Study on the vibration silicon cantilevers under laser excitation

Microcantilevers were used widely in physical, chemical,biological and mechanical system as sensors to detect the tiny change ofenvironment. The resonance frequency and Q-factor were usual outputquantities during detection. So the study of vibration characteristics ofcantilever under different excitation was very important for its uses.In this paper the vibration of silicon cantilever, subjected to a uniformlaser excitation on one surface, was investigated experimentally andtheoretically. The spectrum analyzer was used to obtain the spectrumresponse curve of cantilevers. The result showed that the resonancefrequency obtained from experimental measurement agreed very well with thatobtained from theoretical calculation. To measure the cantilever deflection,an optical experimental apparatus called thermoelastic microscopy, which wasbased on the principle of heterodyne interferometer, was used to obtain theamplitude and phase of the cantilever deflection under different frequenciesof excitation laser. Theoretically, the thermal wave model, along withplasma wave model, was adopted to simulate the vibration of siliconcantilever under optical excitation. The thermal wave model was widely usedto describe the change of sample temperature in the physical process duringlaser operation, while the plasma wave was the specific characterization ofsemiconducting samples under strong laser excitation, and the plasma wavemodel was used to describe the change of excess carrier density in sample.These two models were used together here to study the cantilever vibration.The expressions of excess carrier density and temperature of cantilever wereobtained. Also the curves of amplitude and the phase of silicon cantileverdeflection versus modulation frequency were calculated. The good agreementbetween measurements and simulations was observed from the results. Fromlinear fitting analysis we obtained a linear relationship between thevibration phase and the square root of modulation frequency. This conclusionwas the same as the result from other authors.