Method to analyze spectroscopic ellipsometry data of porous samples utilizing the anisotropic Bruggeman-effective medium theory

A method that enables determining pore size and distribution in a sample selected from the group consisting of:

• a porous thin film having an effective thin layer thickness and a surface;
• and
• a porous surface region of a semi-infinite bulk substrate having a surface;
• said sample comprising skeletal material presenting with a total volumetric porosity %, a % of total pores present in the volume of said thin film which are accessible by solvent presented at said surface thereof, and a % of accessible pores actually filled with solvent at a plurality of times during which the partial pressure of said solvent is changed at said sample surface, said method involving obtaining ellipsometric data at a plurality of times while partial pressure of a solvent is changed in the vicinity of the surface of said sample, and performing a simultaneous regression on said ellipsometric data obtained at at least two of said times, said method not requiring knowledge of effective refractive index values of said porous thin film having an effective thin layer thickness or said porous surface region of a semi-infinite bulk substrate when all pores therein contain no solvent and when they are essentially completely filled, said method comprising:
• a) providing an ellipsometer system comprising a source of electromagnetic radiation, a polarization state generator, a stage for supporting a sample in a chamber that enables controlling the partial pressure of a solvent at the surface of said sample, a polarization state analyzer and a detector of electromagnetic radiation;
• b) while causing said surface of sample to undergo a sequential plurality of solvent partial pressures adjacent thereto in said chamber, obtaining a plurality of ellipsometric data sets that correspond to a plurality of times corresponding to different solvent partial pressures being presented to the surface of said sample;
• c) simultaneous with, or after step a), providing a mathematical model of said sample as a Bruggeman effective medium including as parameters therein, at least:
• variable wavelength dependent refractive index of said skeletal material;
• variable total porosity %;
• variable % of accessible pores;
• variable % of accessible pores that are filled with solvent at a given partial pressure;
• and
• wavelength dependent refractive index values of said solvent;
• and
• d) while assuming fixed values for wavelength dependent solvent refractive indices, and for at least one selection from the group consisting of:
• 100% of all pores are assumed accessible;
• and
• the wavelength dependent refractive indices of said skeletal material are known;
• performing a simultaneous regression on at least two of the plurality of ellipsometric data sets obtained in step b) onto the mathematical model in step c) for said sample to obtain best fit values for the remaining fit parameters in step c).