skip to main content

SciTech ConnectSciTech Connect

Title: Uncertainty in least-squares fits to the thermal noise spectra of nanomechanical resonators with applications to the atomic force microscope

Thermal noise spectra of nanomechanical resonators are used widely to characterize their physical properties. These spectra typically exhibit a Lorentzian response, with additional white noise due to extraneous processes. Least-squares fits of these measurements enable extraction of key parameters of the resonator, including its resonant frequency, quality factor, and stiffness. Here, we present general formulas for the uncertainties in these fit parameters due to sampling noise inherent in all thermal noise spectra. Good agreement with Monte Carlo simulation of synthetic data and measurements of an Atomic Force Microscope (AFM) cantilever is demonstrated. These formulas enable robust interpretation of thermal noise spectra measurements commonly performed in the AFM and adaptive control of fitting procedures with specified tolerances.
Authors:
 [1] ;  [2] ;  [2] ;  [3]
  1. Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010 (Australia)
  2. MicroNanophysics Research Laboratory, RMIT University, Melbourne, Victoria 3001 (Australia)
  3. (Australia)
Publication Date:
OSTI Identifier:
22253527
Resource Type:
Journal Article
Resource Relation:
Journal Name: Review of Scientific Instruments; Journal Volume: 85; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; ATOMIC FORCE MICROSCOPY; COMPUTERIZED SIMULATION; EXTRACTION; LEAST SQUARE FIT; MICROSCOPES; MONTE CARLO METHOD; PHYSICAL PROPERTIES; QUALITY FACTOR; RESONATORS; SPECTRA