Fabrication and Sphericity Measurements of Single-crystal Silicon Spheres

The ultimate roundness achievable on a 90 mm diameter sphere (ball) made from single-crystal silicon depends largely on the mechanics of the grinding and polishing process. Paramount is the uniformity of contact between the ball and lap while grinding or polishing in a totally random way. It is also necessary to have roundness and sphericity measurement capabilities which are able to resolve and reliably characterize surface topography down to the level of several nanometers. During the final fracture mode grinding process of the ball using 1 μm aluminium oxide abrasive a specularly reflecting surface at normal incidence is produced with a roundness deviation referred to the centre of the fitted least-square sphere (LSS) < 100 nm. The character of the error surface strongly reflects the cubic structure of the silicon crystal, with peaks often associated with the ⟨111⟩ crystal axis and valleys associated with the ⟨100⟩ crystal axis. Sphericity is determined from a 3D data set optimally integrated into an error surface with a standard uncertainty of 4 nm, generated from complete sets of 2D roundness profiles measured on regularly sampled great circles with a standard uncertainty below 3 nm. Computer-animated visualizations of the sphericity error surface are used to enhance its topography, resulting in very clear views of the cubic symmetries arising from the fabrication processes and the physical properties of the silicon. After polishing, the ball errors based on a fitted LSS are reduced to less than ± 30 nm.