FABRICATION AND SPHERICITY MEASUREMENTS OF SINGLE-CRYSTAL SILICON SPHERES

The ultimate roundness achievable on a 90 mm diameter sphere (ball) ma de from single-crystal silicon depends largely on the mechanics of the grinding and polishing process. Paramount is the uniformity of contac t between the ball and lap while grinding or polishing in a totally ra ndom way. It is also necessary to have roundness and sphericity measur ement capabilities which are able to resolve and reliably characterize surface topography down to the level of several nanometers. During th e final fracture mode grinding process of the ball using 1 mu m alumin ium 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 su rface strongly reflects the cubic structure of the silicon crystal, wi th peaks often associated with the <111> crystal axis and valleys asso ciated with the <100> crystal axis. Sphericity is determined from a 3D data set optimally integrated into an error surface with a standard u ncertainty of 4 nm, generated from complete sets of 2D roundness profi les measured on regularly sampled great circles with a standard uncert ainty below 3 nm. Computer-animated visualizations of the sphericity e rror surface are used to enhance its topography, resulting in very cle ar views of the cubic symmetries arising from the fabrication processe s and the physical properties of the silicon. After polishing, the bal l errors based on a fitted LSS are reduced to less than +/- 30 nm.