Various solid-state mechanisms for the amplification of the small stroke, produced by piezoelectric materials, have been presented in the literature. A designer tasked with designing a device such as a micro-positioner must choose between these mechanisms. In this paper, the use of topological optimization to produce characteristic functions for amplification mechanisms, forming a basis for comparison of different designs, is investigated. The optimization problem was formulated as a variable thickness sheet problem where the stiffness was maximized subject to a constraint on the free stoke. Apart from specifying the design domain, no volume constraints were imposed. The design domain, comprising a piezoelectric and a metallic region, was discretized with eight-noded, plane-strain finite elements. This formulation was found to produce designs with negligible intermediate thickness. These designs are non-unique and repeatedly solving the problem from different starting material distributions results in slightly different 'optimal' stiffness values. The resulting maximum stiffness can be plotted as a function of free stroke producing a curve that is characteristic of the amplification mechanism. Irregularities in this curve would indicate that a local maximum with poor performance has been found. The method is demonstrated by computing the characteristic curve for two amplifier mechanisms.