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Optical characterisation of SiOxCyHz thin films non-uniform in thickness using spectroscopic ellipsometry, spectroscopic reflectometry and spectroscopic imaging reflectometry
Thin Solid Films 519 (2011) 2874–2876
Contents lists available at ScienceDirect
Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Optical characterisation of SiOxCyHz thin films non-uniform in thickness using spectroscopic ellipsometry, spectroscopic reflectometry and spectroscopic imaging reflectometry Ivan Ohlídal a,⁎, Miloslav Ohlídal b, David Nečas a, Daniel Franta a, Vilma Buršíková a a b
Department of Physical Electronics, Faculty of Science, Masaryk University, Kotlářská 2, Brno, 61137, Czech Republic Institute of Physical Engineering, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2896/2, Brno, 61669, Czech Republic
a r t i c l e
i n f o
Available online 21 December 2010 Keywords: Optical characterisation Non-uniform films Spectroscopic ellipsometry Spectroscopic reflectometry Spectroscopic imaging reflectometry
a b s t r a c t The combined optical method enabling us to perform the complete optical characterisation of weakly absorbing non-uniform thin films is described. This method is based on the combination of standard variable angle spectroscopic ellipsometry, standard spectroscopic reflectometry at near normal incidence and spectroscopic imaging reflectometry applied at normal incidence. The spectral dependences of the optical constants are determined using the non-imaging methods by using the dispersion model based on parametrisation of the density of electronic states. The local thickness distribution is then determined by imaging reflectometry. The method is illustrated by means of the complete optical characterisation of SiOxCyHz thin films. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Many thin films employed in practice exhibit non-uniformity along substrate areas [1–3]. Area non-uniformity misrepresents results of the thin film characterisation if this non-uniformity is not taken into account. The foregoing statement is also true for the optical characterisation of thin films performed using spectroscopic ellipsometry or spectroscopic ellipsometry combined with the other optical techniques (e.g. with spectrophotometry). Thus, it is necessary to develop new original methods for performing the correct and complete optical characterisation of the non-uniform thin films. Here it will be shown that the combination of spectroscopic ellipsometry (SE), spectroscopic reflectometry (SR) and spectroscopic imaging reflectometry (SIR) is an efficient method for performing the correct and complete optical characterisation of weakly absorbing thin films exhibiting area non-uniformity in thickness. 2. Description of the method The method has two basic steps: 1. Determination of the optical constants. The spectral dependences of the optical constants of the non-uniform thin film, i.e. the refractive index n and extinction coefficient k, are determined using the combined method based on simultaneous treatment of the exper-
⁎ Corresponding author. E-mail address: [email protected] (I. Ohlídal). 0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2010.12.069
imental data obtained by the following techniques: variable angle of incidence spectroscopic ellipsometry (VASE) and near-normal SR. 2. Determination of the thickness distribution. A distribution of the local thickness (map of thickness) of the film is determined using SIR under the assumption that the thin film optical constants do not exhibit non-uniformity. The optical constants are fixed in values determined using the combined method of SE and SR (see point 1) at treatment of the SIR experimental data. Ad 1. VASE is applied within the phase modulated ellipsometry. The associated ellipsometric parameters Is, IcII, and IcIII measured in this technique are given for the non-uniform thin films as follows [4]:
Is;cII;cIII =
∫Is;cII;cIII ðhÞRðhÞϱðhÞdh ∫RðhÞϱðhÞdh
;
ð1Þ
where R denotes the reflectance, h is the local film thickness, and ϱ(h) is the density of thickness distribution. The reflectance of absorbing non-uniform thin films is expressed as follows: R = ∫RðhÞϱðhÞdh:
ð2Þ
Integrations in (1) and (2) are performed over the interval of local thicknesses in which ϱ(h) is non-zero. The formulae for Is(h), IcII(h), IcIII(h) and R(h) are the well-known formulae for uniform thin films [5]. The density ϱ(h) expresses the geometrical shape of the thickness non-uniformity. In this paper, the wedge-shaped thickness non-
I. Ohlídal et al. / Thin Solid Films 519 (2011) 2874–2876
1 2πσϑ2
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 4σϑ2 − h−h
2
;
ð3Þ
where h is mean film thickness within the illuminated spot and σϑ is the rms of thickness differences from the mean thickness. For the wedge-shaped non-uniformity, it depends on the angle of incidence ϑ as follows [4]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cos2 α σϑ = σ0 sin2 α + ; cos2 ϑ
ð4Þ
where α is the angle between the plane of incidence and thickness gradient direction. The spectral dependences of the optical constants of the weakly absorbing non-uniform thin films under investigation are expressed by means of the dispersion model of amorphous materials based on parametrisation of the density of electronic states (this model is known as the PDOS model). The PDOS model corresponding to SiO2-like films is specifically utilised in this study (for details see [7]). For each of the non-uniform thin films analysed the least-squares method is applied to the ellipsometric and reflectometric data simultaneously. In this way the values of the following parameters are determined for the individual films: material parameters occurring in dispersion model, mean thickness and parameters describing the wedge-shaped non-uniformity. The spectral dependences of the refractive index n and extinction coefficient k of the non-uniform films studied are then calculated using corresponding formulae of the dispersion model. Ad 2. The SIR data are measured using our self-made spectroscopic imaging spectrophotometer whose detector is a CCD camera [8]. By means of the individual pixels of the CCD camera the spectral reflectances corresponding to small thin film areas are measured. Within these small areas the thickness value can be assumed to be constant. Thus, the reflectance formula for the uniform thin film [5] can be used to interpret the pixel data. Since the optical constants values of the films n and k are fixed in values determined in the first step only the local thickness values are evaluated using the pixel reflectance data. The obtained thickness
3. Experimental arrangements A spectroscopic phase modulated Jobin Yvon UVISEL ellipsometer was used to measure the spectral dependences of the associated ellipsometric parameters for five incidence angles in interval 55–75∘ within the spectral region 0.6–6.5 eV. A spectrophotometer PerkinElmer Lambda 45 was used to measure the spectral reflectance for an incidence angle of 6∘ within the spectral region 1.125–6.5 eV. The spectral dependences of the local reflectance were measured using the spectral imaging spectrophotometer at normal incidence within the spectral region 1.5–3.8 eV. The pixel size was 20 × 20 μm and the corresponding light spot on the film was 40 × 40 μm.
1.00
0.50
Is
ϱðhÞ =
values in each pixel create the area thickness distribution (map of thickness).
0.00
-0.50
-1.00 1.00
0.50
IcII
uniformity is assumed that corresponds to the following density [6]:
2875
0.00
-0.50
-1.00 1.00
0.50 n
IcIII
1.65 1.60
0.00
-0.50
1.55 1.50
-1.00
1.45
0.70
0.04 0.03 0.02
0.50 0.40 0.30 0.20 0.10
0.01
0.00 0.00
meas fit
0.60
k
0.05
reflectance R
extinction coefficient
index of refraction
1.70
0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
photon energy [eV]
photon energy [eV] Fig. 1. Spectral dependences of refractive index n and extinction coefficient k for the characterised SiOxCyHz film.
Fig. 2. Spectral dependences of the associated ellipsometric parameters at a selected angle of incidence of 65∘ and reflectance at near-normal incidence: points and curves denote the experimental and theoretical values, respectively.
2876
I. Ohlídal et al. / Thin Solid Films 519 (2011) 2874–2876
single-pixel reflectance
0.60 0.50
meas fit
0.40 0.30 0.20 0.10 0.00 1.5
2.0
2.5
3.0
3.5
4.0
photon energy [eV]
Fig. 3. Distribution of local thicknesses in a certain part of the SiOxCyHz thin film.
4. Sample preparation The method presented is illustrated by characterising SiOxCyHz films prepared onto silicon single crystal wafers. These films were prepared by plasma-enhanced chemical vapour deposition (PECVD) in capacitatively coupled r.f. (13.56 MHz) glow discharge from mixture of hexamethyldisilazane (C6H19NSi2, HMDSZ) and nitrogen. The HMDSZ flow rate was 10 sccm, the nitrogen flow rate was in the range from 15 to 30 sccm and the working pressure ranged from 10 to 13 Pa. The applied power was 100 W, the negative self bias voltage was in the range from −10 to −40 V depending on the gas mixture. 5. Results and discussion In this contribution the results concerning the selected nonuniform thin film are presented. In Fig. 1 the spectral dependences of the optical constants of this selected film determined within the first step are plotted. In Fig. 2 there are the experimental and theoretical spectral dependences of the associated ellipsometric parameters for the selected incidence angle together with the spectral dependence corresponding to the reflectance for this film. The good agreement between the theoretical and experimental data supports the correctness of the presented results. In Fig. 3 the area thickness distribution is displayed for a certain part of the film area. From this figure it can be seen that the map of local thickness corresponds the wedge-type non-uniformity of the film even though the film also exhibits local deviations from this overall shape (see e.g. the dark spot in the left part). This supports the assumption concerning the wedge-shaped thickness non-uniformity employed in the first step of the method. From the map of local thickness it was determined that the range of thicknesses within the measured area was 870–1030 nm and the thickness gradient was of 2.3 × 10− 5. Hence, the differences in local thickness within one pixel were about 0.9 nm. This means that within one pixel it was not necessary to take into account the non-uniformity of the film. In Fig. 4 the good agreement between the theoretical and experimental spectral dependences of the local reflectance of the film is illustrated for one selected pixel. The correctness of the presented results is also supported by their self-consistency, i.e. the optical constants of the film were obtained using VASE and SR under the assumption that the non-uniformity is of wedge-shape type (step 1). Subsequently, these optical constants
Fig. 4. Spectral dependence of the local reflectance of the SiOxCyHz film corresponding to the selected pixel: points and curves denote the experimental and theoretical values, respectively.
were used to determine the thickness non-uniformity using SIR (step 2) and it was indeed found that the non-uniformity was of the wedgeshaped type. Of course, the presented method can also be applied to characterisation of non-absorbing non-uniform thin films. From the foregoing it is evident that the method described enables us to perform the complete optical characterisation of the nonabsorbing and weakly absorbing non-uniform thin films. 6. Conclusion The combined optical method allowing to perform the complete optical characterisation of the non-absorbing or weakly absorbing non-uniform thin films, i.e. the determination of the spectral dependences of the optical constants and thickness distribution, is presented. This method is based on combining standard VASE and standard SR with SIR. Using the combination of VASE and SR the spectral dependences of the optical constants are determined together with the mean thickness and parameters characterising the overall thickness non-uniformity shape. The distribution of the local thicknesses is then determined using SIR. The method was successfully applied to the complete optical characterisation of the nonuniform SiOxCyHz thin films. Acknowledgements This work was supported by the Czech Ministry of Education research plans MSM 0021622411 and MSM 0021630518; and by the Czech Ministry of Trade project FT-TA5/114. References [1] M.A. Lieberman, J.P. Booth, P. Chabert, J.M. Rax, M.M. Turner, Plasma Sources Sci. Technol. 11 (3) (2002) 283. [2] Y. Yin, L. Hang, M. Proschek, D.R. McKenzie, M.M.M. Bilek, Surf. Coat. Technol. 200 (14–15) (2006) 4339. [3] A.A. Howling, L. Sansonnens, J. Ballutaud, C. Hollenstein, J.P.M. Schmitt, J. Appl. Phys. 96 (2004) 5429. [4] I. Ohlídal, D. Nečas, D. Franta, V. Buršíková, Diamond Relat. Mater. 18 (2009) 364. [5] I. Ohlídal, D. Franta, in: E. Wolf (Ed.), Ellipsometry of thin film systems, Progress in Optics, 41, Elsevier, Amsterdam, 2000, p. 181. [6] D. Nečas, I. Ohlídal, D. Franta, J. Opt. A-Pure Appl. Opt. 11 (2009) 045202. [7] D. Franta, D. Nečas, L. Zajíčková, Opt. Express 15 (2007) 16230. [8] M. Ohlídal, V. Čudek, I. Ohlídal, P. Klapetek, Optical characterization of non-uniform thin films using imaging spectrophotometry, in: C. Amra, N. Kaiser, H.A. Macleod (Eds.), Advances in Optical Thin Films II, Proc. SPIE, 2005, p. 596329-1.
Contents lists available at ScienceDirect
Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Optical characterisation of SiOxCyHz thin films non-uniform in thickness using spectroscopic ellipsometry, spectroscopic reflectometry and spectroscopic imaging reflectometry Ivan Ohlídal a,⁎, Miloslav Ohlídal b, David Nečas a, Daniel Franta a, Vilma Buršíková a a b
Department of Physical Electronics, Faculty of Science, Masaryk University, Kotlářská 2, Brno, 61137, Czech Republic Institute of Physical Engineering, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2896/2, Brno, 61669, Czech Republic
a r t i c l e
i n f o
Available online 21 December 2010 Keywords: Optical characterisation Non-uniform films Spectroscopic ellipsometry Spectroscopic reflectometry Spectroscopic imaging reflectometry
a b s t r a c t The combined optical method enabling us to perform the complete optical characterisation of weakly absorbing non-uniform thin films is described. This method is based on the combination of standard variable angle spectroscopic ellipsometry, standard spectroscopic reflectometry at near normal incidence and spectroscopic imaging reflectometry applied at normal incidence. The spectral dependences of the optical constants are determined using the non-imaging methods by using the dispersion model based on parametrisation of the density of electronic states. The local thickness distribution is then determined by imaging reflectometry. The method is illustrated by means of the complete optical characterisation of SiOxCyHz thin films. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Many thin films employed in practice exhibit non-uniformity along substrate areas [1–3]. Area non-uniformity misrepresents results of the thin film characterisation if this non-uniformity is not taken into account. The foregoing statement is also true for the optical characterisation of thin films performed using spectroscopic ellipsometry or spectroscopic ellipsometry combined with the other optical techniques (e.g. with spectrophotometry). Thus, it is necessary to develop new original methods for performing the correct and complete optical characterisation of the non-uniform thin films. Here it will be shown that the combination of spectroscopic ellipsometry (SE), spectroscopic reflectometry (SR) and spectroscopic imaging reflectometry (SIR) is an efficient method for performing the correct and complete optical characterisation of weakly absorbing thin films exhibiting area non-uniformity in thickness. 2. Description of the method The method has two basic steps: 1. Determination of the optical constants. The spectral dependences of the optical constants of the non-uniform thin film, i.e. the refractive index n and extinction coefficient k, are determined using the combined method based on simultaneous treatment of the exper-
⁎ Corresponding author. E-mail address: [email protected] (I. Ohlídal). 0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2010.12.069
imental data obtained by the following techniques: variable angle of incidence spectroscopic ellipsometry (VASE) and near-normal SR. 2. Determination of the thickness distribution. A distribution of the local thickness (map of thickness) of the film is determined using SIR under the assumption that the thin film optical constants do not exhibit non-uniformity. The optical constants are fixed in values determined using the combined method of SE and SR (see point 1) at treatment of the SIR experimental data. Ad 1. VASE is applied within the phase modulated ellipsometry. The associated ellipsometric parameters Is, IcII, and IcIII measured in this technique are given for the non-uniform thin films as follows [4]:
Is;cII;cIII =
∫Is;cII;cIII ðhÞRðhÞϱðhÞdh ∫RðhÞϱðhÞdh
;
ð1Þ
where R denotes the reflectance, h is the local film thickness, and ϱ(h) is the density of thickness distribution. The reflectance of absorbing non-uniform thin films is expressed as follows: R = ∫RðhÞϱðhÞdh:
ð2Þ
Integrations in (1) and (2) are performed over the interval of local thicknesses in which ϱ(h) is non-zero. The formulae for Is(h), IcII(h), IcIII(h) and R(h) are the well-known formulae for uniform thin films [5]. The density ϱ(h) expresses the geometrical shape of the thickness non-uniformity. In this paper, the wedge-shaped thickness non-
I. Ohlídal et al. / Thin Solid Films 519 (2011) 2874–2876
1 2πσϑ2
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 4σϑ2 − h−h
2
;
ð3Þ
where h is mean film thickness within the illuminated spot and σϑ is the rms of thickness differences from the mean thickness. For the wedge-shaped non-uniformity, it depends on the angle of incidence ϑ as follows [4]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cos2 α σϑ = σ0 sin2 α + ; cos2 ϑ
ð4Þ
where α is the angle between the plane of incidence and thickness gradient direction. The spectral dependences of the optical constants of the weakly absorbing non-uniform thin films under investigation are expressed by means of the dispersion model of amorphous materials based on parametrisation of the density of electronic states (this model is known as the PDOS model). The PDOS model corresponding to SiO2-like films is specifically utilised in this study (for details see [7]). For each of the non-uniform thin films analysed the least-squares method is applied to the ellipsometric and reflectometric data simultaneously. In this way the values of the following parameters are determined for the individual films: material parameters occurring in dispersion model, mean thickness and parameters describing the wedge-shaped non-uniformity. The spectral dependences of the refractive index n and extinction coefficient k of the non-uniform films studied are then calculated using corresponding formulae of the dispersion model. Ad 2. The SIR data are measured using our self-made spectroscopic imaging spectrophotometer whose detector is a CCD camera [8]. By means of the individual pixels of the CCD camera the spectral reflectances corresponding to small thin film areas are measured. Within these small areas the thickness value can be assumed to be constant. Thus, the reflectance formula for the uniform thin film [5] can be used to interpret the pixel data. Since the optical constants values of the films n and k are fixed in values determined in the first step only the local thickness values are evaluated using the pixel reflectance data. The obtained thickness
3. Experimental arrangements A spectroscopic phase modulated Jobin Yvon UVISEL ellipsometer was used to measure the spectral dependences of the associated ellipsometric parameters for five incidence angles in interval 55–75∘ within the spectral region 0.6–6.5 eV. A spectrophotometer PerkinElmer Lambda 45 was used to measure the spectral reflectance for an incidence angle of 6∘ within the spectral region 1.125–6.5 eV. The spectral dependences of the local reflectance were measured using the spectral imaging spectrophotometer at normal incidence within the spectral region 1.5–3.8 eV. The pixel size was 20 × 20 μm and the corresponding light spot on the film was 40 × 40 μm.
1.00
0.50
Is
ϱðhÞ =
values in each pixel create the area thickness distribution (map of thickness).
0.00
-0.50
-1.00 1.00
0.50
IcII
uniformity is assumed that corresponds to the following density [6]:
2875
0.00
-0.50
-1.00 1.00
0.50 n
IcIII
1.65 1.60
0.00
-0.50
1.55 1.50
-1.00
1.45
0.70
0.04 0.03 0.02
0.50 0.40 0.30 0.20 0.10
0.01
0.00 0.00
meas fit
0.60
k
0.05
reflectance R
extinction coefficient
index of refraction
1.70
0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
photon energy [eV]
photon energy [eV] Fig. 1. Spectral dependences of refractive index n and extinction coefficient k for the characterised SiOxCyHz film.
Fig. 2. Spectral dependences of the associated ellipsometric parameters at a selected angle of incidence of 65∘ and reflectance at near-normal incidence: points and curves denote the experimental and theoretical values, respectively.
2876
I. Ohlídal et al. / Thin Solid Films 519 (2011) 2874–2876
single-pixel reflectance
0.60 0.50
meas fit
0.40 0.30 0.20 0.10 0.00 1.5
2.0
2.5
3.0
3.5
4.0
photon energy [eV]
Fig. 3. Distribution of local thicknesses in a certain part of the SiOxCyHz thin film.
4. Sample preparation The method presented is illustrated by characterising SiOxCyHz films prepared onto silicon single crystal wafers. These films were prepared by plasma-enhanced chemical vapour deposition (PECVD) in capacitatively coupled r.f. (13.56 MHz) glow discharge from mixture of hexamethyldisilazane (C6H19NSi2, HMDSZ) and nitrogen. The HMDSZ flow rate was 10 sccm, the nitrogen flow rate was in the range from 15 to 30 sccm and the working pressure ranged from 10 to 13 Pa. The applied power was 100 W, the negative self bias voltage was in the range from −10 to −40 V depending on the gas mixture. 5. Results and discussion In this contribution the results concerning the selected nonuniform thin film are presented. In Fig. 1 the spectral dependences of the optical constants of this selected film determined within the first step are plotted. In Fig. 2 there are the experimental and theoretical spectral dependences of the associated ellipsometric parameters for the selected incidence angle together with the spectral dependence corresponding to the reflectance for this film. The good agreement between the theoretical and experimental data supports the correctness of the presented results. In Fig. 3 the area thickness distribution is displayed for a certain part of the film area. From this figure it can be seen that the map of local thickness corresponds the wedge-type non-uniformity of the film even though the film also exhibits local deviations from this overall shape (see e.g. the dark spot in the left part). This supports the assumption concerning the wedge-shaped thickness non-uniformity employed in the first step of the method. From the map of local thickness it was determined that the range of thicknesses within the measured area was 870–1030 nm and the thickness gradient was of 2.3 × 10− 5. Hence, the differences in local thickness within one pixel were about 0.9 nm. This means that within one pixel it was not necessary to take into account the non-uniformity of the film. In Fig. 4 the good agreement between the theoretical and experimental spectral dependences of the local reflectance of the film is illustrated for one selected pixel. The correctness of the presented results is also supported by their self-consistency, i.e. the optical constants of the film were obtained using VASE and SR under the assumption that the non-uniformity is of wedge-shape type (step 1). Subsequently, these optical constants
Fig. 4. Spectral dependence of the local reflectance of the SiOxCyHz film corresponding to the selected pixel: points and curves denote the experimental and theoretical values, respectively.
were used to determine the thickness non-uniformity using SIR (step 2) and it was indeed found that the non-uniformity was of the wedgeshaped type. Of course, the presented method can also be applied to characterisation of non-absorbing non-uniform thin films. From the foregoing it is evident that the method described enables us to perform the complete optical characterisation of the nonabsorbing and weakly absorbing non-uniform thin films. 6. Conclusion The combined optical method allowing to perform the complete optical characterisation of the non-absorbing or weakly absorbing non-uniform thin films, i.e. the determination of the spectral dependences of the optical constants and thickness distribution, is presented. This method is based on combining standard VASE and standard SR with SIR. Using the combination of VASE and SR the spectral dependences of the optical constants are determined together with the mean thickness and parameters characterising the overall thickness non-uniformity shape. The distribution of the local thicknesses is then determined using SIR. The method was successfully applied to the complete optical characterisation of the nonuniform SiOxCyHz thin films. Acknowledgements This work was supported by the Czech Ministry of Education research plans MSM 0021622411 and MSM 0021630518; and by the Czech Ministry of Trade project FT-TA5/114. References [1] M.A. Lieberman, J.P. Booth, P. Chabert, J.M. Rax, M.M. Turner, Plasma Sources Sci. Technol. 11 (3) (2002) 283. [2] Y. Yin, L. Hang, M. Proschek, D.R. McKenzie, M.M.M. Bilek, Surf. Coat. Technol. 200 (14–15) (2006) 4339. [3] A.A. Howling, L. Sansonnens, J. Ballutaud, C. Hollenstein, J.P.M. Schmitt, J. Appl. Phys. 96 (2004) 5429. [4] I. Ohlídal, D. Nečas, D. Franta, V. Buršíková, Diamond Relat. Mater. 18 (2009) 364. [5] I. Ohlídal, D. Franta, in: E. Wolf (Ed.), Ellipsometry of thin film systems, Progress in Optics, 41, Elsevier, Amsterdam, 2000, p. 181. [6] D. Nečas, I. Ohlídal, D. Franta, J. Opt. A-Pure Appl. Opt. 11 (2009) 045202. [7] D. Franta, D. Nečas, L. Zajíčková, Opt. Express 15 (2007) 16230. [8] M. Ohlídal, V. Čudek, I. Ohlídal, P. Klapetek, Optical characterization of non-uniform thin films using imaging spectrophotometry, in: C. Amra, N. Kaiser, H.A. Macleod (Eds.), Advances in Optical Thin Films II, Proc. SPIE, 2005, p. 596329-1.