Static grids, which are structures with a given profile that are artificially created on the surface, can also be used as a measuring gauge. Such grids, made of silicon and other materials, are subject to degradation, surface contamination, wear (Fig.2). In addition, they are quite expensive and, very significantly, do not allow to calibrate the SPM directly during measuring, for example, biological objects.
MATERIALS AND METHODS
If a voltage (U) is applied to the piezoelectric plate in the form of a step signal (Fig.3), then its thickness will change by virtue of the inverse piezoelectric effect. SPM allows to register a change in thickness (Z), which is determined by the formula:
Z = d33 U,
where d33 is the piezoelectric modulus. Using software, we can select the value of the voltage amplitude, so that the change in plate thickness is exactly 1 nm.
As a material for the measuring gauge it is convenient to use a piezoceramic plate in the form of a round tablet with a thickness of 0.5–2.0 mm and a radius of 5–15 mm. The connecting wires are attached to the electrodes located at the ends of the plate (Fig. 4). If the piezoelectric module of the CTS-19 piezoceramics, which we use in our work, is d33 = 200 ∙ 10–12 C/N, then after application of the voltage U = 5 V the variation of the thickness of the plate (Z) is exactly 1 nm.
The Arduino mega 2560 hardware platform (Fig.5) with pulse-width modulation of the output voltage is well suited as a voltage source . To use the Arduino card, you need the free Arduino Software.
When using the measuring gauge in the SPM (Fig.6), vertical bands appear on the image. The width of these bands can be controlled by changing the frequency of the voltage applied to the electrodes of the measuring gauge. For use in a microscope, the gauge is made in a metal casing, while the top cover of the casing moves by 1 nm.
The measuring gauge is placed on a microscope stage. Connections of the measuring gauge are connected to the outputs of the Arduino board, which is connected to a personal computer (Fig.7) with the installed software. The code of the software allowing to produce a voltage that is constant in amplitude and frequency is shown in Fig.8.
The value "input_voltage= 5" in the program provides a voltage amplitude of 5 V. The scanning frequency of the microscope is set to 0.636 Hz (frequency= 3 Ч 0.636).
During scanning, parallel bands appear on the screen (Fig.9), which correspond to two values of the thickness of the piezo plate – the nanometer standard.
It is important to note that, since the Arduino card uses pulse-width modulation for voltage regulation, it is necessary to use a low-pass filter in the form of an RC circuit so that the thickness of the plate does not change under the influence of the high-frequency component of the voltage.
To determine the change in plate height, a histogram of the topographic image (the distribution of the points of the surface image in height) is plotted on which two peaks correspond to two values of the height of the piezoceramic plate. The approximation of the graph (Fig.10) created on the basis of the histogram data, allows to determine the exact values of the coordinates of the two peaks. The difference between the coordinates of these peaks along the horizontal axis is the average change in the height of the piezoceramic plate.
As a result, a simple and affordable nanometer standard was created, the design of which allows multiple uses. SPM is able to achieve measurement accuracy of the order of 0.001 nm, which indicates the high accuracy of the gauge.
It should be noted that such disadvantages of ceramics as creep, nonlinearity and hysteresis do not affect the accuracy of measurements, since a constant amplitude, frequency and polarity signal is fed to electrodes of nanometer standard.
The sizes of many objects of the "nano-world" are in the range of 0.1–100 nm. Accurate measurement of these dimensions is important in modern technology, biology and medical diagnostics . This fact confirms the relevance of the proposed version of the length gauge of 1 nm. Manufacturing of the proposed measuring gauge does not require expensive equipment or materials, which indicates the accessibility of the standard.
In conclusion, it should be noted that on the basis of a nanometer standard it is possible to create a picometer standard, reducing the applied voltage by several orders and using a material with a smaller value of the piezoelectric module, for example, crystalline quartz. Thus, the method used to create the standard can be considered as promising. ■
The study was carried out with the financial support of the RFBR within the framework of the scientific project 16-29-06290.