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Application of spectroscopic imaging reflectometry to analysis of area non-uniformity in diamond-like carbon films
Diamond & Related Materials 18 (2009) 384–387
Contents lists available at ScienceDirect
Diamond & Related Materials 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 / d i a m o n d
Application of spectroscopic imaging reflectometry to analysis of area non-uniformity in diamond-like carbon films Miloslav Ohlídal a,⁎, Ivan Ohlídal b, Petr Klapetek c, David Nečas b, Vilma Buršíková b a b c
Institute of Physical Engineering, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic Department of Physical Electronics, Faculty of Science, Masaryk University, Kotlářská 2, Brno Czech Republic Czech Metrology Institute, Okružní 31, 638 00 Brno, Czech Republic
a r t i c l e
i n f o
Available online 30 October 2008 Keywords: Diamond-like carbon films Optical properties characterization
a b s t r a c t Complete optical characterization of diamond-like carbon (DLC) films non-uniform in thickness is performed using spectroscopic imaging reflectometry (SIR). It is shown that by using this technique it is possible to determine the area distribution (area map) of the local thickness of these films with arbitrary shape of this thickness non-uniformity. Furthermore, it is shown that in principle it is possible to determine the distributions of the refractive index and extinction coefficient of these films simultaneously with the thickness distribution, if a suitable dispersion model of these optical constants is chosen. In this paper the dispersion model of the optical constants of the DLC films based on parameterization of density of electronic states (DOS) is used. The values of the material parameters of this dispersion model are determined too. It is shown that the DLC films studied do not exhibit the area non-uniformity in material parameters and optical constants. The method presented can be used to characterize the non-uniform films consisting of other materials. © 2008 Elsevier B.V. All rights reserved.
1. Introduction In practice one can encounter many thin films exhibiting nonuniformity. This is also the case of deposition in capacitively coupled RF plasma reactors equipped with parallel electrodes, which are often used to prepare DLC films. The changes of various technological parameters during the deposition can cause the existence of thickness non-uniformity of the DLC film prepared in this way (e.g. the changes in input power, gas flux, working pressure and substrate temperature stabilization often cause this non-uniformity). A very important effect causing the thickness non-uniformity of the DLC films is also the electric field distortion near edges and corners of substrates [1,2]. This is why it is very important to consider the non-uniformity of the DLC films in their optical characterization because without taking the nonuniformity into account misrepresented results are obtained in this characterization. Moreover, in general a certain non-uniformity of such DLC films can arise in the optical constants. So far several papers dealing with the optical characterization of various thin films exhibiting special wedge-shaped non-uniformity in thickness have been published (see e.g. refs [1–5]). In these papers, the optical characterization of the non-uniform films is based on interpreting standard spectrophotometric data, i.e. the data corresponding to spectral dependences of reflectance and transmittance measured by standard spectrophotometers. However, in the case of the general ⁎ Corresponding author. E-mail address: [email protected] (M. Ohlídal). 0925-9635/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2008.10.012
non-uniformity in thickness, the procedures presented in the papers mentioned above are not usable. Thus, other methods must be used to perform the optical characterization of the thin films exhibiting this general thickness non-uniformity. From our previous studies it followed that the methods based on employing spectral imaging reflectometry (SIR) were promising for this purpose. We developed a method employing the interpretation of the experimental data obtained using an imaging spectrophotometer operating in the reflectance mode [6,7]. This method enables us to determine simultaneously the area distributions of the thickness and optical constants (i.e. refractive index and extinction coefficient). Moreover, this method is usable for determining these distributions even when general shapes of these non-uniformities occur in thin films. Thus, SIR mentioned above is very suitable for the complete optical characterization of the non-uniform DLC films. The reason is that the uniformity in the optical constants of the non-uniform DLC films needs not be assumed a priori as in the spectrophotometric methods cited above and the area distribution of the thickness can be determined together with the distributions of the area non-uniformity of the optical constants simultaneously. 2. Sample preparation and experimental arrangement The DLC films were prepared by PECVD in RF capacitive discharge at low pressure (16.5 Pa). The reactor was a glass cylinder with two, inner parallel electrodes, made of graphite. The bottom electrode, with a diameter of 150 mm, was coupled to the RF generator
M. Ohlídal et al. / Diamond & Related Materials 18 (2009) 384–387
385
ki1, j, n and k denote the local real refractive index of the film, local extinction coefficient of the film, real refractive index of the substrate and extinction coefficient of the substrate, respectively. Symbol λ represents the wavelength of incident light. The least square method (LSM) is used to treat the experimental data using Eq. (1). Of course, the LSM must be applied for each local area on the film corresponding to the given pixel of the CDD camera. Within the LSM, the following merit function Si,j was employed: i; j
K
Rsi; j −R0s i; j
s=1
σ i;s j
S = ∑
Fig. 1. Image of the DLC film investigated for the wavelength of 720 nm.
(13.56 MHz) via a blocking capacitor [8]. The depositions were performed at applied power of 50 W. The silicon single crystal substrates were placed on different substrate holders. The substrate holders were situated on the bottom r.f. electrode made of graphite, the r.f. voltage of which was superimposed with a negative d.c. self-bias in the range from -300 to 350 V. For measuring the experimental data the self-made two-channel spectroscopic imaging reflectometer containing a CCD camera as a detector was employed. The reflectance experimental data was measured at a normal incidence of light within the spectral region 320–850 nm. A detailed description of this arrangement is presented in our earlier paper [7]. 3. Data processing Owing to the fact that the dimensions of the local areas on the nonuniform film corresponding to individual pixels of the CCD camera are relatively very small, it is possible to assume that over these areas the film is uniform. This means that the spectral dependences of the reflectance Ri, j measured by a pixel are given by the formulae valid for the uniform films (i and/or j denotes the ith row and/or jth column in which a certain pixel is placed in the matrix of the CCD chip), i.e. 2 i; j i; j i; j i; j jbr 1 j2 + jbr 2 j2 U i; j + 2jbr 1 jjbr 2 jU i; j cos X0i; j −δi;1 j + δ2i; j i; j ; R = i; j i; j i; j i; j 2 1 + jbr 1 j2 jbr 2 j2 ðU i; j Þ + 2jbr 1 jjbr 2 jU i; j cos X0i; j + δi;1 j + δi;2 j
ð1Þ
!2 ;
,j denotes the theoretical and/or experimental where Ris, j and/or R′i s value of the local absolute reflectance corresponding to the (i,j)th pixel and wavelength λs. Symbol σsi, j and/or K represents the standard ,j deviation of R′i and/or the number of the measurements of the s absolute reflectance, i.e. the number of wavelengths, for which the absolute reflectance was measured in each pixel. Within the processing of the experimental data, the dispersion model based on parameterization of DOS [11–13] was used to express the spectral dependences of the refractive index and extinction coefficient of the DLC films. Thus, using the LSM the values of the local thickness di, j and material parameters occurring in the dispersion model are determined for each local area. The dispersion model parameters are as follows [12,13]: the band gaps of σ and π electrons Egσ and Egπ, highenergy limits of σ and π electronic transitions Ehσ and Ehπ, and parameters proportional to the σ and π electron densities Q σ and Q π. Using the parameters found in the procedure described above one can calculate the true spectral dependences of the refractive index and extinction coefficient of the DLC films studied in all the local areas corresponding to the pixels of the CCD camera. This means that distributions (maps) of the thickness and optical constants are determined in this way. Note that the spectral dependences of the optical constants of the silicon substrate were taken from the literature [14] and fixed within the LSM.
4. Results and discussion In this section the results of the optical characterization of a selected non-uniform DLC film are presented. These results are typical of the optical characterization of DLC films being studied using spectroscopic imaging reflectometry (SIR) in this work.
where rˆi1, j, rˆi2, j, Xi0, j, Ui, j, δi1, j and δi2, j denote the local complex reflection Fresnel coefficient of the upper boundary of the film, local complex reflection Fresnel coefficient of the lower boundary of the film, local phase change inside the film, local extinction factor, local phase shift corresponding to the upper boundary and local phase shift corresponding to the lower boundary, respectively. These quantities are expressed as follows [9,10]: i; j n −n 0 b1 i; j br i;j bi; j = ; 1 = j r 1 j exp iδ1 b i;1 j n0 + n
X0i; j =
4π i; j i; j d n1 ; λ
n b b i; j −n br i;2 j = jbr i;2 j j exp iδi;2 j = 1 ; i; j b b1 + n n
4π U i; j = exp − di; j ki;1 j : λ
ð2Þ
In Eq. (2) symbols nˆi1, j, nˆ and di, j represent the local complex refractive index of the absorbing film studied, complex refractive index of the absorbing substrate and local thickness of this film corresponding to the (i,j)th pixel, respectively (n0 = 1 because the ambient is formed by air). In our work we employed the following convention of the complex refractive indices nˆi1, j = ni1, j − iki1, j and nˆ = n − ik, where ni1, j,
ð3Þ
Fig. 2. The distribution of the local thickness of the film under investigation.
386
M. Ohlídal et al. / Diamond & Related Materials 18 (2009) 384–387
In Fig. 1, the CCD image of the sample under study is plotted for the wavelength 720 nm. In this figure the dark and bright areas are seen which indicate an area optical non-uniformity of the film studied. In Fig. 2, the local thickness distribution (map) corresponding to the selected area of this non-uniform DLC film is presented. This figure shows that the selected DLC film exhibits the evident thickness non-uniformity. Its local thickness distribution presented in Fig. 2 corresponds to the CCD image presented in Fig. 1. The local peaks in the local thickness distribution in Fig. 2 are caused by dust particles on the film and local defects of the film. It was found that the values of the material parameters of the dispersion model were practically identical for all the local areas belonging to individual pixels. From this fact it is possible to deduce that the non-uniform DLC film investigated exhibits area uniformity in the material parameters. Of course, this fact also implies that this film is uniform in the optical constants along the area of the film. Thus, the DLC film analyzed only exhibits the thickness area non-uniformity. This conclusion could be achieved on the basis of the fact that this characterization method allows us to determine the distributions of the local thickness and local optical constants in an independent way. The values of the material parameters found are summarized for this DLC film in Table 1. The spectral dependences of the refractive index and extinction coefficient characterizing the selected DLC film non-uniform in thickness calculated using the values of the material parameters found (see Table 1) are plotted in Fig. 3. Similar thickness distributions and spectral dependences of the optical constants were determined for remaining samples of the nonuniform DLC films studied. Note that the non-uniform DLC films under investigation were also characterized using standard, i.e. non-imaging, spectroscopic ellipsometry (see e.g. [15]) under assumption that wedge-shaped thickness non-uniformity occurs in the case of these films. The values of the dispersion parameters and spectral dependences of the optical constants of these non-uniform DLC films determined using this spectroscopic ellipsometry were practically identical with those found by means of SIR. This fact supports a correctness of the results achieved for the DLC films in their characterization using SIR. The spectral dependences of the optical constants of the DLC films prepared under different technological conditions are presented, for example, in papers [16–19]. From the foregoing results it is seen that SIR is the efficient method for the complete optical characterization of the DLC films exhibiting the thickness area non-uniformity. If DLC films exhibit area nonuniformity in thickness and optical constants simultaneously, the method presented will be successful too. Note that within SIR the local thickness distribution can only be determined if the local thicknesses are smaller than a certain limit. This limit depends on the optical constants, spectral region of interest and experimental accuracy of measured reflectance Ri, j. In our case the thickness limit was estimated in value of about 2 µm. It should be noted that we applied SIR for the successful characterization of non-uniform films consisting of materials strongly different from DLC. For example, we also characterized SiOx and carbon-nitride thin films exhibiting thickness non-uniformity in a successful way (results concerning the characterization of these films will be presented elsewhere). The SiOx and carbon-nitride films have the considerably different optical constants in comparison with the DLC films. This fact implies that SIR represents a general method Table 1 The values of the material parameters of the dispersion model for the DLC film selected Parameter
Egσ [eV]
Ehσ [eV]
Qσ [eV3/2]
Egπ [eV]
Ehπ [eV]
Qπ [eV3/2]
1.35
46.90
121.00
1.51
7.49
5.10
Fig. 3. Spectral dependences of the refractive index n1 and extinction coefficient k1 of the non-uniform DLC film selected.
serving as a useful tool for characterizing non-uniform thin films consisting of miscellaneous materials. 5. Conclusion This paper presents the results concerning the complete optical characterization of non-uniform DLC films prepared by PECVD in RF capacitive discharge at low pressure onto the silicon single crystal substrates obtained by means of SIR. From these results it is concluded that these DLC films only exhibit area non-uniformity in thickness and that they are uniform in the optical constants along their areas. The distribution of the local thickness (map of the local thickness) is presented for the selected sample for illustration. The spectral dependences of the refractive index and extinction coefficient of this sample calculated using the values of the material parameters of the dispersion model found are presented too. These spectral dependences were verified using standard spectroscopic ellipsometry. The values of the local thickness and values of the material parameters are found using the LSM applied separately for all local areas corresponding to the individual pixels of the CCD camera. Thus, using SIR it is possible to determine simultaneously the area distributions (maps) of the local thicknesses, local refractive index and local extinction coefficient of the non-uniform DLC films. The same conclusion is valid for non-uniform thin films consisting of other materials. This means that SIR is a very useful general tool for the optical characterization of the thin films exhibiting area non-uniformity. Acknowledgements This work was supported by the Ministry of Education, Youths and Sports of the Czech Republic under contracts MSM 0021630518, MSM 0021622411 and the Ministry of Industry and Trade of the Czech Republic under contract FT-TA3/142. References [1] A.A. Howling, L. Sansonnens, J. Ballutaud, C. Hollenstein, J.P.M. Schmitt, J. Appl. Phys. 96 (2004) 5429. [2] M.A. Lieberman, J.P. Booth, P. Chabert, J.M. Rax, M.M. Turner, Plasma Sources Sci. Technol. 11 (3) (2002) 283. [3] M.I. Török, Opt. Acta 32 (1985) 479. [4] T. Pisarkiewicz, T. Stapinski, H. Czternasek, P. Rava, J. Non-Cryst. Solids 137/138 (1991) 619. [5] T. Pisarkiewicz, J. Phys. D: Appl. Phys. 27 (1994) 160. [6] M. Ohlídal, I. Ohlídal, P. Klapetek, M. Jákl, V. Čudek, Jpn. J. Appl. Phys. 42 (2003) 4760. [7] M. Ohlídal, V. Čudek, I. Ohlídal, P. Klapetek, in: C. Amra, N. Kaiser, H.A. Macleod (Eds.), Advances in Optical Thin Films II, vol. 5963, SPIE, Bellingham, Washington, 2005, p. 596329.
M. Ohlídal et al. / Diamond & Related Materials 18 (2009) 384–387 [8] [9] [10] [11] [12]
L. Zajíčková, V. Buršíková, D. Franta, Czech. J. Phys 49 (1999) 1213. A. Vašíček, Optics of Thin Films, North Holland, Amsterdam, 1960. Z. Knittl, Optics of Thin Films, John Wiley, Chichester, 1976. D. Franta, I. Ohlídal, M. Frumar, J. Jedelský, Appl. Surf. Sci. 212–213 (2003) 116. D. Franta, I. Ohlídal, V. Buršíková, L. Zajíčková, Diamond Relat. Mater. 12 (2003) 1532. [13] D. Franta, D. Nečas, L. Zajíčková, Opt. Express 15 (2007) 16230. [14] C.M. Herzinger, B. Johs, W.A. McGahan, J.A. Woolan, W. Paulson, J. Appl. Phys. 83 (1988) 3323.
387
[15] I. Ohlídal, D. Franta, E. Pinčík, M. Ohlídal, Surf. Interface Anal. 28 (1999) 240. [16] D. Franta, L. Zajíčková, I. Ohlídal, J. Janča, K. Veltruská, Diamond Relat. Mater. 11 (2002) 105. [17] S. Logothetidis, G. Stergioudis, Appl. Phys. Lett. 71 (1997) 2463. [18] J. Lee, R.W. Collins, V.S. Veerasamy, J. Robertson, Diamond Relat. Mater. 7 (1998) 999. [19] T. Mori, N. Fujii, Y.M. Xiong, T. Saitoh, Thin Solid Films 270 (1995) 215.
Contents lists available at ScienceDirect
Diamond & Related Materials 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 / d i a m o n d
Application of spectroscopic imaging reflectometry to analysis of area non-uniformity in diamond-like carbon films Miloslav Ohlídal a,⁎, Ivan Ohlídal b, Petr Klapetek c, David Nečas b, Vilma Buršíková b a b c
Institute of Physical Engineering, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic Department of Physical Electronics, Faculty of Science, Masaryk University, Kotlářská 2, Brno Czech Republic Czech Metrology Institute, Okružní 31, 638 00 Brno, Czech Republic
a r t i c l e
i n f o
Available online 30 October 2008 Keywords: Diamond-like carbon films Optical properties characterization
a b s t r a c t Complete optical characterization of diamond-like carbon (DLC) films non-uniform in thickness is performed using spectroscopic imaging reflectometry (SIR). It is shown that by using this technique it is possible to determine the area distribution (area map) of the local thickness of these films with arbitrary shape of this thickness non-uniformity. Furthermore, it is shown that in principle it is possible to determine the distributions of the refractive index and extinction coefficient of these films simultaneously with the thickness distribution, if a suitable dispersion model of these optical constants is chosen. In this paper the dispersion model of the optical constants of the DLC films based on parameterization of density of electronic states (DOS) is used. The values of the material parameters of this dispersion model are determined too. It is shown that the DLC films studied do not exhibit the area non-uniformity in material parameters and optical constants. The method presented can be used to characterize the non-uniform films consisting of other materials. © 2008 Elsevier B.V. All rights reserved.
1. Introduction In practice one can encounter many thin films exhibiting nonuniformity. This is also the case of deposition in capacitively coupled RF plasma reactors equipped with parallel electrodes, which are often used to prepare DLC films. The changes of various technological parameters during the deposition can cause the existence of thickness non-uniformity of the DLC film prepared in this way (e.g. the changes in input power, gas flux, working pressure and substrate temperature stabilization often cause this non-uniformity). A very important effect causing the thickness non-uniformity of the DLC films is also the electric field distortion near edges and corners of substrates [1,2]. This is why it is very important to consider the non-uniformity of the DLC films in their optical characterization because without taking the nonuniformity into account misrepresented results are obtained in this characterization. Moreover, in general a certain non-uniformity of such DLC films can arise in the optical constants. So far several papers dealing with the optical characterization of various thin films exhibiting special wedge-shaped non-uniformity in thickness have been published (see e.g. refs [1–5]). In these papers, the optical characterization of the non-uniform films is based on interpreting standard spectrophotometric data, i.e. the data corresponding to spectral dependences of reflectance and transmittance measured by standard spectrophotometers. However, in the case of the general ⁎ Corresponding author. E-mail address: [email protected] (M. Ohlídal). 0925-9635/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2008.10.012
non-uniformity in thickness, the procedures presented in the papers mentioned above are not usable. Thus, other methods must be used to perform the optical characterization of the thin films exhibiting this general thickness non-uniformity. From our previous studies it followed that the methods based on employing spectral imaging reflectometry (SIR) were promising for this purpose. We developed a method employing the interpretation of the experimental data obtained using an imaging spectrophotometer operating in the reflectance mode [6,7]. This method enables us to determine simultaneously the area distributions of the thickness and optical constants (i.e. refractive index and extinction coefficient). Moreover, this method is usable for determining these distributions even when general shapes of these non-uniformities occur in thin films. Thus, SIR mentioned above is very suitable for the complete optical characterization of the non-uniform DLC films. The reason is that the uniformity in the optical constants of the non-uniform DLC films needs not be assumed a priori as in the spectrophotometric methods cited above and the area distribution of the thickness can be determined together with the distributions of the area non-uniformity of the optical constants simultaneously. 2. Sample preparation and experimental arrangement The DLC films were prepared by PECVD in RF capacitive discharge at low pressure (16.5 Pa). The reactor was a glass cylinder with two, inner parallel electrodes, made of graphite. The bottom electrode, with a diameter of 150 mm, was coupled to the RF generator
M. Ohlídal et al. / Diamond & Related Materials 18 (2009) 384–387
385
ki1, j, n and k denote the local real refractive index of the film, local extinction coefficient of the film, real refractive index of the substrate and extinction coefficient of the substrate, respectively. Symbol λ represents the wavelength of incident light. The least square method (LSM) is used to treat the experimental data using Eq. (1). Of course, the LSM must be applied for each local area on the film corresponding to the given pixel of the CDD camera. Within the LSM, the following merit function Si,j was employed: i; j
K
Rsi; j −R0s i; j
s=1
σ i;s j
S = ∑
Fig. 1. Image of the DLC film investigated for the wavelength of 720 nm.
(13.56 MHz) via a blocking capacitor [8]. The depositions were performed at applied power of 50 W. The silicon single crystal substrates were placed on different substrate holders. The substrate holders were situated on the bottom r.f. electrode made of graphite, the r.f. voltage of which was superimposed with a negative d.c. self-bias in the range from -300 to 350 V. For measuring the experimental data the self-made two-channel spectroscopic imaging reflectometer containing a CCD camera as a detector was employed. The reflectance experimental data was measured at a normal incidence of light within the spectral region 320–850 nm. A detailed description of this arrangement is presented in our earlier paper [7]. 3. Data processing Owing to the fact that the dimensions of the local areas on the nonuniform film corresponding to individual pixels of the CCD camera are relatively very small, it is possible to assume that over these areas the film is uniform. This means that the spectral dependences of the reflectance Ri, j measured by a pixel are given by the formulae valid for the uniform films (i and/or j denotes the ith row and/or jth column in which a certain pixel is placed in the matrix of the CCD chip), i.e. 2 i; j i; j i; j i; j jbr 1 j2 + jbr 2 j2 U i; j + 2jbr 1 jjbr 2 jU i; j cos X0i; j −δi;1 j + δ2i; j i; j ; R = i; j i; j i; j i; j 2 1 + jbr 1 j2 jbr 2 j2 ðU i; j Þ + 2jbr 1 jjbr 2 jU i; j cos X0i; j + δi;1 j + δi;2 j
ð1Þ
!2 ;
,j denotes the theoretical and/or experimental where Ris, j and/or R′i s value of the local absolute reflectance corresponding to the (i,j)th pixel and wavelength λs. Symbol σsi, j and/or K represents the standard ,j deviation of R′i and/or the number of the measurements of the s absolute reflectance, i.e. the number of wavelengths, for which the absolute reflectance was measured in each pixel. Within the processing of the experimental data, the dispersion model based on parameterization of DOS [11–13] was used to express the spectral dependences of the refractive index and extinction coefficient of the DLC films. Thus, using the LSM the values of the local thickness di, j and material parameters occurring in the dispersion model are determined for each local area. The dispersion model parameters are as follows [12,13]: the band gaps of σ and π electrons Egσ and Egπ, highenergy limits of σ and π electronic transitions Ehσ and Ehπ, and parameters proportional to the σ and π electron densities Q σ and Q π. Using the parameters found in the procedure described above one can calculate the true spectral dependences of the refractive index and extinction coefficient of the DLC films studied in all the local areas corresponding to the pixels of the CCD camera. This means that distributions (maps) of the thickness and optical constants are determined in this way. Note that the spectral dependences of the optical constants of the silicon substrate were taken from the literature [14] and fixed within the LSM.
4. Results and discussion In this section the results of the optical characterization of a selected non-uniform DLC film are presented. These results are typical of the optical characterization of DLC films being studied using spectroscopic imaging reflectometry (SIR) in this work.
where rˆi1, j, rˆi2, j, Xi0, j, Ui, j, δi1, j and δi2, j denote the local complex reflection Fresnel coefficient of the upper boundary of the film, local complex reflection Fresnel coefficient of the lower boundary of the film, local phase change inside the film, local extinction factor, local phase shift corresponding to the upper boundary and local phase shift corresponding to the lower boundary, respectively. These quantities are expressed as follows [9,10]: i; j n −n 0 b1 i; j br i;j bi; j = ; 1 = j r 1 j exp iδ1 b i;1 j n0 + n
X0i; j =
4π i; j i; j d n1 ; λ
n b b i; j −n br i;2 j = jbr i;2 j j exp iδi;2 j = 1 ; i; j b b1 + n n
4π U i; j = exp − di; j ki;1 j : λ
ð2Þ
In Eq. (2) symbols nˆi1, j, nˆ and di, j represent the local complex refractive index of the absorbing film studied, complex refractive index of the absorbing substrate and local thickness of this film corresponding to the (i,j)th pixel, respectively (n0 = 1 because the ambient is formed by air). In our work we employed the following convention of the complex refractive indices nˆi1, j = ni1, j − iki1, j and nˆ = n − ik, where ni1, j,
ð3Þ
Fig. 2. The distribution of the local thickness of the film under investigation.
386
M. Ohlídal et al. / Diamond & Related Materials 18 (2009) 384–387
In Fig. 1, the CCD image of the sample under study is plotted for the wavelength 720 nm. In this figure the dark and bright areas are seen which indicate an area optical non-uniformity of the film studied. In Fig. 2, the local thickness distribution (map) corresponding to the selected area of this non-uniform DLC film is presented. This figure shows that the selected DLC film exhibits the evident thickness non-uniformity. Its local thickness distribution presented in Fig. 2 corresponds to the CCD image presented in Fig. 1. The local peaks in the local thickness distribution in Fig. 2 are caused by dust particles on the film and local defects of the film. It was found that the values of the material parameters of the dispersion model were practically identical for all the local areas belonging to individual pixels. From this fact it is possible to deduce that the non-uniform DLC film investigated exhibits area uniformity in the material parameters. Of course, this fact also implies that this film is uniform in the optical constants along the area of the film. Thus, the DLC film analyzed only exhibits the thickness area non-uniformity. This conclusion could be achieved on the basis of the fact that this characterization method allows us to determine the distributions of the local thickness and local optical constants in an independent way. The values of the material parameters found are summarized for this DLC film in Table 1. The spectral dependences of the refractive index and extinction coefficient characterizing the selected DLC film non-uniform in thickness calculated using the values of the material parameters found (see Table 1) are plotted in Fig. 3. Similar thickness distributions and spectral dependences of the optical constants were determined for remaining samples of the nonuniform DLC films studied. Note that the non-uniform DLC films under investigation were also characterized using standard, i.e. non-imaging, spectroscopic ellipsometry (see e.g. [15]) under assumption that wedge-shaped thickness non-uniformity occurs in the case of these films. The values of the dispersion parameters and spectral dependences of the optical constants of these non-uniform DLC films determined using this spectroscopic ellipsometry were practically identical with those found by means of SIR. This fact supports a correctness of the results achieved for the DLC films in their characterization using SIR. The spectral dependences of the optical constants of the DLC films prepared under different technological conditions are presented, for example, in papers [16–19]. From the foregoing results it is seen that SIR is the efficient method for the complete optical characterization of the DLC films exhibiting the thickness area non-uniformity. If DLC films exhibit area nonuniformity in thickness and optical constants simultaneously, the method presented will be successful too. Note that within SIR the local thickness distribution can only be determined if the local thicknesses are smaller than a certain limit. This limit depends on the optical constants, spectral region of interest and experimental accuracy of measured reflectance Ri, j. In our case the thickness limit was estimated in value of about 2 µm. It should be noted that we applied SIR for the successful characterization of non-uniform films consisting of materials strongly different from DLC. For example, we also characterized SiOx and carbon-nitride thin films exhibiting thickness non-uniformity in a successful way (results concerning the characterization of these films will be presented elsewhere). The SiOx and carbon-nitride films have the considerably different optical constants in comparison with the DLC films. This fact implies that SIR represents a general method Table 1 The values of the material parameters of the dispersion model for the DLC film selected Parameter
Egσ [eV]
Ehσ [eV]
Qσ [eV3/2]
Egπ [eV]
Ehπ [eV]
Qπ [eV3/2]
1.35
46.90
121.00
1.51
7.49
5.10
Fig. 3. Spectral dependences of the refractive index n1 and extinction coefficient k1 of the non-uniform DLC film selected.
serving as a useful tool for characterizing non-uniform thin films consisting of miscellaneous materials. 5. Conclusion This paper presents the results concerning the complete optical characterization of non-uniform DLC films prepared by PECVD in RF capacitive discharge at low pressure onto the silicon single crystal substrates obtained by means of SIR. From these results it is concluded that these DLC films only exhibit area non-uniformity in thickness and that they are uniform in the optical constants along their areas. The distribution of the local thickness (map of the local thickness) is presented for the selected sample for illustration. The spectral dependences of the refractive index and extinction coefficient of this sample calculated using the values of the material parameters of the dispersion model found are presented too. These spectral dependences were verified using standard spectroscopic ellipsometry. The values of the local thickness and values of the material parameters are found using the LSM applied separately for all local areas corresponding to the individual pixels of the CCD camera. Thus, using SIR it is possible to determine simultaneously the area distributions (maps) of the local thicknesses, local refractive index and local extinction coefficient of the non-uniform DLC films. The same conclusion is valid for non-uniform thin films consisting of other materials. This means that SIR is a very useful general tool for the optical characterization of the thin films exhibiting area non-uniformity. Acknowledgements This work was supported by the Ministry of Education, Youths and Sports of the Czech Republic under contracts MSM 0021630518, MSM 0021622411 and the Ministry of Industry and Trade of the Czech Republic under contract FT-TA3/142. References [1] A.A. Howling, L. Sansonnens, J. Ballutaud, C. Hollenstein, J.P.M. Schmitt, J. Appl. Phys. 96 (2004) 5429. [2] M.A. Lieberman, J.P. Booth, P. Chabert, J.M. Rax, M.M. Turner, Plasma Sources Sci. Technol. 11 (3) (2002) 283. [3] M.I. Török, Opt. Acta 32 (1985) 479. [4] T. Pisarkiewicz, T. Stapinski, H. Czternasek, P. Rava, J. Non-Cryst. Solids 137/138 (1991) 619. [5] T. Pisarkiewicz, J. Phys. D: Appl. Phys. 27 (1994) 160. [6] M. Ohlídal, I. Ohlídal, P. Klapetek, M. Jákl, V. Čudek, Jpn. J. Appl. Phys. 42 (2003) 4760. [7] M. Ohlídal, V. Čudek, I. Ohlídal, P. Klapetek, in: C. Amra, N. Kaiser, H.A. Macleod (Eds.), Advances in Optical Thin Films II, vol. 5963, SPIE, Bellingham, Washington, 2005, p. 596329.
M. Ohlídal et al. / Diamond & Related Materials 18 (2009) 384–387 [8] [9] [10] [11] [12]
L. Zajíčková, V. Buršíková, D. Franta, Czech. J. Phys 49 (1999) 1213. A. Vašíček, Optics of Thin Films, North Holland, Amsterdam, 1960. Z. Knittl, Optics of Thin Films, John Wiley, Chichester, 1976. D. Franta, I. Ohlídal, M. Frumar, J. Jedelský, Appl. Surf. Sci. 212–213 (2003) 116. D. Franta, I. Ohlídal, V. Buršíková, L. Zajíčková, Diamond Relat. Mater. 12 (2003) 1532. [13] D. Franta, D. Nečas, L. Zajíčková, Opt. Express 15 (2007) 16230. [14] C.M. Herzinger, B. Johs, W.A. McGahan, J.A. Woolan, W. Paulson, J. Appl. Phys. 83 (1988) 3323.
387
[15] I. Ohlídal, D. Franta, E. Pinčík, M. Ohlídal, Surf. Interface Anal. 28 (1999) 240. [16] D. Franta, L. Zajíčková, I. Ohlídal, J. Janča, K. Veltruská, Diamond Relat. Mater. 11 (2002) 105. [17] S. Logothetidis, G. Stergioudis, Appl. Phys. Lett. 71 (1997) 2463. [18] J. Lee, R.W. Collins, V.S. Veerasamy, J. Robertson, Diamond Relat. Mater. 7 (1998) 999. [19] T. Mori, N. Fujii, Y.M. Xiong, T. Saitoh, Thin Solid Films 270 (1995) 215.