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Realtime imaging of force fields at the nanoscale with a 2D nano-mechanical probe

Abstract : Over the last decades, nanotechnology became a flourishing field of discoveriesin science, enabled by the constant progress made in microfabrication andcharacterization capabilities. Following the original developments of the atomicforce microscope, the field of nanomechanical force microscopy significantlyevolved, offering a new approach for imaging on the nanoscale complementary todirect optical or electronic microscopy. It now represents a standard tool forthe characterization of structures with sub-nanometer resolution. In thisthesis, we employ an ultrasensitive force sensor in the form of a suspendedvibrating nanowire to image force fields above nanostructures in the vicinity ofthe vibrating extremity of the nanowire.While an AFM probe is sensitive to forces perpendicular to the surface, thenanowire probe measures forces in the horizontal plane. Its ability to vibrateequally along both transverse directions allows to realise measurement of 2Dforce fields. An optical readout serves to probe the mechanical vibrations ofthe subwavelength-sized nanowires, which function as a force transducer.While former experiments were based on time-consuming measurements of thenanowire's random, thermal noise trajectories in 2D, followed by a large analysiseffort, the methods and protocols developed in this thesis allow the realizationof force field imaging in quasi-realtime (10 measurements per second). This isachieved by recording resonantly driven trajectories in the 2D space, whosefrequency shifts are tracked by a double phase lock loop and multiple lock-indemodulators, which allow determining the nanowire's eigenmodeorientations. The 2D force field under investigation can then be determined byanalyzing the perturbation of the nanowire's eigenmodes.With these achievements we extended the use cases towards the measurement ofproximity forces which requires good controllability and stability of theexperiment due to the both the small separations between the nanowire extremity and thesample, and the large force gradients found above nanostructuredsurfaces.We present measurements of the electrostatic force fields above nanostructuredsurfaces that are caused by electric field gradients generated by the sample'sgeometric structuration as well as by residual surface fields. The former causea quadratic dependence on an externally applied voltage, while the surfacefields are independent of the applied sample bias voltage. The different fieldcontributions are analyzed using the Maxwell stress tensor formalism whichallows compensating the linear contribution of the residual electrostatic field,and estimating the residual force field gradient. The latter is found in goodqualitative agreement with the numerical estimation of the Casimir force werealized, both in magnitude and shape. For a quantitative comparison of theexperimental results with the theoretical expectations, we subsequently proposea method to compensate the residual surface fields in all three directions,which is already being tested experimentally.The last topic of this thesis concerns the control and analysis of the nanowire'sdynamics by an artificial force field produced by a realtime feedback in 2D thatallows to create any structure of force field. We realized a proof of concept,applying a control force in an arbitrary direction, whose magnitude isproportional to the vibrations of the nanowire along a chosen arbitrarydirection. We explored different configurations of the application of an uniaxialparallel and a transverse feedback. Additionally, we show that a delayedfeedback scheme can be used to realize cold-damping of a single nanowire mode.Furthermore, we use a single transverse feedback to squeeze the nanowire's noise ifposition and velocity space up to values close to the theoretical limit.
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Submitted on : Thursday, February 17, 2022 - 6:18:10 PM
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Philip Heringlake. Realtime imaging of force fields at the nanoscale with a 2D nano-mechanical probe. Condensed Matter [cond-mat]. Université Grenoble Alpes [2020-..], 2021. English. ⟨NNT : 2021GRALY063⟩. ⟨tel-03579099⟩

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