  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 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 distributions in these designs.
By adjusting geometrical features in this model, we identified ideal parameter
combinations 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.
