بررسي رفتار ارتعاشي ميكرو‌تيرك پيزوالكتريك AFM در محيط مايع

INVESTIGATION OF VIBRATION BEHAVIOR OF AFM PIEZOELECTRIC MICRO-BEAM IN LIQUID

ميكروتيرك‌هاي پيزوالكتريك ميكروسكوپ نيروي اتمي1 (AFM)، تيرهايي هستند كه با قرارگيري لايه پيزوالكتريك بر روي آن‌ها مي‌توانند به‌عنوان يك خود‌محرك مورد استفاده قرار بگيرند. هدف اين مقاله بررسي رفتار حركت ارتعاشي اين نوع از ميكروتيرك‌ها در محيط مايع است. مدل‌سازي حركت ارتعاشي تير به‌كمك دو مدل تير غير‌يكنواخت بر پايه‌ي نظريه‌ي اويلر ـ برنولي، و مدل جرم متمركز پيشنهادي شامل سه كره كه هريك معادل يكي از قسمت‌هاي ميكرو‌تيرك غير يكنواخت‌اند، انجام شده است. علاوه بر اين تاثير خواص مكانيكي مهم سيال، فاصله‌ي ميكرو‌تيرك تا سطح نمونه، زاويه‌ي قرارگيري ميكرو‌تيرك نسبت به سطح نمونه، و همچنين تاثير شعاع پراب نيز مورد بررسي قرار مي‌گيرد. نتايج حاصله نشان‌گر وابستگي حركت ارتعاشي به نيروهاي هيدروديناميكي، فشردگي و همچنين برهمكنش بين نوك پراب و سطح نمونه (در فواصل در حد نانومتر) است.

Piezoelectric microbeams are special types of beams applicable to the atomic force microscope (AFM). Having piezoelectric layers, they are capable of self-actuating using the voltage imposed on the piezoelectric layer. The present paper discusses the vibrating behavior of piezoelectric microbeams, with respect to the hydrodynamic forces imposed by a fluid. To do so, considering Hamiltonʹs principle and assumptions of the Euler-Bernoulli theory, the dynamic modeling of a microbeam was carried out and the differential equation of vibrating motion was extracted. As it is very difficult to determine the exact amount of hydrodynamic force imposed on a beam, the hydrodynamic forces were approximated using string sphere modeling. The results obtained from dynamic modeling were compared with experimental ones. The results show that sphere string modeling can favorably model natural frequency and the resonance amplitude of piezoelectric microbeams in a liquid environment. The results show that the vibrating motion (natural frequency and resonance amplitude) of a microbeam in liquid is under the influence of fluid density, due to the damping of liquid and additional mass; it is also seen in the higher vibrating modes. By approaching the microbeam to the sample surface and intensifying squeeze force, the results show further amplitude decrease. The amplitude reduction at higher densities and low angles of the microbeam to the horizon is due to the intensification of compression force. When the interaction force between the probe tip and sample surface is intensified, and when there is a very short distance between the probe tip and sample surface (as small as a nanometer), amplitude is affected. According to the DMT model, there is a direct relationship between the interaction force between the tip and sample surface and the radius of the probe tip. Therefore, the more the radius of the probe tip, the more the interaction force will be. The increase of this force will be followed by a decrease in vibrational motion amplitude.