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2. Lecture 5 Advanced Topics II Signal, Noise and Bandwidth. Fundamental Limitations of force measurement metallurgha.ir2

3. Fundamental Limitations of AFM Noise –From detection system –Thermal fluctuations of Cantilever Signal –Deflection of Cantilever –Gain in system (amplification and feedback) Speed –Mechanical Bandwidth ( Q and  0 of cantilever) –Electronic Bandwidth There is a trade-off between these three when the system is designed for optimum performance. Specific Application determines choice of design. metallurgha.ir3

4. Thickness, t Review Rectangular cantilevers For cantilever of rectangular cross section of a single material where L>b>t where E is the Young’s Modulus. Resonant Frequency metallurgha.ir4

5. Review of resonance Assume a white noise source drives cantilever, F(  )=constant G( ) is the “response function of the Cantilever”, R is the coefficient of viscous damping Damped Harmonic oscillator force equation metallurgha.ir5

6. Small Cantilevers improve general design Viani et al. Jour. Appl. Phys, 86, 2258 (1999) Signal to Noise Ratio Equipartition noise (thermal equilibrium) Force we are trying to sense Assume that we can design detector so well that noise is dominated by the fluctuations of the Cantilever, then SNR is independent of k. Reduction of R (viscous damping) will give better SNR for same bandwitdth B Smaller Cantilevers experience less viscous damping. metallurgha.ir6

7. Viani et al. Jour. Appl. Phys, 86, 2258 (1999) metallurgha.ir7

8. Small Cantilever has higher resonance frequency for same k value, therefore there is more available bandwidth (possible to scan faster). Better SNR for small Cantilever due to smaller damping. Viani et al. Jour. Appl. Phys, 86, 2258 (1999) metallurgha.ir8

9. Detection System Optical lever requires reflection of LASER spot Metal reflective surface causes stress, bending Small cantilever means less reflected signal, more power causes heating Focus and alignment becomes more difficult. Metal pad for better reflection Would like a sensitive method to measure cantilever deflection without LAZER metallurgha.ir9

10. Dynamic Force Measurements z z0z0 Contact region Force Large Q is important for low force imaging and therefore high resolution with soft samples Force applied to sample is or order Oscillating Cantilever can be regarded as a Force Amplifier Typical parameters in Liquid: metallurgha.ir10

11. Imaging soft agarosegel in PBS buffer Tamayo et. al., Applied Phys. Lett. 77, 582, (2000) Standard Tapping mode in Liquid (Acoustic or MAD drive) With Q control metallurgha.ir11

12. Extremely high Q with tuning fork Grober et al. Rev. Sci. Inst. 71, 2776 (2000) Tuning Fork requires no optical lever Piezo electric effect is used to both drive and read oscillation of the fork. Calibrate the fork Q with driving oscillation metallurgha.ir12

13. Grober et al. Rev. Sci. Inst. 71, 2776 (2000) Analyze noise due to thermal fluctuations of arms of the tuning fork. Noises due to thermal fluctuations, converted to force on fork. Spring Constant from thermal fluctuations:Huge! metallurgha.ir13

14. Grober et al. Rev. Sci. Inst. 71, 2776 (2000) Frequency shift in last few nm of approach Q reduction means dissipative Sample-Tip forces Tunneling current used to monitor distance metallurgha.ir14

15. New Directions ? Small tuning fork or other oscillator with smaller spring constant? Small, soft cantilever with new means of sensing deflection (capacitive change, resistive change)? FM techniques to get more information from dynamic (oscillating cantilever) methods ? metallurgha.ir15

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