# Measurement of Sub-Surface Microstructures Based on a Developed Ultrasonic Atomic Force Microscopy
## 2 Materials and Methods  
### Contact-Resonance AFM  
Figure 1 shows a schematic of the developed contact-resonance AFM (CR-AFM) for subsurface profile measurement. It is operated to obtain the information of subsurface microstructure via a probe applied with ultrasonic excitation where the frequency is near the contact resonance frequency of the probe and the sample. In this system, for the sake of easy operation and application, a piezoresistive cantilever probe is used in the system instead of traditional cantilever probe requiring a laser detection unit. The vibration signal of the piezoresistive probe is controlled by a lock-in amplifier in the process of probe scanning over the measured surface. During the scanning procedure, the vibration amplitude or frequency change of the probe is used as the feedback control signal to control the piezoelectric actuator carrying the probe up and down afterwards corresponding to the feedback signal. Since the subsurface microstructures would generate variation of the contact resonant frequency on the surface of the sample and thus change the tracking path of the probe controlled by the feedback control, the scanning image of the sub-surface structure can be obtained.  
In the existing CR-AFM-based subsurface topography studies [22; 23], the probe is given a constant external excitation signal for vibration and the contact force between the probe and the sample is adopted as the feedback signal and maintained constant during the scanning process. The frequency for the external excitation signal is the contact resonance frequency of the probe-sample system. In the scanning, if the sample has subsurface microstructures, it would lead to the change of the probe vibration amplitude, so that the amplitude signal of the probe vibration during the whole scanning process can be drawn to obtain the topography of the subsurface microstructure. The study in this paper adopts a new method based on CR-AFM. The main difference is that in this study, the contact resonance frequency of the probe-sample system is set as the feedback signal instead of the contact force in traditional method. During the scanning, the actual contact resonance frequency of each scanned point is detected in real time and the difference of the detected frequency from the reference frequency is used as the driving signal to the piezoelectric ceramic scanner. Since the subsurface microstructure will influence the resonance frequency of the probe-same system, the signals drawn by the piezoelectric ceramic scanner servo displacement during the scanning process could represent the subsurface topography of the sample. The advantage of using the resonance frequency over the conventionally used contact force as the feedback signal comes from the ability to acquire information from deeper subsurface structures. When using contact force as the feedback signal, the amplitude of the probe vibration differs along the scan path: the amplitude may be  
Figure 1: Schematic of the CR-AFM for measuring subsurface microstructures.  
drastically suppressed when the probe vibration is at the off-resonant mode, resulting in a reduction of the energy transmitted from the probe into the sample and thus making it difficult to reach deeper subsurface structures. In our method, on the other hand, the energy of the vibration holds still at its maximum value for each measurement point, yielding a much better penetration capability.  
The subsequent simulations and experiments will mainly discuss the proposed method, the detection capability of the method for subsurface topography at different burial depths will be studied, and the advantage with the traditional CR-AFM method will be compared.