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A compact vertical scanner for an atomic force microscope (AFM) is developed. The vertical scanner is designed to have no interference with the optical microscope for viewing the cantilever. The theoretical stiffness and resonance of the scanner are derived and verified via finite element analysis. An optimal design process that maximizes the resonance frequency is performed. To evaluate the scanner’s performance, experiments are performed to evaluate the travel range, resonance frequency, and feedback noise level. In addition, an AFM image using the proposed vertical scanner is generated.

An atomic force microscope (AFM) is composed of a micro-machined cantilever with nulling control devices, vertical and horizontal scanners (usually, monolithic tube piezoelectric scanners), an optical microscope for viewing the cantilever and samples, and coarse positioning devices for the cantilever and the sample [

We have developed a compact vertical scanner that has no interference with the viewing angle of the optical microscope. The scanner is composed of a linear flexure guide, a piezoelectric actuator, and a feedback sensor. The theoretical stiffness of the flexure guide is analyzed, and its resonance is calculated and verified using finite element analysis. The optimal design technique is used to maximize the feedback speed, and the result is verified using finite element analysis. The travel range, feedback noise, nulling resolution, and resonances were evaluated experimentally and compared to the theoretical findings. Finally, we present an AFM image from the developed vertical scanner.

A

For the model, the _{h}_{h}_{0}

The static stiffness of the flexure guide is given by [^{3}/12) is the second moment of inertia of the flexure guide. The stiffness (N/m) of the rotational hinge for changing of the force exerted by the PZT actuator is calculated as follows:

Therefore, the total stiffness of the

Using _{max}_{max}_{0}

Using _{f}

The optimal design is determined with the objective of maximizing the resonant frequency. Thus, the cost function is given by:

The cost function has two constraints: the maximum displacement should be larger than 17 μm, and the maximum stress should be lower than 20% of the ultimate strength of the material. The maximum stress was selected considering the fatigue fracture based on the following equation:
_{n}^{8} cycles, _{L}_{G}_{S}_{nn}_{u}_{n}_{u}

The optimal parameters were selected as shown in

Using the sequential quadratic programming (SQP) method of MATLAB^{®} Optimization Toolbox™ (The MathWorks), the convergence plot after completion of the optimization process was determined as shown in

To ensure a global minimum value, eight optimization processes with random initial values were performed as shown in

To validate the optimal design, finite element analyses using the commercial program Pro/ENGINEER Mechanica™ were performed, and the results are shown in

The assembled

As a first measurement, the vertical nulling resolution of the total system is an important factor that determines the quality of the AFM image. The vertical nulling resolution characterizes the stability of maintaining the gap between the tip and sample. After approaching the tip close to the sample surface, we measured the gap between the tip and sample using the optical lever of the AFM head at the null state of the cantilever with no

The step height (20 nm) standard sample was measured using our homemade AFM with the proposed vertical scanner as shown in

A compact AFM vertical scanner that has no interference with the viewing angle of the optical microscope was developed. The theoretical stiffness of the flexure guide was analyzed, and the resonance was calculated and verified via finite element analysis. A design optimization process to maximize the feedback speed was performed and verified via finite element analysis. The travel range, feedback noise, nulling resolution, and resonances were experimentally evaluated and compared to the theoretical findings. The travel range was measured as 10.5 μm for a 120 V input. The feedback noise was about 1.2 nm peak-to-peak. The first resonance is about 2 kHz, which is close to the optimal design results. Finally, a non-contact AFM image of the 20 nm height standard sample was generated. As a final comment, the travel range of the scanner is about 10 μm that seems to be large for the specialized wafer industries. Because the usual measuring height is less than 1 μm in the wafer industries, so the small actuator could be used for the above specialized application field. If the nano-scanner is made from the vacuum compatible materials, the nano-scanner could be used in the scanning electron microscope.

This research was supported by Yeungnam University research grants in 2009.

Schematic diagram of the

A simplified model of the

Convergence plot of the optimization process.

Convergence of the cost function at eight different initial values. This plot shows that the optimized results are global minimums.

Static FEA of the

Dynamic FEA of the

Photo of the

Travel range of the

Noise level of the

Resonances of the

Vertical nulling resolution of the TS-AFM. Top: NC-AFM image. Middle: statistics. Bottom: histogram.

Non-contact AFM image of the 20 nm standard height grating.

Optimization parameters.

Preload (_{0} |
5 | 20 | Random value within lower and upper bounds. |

Thickness ( |
0.2 | 0.5 | |

| |||

Length ( |
4 | 9 |

Optimized results of parameters

| ||
---|---|---|

Thickness (mm) | 0.32 | 0.3 |

Length (mm) | 4.8 | 4.8 |

Preload (_{0} |
20 | 20 |

Resonance frequency (kHz) | 1.95 | |

| ||

Maximum displacement = 17.4 μm, Maximum stress = 54 MPa |

Comparison between the optimal and FEA solutions.

| |||
---|---|---|---|

Stiffness of the guide (N/μm) | 0.71 | 0.67 | 5.6 |

First resonant frequency of the guide (kHz) | 1.95 | 1.78 | 8.7 |

Moving mass of |