1. Tuning Fork Scanning Probe Microscopy Mesoscopic Group Meeting November 29, 2007

2. Force microscopy: tuning-fork transducers Another favorite force transducer is a watch crystal, which is in the form of a quartz tuning fork. This has the advantage of being self-actuated and self-detected. The actuation is provided by applying a voltage (usually at a frequency corresponding to the resonant frequency of the tuning fork) and detection is accomplished by measuring the resulting current, which is proportional to the deflection. V I

3. - Self actuating - Self sensing - No light - No alignment - optical deflection - laser diode - photo diode - optical alignment - addition actuator Quartz Crystal Tuning fork Quartz Tuning Fork as a Force Sensor Micro-machined Cantilever

4. Force sensitivity  (Qf/k) 1/2 f ~ 10 - 100 kHz k ~ 0.01 - 100 N/m Q ~ 10 2 ~ 10 nm dithering f ~ 32 - 100 kHz k ~ 10 3 - 10 5 N/m Q ~ 10 4 (10 6 in vacuum) < 1 nm dithering CantileverTuning Fork Force Sensitivity of Quartz Tuning Fork Low force sensitivity Low thermal noise due to high stiffness High resolution by small dithering amplitude

5. Force Sensitivity of Quartz Tuning Fork Spring constant is given by Where the Young’s modulus for quartz is given by E=7.87 x 10 10 N/m^2 Force sensitivity is proportional to

6. Putting a tip on a tuning fork Most groups use thin etched wire tips Todorovic and Schultz (1998) Problem is that mass of wire loads tuning fork--changes quality factor and frequency

7. Putting a tip on a tuning fork Our group--use commercial cantilever tips Rozhok et al.

8. Putting a tip on a tuning fork Our group--use commercial cantilever tips Rozhok et al.

9. Putting a tip on a tuning fork Our group--use commercial cantilever tips Rozhok et al. Surface of HOPG graphite

10. Measurements using a tuning fork As the tip is brought close to the surface, the amplitude, phase and frequency of the tuning force changes as a consequence of the force interaction with the surface f = 32.768 KHz k = 1300 N/m Q = 1300 f = 32.768 KHz k = 1300 N/m Q = 1300 L = 2.2 mm, t = 190  m, w = 100  m

11. Damped forced harmonic oscillator On resonance, the response of the tuning fork is 90 degrees out of phase with the drive

12. Amplitude and phase mode operation As tip approaches surface, interaction of tip with surface reduces amplitude of tuning fork oscillation Use z-piezo feedback to maintain amplitude at set value Problem: For high Q tuning forks, it takes a long time for oscillation amplitude to reach steady-state value after any change (milliseconds) Results in very long scan times Same problem with phase mode operation (although very sensitive)

13. Frequency mode operation As tip approaches surface, interaction of tip with surface also changes frequency of tuning fork oscillation This change is more instantaneous In dynamic mode AFM, frequency shift is proportional to gradient of force

14. Frequency mode operation Methods of detection Simplest is self-excitation I->Vamp Phase shift Feedback amplitude control Frequency measurement To feedback and/or plot Voltage divider Amplitude control gives information about dissipation

15. Frequency mode operation More sophisticated techniques Frequency modulation + VCO Lock-in I->V Feedback dc sum DC Frequency offset

16. Frequency mode operation More sophisticated techniques Phase-locked loop Phase comp VCO I->V amp LPF

17. Frequency mode operation Some comparisons: Conventional AFM, 5 mHz resolution, f= 10 4 Hz, k=1 N/m Minimum gradient resolution is 10 -6 N/m For tuning fork, we have k=1000 N/m, so we need to do 1000 times better on frequency resolution, i.e., 5 microhertz

18. Frequency mode operation More sophisticated techniques Goal is to replace analog circuit with software (Labview) Phase comp DDS I->V amp LPF