Tef–Si–Substrate case considered here, we find that $T>0$ corrections to the $T=0$ forces are no more than 2% over the entire range of separations considered here, and hence they can be neglected.

The presence of Brownian motion proves a much more difficult experimental complication to overcome. First, Brownian motion will lead to random fluctuations in the position of the spheres, making it hard to measure their stable separations in an experiment  [@Risken]. Second, and more importantly, sufficiently large fluctuations can drive the Si sphere to “tunnel” past its unstable equilibrium position with the gold plate, leading to stiction [@Risken] since the Si–Au interaction is purely attractive for small separations. The remainder of this section will revolve around the question of how and whether one can overcome both of these difficulties to observe suspension in experiments. In particular, we consider observation of the average separation of the spheres over a sufficiently long time, but not so long that stiction occurs, and analyze the separation statistics and the stiction timescale. First, however, we describe how the parameters are chosen so that Brownian fluctuations are not so severe.

The sphere geometry that we consider is depicted in [Fig. \[fig:fig5\]]{}: a hollow spherical shell 