suspended by a surface–surface separation $h$ above a layered substrate, consisting of a thin indium tin oxide (ITO) film of thickness $H$ deposited on a gold substrate, where the purpose of the ITO layer is to eliminate the Si-sphere instability as explained below. The thickness of the shell is denoted as $t=\alpha
R$, where $\alpha$ is a convenient fill-fraction parameter. We consider hollow spheres in order to increase $R$ and thereby reduce Brownian fluctuations. In particular, both the Brownian fluctuations and the probability of stiction in the case of the silicon sphere are reduced by increasing the strength of the Casimir force, which can be achieved by increasing $R$ since the Casimir force scales roughly with surface area, and below we consider radii from 1 to 10 $\mu$m. In this regime, as quantified in the previous section, a simple PFA approximation is sufficient to accurately compute the forces and separations. However, because the gravitational force scales as $R^3$, for large $R$ the gravitational force will overcome the Casimir force and push the Si sphere past its unstable equilibrium into stiction. In order to reduce the gravitational force while keeping the surface area fixed, we propose using a hollow Si sphere. 