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Heinrich Diesinger1, Dominique Deresmes1, Thierry Mélin1

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Summary

This study models noise in phase-locked loop (PLL) based frequency modulation Kelvin force microscopy (FM-KFM). It shows PLL components don't add noise, enabling optimized probe design for better performance.

Keywords:
Kelvin force microscopydynamicfrequency noisenoise performancephase noisethermal excitation

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Area of Science:

  • Surface science and nanotechnology
  • Atomic force microscopy techniques
  • Metrology and instrumentation

Background:

  • Phase-locked loop (PLL) systems are crucial for advanced microscopy techniques like frequency modulation Kelvin force microscopy (FM-KFM).
  • Understanding and mitigating noise is essential for improving the resolution and reliability of FM-KFM measurements.
  • Existing noise analysis often focuses on single components, lacking a holistic approach.

Purpose of the Study:

  • To comprehensively assess the noise performance of PLL-based FM-KFM systems.
  • To develop a systematic method for noise modeling and analysis within the FM-KFM setup.
  • To provide guidelines for optimizing probe design and experimental parameters to minimize noise.

Main Methods:

  • Modeling noise propagation through the PLL system using exact closed-loop noise gains and operational amplifier (OpAmp) noise gain approximations.
  • Analyzing noise contributions from thermal and detector sources.
  • Investigating Kelvin output noise by modeling the bias feedback loop.
  • Developing a crossover criterion to determine dominant noise sources based on system parameters.

Main Results:

  • PLL components were found to neither modify nor contribute noise, aligning with theoretical values and measurements.
  • A design rule was proposed for selecting AC modulation frequency to optimize bandwidth sharing between Kelvin and topography loops.
  • A crossover criterion effectively identifies whether thermal or detector noise dominates based on bandwidth, temperature, and probe parameters.
  • Probe merit factors were established for different noise dominance scenarios, offering insights into probe design.

Conclusions:

  • The study provides a comprehensive framework for assessing FM-KFM noise performance, moving beyond single-aspect optimization.
  • The findings demonstrate that PLL components do not introduce additional noise, validating the system's intrinsic noise floor.
  • The proposed design rules and criteria enable informed choices for optimizing experimental parameters and probe design, leading to enhanced measurement sensitivity and accuracy.