The article analyzes the existing methods and means of measuring objects in the nanometer range and develops their classification based on the main principles of use. The main parameters on which each described method is based are considered and the conditions for their most efective application are determined. It is proved that the chemical and electrical sets of properties of the nanomaterial can change when the particle size decreases to the nanometer size, which requires the inclusion of additional chemical and electrical tests in existing methods. Based on the analysis, it was determined that the most functional and universal in solving a wide range of problems is the method of scanning probe microscopy. The classification of existing methods of scanning probe microscopy based on the nature of their applications is developed. The main information parameters on which each described method is based are considered, and the conditions of their most efective application are determined. To increase the accuracy of nanomeasurements, a methodology based on the principle of integration of information provided by diferent methods has been developed. The use of the diferential-digital method is proposed, which includes the use of an additional information parameter in the mathematical model. An algorithm for including additional (a priory) information in the conditions for measuring the nanostructures has been developed, which leads the problem to the correct one according to the method of the control link, which characterizes the deviation of the parameters of measuring nanoobjects from their nominal values. It is proved that increasing the number of measurement methods used in the metrological analysis of nanoobjects will increase the reliability and accuracy of measurement results, and each method will provide additional information parameters to create a computerized method of calculating the control link. The main condition for correct comparison of the result is knowledge of the specific parameters on which each method is based.
In recent years, the study of submicron, nano-, and cluster materials has developed rapidly in
many fields of science and technology [
Improving production eficiency and product quality, development of electronic equipment and biomedical devices, as well as the creation of new nanostructured materials with special properties are largely determined by the accuracy and precision of metrological support. It should be noted that research aimed at improving the instrumentation of nanotechnology has reached a new progressive level. Of course, large-scale development of the nanoindustry is impossible without appropriate metrological (MS) and software support.
Most of the theoretical and applied studies of new measurement methods with a minimum
error have no practical application. The existing methods [
In this regard, the problem of improving existing and developing new automated methods for measuring and evaluating the physical and mechanical properties of nanoobjects is relevant.
Therefore, the aim of the work is a thorough analysis of existing methods and measuring instruments in the nanometer range, their classification, and determination of the main characteristics. The analysis is carried out to create a new unified computer program for automatic correction of nano-measurements errors online.
The essence of nano-measurements is to work at the molecular level, to study structures with
fundamentally new properties. One of the main problems when working with nano-objects
and nanostructures is associated with ultra-low signal levels. Another problem [
The essence of nano-measurements is to work at the molecular level, to study structures with
fundamentally new properties. One of the main problems when working with nanoobjects and
nanostructures is related to ultra-low signal levels. Another problem [
For example [
Also, a prominent aspect is that DC measurements may require the characterization of some
devices and structures by radio frequency signals. This requires a strict design of measuring
instruments with reliable RF connections with low losses of the measuring head and a special
electronic circuit for each signal path [
Nowadays, raster electron microscopy (SEM), transmission electron microscopy (TEM), atomic force microscopy (AFM), scanning tunneling microscopy (STM), microscopy, and focusing on microscopy have become the most widespread. mass spectrometry, Auger spectroscopy, etc. From the point of view of research of the relief and physical properties of structures with high lateral resolution (less than 10 nm), one of the most perspectives is scanning probe microscopy (SPM).
The size and structure of the nanoobject have a great influence on the type of technique and
the characteristics of the measurement methods used [
SPM, STM, AFM methods are especially useful for the structures of crystalline nanoparticles. Figure 1 shows the atomic structures for some typical crystals of well-known shapes, such as a simple cube, a volume-centered cube, and a border-centered cube. Knowing the location of atoms in these structures helps to predict the properties of particles.
However [
Importantly, the chemical and electrical sets of properties of the nanomaterial can change as the particle size decreases to nanometer size. Therefore, in practice, additional chemical and electrical tests are required to determine the characteristics of most of these materials, which also afects the choice of the measurement method. Depending on the means of measurement, methods of analysis of nanomaterials can be divided into two main groups: discrete and ensemble methods of measurement.
Discrete methods of measuring nanoobjects typically use powerful microscopes, such as
scanning electron microscopy (SEM), transmission electron microscopy (TEM), electron
microscopy (SEM), atomic force microscopy (AFM), and scanning probe microscopy (SPM). EM
and SPM are fairly simple methods and reflect particle shapes, but are insuficient in terms of
statistics [
These methods have a resolution much higher than optical microscopy and can detect and measure discrete particles by scattering a high-energy electron beam (SEM and TEM), or by detecting through a probe attached to a slightly sprung console (AFM). In figure 2 shows a comparison of discrete methods of nano measurement concerning the indicators of the speed of obtaining results and price.
Ensemble methods are usually indirect methods when information from many nanoparticles is obtained simultaneously. The methods of this group make it possible to establish the average size of nanoparticles as low-angle X-ray scattering (SAXS) and to detect photon interference.
One of the most frequently used and user-friendly methods for determining the size of nanoobjects in this group is the method of dynamic light scattering (DRS), which is based on the principles of coherence of light waves, and metrological characteristics are obtained by determining the phase diference of these waves after interaction with nanoparticles.
One method that potentially combines the advantages of a group of discrete methods and an ensemble approach is the nanoparticle tracking method, which involves determining the position of particles suspended in a liquid by detecting the light they scatter when irradiated by a laser source and viewing the suspension by using a camera with a charged connected device.
In figure 3 presents the ratio of the main methods of research of nanomaterials with diferent relief characteristics of nanoobjects.
Based on the analysis, it was determined that the most functional and universal in solving
a wide range of problems is the method of scanning probe microscopy. SPM, in turn, covers
several diferent experimental methods for studying the structure and properties of the surface,
both at the micro-level and the level of individual molecules and atoms [
The indisputable advantage of this method is the fact that with the help of SPM you can get information directly from a relatively large area of the surface, which allows you to use this method on-line. Therefore, it is not surprising that they are now widely used for the research, diagnosis, and modification of surfaces.
Common to all methods is the presence of a pointed probe as a tool for working with the surface of the samples. There are contact, semi-contact, and non-contact modes of operation, as well as various modes of operation, including tunnel mode, atomic force mode, spectroscopy mode, Kelvin probe method, electric power, magnetic force, near field, optical, confocal microscopy, etc.
With these methods, you can measure not only the topology of the structure but also many special properties, such as modulus of elasticity, distribution of various substances on the surface, the degree of surface roughness, static charge distribution, the orientation of magnetic domains, etc. [16].
Based on the nature of the applications of existing methods in SPM, they can be classified as follows (figure 4).
Despite the variety of types and applications of modern scanning microscopes, their work is based on similar principles, and their designs difer little from each other.
Another common feature that unites not only sounding instruments, but also other measuring equipment presented in the article for measuring in the nanomaterial range is their increased sensitivity to external destabilizing factors, such as the composition and properties of the environment, lighting, potential diference, and magnetic field, temperature, etc. Because the properties of certain nanomaterials are diferent from conventional ones, the efect of destabilizing factors on the measurement results can be completely unpredictable.
Therefore, when choosing an existing or developing a new measurement method, the features of the kinetics and mechanism of the interaction of the measuring nanoobject with the environment should be thoroughly studied, the properties of nanostructures, process parameters, and the model of their mathematical description should be determined.
A necessary condition for the choice of measurement conditions, such assessments, and subsequent interpretation of the data is the reproducibility of the results and the invariance of the sample for a set of properties.
When changing the size can change not only the values of certain values but also the nature of their dependencies on properties, environments, and influences.
The main directions of creation and use of methods of measurement of micro- and nanosystems are defined: • creation of model representations of connections of topological characteristics and reaction of the object to external influences • establishing links between the properties of the element or system and the topology of the composition, structure, charges, and fields • establishing links between technological factors, the kinetics of formation, and the properties of nanostructures • creation of models that link the functional parameters of devices with the properties of structures that are determined during their manufacture Therefore, to obtain more reliable results, the method of nano measurements should take into account the efects of external destabilizing factors on the nanoobject and ensure the possibility of correcting the deviations caused by them.
Based on the analysis, a method for measuring nanoobjects in static and dynamic modes is proposed. This method will take into account the influence of destabilizing factors for nanostructures of diferent types. The method consists of the continuous determination of the coordinates of the points on the surface of the nanoobject, their processing, and presented in the form of a three-dimensional image. A cluster is introduced to determine the compensating link that corresponds to the tolerance field according to the spectrum of the color image.
The color value of the discrete points of the digital image forms the area, which is represented as isolines. Mathematical software includes geometric parameters of the reference nanostructure. As a result, a region of the color image is formed, which corresponds to the deviations from the shape and location of the surfaces and difers from each other in color (figure 5).
In addition to measuring flat nanostructures, a big task is to determine the topographic features of the surface and the angle of rotation of the plane of the nanoobject. This dependence is formed in the form of a three-dimensional array, in which one column occupies the angle of inclination of the plane, the second – the topographic features of the surface, the third – the coordinate. When scanning the surface of the part, a function based on a mathematical model of the process of traversing the measuring object is used.
The obtained values of the angle of inclination of the plane and topographic features, as well as the values of the coordinates, are compared with the tolerance field, which is presented in the color image (figure 6).
The diferential-digital method makes it possible to study errors, determine the parameters of the nanoobject and obtain cross-sections using the developed methods of algorithmic error compensation, which provides zero ofsets for the operating conditions of the measurement after the training procedure to obtain a statistical result. The development of the diferentialdigital method involves the use of an additional information parameter in the mathematical model in the form of a compensating link. The introduction of additional (a priori) information leads the problem to the correct according to the method of regularization for the functional Ω(, ) = |
− |2 + | − 0|, where →− ∞, 0 – is the a priori solution vector that coincides with the regularization coeficient.
Using this approach to the problem of determining the geometric parameters of the aviation part of a complex spatial surface in small segments, using Delaunay triangulation, using the operation of minimizing the sum of the squares of the deviation, we obtain the following expression:
( =1)
2 Φ( ) = ∑ + (, ), part; constructed surface; (,
) the geometric parameter and the regularization coeficient :
= 0, 1, . . . , , . . . , where ∑( =1) 2 – the sum of the squares of the deviation of n measured points, then from the
– the required geometric parameters of the aviation - regulatory member, which includes information about the nominal value of (, ) = ∑ ( − ) .
2
Thus, we obtain the problem of the regularizing link, which characterizes the deviation of the parameters of nanoobjects from their nominal values, we can obtain a clear point of minimum in the minimization function. The obtained results were stable and satisfied the value of the tolerance field of the measuring part.
( =1)
There are many advantages and disadvantages in choosing a specific measurement method to measure the topography of non-objects. There is no best general method. The use of integration of information provided by diferent methods is proposed, but the results of diferent methods may be contradictory in some cases, namely: 1. Each method is based on the need to study the diferent properties of nanoobjects 2. The steps of sample preparation can modify the results by further unintentional movements of the particles in the matrix, changing the average diameter detected by the SPM 3. Uncertainty that is not taken into account may also afect the final measurements 4. The use of diferent weighing in determining the average diameter of the size distribution. Comparing the results of diferent measurements of the same methodology will be less problematic in this sense because the existing error is constant
Comparing the results of diferent measurements of the same methodology will be less problematic in this sense because the existing error is constant. Therefore, to test the method, the error must be accurately measured, and the results must be consistent with other methods. Therefore, increasing the number of measurement methods used in the metrological analysis of nanoobjects will increase the reliability and accuracy of measurement results and each method will provide additional information. The main condition for correct comparison of the result is knowledge of the specific parameters on which each method is based. The analysis was conducted to obtain the most complete information for the development of a computer program based on a discrete-digital measurement method, which would take into account the measurement information obtained by diferent measurement methods, taking into account the impact of destabilizing factors. in Theory, Practice and Applications (Cat. No. 98CH36190), volume 3, IEEE, 1998, pp. 1739–1746. [15] M. Sitti, H. Hashimoto, Two-dimensional fine particle positioning under an optical microscope using a piezoresistive cantilever as a manipulator, journal of Micromechatronics 1 (2000) 25–48. [16] Digital Instruments, 2021. URL: https://www.digital-instruments.com/.