Shape Detection of Silicon Single Crystal Based on the MUSIC Algorithm

To improve the accuracy and speed of detecting crystal shape during the growth of Czochralski silicon single crystals, a straight line detection method is proposed based on the multiple signal classification (MUSIC) algorithm. First, in order to obtain multi-snapshot signals to meet the MUSIC algorithm requirements, we add multiple sets of zero-mean Gaussian noise. These sets of noise obey the same distribution (i.e., zero-mean Gaussian). This supports the generation of multiple images, which are converted into multi-snapshot signals of a virtual sensor array. These multi-snapshot signals are used to construct a far-field model; the tilt angle estimation problem of a straight line is transformed into a search problem, which seeks the direction of arrival in the virtual input sources. Finally, a near-field model is constructed, and the estimated potential offsets corresponding to the tilt angles are calculated to determine the parameters of the straight line. The simulation and engineering experiments show that the proposed method can accurately and quickly detect the tilt angle and the offset of the straight line, and is superior to existing methods.