  Atomic layer crystals are emerging building blocks for enabling new
two-dimensional (2D) nanomechanical systems, whose motions can be coupled to
other attractive physical properties in such 2D systems. Optical interferometry
has been very effective in reading out the infinitesimal motions of these 2D
structures and spatially resolving different modes. To quantitatively
understand the detection efficiency and its dependence on the device parameters
and interferometric conditions, here we present a systematic study of the
intrinsic motion responsivity in 2D nanomechanical systems using a
Fresnel-law-based model. We find that in monolayer to 14-layer structures, MoS2
offers the highest responsivity among graphene, h-BN, and MoS2 devices and for
the three commonly used visible laser wavelengths (633, 532, and 405nm). We
also find that the vacuum gap resulting from the widely used 300nm-oxide
substrate in making 2D devices, fortunately, leads to close-to-optimal
responsivity for a wide range of 2D flakes. Our results elucidate and
graphically visualize the dependence of motion transduction responsivity upon
2D material type and number of layers, vacuum gap, oxide thickness, and
detecting wavelength, thus providing design guidelines for constructing 2D
nanomechanical systems with optimal optical motion readout.
