Projection-Based Statistical Analysis ofFull-Chip Leakage PowerwithNon-Log-Normal Distributions

difficulty ofleakage estimation. Asdemonstrated in[3], leakage Inthis paper wepropose anovel projection-based algorithm to variations canreach 20x, while delays only varyabout 30%.Ithas estimate thefull-chip leakage powerwithconsideration ofboth also beenobserved that leakage powerissensitive tobothinterinter-die andintra-die process variations. Unlike manytraditional dieandintra-die variations. Intra-die variations modelthe approaches that rely onlog-Normal approximations, theproposed individual, butspatially correlated, local variations within the algorithm applies anovel projection method toextract alow-rank samedie. Theseintra-die variations mustbemodeled bymany quadratic model ofthelogarithm ofthefull-chip leakage current additional random variables, thereby significantly increasing the and,therefore, isnotlimited tolog-Normal distributions. By problem size ofleakage analysis. Forexample, thetotal number of exploring theunderlying sparse structure oftheproblem, an randomvariables canreach103106tomodelthefull-chip efficient algorithm isdeveloped toextract thenon-log-Normal variations forapractical industry design. leakage distribution withlinear computational complexity in Manyworkshavebeendeveloped tocapture theleakage circuit size. Inaddition, anincremental analysis algorithm is variations [4]-[10]. Mostofthese approaches approximate the proposed toquickly update theleakage distribution after changes leakage variation asalog-Normal distribution. Forthat purpose, a toacircuit aremade.Ournumerical examples inacommercialfirst-order (i.e., linear) Taylor expansion isusedtoapproximate 90nmCMOS process demonstrate that theproposed algorithmthelogarithm oftheleakage current. Given theincreasingly larger provides 4x errorreduction compared withthepreviouslyvariations innanoscale technologies, suchalinear approximation proposed log-Normal approximations, while achieving orders of canresult ininaccurate results, especially because theleakage magnitude moreefficiency thanaMonteCarlo analysis with104 current hasastrongly nonlinear dependency onprocess variations. samples. Aswill bedemonstrated bythenumerical examples inSection 4, a 20% estimation errorisobserved byusing thelinear Categories andSubject Descriptors