Capacitance of spherical dielectric layers

A capacitor device is modeled consisting of a close-packed arrangement of spheres as the dielectric layer. The top electrode is deposited directly on the upper half of the top layer of spheres and bottom electrode is a flat conductor. Expressions are derived for the capacitance for both single and multiple layers of spheres. It is found that a single layer of spheres has the largest increase in capacitance over that of a perfect parallel plate capacitor that has a dielectric thickness equal to the diameter of the spheres. The model predicts a decrease in capacitance as the number of sphere layers increases. The relative uncertainty in capacitance equals the relative uncertainty in the diameter of the spheres for both single and multiple layers.