## 3 Results and Discussion
### Limitations and Further Improvements  
As the developed AFM is the first prototype constructed from the preliminary design, it has several limitations. One of the main limitations is the resolution limit of imaging. The piezo stage used in our setup adopts open-loop design and does not contain an internal strain gauge sensor, limiting the resolution to 20 nm in all directions (\(X\), \(Y\), and \(Z\) axes). In addition, the maximum travel range of the piezo stage is 20 \(\upmu\)m. Therefore, an AFM image that is acquired with the system is limited to a maximum scan size of 20 \(\upmu\)m \(\times\) 20 \(\upmu\)m. The resolution limit and the scan range of our AFM setup can be improved by using piezo stage with better specifications. However, a complete redesign on some of the custom-built mechanical parts might be necessary to incorporate the new piezo stage with different mechanical dimensions.  
Calibration on the scanner was attempted using a silicon calibration grating with 4 \(\upmu\)m period and 25 nm step height. Unfortunately, the features on the calibration grids cannot be resolved in the AFM images obtained with our AFM. This is mainly due to the resolution limit of the piezo stage. Therefore, calibration on the scanner was not carried out successfully in our setup. The scan size of the AFM images wascalculated based on the piezo stage specifications (provided by the manufacturer). A maximum travel range of 20 \(\upmu\)m requires 75 V of output voltage (or 10 V of input voltage to the piezo's controller). Therefore, 7.5 V of output voltage (or 1 V of input voltage) corresponds to 2 \(\upmu\)m of travel range.  
On the whole, there are several pros and cons of our developed AFM as compared to a commercially available system. Using resources commonly available from the undergraduate laboratory, our AFM costs considerably less than a typical commercial AFM, where the price may start from $26k USD. A high-end machine may cost more than $100k USD per unit. In terms of imaging performance, our AFM is capable of performing imaging at the microscopic scale, while a commercial  
Figure 12: Line scans for trace and retrace extracted from AFM images in Figure 10: (**a**) Trace and retrace of line 75 extracted from Figure 11a,b, respectively; (**b**) Trace and retrace of line 75 extracted from Figure 11c,d, respectively; (**c**) Trace and retrace of line 75 extracted from Figure 11e,f, respectively.  
AFM would be able to resolve features at two or three orders of magnitude smaller (nanometer scale). The fundamental limitation of the existing system is the imaging mode which is restricted to contact mode imaging only.  
Currently, the AFM system is not able to generate a force-distance curve. Therefore, calibration on the force constant of a cantilever cannot be performed. A sub-program will need to be developed to perform this measurement. This can be achieved in LabVIEW environment without any extra hardware. More advanced imaging modes such as non-contact imaging and tapping mode imaging are some of the possible improvements that can be implemented in the existing system. However, the cantilever holder will have to be redesigned in order to oscillate the AFM cantilevers in the various frequencies.