Graduation Year


Document Type




Degree Granting Department

Electrical Engineering

Major Professor

Sergei Ostapenko, Ph.D.

Co-Major Professor

Rudy Schlaf, Ph.D.

Committee Member

John Wolan, Ph.D.

Committee Member

Ashok Kumar, Ph.D.

Committee Member

Julie Harmon, Ph.D.


Photovoltaics, Silicon wafers, Stress, Cracks, Transducers


Non-destructive monitoring of residual elastic stress in silicon wafers is a matter of strong concern for modern photovoltaic industry. The excess stress can generate cracks within the crystalline structure, which further may lead to wafer breakage. Cracks diagnostics and reduction in multicrystalline silicon, for example, are ones of the most important issues in photovoltaics now. The industry is intent to improve the yield of solar cells fabrication. There is a number of techniques to measure residual stress in semiconductor materials today. They include Raman spectroscopy, X-ray diffraction and infrared polariscopy. None of these methods are applicable for in-line diagnostics of residual elastic stress in silicon wafers for solar cells. Moreover, the method has to be fast enough to fit in solar cell sequential production line. In photovoltaics, fast in-line quality control has to be performed within two seconds per wafer to match the throughput of the production lines.

During this Ph.D. research we developed the resonance ultrasonic vibration (RUV) approach to diagnose residual stress non-destructively in full-size multicrystalline silicon wafers used in solar cell manufacturing. This method is based on excitation of longitudinal resonance ultrasonic vibrations in the material using an external piezoelectric transducer combined with high sensitive ultrasonic probe and data acquisition of the frequency response to make the method suitable for in-line diagnostics during wafer and cell manufacturing. Theoretical and experimental analyses of the vibration mode in single crystal and multicrystalline silicon wafers were used to provide a benchmark reference analysis and validation of the approach. Importantly, we observed a clear trend of increasing resonance frequency of the longitudinal vibration mode with higher average in-plane stress obtained with scanning infrared polariscopy.

Using the same experimental approach we assessed a fast crack detection and length determination in full-size solar-grade crystalline silicon wafers. We demonstrated on a set of identical non-processed crystalline Si wafers with introduced periphery cracks that the crack shifts a selected RUV peak to a lower frequency and increases the resonance peak’s half-width. Both characteristics are gradually increased with the length of the crack. This was confirmed also theoretically by performing finite element analysis of longitudinal vibrations of wafers with cracks. The frequency shift and peak half-width were found to be reliable indicators of the crack appearance in silicon wafers suitable for mechanical quality control and fast wafer’s inspection.

Resonance ultrasonic vibrations metrology is a promising technique to provide quality control in full-size silicon wafers. This approach has the potential to be further developed into a diagnostic tool to address the needs of silicon wafer manufacturers, both in the microelectronic and the solar cell industries