Piezoresistive Ring-Shaped AFM Sensors with Pico-Newton Force Resolution

Mechanical Design

The ring probe is designed to resonate at about 1 MHz (elliptic mode). A simple formula of the ring’s resonance frequency is given by J.Kirkhope (Kirkhope, 1976).

Where R is the central radius, E, the Young’s modulus, I, the moment of inertia, A, the ring cross section, ρ, the mass density, G, the shear modulus, and K, the shear coefficient which is 5/6. The elliptic mode is found for n=2. Two rings are designed to resonate around 1 MHz. The outer radii are set to 250 µm and 200 µm, respectively, with a width of 50 µm and a thickness of 20 µm. The tip is designed in a triangular form (200 µm in length and 60 µm in width) and placed in a face-to-face position to keep the structure symmetrical (Figure 1).

Figure 1.

ANSYS modal simulation of the ring probe vibrating in the elliptic mode. The dash lines indicate the non-deformed structure. The simulated frequency is 1.47 MHz.

Table 1 shows the ring dimensions and the elliptic mode resonance frequency given by analytical modeling and Finite Element Modeling (FEM) simulation.