This thesis summarizes my graduate study under the National Institute of Standards and Technology (NIST) Atom-Based Dimensional Metrology Project, in which we are developing methods for measuring sub-micrometer dimensions including directly counting atom spacings on a silicon-surface lattice.

Atomically flat, hydrogen-terminated Si(111) surfaces are prepared using wet chemistry. The surface morphology after the wet-chemistry preparation was found to be dependent on both the initial etching time and wafer miscut. These two factors have been neglected in literature. To produce a morphology of uniform, long-range steps and terraces, the miscut angle has to be larger than a certain angle. The development and dynamics of the surface morphology was explained by preferential etching. A kinetic Monte-Carlo simulation was used to quantitatively study some of the key aspects of the surface-morphology evolution, such as step flow, pit expansion, and step?pit collision.

The hydrogen-terminated silicon surfaces prepared using wet-chemical etching method were used as substrates to create nanometer-scale patterns using a scanning tunneling microscope (STM)-probe-induced surface modification in both ultra-high vacuum (UHV) and low-vacuum environments. Patterns created in UHV have linewidths below 10 nm, while patterns created in low vacuum had a minimum linewidth of nominally 20 nm. The pattern created in a low vacuum environment was further processed using SF6 reactive-ion etching, resulting in patterns whose aspect ratio had increased more than 5 times.

To enable accurate measurement of atom spacings, a Michelson interferometer of novel design was implemented in this research, based on the principle that during operation, the interference-fringe signal is locked at a zero point by tuning the laser frequency, thus transferring the displacement measurement into a laser-frequency measurement and greatly increasing the measurement resolution. The interferometer is designed to be integrated into an ultra-high-vacuum scanning tunneling microscope for atom-resolved measurements. This unique implementation achieves a nominal resolution of sub-angstrom. In this thesis, the principles of the interferometer design and the uncertainty budget of the interferometer are discussed.