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

2. Scanning Probe Schematic

3. Scanner

4. What makes the SPM work is the scanner, which is made out of a piezoelectric element A piezoelectric is a material that extends or contracts when a voltage is applied to it The reverse also applies: when a piezoelectric is deformed, a voltage is developed (this is the way a gas lighter works)

5. Piezoelectric materials and scanners The extension or contraction of a piezoelectric element is small For example, for a 5 cm long piezoelectric element, a voltage of 100 V will result in an extension of 1 micron Since voltages can be controlled on the level of at least 10 mV, this gives a resolution of 0.1 nm or 1 Angstrom One can put three of them together to form a scanner in three dimensions

6. Tube scanners Another favorite design of the scanner is the tube scanner. In this geometry, the electrodes on the scanner are cut into four quadrants Applying opposite voltages on two X or Y electrodes with to the inner electrode will bend the tube one way or the other. Applying the same voltage to all the 4 electrodes will extend or contract the tube in the Z direction Either tip or sample is attached to scanner

7. Scanning Probe Schematic Coarse approach mechanism

8. Coarse Approach Mechanism Since the scanner can move either tip or sample only by a few microns, we need a mechanism to bring the tip and sample within “striking distance” of each other. The simplest coarse approach mechanism is a threaded mechanism of some type driven by a stepper motor How small a step size can we achieve with this? The smallest typical screw that one can buy readily has an 0-80 thread=80 threads per inch. A typical stepper motor will have about 200 steps per revolution Resolution: 25.4 mm / 80 / 200 = 1.5 microns With a finer resolution stepper (500 steps per revolution) =0.6 microns

9. Coarse Approach Mechanism Scan tube Support Piezo Contact Slowly extend piezo Rapidly contract piezo Apply a sawtooth waveform voltage to the piezo Voltage time slip Can move in small steps (50 nm) and very rapidly For finer control, one can use a “slip-stick” mechanism

10. Slip-stick Coarse Approach Mechanism Some examples from the Mesoscopic Physics Lab

11. Coarse Approach Mechanism Scan tube Slip-stick mechanism can be very fickle--depends on friction Walker mechanism (Pan design) Scan tube Typically use 6 shear piezos--high voltage pulses need to be precisely timed

12. Coarse Approach Mechanism Modified Pan design (Anjan Gupta) Use a slotted scan tube

13. Coarse Approach Procedure It is clear that one does not want to crash the tip into the sample, so we need to establish a procedure to get within “striking distance” of the sample. This is done as in the following flow diagram: Use Z piezo to check for feedback In feedback? Yes No Advance one step Start scanning

14. Scanning Probe Schematic Tip-sample interaction

15. Tip-sample interaction: Tunneling The first scanning probe microscope to be invented was the scanning tunneling microscope, or STM. This depends on a tip-sample interaction that involves tunneling of electrons from the metallic tip to the substrate. The tunneling current depends exponentially on the tip- substrate distance, making it a very sensitive instrument. It gives information not only about topography, but also about the spatial variation of the density of electrons. It can be used to image atoms and electron orbits. However, a major drawback is that the sample substrate must be conducting, restricting its use. I

16. Tip-sample interaction: Force microscopy The force microscope was invented after the scanning tunneling microscope. The simplest force microscope depends on the van der Waal’s (or fluctuating dipole) attractive interaction between the tip and the sample Force distance van der Waal’s interaction Coulomb repulsion

17. Force microscopy: optical detection In a conventional cantilever AFM, the interaction between the tip and the surface results in a deflection of the cantilever holding the tip, or a change in the resonant frequency of the cantilever. This can be detected by many techniques, the most widely used in commercial systems being optical detection: Laser mirror 4-quadrant photodetector The signal in the detector is used to keep the deflection or the resonant frequency of the cantilever constant by moving the z piezo

18. Contact mode AFM The simplest mode of operation is contact mode AFM. In this mode, the tip is essentially placed in contact with the surface, and either the deflection of the cantilever or the movement in the z piezo required to keep the deflection is recorded as a function of the x-y displacement Force distance van der Waal’s interaction Coulomb repulsion Force constants of commercial cantilevers are typically 0.1 N/m. Hence a displacement of 1 nm corresponds to a force 0.1 nN

19. Non-contact mode AFM A more complicated technique of using AFM is non-contact AFM. In this mode, the cantilever is set into oscillation at its natural frequency, usually with another piezo. As the tip approaches the surface, the attractive force tip-sample force changes the frequency, amplitude and phase of oscillation. Any of these parameters can be used in the feedback circuit. Force distance van der Waal’s interaction Coulomb repulsion

20. Tapping mode AFM Contact mode AFM has high resolution, but wears out the tip, and may modify the surface especially if it is soft. Non contact mode does not have as good resolution. Intermittent contact or tapping mode AFM, where the tip touches the surface each half-cycle of an oscillation, has advantages of both. Force distance van der Waal’s interaction Coulomb repulsion

21. 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

22. - 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

23. 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

24. 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

25. 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

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

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

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

29. 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

30. Damped forced harmonic oscillator On resonance, the response of the tuning fork is 90 degrees out of phase with the drive Exploit this to self-excite the tuning fork

31. Lift-mode MFM However, at short distances, it is difficult to separate the magnetic interactions from van der Waal’s interactions. Taking advantage of the fact that van der Waal’s interactions are short range while magnetic interactions are long range, one uses the “lift-mode” technique: take an image of the sample at short distances to obtain primarily topographic information, then use this information to keep the tip a fixed height above the sample, following the topography, and thereby obtain a (almost) purely magnetic image. AFM and MFM images of an array of elliptical permalloy (ferromagnetic) particles

32. Other microscopies (a partial list) Electrostatic force microscopy (EFM) Lateral force microscopy (LFM) Kelvin force microscopy Scanning capacitance microscopy (SCM) Scanning gate microscopy Scanning SET microscopy Scanning SQUID microscopy Scanning thermal microscopy Magnetic resonance force microscopy (MRFM) Scanning Hall probe microscopy Near field scanning optical microscopy (NSOM)

33. Other uses of scanned probe techniques Lithography (electric field, DPN, atom-by-atom) Local voltage probes Biomolecular force detection Nanomanipulation ……………………………….