without resorting to practical measurements. Thus, it is possible to significantly
accelerate the course of research in the price of minor errors.
Let’s consider the features of numerous algorithms for solving problems in the
simulation of resonator probes by directly integrating the field equations, paying
attention also to the radiation field from the microprobe. The radiation source is the
measuring aperture of the microprobe, which is considered as an aperture antenna,
which radiates into the diagnosed medium [17].
To calculate the input impedance and the directional pattern (DP) of such an
aperture antenna, one can use the moment method (MM) [18]. However, the use of
MM to solve this problem leads to obtaining a full matrix and, consequently, the
method requires extremely large computer memory and processor time. The finite
element method (FEM) is more suitable for solving such problems, since it has a
relatively simple formulation for complex penetrating structures and leads to the
production of sparse matrices for which there are sufficiently effective algorithms for
solving. However, the FEM method, applied "alone" for unlimited volumes, does not
satisfy the Sommerfeld radiation condition. The radiation conditions at finitely remote
boundaries must be ensured by introducing the appropriate limiting absorption
conditions. In [19], in order to reduce the discretization region, absorbing boundary
conditions are proposed that allow their placement quite close to the emitting aperture.
However, the accuracy of these approximate boundary conditions depends on specific
problems, leading to unpredictable error results of the calculation result. To eliminate
the shortcomings of MM and FEM methods, a number of works [20, 21] proposed the
combined use of numerical methods: the FEM method is used inside the resonant
cavity, and the method of moments is used outside of it.
Also, when the scanning microwave microscope operates, there are certain
factors, the influence of which either introduces certain errors or noises, or complicates
the correct interpretation of the measured parameters. Such disturbing factors, as a rule,
consists of: all kinds of vibrations to which the installation is exposed, various
temperature deviations, the microclimate of the room, the unevenness of the surface of
the object, etc. And if most of them can be fought with known methods, then the strong
influence of the gap between the tip of the probe on the conversion characteristics (Fig.
3) may allow us, as well as in, for example, the AFM or STM to extract data on the
surface profile of the investigated object.
However, unlike Atomic Force Microscopy (AFM) or Scanning Tunneling
Microscopy (CTM) in SMM, as mentioned above, it is possible to derive from the
conversion characteristics not only data on surface roughness, but also data on the
surface distribution of such electrophysical parameters as: specific resistance,
dielectric permittivity, concentration of free charge carriers, their lifetime and mobility,
etc. In other words, the diagnosis of materials with the help of SMM is multiparameter.
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