Complex Influence of Probe–Sample System Parameters on the Probe Oscillation Mode and Formation of Bistability in Tapping Atomic Force Microscopy

Engaging the tapping mode in atomic force microscopy does not guarantee intermittent-contact interaction; depending on the parameters combination, the probe–sample system may instead exhibit non-contact (attractive) or mixed behavior. The mixed mode is undesirable due to scanning instability, known as bi-stability of probe oscillations. Aim of this work was to identify influence of probe (spring constant and quality factor), sample (the Young modulus, the Hamaker constant), and scanning (oscillation amplitude of the piezoelectric generator) parameters on the implementation of the bistable interaction mode, as well as to find conditions for achieving stable semi-contact interaction between the tip and sample. Еquation of probe tip oscillations was solved taking into account elastic-adhesive contact of the tip and the sample according to the Johnson–Kendall–Roberts model. Dependencies of the dynamic interaction characteristics of the probe and sample on the distance between them were obtained. These dependencies were analyzed to determine if there was switching between repulsive and attractive interaction modes. Results clearly demonstrated which of the dynamic interaction modes was realized with a particular combination of parameters. Conclusions are applicable in practice to choose probes. The following regularities were obtained. The elastic (actually semi-contact, tapping) interaction mode is realized with an increase in the amplitude of piezoelectric generator oscillations, higher values of the spring constant and quality factor of the probe, the Young modulus of the sample material and/or at lower values of the Hamaker constant of the sample. Higher values of the Hamaker constant and/or lower values of other parameters lead to a mixed interaction regime. Having even higher Hamaker constant and further reduction in other parameters, the adhesion mode (non-contact atomic force microscopy) can be realized.

1. Abetkovskaia SO, Chizhik SA. Complex influence of probe and material characteristics, amplitude of piezogenerator vibration on probe oscillation mode in tapping atomic force microscopy. Methodological aspects of scanning probe microscopy : XIV International Conf., dedicated to the memory of Tatiana Anatolievna Kuznetsova, Minsk, October 21–24, 2025: proceedings. 2025;99-103. (In Russ.).

2. Derjaguin BV, Muller VM, Toporov YuP. Effect of contact deformations on the adhesion of particles. J. of Colloid and Interface Sci. 1975;53(2):314-326. DOI: 10.1016/0021-9797(75)90018-1

3. García R, Pérez P. Dynamic atomic microscopy methods. Surf. Sci. Rep. 2002;47:197-301. DOI: 10.1016/S0167-5729(02)00077-8

4. Keyvani A. Tamer MS, van Wingerden J-W, Goosen JFL, van Keulen F. A comprehensive model for transient behavior of tapping mode atomic force microscope. Nonlinear Dynamics.2019;97:1601-1617. DOI: 10.1007/s11071-019-05079-2

5. Gleyzes P, Kuo PK, Boccara A. Bistable behavior of a vibrating tip near a solid surface. Appl. Phys. Lett. 1991;58(25):2989-2991. DOI: 10.1063/1.104690

6. Sarid D. Scanning force microscopy with applications to electric, magnetic and atomic forces. New York; 1994.263 p.

7. Anczykowski B, Krüger D, Babcock KL, Fuchs H. Basic properties of dynamic force spectroscopy with the scanning force microscope in experiment and simulation. Ultramicroscopy. 1996;66(3-4):251-259. DOI: 10.1016/S0304-3991(97)00002-8

8. Nony L, Boisgard R, Aime JP. Nonlinear dynamical properties of an oscillating tip–cantilever system in the tapping mode. J. of Chem. Phys. 1999;111(4):1615-1627. DOI: 10.1063/1.479422

9. García R, San Paulo A. Attractive and repulsive tip-sample interaction regimes in tapping-mode atomic force microscopy. Phys. Rev. B. 1999;60(7):4961-4967. DOI: 10.1103/PhysRevB.60.4961

10. San Paulo Á, García R. Unifying theory of tapping-mode atomic-force microscopy. Phys. Rev. B. 2002;66:041406(R). DOI: 10.1103/PhysRevB.66.041406

11. Kiracofe D, Melcher J, Raman A. Gaining insight into the physics of dynamic atomic force microscopy in complex environments using the VEDA simulator. Rev. of Sci. Instr. 2012;83(1):013702. DOI: 10.1063/1.3669638

12. Li YingZi, Qian JianQiang, Li XiaoFeng, Li Yuan, Hua BaoCheng, Yao JunEn. Elimination of bistability in constant-phase mode in atomic force microscopy. Appl. Phys. 2012;57(5):460-465. DOI: 10.1007/s11434-011-4825-0

13. Söngen H, Bechstein R, Kühnle A. Quantitative atomic force microscopy. J. of Phys.: Condensed Matter. 2017;29:274001. DOI: 10.1088/1361-648X/aa6f8b

14. Abetkovskaia SО, Chizhik SА. Influence of the probe spring constant and the quality factor on its oscillation characteristics in dynamic mode of atomic force microscopy. Doklady of the National Academy of Sciences of Belarus. 2024;68(6):513-518. DOI: 10.29235/1561-8323-2024-68-6-513-518

15. Abetkovskaia SO, Chizhik SA, Guangbin Yu. Tapping mode of an atomic force microscope with a probe cantilever of a low spring constant. Vestsi Natsyyanal’nai akademii navuk Belarusi. Seryya fizika-tekhnichnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physical-technical series. 2025;70(1):57-68. DOI: 10.29235/1561-8358-2025-70-1-57-68