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.

In this paper, we propose a new 2D displacement atom encoder using only one lateral-dithered scanning tunneling microscope (STM) tip and one mono-crystalline area of the highly oriented pyrolytic graphite (HOPG) crystal. A high-speed lateral circular dither modulation with proper amplitude is applied to a tip scanner to position the STM tip on six specific points on the HOPG crystalline surface. Multi-tunneling-current signals obtained from the six specific points are utilized to determine the lateral 2D displacement based on the two unit lattice vectors on the HOPG crystalline surface. In addition, the interpolation method can be used in the newly proposed method to measure displacement less than the lattice spacing. In the paper, instrumentation and experiments of the new 2D displacement measurement technique are discussed. The experimental results show that the proposed technique has the capability to measure 2D displacement with a resolution of 10 pm order.

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