# Measurement of Sub-Surface Microstructures Based on a Developed Ultrasonic Atomic Force Microscopy
## 3 Results and Discussion
### Experimental Results  
Experiments are carried out to demonstrate the capability of the established CR-AFM system. In the experiments, the contact resonance frequency of the probe and the sample is firstly determined by sweeping the excitation signal for driving the probe vibrating. In this experiment, the first-order contact resonance frequency of the probe-sample is determined to be 220 kHz, which is tested by sweeping the frequency of the probe in contact with an unetched silicon wafer covered by a 30 \(\upmu\)m HOPG film. The result of the frequency sweep on the single point is shown in Figure 6. Then, an exciting signal with the frequency of 220 kHz and an amplitude of about 500 mV is applied to the thermally driven probe. First, the probe is brought into contact with the sample, and a sweep signal is applied to the probe to determine the contact resonance frequency between the probe and the sample at a single point. Then, use this frequency as the reference oscillation frequency in the probe scanning process. When the topography of the subsurface changes, the contact resonance frequency of the surface changes, and the vibration frequency of the probe also varies. After that, the difference between the collected real-time probe contact resonance frequency and the reference frequency is used as a feedback signal, and the piezoelectric ceramic is controlled to drive the probe to move up and down to complete the scan process and the probe can trace the subsurface profile in this way. To briefly summarize, the deviation of the actual vibration frequency of the probe from the reference frequency at each measurement point  
Figure 5: Finite element simulation results. (**a**) shows the change in the contact resonance frequency of the probe sweeping across the sample surface of 8 \(\upmu\)m when the surface HOPG film thickness is different. (**b**) shows the variation of the maximum contact resonance frequency difference during the scanning process with the increase of the HOPG film thickness. is used as the control signal, and the subsurface morphology of the sample is characterized by the motion profile of the \(Z\)-axis piezoelectric ceramic. Figure 7 shows the characterizations of the three samples used in the experiments. As shown in the figure, the upper figures illustrate the surface topography of the sample. The sectional profile that marked in the upper figures are shown in the lower figures. As the thickness of the sample in Figure 7c is beyond the measurement range of AFM, a white light interferometer was used to measure the HOPG film thickness while AFM is used for the first two samples. The HOPG film thicknesses covered on the three samples were evaluated to be 485 nm, 805 nm and 34.469 \(\upmu\)m, respectively. It should be noted that the thickness values are obtained by averaging multiple sectional profile to reduce the estimation random error. Figure 6: The spectrum of the contact resonant frequency around a local maximum at the start point of the experiment. Figure 7: Characterization of the three samples prepared in the experiments. (**a**,**b**) show the AFM scan images at the edge of the HOPG films with two different film thicknesses covered on the Si substrates. (**c**) shows the white light interference image of the third sample with a different film thickness from the first two samples. (**d**–**f**) show the height difference of samples (**a**–**c**) on line 1, line 2, and line 3, respectively. The measurement results of the three samples by the built CR-AFM are shown in Figure 8. The piezoresistive cantilever probe used in the experiment has a resonant frequency of 30 kHz and it has a contact resonance frequency of 220 kHz with the sample surface with subsurface microstructures. The scan rate of the probe is 100 nm/s. The sampling frequency of the scanned point data in the experiment is 1000 kHz and every 100 acquired data are averaged.