Modeling the eddy current damping of a typical room- and low-temperature scanning tunneling microscope

The sensitivity of a scanning tunneling microscope (STM), which enables subatomic resolution, depends critically on the efficiency of its mechanical damping. Here, we model and experimentally characterize the eddy current damping system of a typical room- and low-temperature STM. The classical description of a point mass suspended by a spring is extended by treating the STM scanner as a rigid body suspended by three equidistant independent springs, whose translational and rotational dynamics are described using the Lagrange formalism. After simulating the vertical, lateral, and torsional motion of the scanner, the method of mirrors is applied to calculate the eddy current damping coefficient for the cylindrical magnet and copper plate geometry. The experimental characterization is performed using an optoelectronic acquisition system developed to directly measure the vertical decay of the suspended scanner. Measurements are carried out for two spring constants, 145 and 111 N/m, and for different magnet–plate separation distances. The calculated damping coefficients are compared with the experimentally measured decay constants, linking the rigid-body mechanical model, the eddy current calculation, and the measured damping response. Finally, the characterized damping system is implemented in a homemade low-temperature STM, and STM images of Au(111) acquired under ultra-high vacuum conditions at 77 K show stable cryogenic operation with atomic resolution.