Method for determining properties of a sample by ellipsometry
A method for determining properties of a sample ( 12 ) by ellipsometry includes positioning the sample ( 12 ) in an ellipsometer ( 10 ) so that a surface normal (n) of a measurement region of the sample surface is tilted relative to a reference axis (z) of the ellipsometer ( 10 ) and measuring a Mueller matrix for the measurement region. The method then includes creating an equation system by equating the measured Mueller matrix and a matrix product formed of: a rotation matrix about an input rotation angle (γ); an isotropic Mueller matrix in normalized NCS form and a rotation matrix about an output rotation angle (−δ). The method then solves the equation system for the parameters representing the sample properties to be determined. The input rotation angle (γ) and the output rotation angle (−δ) are set as parameters independent of one another when setting up the equation system.
1. A method for determining properties of a sample ( 12 ) by ellipsometry, comprising the steps of:
providing an ellipsometer ( 10 ) having a reference axis (z),
positioning the sample ( 12 ) in the ellipsometer ( 10 ) so that a surface normal (n) of a measurement region of the sample surface is tilted relative to the reference axis (z) of the ellipsometer ( 10 ),
measuring a Mueller matrix for the measurement region,
creating an equation system that is not underdetermined, the equation system equating the measured Mueller matrix to a matrix product formed of
a rotation matrix about an input rotation angle (γ),
an isotropic Mueller matrix in normalized NCS form and
a rotation matrix about an output rotation angle (−δ) that is applied independently of the input rotation angle (γ), and
solving the equation system for the parameters representing the sample properties to be determined.
2. The method of claim 1 , wherein as part of solving the equation system, the Mueller parameters N, S, C and/or the ellipsometric transfer variables Δ and Ψ equivalent to these are explicitly calculated.
3. The method of claim 2 , further comprising the step of:
determining optical and/or mechanical sample properties from the calculated ellipsometric transfer variables Δ and Ψ by a numerical error minimization method by variation of parameters of a sample model.
4. The method of claim 3 , wherein as part of the error minimization method the angle of incidence (φ) is used as an additional parameter to be varied.
5. The method of claim 1 , wherein as part of solving the equation system, the input rotation angle (γ) and the output rotation angle (−δ) are calculated explicitly.
6. The method of claim 5 , wherein the rotation angles (γ, −δ) determined by solving the equation system are used to calculate the alignment of the surface normal (n) of the sample surface in the measurement region relative to the reference axis (z) of the ellipsometer ( 10 ).
7. The method of claim 1 , wherein the solving of the equation system is performed by a numerical error minimization method by variation of parameters of a sample model.
8. The method of claim 1 , wherein the ellipsometer ( 10 ) is an imaging ellipsometer ( 10 ).
9. The method of claim 8 , wherein the sample surface is curved, the step of solving the equation system for the parameters representing the sample properties includes calculating the input rotation angle (γ) and the output rotation angle (−δ), and the method further comprising creating maps by solving the equation system pixel by pixel for each of plural reference points on the curved surface and assigning ellipsometric transfer variables Δ and Ψ to each of the reference points.
10. The method of claim 1 , wherein the sample has a plurality of measurement regions on the measurement surface, the steps of the method are carried out for at least two of the plurality of measurement regions, and the method further comprising creating at least one map comprised of the parameters representing the sample properties at the at least two measurement regions.