Symmetrical buffer placement in clock trees for minimal skew immune to global on-chip variations

As the feature size of VLSI circuits scales down and clock rates increases, circuit performance is becoming more sensitive to process variations. This paper proposes an algorithm of symmetrical buffer placement in symmetrical clock trees to achieve zero-skew in theory, as well as robust low skew under process or environment variations. With the completely symmetrical structure, we can eliminate many factors of clock skew such as model inaccuracy, environment temperature and intra-die process variations. We devise a new dynamic programming scheme to handle buffer placement and wire sizing under the constraint of symmetry. By classifying the wires by tree levels and defining the level-dependent blockages, the potential candidate points in the gaps of circuit blocks can be fully explored. The algorithm is efficient for minimizing source-sink delay as well as other linear cost functions. Experiments show that our method helps to obtain a balanced design of clock tree with low delay, skew and power.