Quantitative atomic force microscopy.

Area of Science:

• Surface Science
• Nanotechnology
• Materials Science

Background:

• Atomic Force Microscopy (AFM) is crucial for surface science, with Amplitude Modulation (AM) and Frequency Modulation (FM) being prominent modes.
• Existing data analysis methods for different AFM modes rely on mode-specific assumptions, complicating comparisons and validity checks.
• A unified approach is needed to simplify AFM data interpretation across various modes.

Purpose of the Study:

• To develop a unifying set of equations for analyzing AFM data.
• To enable straightforward comparison of data acquired using different AFM modes.
• To provide a universal method for extracting tip-sample force information within the harmonic approximation.

Main Methods:

• Combining existing, mode-specific AFM data evaluation methods.
• Developing a unifying set of three equations applicable to the harmonic approximation.
• Quantitatively analyzing 3D AFM data from both AM and FM modes.

Main Results:

• A single set of three AFM equations is presented for unified data analysis.
• These equations allow analysis regardless of the specific AFM mode (AM or FM).
• The three equations yield the complete information about tip-sample forces within the harmonic approximation.

Conclusions:

• The developed unifying equations simplify AFM data analysis across different modes.
• This approach facilitates direct comparison of results obtained from AM and FM modes.
• The method provides a robust framework for understanding tip-sample interactions in surface science.