Déformation photoinduite dans les films minces contenant des ...

Chapter 2. Experimental setup and sample preparation 31the tip-surface interaction forces. So, the ∆V signal decreases. It has been measured [3]that this phenomenon can be described by:∆V = ∆V R[1 − exp(− d )]d 0(2.11)where d = z surf − z is the tip-to-surface distance (z surf and z being the coordinates ofthe tip and of the surface, respectively), d 0 is the characteristic distance (≃ 1 nm), ∆V Ris the maximum amplitude of ∆V at the resonance frequency.Considering the linear relationship between the V z applied on the scan piezo and its zdisplacement (which determines the tip-to-sample separation):pastel-00527388, version 1 - 19 Oct 2010we obtain:z = γ|V z | (2.12)(∆V = ∆V R[1 − exp − V )]z − V surfv 0where V z , V surf , v 0 are the voltages corresponding to the respective z positions.(2.13)∆V is amplified through a gain G = 100 and is filtered via a lock-in amplifier (gain G LI )locked on the tip excitation frequency. This constitutes the shear-force signal:V SF = G · G LI · ∆V RMS (2.14)When the tip is far from the sample surface, V SF takes the value VSF ∞ correspondingto the free vibration amplitude of the tip. When the tip approaches the surface, theshear-force interaction induces a decrease of the tip vibration and V SF decreases. Thus,we process the signal by adding a constant voltage ∆V ∞ to −V SF and we obtain thesignal V in = VSF ∞ − V SF (Figure 2.7(a)). This signal is used in the feedback loop.2.1.3.3 FeedbackThe processed DC voltage V in is used to define the process set-point (Figure 2.7). Anadjustable attenuator G C varies the amplitude of V in . This voltage is compared to a