There is a certain amount of confusion about the number and type of digital converters needed to produce the best scan in an SPM. Most of the hype is due to marketing efforts rather than engineering principles. First of all, there is no benefit to using the DSP to control the PID feedback for the Z axis. One excuse given is so that the software can control the gain settings instead of using knobs. This is bogus, as the Qscope demonstrates. Converting an analog signal to digital always introduces resolution errors and sampling delays. Minimizing the distortion introduced requires sophisticated filters. A good example of this is the design of CD players. Very high order low pass filters are required to minimize distortion.

     The PID terminology is the digital equivalent of the "lead-lag" networks used for many years to improve the stability of analog feedback systems. The problem with using the DSP to control the Z feedback is that it places a heavy real time burden on the DSP and makes it extremely difficult for it to perform other tasks. The PID loop is the simplest type of feedback control, and is not sufficient to suppress the high Q resonance in the Z axis due to the longitudinal resonance of the scanner which occurs at about 10 KHz; analog compensation is required to obtain good performance. It cannot be done by the DSP because too many time elements are required for the finite time response. The Quesant system is able to provide a closed loop frequency response within a factor of three of this resonance. Computer control of the PID parameters is provided by digitally controlled gain elements rather than by numbers down loaded to the DSP. The Z axis response is digitized by 16 bit converters at 100 KHz and accumulated by the DSP to form 32 bit topology information from which the image is formed. By summing many samples per pixel, the full range of the D to A converter is preserved no matter how small the Z deflection is. Because the DSP is not overburdened trying to implement the PID feedback, four separate streams of data can be downloaded to the host system.

     To control the scan in X and Y, it is necessary to provide three independent means of controlling the scan, the size of the scan, and the offset of the scan within the maximum range of the PZT. This is because with only a single converter, the resolution of the scan becomes too low if the scan size is small. Due to the large dynamic range of the deflection, one or two converters do not provide a large enough attenuation. With an 80 micron scanner, zooming down to a 5 nm scan size for atomic resolution is a reduction of 16000 to 1. To do this, the most significant 14 bits of a 16 bit D to A converter are held fixed during the scan, leaving only 2 bits for the scan. Even with a 20 bit converter, only 6 bits would be available. This obviously will not work. In the worst case, most of the resolution bits of the converter must be available for the scan. In the Quesant controller, separate converters are used for the offset, switched gain ranges are used to scale the size of the scan over a range of 200 to 1, and 16 bit converters are dedicated to the scan. Another problem is that even with careful circuit design, and premium components, noise is introduced into the scan signal from external electronic sources. To minimize this, it is essential to reduce the High Voltage amplifier gain at its outputs for small scan sizes that do not require an offset. To control the scan in X and Y, two distinct methods are used for the cases where hard zoom is invoked and where it is not. Hard zoom refers to the ability to scan at the maximum range, and then to select an area within that scan and expand it to an arbitrary size. It is necessary for the high voltage amplifiers to operate at maximum gain for this case. Where this mode is not needed, the high voltage amplifiers can be bypassed for smaller scans, eliminating this possible source of noise.

     Without correction for nonlinearity and accurate calibration, the PZT is inherently a poor element as far as precision is concerned. Anyone who feels that all that is required for precise scans is a few 16 bit D to A converters is quite naïve. The PZT by itself is only good for about 20% accuracy. There is also coupling between Z and X and Y unless they are mechanically separated as in the Quesant system. Two sources of PZT inaccuracy are observed and have been studied by us: creep and cubic nonlinearity. Creep is a linear effect in electronic terms, and is primarily a function of time. Other notes describe its effects. Cubic nonlinearity, on the other hand is primarily a function of the voltage applied to the PZT. It is important to remove both of these artifacts for a precise scan because they scale differently in time and scan size. In the Quesant system, the creep is removed by an electronic compensation circuit in all three axes, while the remaining cubic nonlinearity correction is done by a DSP algorithm using a series of Fourier sine terms. Unless the creep is first removed from the scan, the nonlinearity can't be accurately removed. By scanning a diffraction grating in both X and Y and performing a Fourier series expansion of the pitch of the grating lines, an exact correction can be generated. The correction is done by the DSP as the scan is generated using 32 precalculated slope segments. The result produces 0.2% linearity and similar absolute calibration.

     At Quesant, we have striven to provide the most precise design possible regardless of cost, but we have not included useless components just for marketing hype. An examination of our design would reveal many elements not present in other systems such as creep compensation, Bessel filters for resonance suppression, high speed feed forward imaging and the capacitive reactance bridge technology used in the optional metrology head. This technology is the result of many years of experience in electronic circuit design, and years of perfecting the art of scanning probe microscopes.