Scanning probe microscopes universally use PZT material either in the form of cylinders or as stacked elements to position the probe in the X, Y, and Z axes. PZT is a lead zirconate titanate piezoelectric ceramic. The most serious limitation of this material is its tendency to continue to expand after a voltage is applied to it. This phenomenon is generally called Creep or Drift, and continues to occur over at least seven orders of magnitude in time. While the degree of drift may be only a few percent in one decade of time, it makes the difference between a precision instrument and one that is useful only for crude measurements. The manufacturers of the PZT do not provide much information about creep, but may show it as a graph where the PZT extension increases linearly with the logarithm of time. Our measurements have shown this to be only a crude approximation. The amount of creep and time dependence will vary with each type or formulation of PZT material.

        The artifacts caused by creep are present in each axis. The Z axis responds to signals from seconds to milliseconds. The fast scan axis responds to signals from seconds to tenths of a second, and the slow axis responds to signals from hundreds of seconds to seconds. In the X and Y axis, the calibration between the axes will generally differ by 20% with the slow axis having a greater movement. Rotation of the direction of scan by 90 degrees will therefore reverse the difference and cause a 40% distortion in the scan. The first scan will not agree with subsequent scans since the PZT has a memory of at least 5 minutes. The creep causes a phase shift between the Fourier components of the sweep waveforms, resulting in a highly nonlinear scan. The nonlinear correction and calibration change with all parameter of the scan, such as sweep speed, image resolution, and direction. In the Z axis the effect is most obvious in the shift of the baseline and the inability to obtain accurate calibration. Software compensation is not practical due to the long memory of the PZT.
An obvious way to deal with the problem is to use an independent means of sensing the position of the PZT and to use whatever voltage is needed to push the PZT to the right position. There are a number of problems with this idea. If strain gauges are used, the full scale output is typically about 5 millivolts. Obtaining a noise free signal is possible only at fairly large scans, and at low speeds. Capacitive sensors provide a larger output, but add considerably to the system cost, and make the system much more delicate, trouble prone, and may require a factory technician to calibrate the system in the field. Usually, for small scans, the closed loop system is switched off. In any event, the more precise the system is before correction, the better it will be after.

        PZT material is not homogeneous, but consists of millions of grains, and within these grains are domains with random orientation. The capacitance of these grains will vary throughout the material. The resistivity of the material is also not infinite. Like semiconductor materials, the Fermi level lies below the conduction band, and at any temperature above absolute zero, there are thermally excited electrons that are free to move. As a result of this, current will flow through the material in response to local potential gradients.

        When a voltage is applied to the PZT, the potential gradients are immediately determined by the capacitive reactance of the material, and an initial movement occurs. In the long term, the potential distribution will be determined by the bulk resistivity of the material, which is not directly related to capacitance. Creep is caused by the relaxation process whereby the equipotential surfaces adjust themselves to conform to the resistivity of the material. There are short paths of current flow that occur in milliseconds, and much longer paths that require many minutes.

        In an electronic analogy, the PZT is like a large mesh of resistors and capacitors connected between two terminals. The values of the elements vary in a random fashion. The relaxation is a linear phenomenon and therefore proportional to the applied voltage. The I-V response is completely specified by the impulse response, or its integral the step response. The response to an arbitrary voltage waveform is given by the convolution of the PZT response and the applied voltage.

        In addition to providing a metrology head with precise position sensing, a solution pursued at Quesant with every system is to provide electronic compensation networks in series with the PZT drivers that equalize the response over the whole range of time constants, from 5 millisec. to 300 seconds. This effectively makes the PZT material respond to any input signal in an ideal way. A step function for instance results in a step movement with no creep. Software developed for the purpose allows adjustment of each system. With compensation, the hard zoom is free from drift, step calibration gratings have flat tops on the steps, and the calibration does not depend on the orientation of the grating. Nonlinearity of the scans is dramatically reduced and does not depend on the direction of the scan.

        Before purchasing a probe microscope, tests should be performed to see how it will work on meaningful samples:

1. Measure a calibration grid, then rotate the scan direction 90 degrees to see if the calibration holds. Keep the grid fixed.

2. Locate a blemish and position it near the corner of the scan. Do a hard zoom and look for distortion or drift of the blemish on subsequent scans.

3. Measure a step height grating in one orientation and rotate it 90 degrees. If the measurement is not the same, or the baseline is not straight, there is creep in Z.

4. Measure a precise grating like a ruled diffraction grating in 0 degrees and 90 degree orientation. There should be no noticeable change in the line spacing to the eye.

5. Make a slow scan of a diffraction grating (0.5 Hz) and then a fast scan (20 Hz). The images should be exactly the same in calibration and linearity.