Déformation photoinduite dans les films minces contenant des ...

Chapter 2. Experimental setup and sample preparation 28frequency causes a significant capacitance variation. This gives a high sensitivity tofurther variations of the tip vibration amplitude. In particular, when the tip interactswith the sample surface, the consequent vibration amplitude variations reflect to a variationof the piezo capacitance, which constitute the shear-force signal proportional tothe tip-surface interaction shear-forces.pastel-00527388, version 1 - 19 Oct 2010In order to accurately place the vibration resonance frequency, we use a tip-endinglength of a few mm. This allows to precisely set the resonance. We drive the tip-endingfree length of the optical fiber at its second harmonic, since the fundamental vibrationmode gives a very strong mechanical constraint and a large vibration amplitude. Thechoice of the drive frequency is a compromise between the low s/n ratio obtained withlow frequencies (low time constant) and the limitation due to the standard electronics.The frequency is adjusted by choosing the tip-ending free length L with respect to thesyringe apex. The i − th harmonic frequency f i varies as 2 :where k i = α i L and α i is solution of:f i = k2 i2π√EIρS1L 2 (2.1)cosh(α i L) · cos(α i L) + 1 = 0 (2.2)E is the Young modulus of the fiber, I is its inertia moment, ρ is the material density, Sis the fiber section and L is the tip-ending free length (neglecting the tip shape, whosecontribution is not significant). We usually work at the second harmonic frequency f 2 ,with typical values 3 of about 50 ÷ 60 kHz for L = 3.5 ÷ 3 mm.2.1.3.1 DimensioningThe impedance of the dither piezo tube is essentially capacitive 4 , far from the tuberesonance. To avoid thermal effects a fixed resistor R p is put in parallel with C p andshortcuts the resistive part of the piezotube impedance. The total impedance of thispart is Z p . On the detection branch the R c and r c tunable resistors allow to balancethe resistive parts (R p and r p ) of the piezo branch. Together with the C capacitor, theyform the detection impedance Z. The opposite branches (R and r) of the bridge arepurely resistive. The tunable resistors R and r are set to balance the C p /C r ratio athigh frequency.2 See for example [2].3 See also Figure 2.84 A very small resistance r p models the dissipations