various prior art techniques . this invention allows reduced pessimism involved in traditional aocv graph based optimization / analysis . this invention reduces the gap between pba slack and aocv gba slack . this invention allows eda tools to optimize the design with the right slack picture . this invention provides an improved pppa due to a reduced power envelope , reduced area and reduced die size .