Method for the optical characterisation of materials without using a physical model

A method for optical characterization of at least one layer of material in an interval A of values taken by a function α of an optical wavelength λ, when λ varies in an interval of wavelengths, the at least one layer being created on a substrate, the method comprising:

• 1) carrying out a set of reflectometry and/or ellipsometry measurements over the interval A, the set of measurements leading to a measured spectrum, marked ψ, and choosing methods for calculating associated with a nature of the measurements and with a type of layer to be characterized;
• 2) choosing m initial values α1 . . . αm of the function α, belonging to the interval A, m being a whole number at least equal to 1, and defining an interval B as being the set of points α of the interval ranging from the smallest to the biggest number among α1 . . . αm, when m is greater than 1, and as being the interval A when m equals 1;
• 3) choosing m complex initial values of a complex refraction index n*=n+jk for the m points αi, i ranging from 1 to m;
• 4) when m is not 1, choosing an interpolation law that allows calculating the refraction index n(α) of the material over the interval B, from the points (αi, ni), with ni=n(αi), i ranging from 1 to m, and when m equals 1, n(α) is taken equal to the number n1(α1) over the entire interval B;
• 5) choosing M variable parameters, M being less than or equal to 2 m+1;
• 6) choosing an error function Er(ψ,{overscore (ψ)}) that characterizes the difference between a measured spectrum ψ and a theoretical spectrum {overscore (ψ)};
• 7) using a minimizing function of Er(ψ,{overscore (ψ)}) with M parameters, performing:
• a) by applying the interpolation law of (α1, ni) over the interval B, deducing n(α), α belonging to B;
• b) by using n(α) and the thickness ε of the layer, and methods for calculating spectrums, calculating a theoretical spectrum {overscore (ψ)} (n(α),ε);
• c) comparing ψ and {overscore (ψ)} by using Er(ψ,{overscore (ψ)}) and, if Er(ψ,{overscore (ψ)}) is less than a predetermined value e, or is minimal, going to e), otherwise going to d);
• d) making the M variable parameters vary so as to tend to the minimum of Er(ψ,{overscore (ψ)}), and returning to a);
• e) if Er(ψ,{overscore (ψ)}) is less than e, then obtaining a set of M variable parameters, for which Er(ψ, {overscore (ψ)}(n(α,M),ε)) is minimal and the refraction index is then taken equal to the last one obtained, and if Er(ψ,{overscore (ψ)}) is greater or equal to e going to 8);
• 8) increasing the number m of initial values of the function α and returning to 2).

A method for optical characterization of at least one layer of a material in an interval of wavelengths [λ min, λ max], the at least one layer being created on a substrate, the method comprising:

• carrying out a set of reflectometry and/or ellipsometry measurements, the set of measurements leading to a measured spectrum, marked ψ;
• choosing m initial wavelengths λ1 . . . λm belonging to the interval, m being a whole number at least equal to 1, and associating a refraction index to each wavelength;
• choosing an interpolation law at least for the refraction index of the material, for wavelengths lying between the initial wavelengths λ1 . . . λm;
• choosing M initial parameters, M being at least equal to m, an initial refraction index ni for each initial wavelength λi, 1≦i≦m, the initial wavelengths being chosen so as to determine via interpolation at least the refraction index for any wavelength within the interval [λ min, λ max], couples (λi, ni) being nodes;
• choosing reflectometry and ellipsometry methods of calculation;
• choosing an error function Er, representative of the difference between two spectrums ψ1 and ψ2, the spectrums ψ1 and ψ2 being calculated or measured over a number of points greater than the number m of nodes;
• using the m initial wavelengths, the M initial parameters, and the interpolation law, implementing an optimization process of:
• determining a theoretical spectrum, marked {overscore (ψ)}, depending on the chosen methods of calculation, and on the index deduced via interpolation of its value at λi, i ranging from 1 to m, over the spectrum [λmin, λmax];
• determining the error Er(ψ,{overscore (ψ)}), between the measured spectrum and the theoretical spectrum;
• minimizing the error by varying the position of the values of the unknown indexes and/or the thickness of the layer and/or the values of the refraction indexes with initial wavelengths, and obtaining a spectrum;
• adding other wavelengths to the initial wavelengths λi . . . λm, the added wavelengths constituting new nodes;
• repeating the method by choosing a number m′ of initial wavelengths, m′ being greater than m, and M′ initial parameters, M′ being greater than M, until the accuracy of each spectrum thus best represented is equal to a predetermined accuracy.