• If vibrations are to move the tip relative to the sample, they must penetrate the mechanical loop.

• Solutions

(1) keep vibrations away - vibration isolation table - acoustical isolation

(2) make mechanical resonance freq. of loop components high. - small - lightweight - stiff

(3) damp vibrations

• references Mechanical Vibrations by Den Hartog (1956). Formulas for Stress and Strain by Raymond J. Roask (McGraw Hill, NY, 1975). A Physicist's Desk Reference edited by Herbert L. Anderson (Amer. Inst. of Physics,1989).

• How good does it have to be?

NSOM: less important - bigger scans less resolution. - 1Å good, 10Å may be acceptable

NSOM is 'easy' to build.

• Thermal expansion.

STM: worry -- cover, keep light off, etc

NSOM: again, larger scans and less resolution make it less important. - most NSOMs are 'out in the wind'

design: symmetry so uniform thermal expansion is canceled. - problem: usually temp. change is not uniform. - never a problem at low temps.

• Materials

- Macor is machinable, light, stiff, and has an expansion coefficient similar to PZT (piezoelectric material used).

- Titanium is also good.

- Aluminum is light but rather soft.

- Stainless steel is good but dense.

- Ceramics are good but hard to shape.

- Sapphire is very hard and flat.

- shock-absorbing rubber, bungie-cords

• The screws have balls at the end which mount into a kinematic mount for the sample stage.

• One screw is driven by a stepper motor to automate the approach.

• Other types of approach mechanisms are sometimes used in STM's.

The feet are driven out of phase so at least seven are always moving. The other foot slips. The tube is supported solely by the eight feet.

Driving Waveform for Stick-Slip Motion

A simple circuit to generate the sharp waveforms necessary for producing slip-stick motion is shown. A ramp waveform from a function generator triggered by a computer passes through a nonlinear amplifier circuit (consisting of two diodes, an op-amp and a variable resistor) and is then passed through a high voltage amplifier (not shown) before being applied to the piezo's to generate the slip stick coarse motion.

A histogram of the frequency of the step size for several hundred steps.

• To understand, consider a plate piezo.

• theoretical estimate:

- We assume the strain is evenly distributed, then the two sides form arcs of circles with radii differing by the tube width w.

- It then follows that the sideways displacement of the top of the tube is

- similarly, the angle from normal of the upper face of the tube is

- The total motion is then .

• The motion can also be calibrated by measurements.

- These methods can rely on sensing the motion of the tip with an external instrument: an interferometer (accurate) a very precise dial gauge (these exist with < 1 µm resolution) capacitance gauges (accurate) optical microscope (crude, but O.K. for very large range)

- Other methods use the probe on a well - characterized sample: latex spheres (come in a variety of sizes) C (graphite) or Au on mica work if you mount an STM tip. structures produced by precision electron beam lithography. (this is perhaps the most accurate)

- hysteresis is controlled by either measuring the shape of the curve and compensating, or more accurately (and rarely) by in-situ capacitance sensors of position (Joe Griffith, Phil Russell, et al.).

- It can be ignored if the scans are not very large and data is stored separately for scanning in opposite directions.

• creep (after a voltage step, the motion does not come to an immediate stop but the motion falls exponentially to zero).

- Creep is worst after large voltage steps, and appears as a drift in the image (as that from thermal deformations of the microscope).

- It is minimized by waiting a few minutes after large voltage steps.

- Creep does not occur at cryogenic temps.

• Distortion due to the path the probe takes not being exactly a plane (pin-cushion distortion) can be a problem on instruments with very large scan ranges. - Correct by calculating and pre-compensating.

so the feedback can remain closer to the setpoint value (remember the linear approx).

• There is nothing unique about these configurations.

• An instrument that does both (A. LaRosa):

- Least squares fit to all or part of an image. Recommended.

• Spike (glitch) removal.

- Occasionally data may contain one bad point for a variety of reasons.

- It is often replaced with an average of the neighboring points.

• Smoothing

- Mild: multiply by .25 .5 .25 in a sliding average, in both directions.

- FFT: cut out whatever frequencies are not desired.

• Our recommendation:

- If the data needs much massaging, throw it out and take better data.

- Don't rely on heavy filtering -- you want to know if your data is trustworthy or not.

- Commercial instrument users: know how your data is being filtered.

- Filter data as you take it -- analog or averaging. There is no reason why you should use a wide bandwidth with slow sampling. But leave enough time constants between data points so that you do not smear the data. Also take a look at the unfiltered signals to be sure it is just white noise (no sample bumping or oscillations which could signal trouble).

• Many modes, generally fall into two categories.

- view from directly above Image is seen through the color (gray) scale.

- Perspective -- Usually the z in topography is greatly exaggerated over x and y. An optical image doesn't even have the same units.

• Color by

- gray scale / color by data range (color bar).

- light source (good when fine contrast within several regions separated by large contrast).

- derivative coloring.

- Overlay several images, giving each its own primary color -- to show correlations.

- You learn more about this by going to the instrument show.

• Color bars.

- Uniform range of colors:

- Non-uniform color gradient Used to highlight part of the image. Also used to hide spiked noise. Be suspicious if you see large areas of endpoint colors or randomly spaced dots of them -- it may be hiding bad data.