Method for measuring dynamic thermal expansion property of nano-film

A method for measuring a dynamic thermal expansion property of a nano-film, wherein the method for measuring a dynamic thermal expansion property of a nano-film is applied to an ellipsometer equipped with a temperature-controlled heating stage;

• the temperature-controlled heating stage is configured to carry a film sample;
• the temperature-controlled heating stage is also configured to control a temperature of the film sample according to a temperature modulation program;
• and the temperature modulation program comprises a linear temperature change program and a resonant temperature modulation program that are superimposed;
• and
• the method for measuring a dynamic thermal expansion property of a nano-film comprises:
• controlling the temperature of the film sample on the temperature-controlled heating stage according to the temperature modulation program, to obtain a thickness-time curve of the film sample;
• determining an apparent thickness-time curve of the film sample by using a numerical integral averaging formula based on an average temperature and frequency of the temperature modulation program and the thickness-time curve of the film sample;
• determining an amplitude-time curve and a phase-time curve of the film sample by using a digital signal processing method based on the average temperature and frequency of the temperature modulation program and the thickness-time curve of the film sample, wherein both the amplitude-time curve and the phase-time curve are used to describe a resonant dynamic change of a thickness of the film sample in response to resonant temperature modulation;
• determining a coefficient of apparent thermal expansion of the film sample under the temperature modulation program by using a numerical derivation formula based on the average temperature and frequency of the temperature modulation program and the apparent thickness-time curve of the film sample;
• determining a coefficient of reversible thermal expansion of the film sample under the temperature modulation program by using a formula for the reversible thermal expansion, and real and imaginary parts of the coefficient of the reversible thermal expansion based on the average temperature, the average frequency, an average amplitude, and an average phase of the temperature modulation program, as well as the amplitude-time curve and the phase-time curve of the film sample;
• and
• determining a coefficient of irreversible thermal expansion of the film sample under the temperature modulation program by using a difference formula based on the coefficients of the apparent thermal expansion and the reversible thermal expansion of the film sample.