Optical Detection Of Atomically-thin Membrane Vibrations

The discovery of graphene in 2004 opened new cognition and research on the new twodimensional material.Nanomechanical systems based on graphene and other twodimensional membrane have opened up a new field of science research.Nanomechanical systems are mainly used for the measurement of extremely small forces,which we call nanomechanical force detectors.Such nanomechanical force detectors have very strong application prospects in microtechnology and induction.Improving the sensitivity of mechanical force detectors will enable people to explore novel and unknown physics phenomena,which can be used to develop the new and powerful potential applications according to these measurement..Mechanical resonators based on suspended twodimensional membranes such as graphene and monolayer transition metal dichalcogenides(TMD)are promising systems for developing sensitive detectors of mass,charge and force.What make these membranes suitable for such applications are their low mass density and their low resistance against bending deformation.These features enable the membrane to move by a measurable amount in response to external stimuli,especially when the membrane is driven to resonance.To measure the flexural vibrations of the membrane,it is important to employ a technique capable of resolving tiny fluctuations of vibration amplitude whose power spectral density typically falls within the range of a few picometers per square root of Hertz.Capacitive detection methods employed to detect the vibrations of graphene membranes are less appropriate for TMD membranes;this is because the latter are semiconducting materials,so the cutoff frequency of such a capacitive detection is low.Alternatively,researchers have been developing optical detection methods based on Fabry-Perot interferences of light between the membrane and a mirror-like substrate,which relate the intensity of light reflected by the device to the distance between the membrane and the substrate.In this work,we calculate the membrane-to-substrate distances that maximize the optical responsivity of the resonator,which we define as the derivative of the resonator's reflectivity with respect to membrane's displacement.In addition,we examine how various substrates with different refractive indices affect this optical responsivity,including bare silicon,silicon coated with silicon oxide,dissipative metal mirrors,and non-dissipative Bragg reflectors.Our calculation method is based on the transfer matrix method for propagating electromagnetic fields,which is an interesting alternative to timing diagrams that are more frequently used in this context.Our results are consistent with earlier theoretical and experimental result,and offer perspectives to enhance the optical responsivity of these mechanical resonators.