Tailoring stresses in piezoresistive microcantilevers for enhanced surface stress sensing: insights from topology optimization

Abstract

In assessing piezoresistive microcantilever sensitivity for surface stress sensing, the key is its capacity to translate surface stress into changes in resistance. This change hinges on the interplay between stresses and piezoresistivity. Traditional optimization has been constrained by rudimentary 1D models, overlooking potentially superior designs. Addressing this, we employed topology optimization to optimize of Si(100) microcantilevers with a p-type piezoresistor. This led to optimized designs with up to 30% enhanced sensitivity over conventional designs. A recurrent "double-cantilever" configuration emerged, which optimizes longitudinal stress and reduces transverse stress at the piezoresistor, resulting in enhanced sensitivity. We developed a simplified model to analyze stress profiles in these designs. By adjusting geometrical features in this model, we pinpointed an ideal parameter combination for optimal stress distribution. Contrary to conventional designs favoring short cantilevers, our findings redefine efficient surface stress sensing, paving the way for innovative sensor designs beyond the conventional rectangular cantilevers.