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We present the design and fabrication of an improved probe for scanning gate microscopy (SGM). Like our previously reported design, the new probe integrates a coaxial tip to produce highly localized electric fields and a piezoresistor to self-sense tip deflection. However, the new design achieves a vertical displacement resolution of 3.7 Å in a 10 kHz bandwidth, enabling the study of both topography and electron organization of semiconductor nanostructures with sub-nanometer features. The design is based on a numerical optimizer for force-sensing piezoresistive cantilevers, which we have extended for SGM.