The fundamental resolution limit of an atomic force microscope (AFM) cantilever is primarily determined by several factors, including the cantilever's stiffness, the noise characteristics of the system, and the effective mass of the cantilever.

1. Cantilever Stiffness: The spring constant (k) of the cantilever affects its sensitivity and resolution. A stiffer cantilever can provide better resolution at high frequencies but may be less sensitive to small forces.

2. Thermal Noise: The thermal fluctuations of the cantilever, which can be described by the equipartition theorem, contribute to the noise in the measurement. The thermal noise level can be quantified using the formula: [ \text{Noise} \propto \sqrt{\frac{k_B T}{k}} ] where (k_B) is the Boltzmann constant, (T) is the temperature, and (k) is the spring constant of the cantilever. Lowering the temperature or using a cantilever with a higher stiffness can help reduce noise and improve resolution.

3. Effective Mass: The effective mass of the cantilever affects its response to forces. A lighter cantilever can respond more rapidly to changes, potentially improving resolution.

4. Tip-Sample Interaction: The nature of the interaction between the AFM tip and the sample also plays a critical role. The forces involved (van der Waals, electrostatic, etc.) should be well understood to optimize the resolution.

5. Mode of Operation: Different AFM modes (contact mode, non-contact mode, tapping mode) have varying impacts on resolution. Tapping mode, for instance, can enhance resolution by reducing lateral forces on the sample.

In summary, the resolution limit of an AFM cantilever is determined by a combination of mechanical properties, thermal noise, and interaction forces at the nanoscale. Optimizing these parameters is essential for achieving high-resolution imaging in AFM applications. For further detailed reading, you can refer to relevant literature on AFM technology and principles.