NTH order circular symmetry pattern and hexagonal tesselation: two new layout techniques cancelling nonlinear gradient

This paper discusses systematic mismatch due to gradient in IC fabrication and presents a generic layout strategy to enhance matching characteristics for passive and active devices in VLSI. Circular symmetry pattern, a new type of layout structure, was proposed and its effect on high order gradient cancellation was discussed. Analytical deviations suggested circular symmetry pattern has the potential to cancel high order gradient mismatching between two devices. This paper also proposed two layout structures, the second circular symmetry pattern and a hexagonal tessellation, which can cancel linear quadratic gradient in resistors, capacitors and threshold voltages of transistors. Simulation results of proposed second circular symmetry patter and hexagonal tessellation have a better matching performance than existing layout structure.