R. M. A. Azzam and N. M. Bashara, "Unified Analysis of Ellipsometry Errors Due to Imperfect Components, Cell-Window Birefringence, and Incorrect Azimuth Angles*," J. Opt. Soc. Am. 61, 600-607 (1971)
Coupling constants are introduced that determine the extent to which a component imperfection, window birefringence, or azimuth-angle error couple to cause an error of the specimen reflectance ratio. A unified scheme for treating these sources of error is presented. By expressing the coupling constants as functions of the nulling angles, any of the nulling methods can be considered. Results are presented for the compensator at ±π/4 and nulling by the polarizer and analyzer, which show the contributions of the different sources of error to ψ and Δ in the four ellipsometry zones. The limitations of one- and two-zone measurements are discussed. A procedure is described and demonstrated experimentally for determining the quantities characterizing the different sources of error in the ellipsometer. These results can be used in correcting data from one-, two-, or four-zone measurements.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
P, C, and A are the polarizer, compensator, and analyzer azimuths at null, respectively. The * superscript indicates the azimuth minus C Each optical component is characterized by (1) its principal frame, which is rotated with respect to the ps frame by the azimuthal angle Zi (=P, C, etc) and (2) its complex relative transmittance ρi = ρi0+δρi, ρi0 is the ideal relative transmittance and equals 0, ρC, 0 for the polarizer, compensator, and analyzer respectively and 1 for the windows. The azimuth error δZi and component imperfection δρi couple into errors in the specimen ρ of γi′δZi and γiδρi, respectively.
Table II
Ellipsometry angles ψ and Δ corrected to first order (all effects included).
Nulling azimuthal angles as functions of specimen ψ and Δ and all imperfections.
Zone 1
2
3
4
1
2
3
4
Table IV
Imperfection properties of two ellipsometers from measurements in four zones. ηP,C = 2t1P+2δPc−2δCc, t1P+jt2P = δρP, t1C+jt2C = δρC, where δPc and δCc are polarizer and compensator calibration errors, δρP and δρC are the deviations of the complex relative transmittances of the polarizer and compensator from zero and −j, respectively.
The retardation setting of the compensator slightly changed, accidentally, about halfway during taking the data.
These values are determined from the data corresponding to each azimuth separately, using Eq. (32), neglecting azimuth-angle errors.
P, C, and A are the polarizer, compensator, and analyzer azimuths at null, respectively. The * superscript indicates the azimuth minus C Each optical component is characterized by (1) its principal frame, which is rotated with respect to the ps frame by the azimuthal angle Zi (=P, C, etc) and (2) its complex relative transmittance ρi = ρi0+δρi, ρi0 is the ideal relative transmittance and equals 0, ρC, 0 for the polarizer, compensator, and analyzer respectively and 1 for the windows. The azimuth error δZi and component imperfection δρi couple into errors in the specimen ρ of γi′δZi and γiδρi, respectively.
Table II
Ellipsometry angles ψ and Δ corrected to first order (all effects included).
Nulling azimuthal angles as functions of specimen ψ and Δ and all imperfections.
Zone 1
2
3
4
1
2
3
4
Table IV
Imperfection properties of two ellipsometers from measurements in four zones. ηP,C = 2t1P+2δPc−2δCc, t1P+jt2P = δρP, t1C+jt2C = δρC, where δPc and δCc are polarizer and compensator calibration errors, δρP and δρC are the deviations of the complex relative transmittances of the polarizer and compensator from zero and −j, respectively.
The retardation setting of the compensator slightly changed, accidentally, about halfway during taking the data.
These values are determined from the data corresponding to each azimuth separately, using Eq. (32), neglecting azimuth-angle errors.