Year: 2025
Type: article
Abstract: The paper shows the possibility of using correlation analysis as a means of mathematical modeling for nondestructive testing of semiconductor crystals on the example of doped gallium arsenide.The aim of the study was to analyze the relationships between the physical parameters of single crystals of doped gallium arsenide using multivariate correlation analysis.The following tasks were solved: to determine the algorithm for correlation analysis of the physical parameters of GaAs single crystals with different ligatures and to build the corresponding linear models, to analyze the results obtained.As the material for the study, plates of single crystals of doped gallium arsenide of three types were chosen: with copper impurity, which has an intergranular embedding; with cadmium impurity, which is embedded in the gallium sublattice; with selenium impurity with arsenic embedding in the sublattice.The concentration of impurities, mechanical stresses, and dislocation density were measured at 32 points along the diameter of each plate.Based on the results of the study, linear models were constructed in which the variable y (mechanical stresses) -the response depended on two factors x1 (impurity concentration) and x2 (dislocation density).According to the values of the coefficients of determination, it was found that all models are statistically significant, and according to the coefficients of multiple correlation, the relationship between the parameters is quite close.The significance of the coefficients of determination was assessed using Fisher's F-test with a probability of 0.95, and the significance of the correlation coefficients was assessed using Student's t-statistics with a significance level of 0.05.Thus, the error for all statistical hypotheses and conclusions does not exceed 5%.The regression equations were used to determine the known and previously unknown correlations between the physical properties of crystals.It was found that the sign of the correlation for selenium impurity with respect to mechanical stress response is negative, and the corresponding signs for copper and cadmium impurities are positive.This indicates the existence of a special mechanism for compensating for mechanical stress due to the redistribution of impurities embedded in the arsenic sublattice compared to impurities embedded in the gallium sublattice or in the intergranular spaces.The results obtained are a prerequisite for further improvement of semiconductor crystal modeling using correlation analysis.
Authors: Maryna B. Litvinova, Oleg M. Dudchenko, Oleksandr D. Shtanko, Svitlana O. Karpova
Institution: Admiral Makarov National University of Shipbuilding
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4410244637