We have proposed and demonstrated a novel method that can determine both the geometrical thickness and refractive index of a silicon wafer at the same time using an optical comb. The geometrical thickness and refractive index of a silicon wafer was determined from the optical thickness using phase information obtained in the spectral domain. In a feasibility test, the geometrical thickness and refractive index of a wafer were measured to be 334.85 microm and 3.50, respectively. The measurement uncertainty for the geometrical thickness was evaluated as 0.95 microm (k = 1) using a preliminary setup.

A phase-encoding electronics capable of compensating for the nonlinearity error in a heterodyne laser interferometer is described. The system consists of the phase demodulating electronics and the nonlinearity compensating electronics. For phase demodulation, we use the phase-quadrature mixing technique. For nonlinearity compensation, the offsets, the amplitudes and the phase of two output signals from the demodulator are adjusted electrically so that their Lissajous figure is a circle. As a result, the correct phase can be obtained. An analysis of the nonlinearity in the heterodyne interferometer and the design of the phase-encoding electronics are presented. The experiment was performed in a Michelson-type interferometer using a transverse Zeeman stabilized He-Ne laser. We demonstrate that this method can encode the phase of a heterodyne interferometer with sub-nanometer accuracy.

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The pitch and orthogonality of two-dimensional (2D) gratings have been calibrated by using an optical diffractometer (OD) and a metrological atomic force microscope (MAFM). Gratings are commonly used as a magnification standard for a scanning probe microscope (SPM) and a scanning electron microscope (SEM). Thus, to establish the metertraceability in nano-metrology using SPM/SEM, it is important to certify the pitch and orthogonality of 2D gratings accurately. ODs and MAFMs are generally used as effective metrological instruments for the calibration of gratings in nanometer range. Since two methods have different metrological characteristics, they give complementary information for each other. ODs can measure only mean pitch value of grating with very low uncertainty, but MAFMs can obtain individual pitch value and local profile as well as mean pitch value, although they have higher uncertainty. Two kinds of 2D gratings, each with the nominal pitch of 700 nm and 1000 nm, were measured, and the uncertainties of calibrated values were evaluated. We also investigated the contribution of each uncertainty source to the combined standard uncertainty, and discussed the causes of main ones. The expanded uncertainties (k = 2) of calibrated pitch values were less than 0.05 nm and 0.5 nm for the OD and the MAFM, and the calibration results were coincident with each other within the expanded uncertainty of the MAFM.

We report on a novel compact interferometery system for measuring parasitic motions of a precision stage. It is a combination of a Michelson interferometer with an auto-collimator, of which full physical dimension is mere 70 mm x80 mm x35 mm (WxLxH) including optical components, photo-detectors, and electronic circuits. Since the beams, which measure displacement and angle, can be directed at the same position on the moving mirror, the system is applicable for testing small nano-stages where commercial interferometers are not able to be used. And thus, errors from nano-scale deformation of the moving mirror can be minimized. We find that the residual errors of linear and angular motion measurements are 2.5 nm in peak-to-peak and 0.2'', respectively.