Charakterizace náhodně drsných povrchů pomocí úhlově rozlišeného rozptylu světla a mikroskopie atomové síly

Characterization of randomly rough surfaces using angle-resolved scattering of light and atomic force microscopy

journal article in Web of Science

en

The roughness of four samples of silicon single-crystal surfaces roughened by anodic oxidation is studied using atomic force microscopy (AFM) and angle-resolved scattering of light. The power spectral density functions (PSDFs) are determined on the basis of the measured values of the intensity of the scattered light. This is done on the basis of three models, which establish relation between the intensity of the light scattered in the given direction and the values of the PSDF at a certain spatial frequency. Two of the models are based on the scalar diffraction theory (SDT), while the third is based on the Rayleigh-Rice perturbation theory. The formulae corresponding to the SDT are derived in the theoretical part of the paper. The condition for the Fraunhofer diffraction is not satisfied if the values of the wavelength, distance to the detector and the dimensions of the illuminated spot on the sample used in the experiment are considered. However, it is shown that if the calculation of the intensity of the scattered light is performed in a certain way, then the validity of the expansion only up to the linear terms in the phase terms, i.e. in the same way as in the Fraunhofer diffraction, is not limited by the dimensions of the light spot but by the autocorrelation length of the randomly rough surface. The results obtained by the optical methods are compared with those obtained by AFM. It is shown that there is a good agreement between these results.

Je studována drsnost čtyř vzorků křemíkových monokrystalických povrchů, které byly zdrsněny anodickou oxidací pomocí úhlově rozlišeného rozptylu světla a mikroskopií atomové síly (AFM). Jsou určovány funkce výkonové spektrální hustoty (PSDF) pomocí měření intenzity rozptýleného světla. Jsou k tomu použity tři modely stanovující relaci mezi intenzitou světla rozptýleného v daném směru a hodnotou PSDF v určité prostorové frekvenci. Dva modely jsou založeny na skalární difrakční teorii (SDT), zatímco třetí je založen na Rayleighově-Riceově perturbační teorii. Je ukázáno, že podmínky pro Fraunhoferovu difrakci a použité uspořádání experimentu není vymezena rozměry světelné stopy, ale autokorelační délkou náhodně drsného povrchu. Výsledky získané optickými metodami jsou srovnány s výsledky získanými pomocí AFM. Ukázalo se, že mezi výsledky je dobrý souhlas.

The roughness of four samples of silicon single-crystal surfaces roughened by anodic oxidation is studied using atomic force microscopy (AFM) and angle-resolved scattering of light. The power spectral density functions (PSDFs) are determined on the basis of the measured values of the intensity of the scattered light. This is done on the basis of three models, which establish relation between the intensity of the light scattered in the given direction and the values of the PSDF at a certain spatial frequency. Two of the models are based on the scalar diffraction theory (SDT), while the third is based on the Rayleigh-Rice perturbation theory. The formulae corresponding to the SDT are derived in the theoretical part of the paper. The condition for the Fraunhofer diffraction is not satisfied if the values of the wavelength, distance to the detector and the dimensions of the illuminated spot on the sample used in the experiment are considered. However, it is shown that if the calculation of the intensity of the scattered light is performed in a certain way, then the validity of the expansion only up to the linear terms in the phase terms, i.e. in the same way as in the Fraunhofer diffraction, is not limited by the dimensions of the light spot but by the autocorrelation length of the randomly rough surface. The results obtained by the optical methods are compared with those obtained by AFM. It is shown that there is a good agreement between these results.

úhlově rozlišený rozptyl, náhodně drsné povrchy, skalární difrakční teorie, Rayleighova-Riceova perturbační teorie. mikroskopie atomové síly

angle-resolved scattering; randomly rough surfaces; scalar diffraction theory; Rayleigh-Rice perturbation theory; atomic force microscopy

01.10.2021

IOP PUBLISHING LTD

BRISTOL

2040-8986

23

10

105602– 105602

14