Two-dimensional encoder with picometre resolution using lattice spacing on regular crystalline surface as standard

Abstract

A two-dimensional (2D) encoder with picometre resolution using multi-tunnelling-probes scanning tunnelling microscope (MTP-STM) as detector units and a regular crystalline lattice as a reference is proposed. In experiments to demonstrate the method, a highly oriented pyrolytic graphite (HOPG) crystal is utilized as the reference. The MTP-STM heads, which are set upon a sample stage, observe multi-points which satisfy some relationship on the HOPG crystalline surface on the sample stage, and the relative 2D displacement between the MTP-STM heads and the sample stage can be determined from the multi-current signals of the multi-points. Two unit lattice vectors on the HOPG crystalline surface with length and intersection angle of 0.246 nm and 60°, respectively, are utilized as 2D displacement references. 2D displacement of the sample stage on which the HOPG crystal is placed can be calculated using the linear sum of the two unit lattice vectors, derived from a linear operation of the multi-current signals. Displacement interpolation less than the lattice spacing of the HOPG crystal can also be performed. To determine the linear sum of the two unit vectors as the 2D displacement, the multi-points to be observed with the MTP-STM must be properly positioned according to the 2D atomic structure of the HOPG crystal. In the experiments, the proposed method is compared with a capacitance sensor whose resolution is improved to approximately 0.1 nm by limiting the sensor's bandwidth to 300 Hz. In order to obtain suitable multi-current signals of the properly positioned multi-points in semi-real-time, lateral dither modulations are applied to the STM probes. The results show that the proposed method has the capability to measure 2D lateral displacements with a resolution on the order of 10 pm with a maximum measurement speed of 100 nm s−1 or more.

Generating Sub-nanometer Displacement Using Reduction Mechanism Consisting of Torsional Leaf Spring Hinges

“…There are several other works to carry out picometer measurement that uses the atomic lattice spacing as a reference of positioning [2]- [4]. Aketagawa et al had important trials in which the lattice spacing of HOPS (highly oriented pyrolytic graphite) was used as a reference for a double-tunneling-probe STM (DTP-STM) of twodimensional encoder scale with tens of picometer resolution [2], but the measurement apparatus itself is too complex to use as the picometer displacement generating tool.…”

Real-time cross-correlation filtering of a one-dimensional grating position-encoded signal

“…If several crystalline lattice-encoded signals picked up by STM are employed, two-dimensional displacements with tens of picometers resolution can be measured according to the algorithm in [10,11].…”

Atomic force microscope cantilevers as encoders for real-time forward and backward displacement measurements

“…On the one hand, new optical encoders [1][2][3] are investigated for nanometer-resolution displacement measurements, although their resolutions are limited due to the relatively long optical wavelength, and their accuracies are limited by the nonlinearities in interpolation. But on the other hand, scanning probe microscopes (SPM), a revolutionary family of nanometer-scale measuring instruments, can also undoubtedly be used as encoders [4][5][6][7][8][9][10] for micro displacement measurement with nanometer and higher resolution. In particular in [9,10], a tuning-fork atomic force microscope (AFM) cantilever used as an encoding sensor, due to its compactness, can sense the position change of a line-scale or grating, when it moves with the micro-scanning stage if its parameters are well defined and well calibrated.…”