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An ellipsometric study of Ni, Mo and NixN films deposited on Si
Thin Solid Films 313]314 Ž1998. 314]318
An ellipsometric study of Ni, Mo and Ni x N films deposited on Si A.A. Tarasenko a,U , L. Jastrabık ´ b , D. Chvostovab, J. Sobotac a Institute of Physics, National Academy of Sciences of Ukraine, Prospect Nauki 46, 252028 Kij¨ 28, Ukraine Institute of Physics, Academy of Sciences of the Czech Republic, Na Slo¨ance 2, 180 40 Praha 8, Czech Republic c Institute of Scientific Instruments, Academy of Sciences of the Czech Republic, Kralo¨opolska ´ ´ 147, 612 64 Brno, Czech Republic b
Abstract The results of spectral and angle-dependent ellipsometric measurements of r.f. magnetron-sputtered very thin nickel, molybdenum and nickel nitride films deposited onto w100x oriented silicon substrates have been reported. Ellipsometric data were taken over the spectral range of 348]806 nm. The parameters of the films, namely, film thicknesses and volume fractions for the constituents have been calculated from the ellipsometric data by the best fitting procedure using one-layer ŽairrMetalrSi., two-layer ŽairrMetalrSiO 2rSi. and three-layer ŽairrMetal oxiderMetalrSiO 2rSi. optical models. We have estimated the roughness on the film surfaces and contamination of the films by Si and SiO 2 using the Maxwell-Garnett and Bruggeman effective medium approximations. We have also used a model with an inhomogeneous silicon dioxide interface Ža mixture of SiO 2 and a-Si.. The ellipsometric measurements along with computer data processing will be useful for quality control during the manufacturing of the films, which have applications in soft X-ray optical systems. Q 1998 Elsevier Science S.A. Keywords: Ellipsometry; Thin nickel; Molybdenum and nickel nitride films; Optical constants; Multilayer optical models
1. Introduction The multilayer structures composed of alternating films of low and high atomic number materials deposited on smooth substrates are the most common elements for the manufacturing of vacuum-UV and soft X-ray mirrors and other multilayer optical devices for X-ray telescopes, microscopes and lasers. The technology of deposition is relatively straight forward, but the quality of the multilayer structures, characterized by their reflectivities, is greatly influ-
U
Corresponding author. Optics Division, Institute of Physics Academy of Sciences of the Czech Republic, Na Slovance 2, 18040, Prague 8, Czech Republic. Fax: q4202 8581448; e-mail: [email protected] 0040-6090r98r$19.00 Q 1998 Elsevier Science S.A. All rights reserved PII S0040-6090Ž97.00839-0
enced by the roughness of the films, interface imperfections and variations in the interlayer spacing. A multilayer structure must be fabricated from optically homogeneous continuous layers having thicknesses of several nanometers. Thus, diagnostics to assess the properties and control of the quality of such films are of great importance. Ellipsometry is an effective, non-destructive method which can be used successfully for these purposes. 2. Experimental The r.f. magnetron sputtering system used in this investigation, has been described in detail elsewhere w1,2x. The films of Ni were deposited at rate about 2.7 nmrmin, Mo at 7.1 nmrmin and Ni x N at 4.2 nmrmin.
A.A. Tarasenko et al. r Thin Solid Films 313]314 (1998) 314]318
The ellipsometric measurements were performed on a Rudolph Research, Model 43603]200E spectroscopic ellipsometer. Values of D and C were obtained over 16 wavelengths in the spectral range of 348]806 nm, using a set of interference filters. The incidence angle was varied between 458 and 808. 3. Results and discussion It is well known that thin films deposited on solid surfaces have very complicated microstructures. There are many lattice dislocations, grain boundaries and voids in the films sputtered onto solid surfaces. The properties of these films are different from the bulk materials. A common way in ellipsometry of simulating the variations in film dielectric function with treatment conditions is to model the film as a mixture of constituents. There are two most frequently used approaches. The Maxwell-Garnett theory ŽMG approximation. takes into account the granular structure of the film w3,4x. The film is treated as a mixture of discrete impurity particles embedded in the matrix of the primary constituent Žmetal.. The effective dielectric function of the film e M G is determined from the following equation:
eM G y e 1 e y e1 s Ý qi i eM G q e 1 ei q 2 e 1
Ž1.
i
where qi and e i are the volume fraction and dielectricfunction, respectively, for the i-th constituent Ž i s 1 for metal.. The second approach was suggested by Bruggeman Žeffective medium or approximation EMA for mixed layers. w5x. The film is regarded as a homogeneous mixture of different particles of size less than the wavelength of light l. The effective dielectric function e B is determined from the equation:
Ý qi i
ei y eB s0 ei q 2 eB
Ž2.
It should be mentioned that a problem may arise with the selection of the proper solution of this equation w6x. The roughness of the film is treated as a separate layer consisting of a mixture of metal and air with dielectric function evaluated from the MG or approximation EMA. We applied both approximations in our modeling procedure. For the analysis of the ellipsometric data, we used the common method in which the data are best fit to the appropriate layer model after a grid search within the space of the variable model parameters. To fit the model parameters, an error function d is defined as follows:
ds
1 N
315 1r2
N
Ý
< r y tanCn exp iD n < 2
Ž3.
n
where r s R prR s is the calculated complex ratio of the Fresnel reflection coefficients for light polarized parallel Žp. and perpendicular Žs. to the plane of incidence; Cn and D n are the ellipsometric angles measured at a particular incidence angle and wavelength. It should be mentioned that this function weights the experimental data unequally due to the tan C factor. For C fs 908 even small differences between the data and the fit are enhanced, which may lead to a biasing of the values of the fitted parameters. In the analysis procedure, r was calculated for chosen optical models. A minimization procedure gives the best fit parameters including film thicknesses d i and volume fractions qi for the constituents. The complex refractive indices of Si, a-Si, and SiO 2 were taken from w7x. Refraction index for molybdenum oxide film was taken from w8x. The refractive indices for Ni, Mo and Ni x N over the entire spectral range have been determined from the ellipsometric measurements of thick Ž d, 100 nm. films. Disagreement between the optical data, obtained for Ni and Mo, and the literature data w7x do not exceed 15%. The measured data for the real Ž n. and imaginary parts Ž k . of the complex refractive index for Ni x N are shown in Fig. 1. The dielectric function of the Ni x N film can be approximated by the following equation:
es1y
v p2t v 2t y i v
q
v b2 v 02 y v 2 q i vrt b
Ž4.
where v , v p and t are the light frequency, plasma frequency and the relaxation time of the free electrons; v 0 , v b and t b are the resonance frequency, oscillator strength and relaxation time of the bound electrons, respectively. The second term describes the effect of the free electrons ŽDrude term. and the third term is the contribution from an assembly of damped harmonic oscillators. Rewriting Eq. Ž4. as a function of l, we obtain an analytical expression for the complex refraction index for Ni x N in the investigated spectral range: 2
e ' Ž n y ik . s 1 y q
1 2
Ž 87.1rl. y i37.6rl
1 2 Ž 1 y 338rl. q i238rl
Ž5.
where l is measured in nm. The results of the best fit are plotted as the solid lines in Fig. 1. The simplest one-layer model ŽairrMerSi. has been assumed first for analyzing the ellipsometric data ŽMe
A.A. Tarasenko et al. r Thin Solid Films 313]314 (1998) 314]318
316
Fig. 1. The spectral variations of the refraction and extinction coefficients for a thick Ni x N film.
refers to Ni, Mo and Ni x N.. The only fitting parameter is the thickness of the film d. The quality of the fit is estimated by mean square error d . As a first step this model gives a fairly good approximation. In some cases it fits experimental data with mean square error equals to the experimental error. When the value of d is near the level of the experimental error of the measurements d 0 s 0.01, further improvement of the optical model cannot achieve a significant decrease of d , in principle. The next one-layer models consider the film as a mixture of metal with silicon wairrŽMe q i .rSix, silicon dioxide wairrŽMe q SiO 2 .rSix and air wairrŽMe q air.rSix as described by the MG approximation. These models have two fitting parameters, the film thickness d and volume fraction of the metal q and fit the experimental data slightly better than the first one-layer models. The latter model has a tendency to give very thick films Ž d; 100 nm. with unreasonably low metal content Ž q ; 0.01]0.1.. We also consider two-layer models in order to
account for the presence of the silicon dioxide interface layer between the substrate and the metal. The simplest two-layer model ŽairrMerSiO 2rSi. with two fitting parameters, d M and d 2 , gives mean square errors 3]10 times lower than the one-layer models. We can also estimate the roughness on the metal film, using admixtures of air in the topmost layer wtwo-layer models: airrŽMe q air.rSiO 2rSi and airrŽMe q air.rMerSix, and the presence of the silicon dioxide in the metal film wairrŽMe q SiO 2 .rSiO 2rSix using the EMA both cases. We have also included the model proposed for the SiO 2rSi interface w9x. Terao w9x showed that the thin SiO 2 films are inhomogeneous and the best fit is obtained for a mixture of SiO 2 and a-Si in SiO 2 film. Therefore, we consider the two-layer model wairrMerŽSiO 2 q a-Si.rSix with three fitting parameters, d M , d 2 and qU Žvolume fraction of a-Si in SiO 2 film.. There is also evidence that the surfaces of the molybdenum films are covered by an oxide layer w1x. In order to account the presence of the metal oxide, we consider three-layer model wairrMeOrMer SiO 2rSix. The parameters of the samples were calculated either for a given wavelength or for the entire data file of the sample, obtained over the full spectral range. The results of the best fitting are summarized in Tables 1]3. It is seen from the tables that the thick metal ŽNi a1,2,4 and Mo a3,4. and nickel nitride ŽNi x N a4. films have rather stable values of their thicknesses d and small mean square errors Ž d F 0.01. as compared to the data for the thinner films. The metal content q in these films is close to 1. The surface roughness is about 1 nm. One can conclude that these films are continuous, have a homogeneous composition and are rather smooth. The optical con-
Table 1 One-layer models for Me s Ni, Mo, and Ni x N films on Si wafers using the MG approximation Sample
Model AirrŽMe q Si.rSi
AirrMerSi dM Ni a1 Ni a2 Ni a3 Ni a4 Mo a1 Mo a2 Mo a3 Mo a4 Nix N a1 Nix N a2 Nix N a3 Nix N a4
22.2 12.4 6.05 17.5 4.34 2.18 17.9 16.3 4.19 9.20 5.10 20.0
drd0 0.43 0.63 1.77 0.92 3.67 5.63 0.84 1.02 3.41 2.06 2.40 1.19
d1
q
22.3 12.4 6.05 17.6 4.34 19.8 18.6 17.4 4.19 9.44 5.10 20.4
0.99 1.0 1.0 0.99 1.0 0.13 0.95 0.93 1.0 0.97 1.0 0.97
AirrŽMe q air.rSi
drd0 0.35 0.63 1.77 0.91 3.67 45.43 0.42 0.61 3.41 20.6 2.40 1.09
d1
q
22.2 12.4 6.05 17.5 13.9 9.42 19.6 17.9 7.51 9.20 11.0 20.9
1.0 1.0 1.0 1.0 0.86 0.78 0.99 0.99 0.80 1.0 0.79 0.99
d1 is the thickness of the top layer; q is the volume content of the Me; d 0 s 0.01.
AirrŽMe q SiO2 .rSi
drd0 0.43 0.63 1.77 0.92 3.02 1.56 0.45 0.78 2.82 2.06 2.40 1.10
d1
q
22.2 12.4 6.05 17.5 13.1 9.29 17.9 16.3 7.26 9.20 10.8 22.2
1.0 1.0 1.0 1.0 0.75 0.6 1.0 1.0 0.65 1.0 0.60 0.95
drd0 0.43 0.63 1.77 0.92 2.90 1.43 0.84 10.2 2.77 20.6 2.40 1.17
A.A. Tarasenko et al. r Thin Solid Films 313]314 (1998) 314]318
317
Table 2 Two-layer models for Me s Ni, Mo, and Ni x N films on Si wafers using the EMA Sample
Model AirrMerSiO2rSi
Ni a1 Ni a2 Ni a3 Ni a4 Mo a1 Mo a2 Mo a3 Mo a4 Nix N a1 Nix N a2 Nix N a3 Nix N a4
AirrŽMe q SiO2 .rSiO2rSi
AirrŽMe q air.rSiO2rSi
dM
d2
drd0
d1
d2
q
drd0
d1
d2
q
drd0
21.4 12.2 4.71 16.6 3.32 0.92 17.0 15.4 2.45 7.74 2.76 18.4
3.39 1.03 4.59 3.66 6.43 7.65 4.71 5.02 5.21 5.12 8.20 5.69
0.27 0.61 0.68 0.67 0.65 0.78 0.29 0.34 1.40 0.68 0.58 0.58
21.4 12.2 4.71 16.6 3.32 0.92 17.0 15.4 3.88 7.74 2.76 18.4
3.39 1.03 4.59 3.66 6.43 7.65 4.71 5.02 2.35 5.12 8.20 5.69
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.8 1.0 1.0 1.0
0.27 0.61 0.68 0.67 0.65 0.78 0.29 0.34 1.29 0.68 0.58 0.58
21.4 12.2 4.71 16.6 3.32 0.92 17.0 15.4 3.84 7.74 2.76 18.4
3.39 1.03 4.59 3.66 6.43 7.65 4.71 5.02 2.15 5.12 8.20 5.69
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.8 1.0 1.0 1.0
0.27 0.61 0.68 0.67 0.65 0.78 0.29 0.34 1.33 0.68 0.58 0.58
d1 is the thickness of the top layer; d 2 is the thickness of the SiO 2 interface layer between Me and Si; d M is the thickness of the Me film; 9 is the volume content of the Me.
stants of these films are close to the bulk values. The scattering of the results for thin films ŽNi a3 and Mo a1,2. points out that the refractive indices of the films deviate significantly from the bulk values and that the films are probably discontinuous or have a granular structure with a great number of defects, voids and so on. All Ni films do not appear to have significant oxide layers on their surfaces. The structure of the Ni x N films, however, remains undetermined. It is known that in the Ni]N system two nitrides exist, Ni 4 N, having two modifications Žcubic and tetragonal., and Ni 3 N, having a hexagonal unit cell w10x. All these nitrides exhibit metallic conduction. The composition and properties of the nickel nitride films depend strongly on the deposition condi-
tions. There is no any detectable optical anisotropy of the Ni x N films. The relatively large mean square errors for these films may indicate that the refractive index depends on the thickness of the film. It should be noted that the smallest errors d were obtained for the optical model with a composite SiO 2 interface layer ŽSiO 2 q a-Si., in comparison with the other optical models having the same number of fitting parameters. 4. Summary We have investigated thin Ni, Mo and Ni x N films deposited onto w100x oriented silicon substrates over the spectral range 348]806 nm by means of spectros-
Table 3 Two- and three-layer models for Me s Ni, Mo, and Ni x N films on Si wafers using the EMA Sample
Model AirrMeOrMerSiO2rSi
Ni a1 Ni a2 Ni a3 Ni a4 Mo a1 Mo a2 Mo a3 Mo a4 Nix N a1 Nix N a2 Nix N a3 Nix N a4
AirrŽMe q air.rMerSi
AirrMerŽSiO2 q a-Si.rSi
d1
dM
d2
drd0
d1
dM
q
drd0
dM
d2
qU
drd0
0.0 0.0 0.0 0.0 0.00 2.81 0.12 0.30
214 12.2 4.71 16.6 3.32 0.99 16.8 15.1
3.39 1.03 4.59 3.66 6.43 3.32 4.10 3.33
0.27 0.61 0.68 0.67 0.65 0.76 0.28 0.30
1.10 0.0 6.33 3.27 4.75 20.91 0.61 0.92 4.78 8.68 6.20 2.69
21.8 12.4 0.0 14.1 0.91 1.12 16.5 15.1 0.0 0.83 0.09 16.5
0.05 0.0 0.90 0.95 0.70 0.05 0.30 0.20 0.75 0.90 0.70 0.80
0.31 0.63 1.18 0.81 0.86 1.08 0.33 0.34 1.33 1.02 1.4 0.56
21.4 11.9 4.62 16.6 3.27 0.85 16.8 15.2 2.45 7.55 2.76 18.3
2.65 3.42 3.88 3.1 5.5 6.36 4.01 4.58 5.21 4.79 6.55 5.63
0.15 0.75 0.45 0.5 0.35 0.40 0.45 0.50 0.20 0.50 0.35 0.55
0.27 0.41 0.42 0.62 0.51 0.42 0.27 0.26 1.40 0.32 0.4 0.38
d1 is the thickness of the top layer; d 2 is the thickness of the SiO 2 interface layer between Me and Si; d M is the thickness of the Me film; q is the volume content of the Me; qU is the volume content of the a-Si in SiO 2 interface layer.
318
A.A. Tarasenko et al. r Thin Solid Films 313]314 (1998) 314]318
copic, variable angle ellipsometry. Ten optical models have been used to calculate the thicknesses of the layers and determine the quality of the films, i.e. their homogeneity and roughness. It is shown that thick Ž dG 10 nm. films have a homogeneous composition with refractive indices close to the bulk values and roughness less than 1 nm. The thin metal and nickel nitride films Ž dF 10 nm. are probably discontinuous and have an inhomogeneous granular or island structure, which differs substantially from that of the thick films. The best fitting results were obtained for a two-layer model with inhomogeneous interface silicon dioxide layer. The structure of this layer was proposed in w9x. Acknowledgements This work was supported by the Grant Agency of
the Academy of Science. CR under grant No A2010536. References w1x P. ˇ Siroky, ´ J. Sobota, J. Seidl, L. Jastrabık, ´ Thin Solid Films 234 Ž1993. 500. w2x J. Sobota, V. Perina, O. Renner, et al., Acta Phys. Univ. ˇ Comenianae XXXV 1 Ž1994. 123. w3x J.C. Maxwell-Garnett, Philos. Trans. R. Soc. Lond. A 203 Ž1904. 385. w4x J.C. Maxwell-Garnett, Philos. Trans. R. Soc. Lond. A 205 Ž1906. 237. w5x D.A.G. Bruggeman, Ann. Phys. Leipzig 5 Ž1935. 637. w6x Ph.J. Roussel, J. Vanhellemont, H.E. Maes, Thin Solid Films 233 Ž1993. 423. w7x E.D. Palik ŽEd.., Handbook of Optical Constants of Solids, Academic Press, New York, 1985. w8x M.R. Tubbs, Phys. Stat. Sol. Ža. 21 Ž1974. 253. w9x E.A. Irene, Thin Solid Films 233 Ž1993. 96. w10x N. Terao, J. Phys. Soc. Jpn. 17 Ž1962. 238.
An ellipsometric study of Ni, Mo and Ni x N films deposited on Si A.A. Tarasenko a,U , L. Jastrabık ´ b , D. Chvostovab, J. Sobotac a Institute of Physics, National Academy of Sciences of Ukraine, Prospect Nauki 46, 252028 Kij¨ 28, Ukraine Institute of Physics, Academy of Sciences of the Czech Republic, Na Slo¨ance 2, 180 40 Praha 8, Czech Republic c Institute of Scientific Instruments, Academy of Sciences of the Czech Republic, Kralo¨opolska ´ ´ 147, 612 64 Brno, Czech Republic b
Abstract The results of spectral and angle-dependent ellipsometric measurements of r.f. magnetron-sputtered very thin nickel, molybdenum and nickel nitride films deposited onto w100x oriented silicon substrates have been reported. Ellipsometric data were taken over the spectral range of 348]806 nm. The parameters of the films, namely, film thicknesses and volume fractions for the constituents have been calculated from the ellipsometric data by the best fitting procedure using one-layer ŽairrMetalrSi., two-layer ŽairrMetalrSiO 2rSi. and three-layer ŽairrMetal oxiderMetalrSiO 2rSi. optical models. We have estimated the roughness on the film surfaces and contamination of the films by Si and SiO 2 using the Maxwell-Garnett and Bruggeman effective medium approximations. We have also used a model with an inhomogeneous silicon dioxide interface Ža mixture of SiO 2 and a-Si.. The ellipsometric measurements along with computer data processing will be useful for quality control during the manufacturing of the films, which have applications in soft X-ray optical systems. Q 1998 Elsevier Science S.A. Keywords: Ellipsometry; Thin nickel; Molybdenum and nickel nitride films; Optical constants; Multilayer optical models
1. Introduction The multilayer structures composed of alternating films of low and high atomic number materials deposited on smooth substrates are the most common elements for the manufacturing of vacuum-UV and soft X-ray mirrors and other multilayer optical devices for X-ray telescopes, microscopes and lasers. The technology of deposition is relatively straight forward, but the quality of the multilayer structures, characterized by their reflectivities, is greatly influ-
U
Corresponding author. Optics Division, Institute of Physics Academy of Sciences of the Czech Republic, Na Slovance 2, 18040, Prague 8, Czech Republic. Fax: q4202 8581448; e-mail: [email protected] 0040-6090r98r$19.00 Q 1998 Elsevier Science S.A. All rights reserved PII S0040-6090Ž97.00839-0
enced by the roughness of the films, interface imperfections and variations in the interlayer spacing. A multilayer structure must be fabricated from optically homogeneous continuous layers having thicknesses of several nanometers. Thus, diagnostics to assess the properties and control of the quality of such films are of great importance. Ellipsometry is an effective, non-destructive method which can be used successfully for these purposes. 2. Experimental The r.f. magnetron sputtering system used in this investigation, has been described in detail elsewhere w1,2x. The films of Ni were deposited at rate about 2.7 nmrmin, Mo at 7.1 nmrmin and Ni x N at 4.2 nmrmin.
A.A. Tarasenko et al. r Thin Solid Films 313]314 (1998) 314]318
The ellipsometric measurements were performed on a Rudolph Research, Model 43603]200E spectroscopic ellipsometer. Values of D and C were obtained over 16 wavelengths in the spectral range of 348]806 nm, using a set of interference filters. The incidence angle was varied between 458 and 808. 3. Results and discussion It is well known that thin films deposited on solid surfaces have very complicated microstructures. There are many lattice dislocations, grain boundaries and voids in the films sputtered onto solid surfaces. The properties of these films are different from the bulk materials. A common way in ellipsometry of simulating the variations in film dielectric function with treatment conditions is to model the film as a mixture of constituents. There are two most frequently used approaches. The Maxwell-Garnett theory ŽMG approximation. takes into account the granular structure of the film w3,4x. The film is treated as a mixture of discrete impurity particles embedded in the matrix of the primary constituent Žmetal.. The effective dielectric function of the film e M G is determined from the following equation:
eM G y e 1 e y e1 s Ý qi i eM G q e 1 ei q 2 e 1
Ž1.
i
where qi and e i are the volume fraction and dielectricfunction, respectively, for the i-th constituent Ž i s 1 for metal.. The second approach was suggested by Bruggeman Žeffective medium or approximation EMA for mixed layers. w5x. The film is regarded as a homogeneous mixture of different particles of size less than the wavelength of light l. The effective dielectric function e B is determined from the equation:
Ý qi i
ei y eB s0 ei q 2 eB
Ž2.
It should be mentioned that a problem may arise with the selection of the proper solution of this equation w6x. The roughness of the film is treated as a separate layer consisting of a mixture of metal and air with dielectric function evaluated from the MG or approximation EMA. We applied both approximations in our modeling procedure. For the analysis of the ellipsometric data, we used the common method in which the data are best fit to the appropriate layer model after a grid search within the space of the variable model parameters. To fit the model parameters, an error function d is defined as follows:
ds
1 N
315 1r2
N
Ý
< r y tanCn exp iD n < 2
Ž3.
n
where r s R prR s is the calculated complex ratio of the Fresnel reflection coefficients for light polarized parallel Žp. and perpendicular Žs. to the plane of incidence; Cn and D n are the ellipsometric angles measured at a particular incidence angle and wavelength. It should be mentioned that this function weights the experimental data unequally due to the tan C factor. For C fs 908 even small differences between the data and the fit are enhanced, which may lead to a biasing of the values of the fitted parameters. In the analysis procedure, r was calculated for chosen optical models. A minimization procedure gives the best fit parameters including film thicknesses d i and volume fractions qi for the constituents. The complex refractive indices of Si, a-Si, and SiO 2 were taken from w7x. Refraction index for molybdenum oxide film was taken from w8x. The refractive indices for Ni, Mo and Ni x N over the entire spectral range have been determined from the ellipsometric measurements of thick Ž d, 100 nm. films. Disagreement between the optical data, obtained for Ni and Mo, and the literature data w7x do not exceed 15%. The measured data for the real Ž n. and imaginary parts Ž k . of the complex refractive index for Ni x N are shown in Fig. 1. The dielectric function of the Ni x N film can be approximated by the following equation:
es1y
v p2t v 2t y i v
q
v b2 v 02 y v 2 q i vrt b
Ž4.
where v , v p and t are the light frequency, plasma frequency and the relaxation time of the free electrons; v 0 , v b and t b are the resonance frequency, oscillator strength and relaxation time of the bound electrons, respectively. The second term describes the effect of the free electrons ŽDrude term. and the third term is the contribution from an assembly of damped harmonic oscillators. Rewriting Eq. Ž4. as a function of l, we obtain an analytical expression for the complex refraction index for Ni x N in the investigated spectral range: 2
e ' Ž n y ik . s 1 y q
1 2
Ž 87.1rl. y i37.6rl
1 2 Ž 1 y 338rl. q i238rl
Ž5.
where l is measured in nm. The results of the best fit are plotted as the solid lines in Fig. 1. The simplest one-layer model ŽairrMerSi. has been assumed first for analyzing the ellipsometric data ŽMe
A.A. Tarasenko et al. r Thin Solid Films 313]314 (1998) 314]318
316
Fig. 1. The spectral variations of the refraction and extinction coefficients for a thick Ni x N film.
refers to Ni, Mo and Ni x N.. The only fitting parameter is the thickness of the film d. The quality of the fit is estimated by mean square error d . As a first step this model gives a fairly good approximation. In some cases it fits experimental data with mean square error equals to the experimental error. When the value of d is near the level of the experimental error of the measurements d 0 s 0.01, further improvement of the optical model cannot achieve a significant decrease of d , in principle. The next one-layer models consider the film as a mixture of metal with silicon wairrŽMe q i .rSix, silicon dioxide wairrŽMe q SiO 2 .rSix and air wairrŽMe q air.rSix as described by the MG approximation. These models have two fitting parameters, the film thickness d and volume fraction of the metal q and fit the experimental data slightly better than the first one-layer models. The latter model has a tendency to give very thick films Ž d; 100 nm. with unreasonably low metal content Ž q ; 0.01]0.1.. We also consider two-layer models in order to
account for the presence of the silicon dioxide interface layer between the substrate and the metal. The simplest two-layer model ŽairrMerSiO 2rSi. with two fitting parameters, d M and d 2 , gives mean square errors 3]10 times lower than the one-layer models. We can also estimate the roughness on the metal film, using admixtures of air in the topmost layer wtwo-layer models: airrŽMe q air.rSiO 2rSi and airrŽMe q air.rMerSix, and the presence of the silicon dioxide in the metal film wairrŽMe q SiO 2 .rSiO 2rSix using the EMA both cases. We have also included the model proposed for the SiO 2rSi interface w9x. Terao w9x showed that the thin SiO 2 films are inhomogeneous and the best fit is obtained for a mixture of SiO 2 and a-Si in SiO 2 film. Therefore, we consider the two-layer model wairrMerŽSiO 2 q a-Si.rSix with three fitting parameters, d M , d 2 and qU Žvolume fraction of a-Si in SiO 2 film.. There is also evidence that the surfaces of the molybdenum films are covered by an oxide layer w1x. In order to account the presence of the metal oxide, we consider three-layer model wairrMeOrMer SiO 2rSix. The parameters of the samples were calculated either for a given wavelength or for the entire data file of the sample, obtained over the full spectral range. The results of the best fitting are summarized in Tables 1]3. It is seen from the tables that the thick metal ŽNi a1,2,4 and Mo a3,4. and nickel nitride ŽNi x N a4. films have rather stable values of their thicknesses d and small mean square errors Ž d F 0.01. as compared to the data for the thinner films. The metal content q in these films is close to 1. The surface roughness is about 1 nm. One can conclude that these films are continuous, have a homogeneous composition and are rather smooth. The optical con-
Table 1 One-layer models for Me s Ni, Mo, and Ni x N films on Si wafers using the MG approximation Sample
Model AirrŽMe q Si.rSi
AirrMerSi dM Ni a1 Ni a2 Ni a3 Ni a4 Mo a1 Mo a2 Mo a3 Mo a4 Nix N a1 Nix N a2 Nix N a3 Nix N a4
22.2 12.4 6.05 17.5 4.34 2.18 17.9 16.3 4.19 9.20 5.10 20.0
drd0 0.43 0.63 1.77 0.92 3.67 5.63 0.84 1.02 3.41 2.06 2.40 1.19
d1
q
22.3 12.4 6.05 17.6 4.34 19.8 18.6 17.4 4.19 9.44 5.10 20.4
0.99 1.0 1.0 0.99 1.0 0.13 0.95 0.93 1.0 0.97 1.0 0.97
AirrŽMe q air.rSi
drd0 0.35 0.63 1.77 0.91 3.67 45.43 0.42 0.61 3.41 20.6 2.40 1.09
d1
q
22.2 12.4 6.05 17.5 13.9 9.42 19.6 17.9 7.51 9.20 11.0 20.9
1.0 1.0 1.0 1.0 0.86 0.78 0.99 0.99 0.80 1.0 0.79 0.99
d1 is the thickness of the top layer; q is the volume content of the Me; d 0 s 0.01.
AirrŽMe q SiO2 .rSi
drd0 0.43 0.63 1.77 0.92 3.02 1.56 0.45 0.78 2.82 2.06 2.40 1.10
d1
q
22.2 12.4 6.05 17.5 13.1 9.29 17.9 16.3 7.26 9.20 10.8 22.2
1.0 1.0 1.0 1.0 0.75 0.6 1.0 1.0 0.65 1.0 0.60 0.95
drd0 0.43 0.63 1.77 0.92 2.90 1.43 0.84 10.2 2.77 20.6 2.40 1.17
A.A. Tarasenko et al. r Thin Solid Films 313]314 (1998) 314]318
317
Table 2 Two-layer models for Me s Ni, Mo, and Ni x N films on Si wafers using the EMA Sample
Model AirrMerSiO2rSi
Ni a1 Ni a2 Ni a3 Ni a4 Mo a1 Mo a2 Mo a3 Mo a4 Nix N a1 Nix N a2 Nix N a3 Nix N a4
AirrŽMe q SiO2 .rSiO2rSi
AirrŽMe q air.rSiO2rSi
dM
d2
drd0
d1
d2
q
drd0
d1
d2
q
drd0
21.4 12.2 4.71 16.6 3.32 0.92 17.0 15.4 2.45 7.74 2.76 18.4
3.39 1.03 4.59 3.66 6.43 7.65 4.71 5.02 5.21 5.12 8.20 5.69
0.27 0.61 0.68 0.67 0.65 0.78 0.29 0.34 1.40 0.68 0.58 0.58
21.4 12.2 4.71 16.6 3.32 0.92 17.0 15.4 3.88 7.74 2.76 18.4
3.39 1.03 4.59 3.66 6.43 7.65 4.71 5.02 2.35 5.12 8.20 5.69
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.8 1.0 1.0 1.0
0.27 0.61 0.68 0.67 0.65 0.78 0.29 0.34 1.29 0.68 0.58 0.58
21.4 12.2 4.71 16.6 3.32 0.92 17.0 15.4 3.84 7.74 2.76 18.4
3.39 1.03 4.59 3.66 6.43 7.65 4.71 5.02 2.15 5.12 8.20 5.69
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.8 1.0 1.0 1.0
0.27 0.61 0.68 0.67 0.65 0.78 0.29 0.34 1.33 0.68 0.58 0.58
d1 is the thickness of the top layer; d 2 is the thickness of the SiO 2 interface layer between Me and Si; d M is the thickness of the Me film; 9 is the volume content of the Me.
stants of these films are close to the bulk values. The scattering of the results for thin films ŽNi a3 and Mo a1,2. points out that the refractive indices of the films deviate significantly from the bulk values and that the films are probably discontinuous or have a granular structure with a great number of defects, voids and so on. All Ni films do not appear to have significant oxide layers on their surfaces. The structure of the Ni x N films, however, remains undetermined. It is known that in the Ni]N system two nitrides exist, Ni 4 N, having two modifications Žcubic and tetragonal., and Ni 3 N, having a hexagonal unit cell w10x. All these nitrides exhibit metallic conduction. The composition and properties of the nickel nitride films depend strongly on the deposition condi-
tions. There is no any detectable optical anisotropy of the Ni x N films. The relatively large mean square errors for these films may indicate that the refractive index depends on the thickness of the film. It should be noted that the smallest errors d were obtained for the optical model with a composite SiO 2 interface layer ŽSiO 2 q a-Si., in comparison with the other optical models having the same number of fitting parameters. 4. Summary We have investigated thin Ni, Mo and Ni x N films deposited onto w100x oriented silicon substrates over the spectral range 348]806 nm by means of spectros-
Table 3 Two- and three-layer models for Me s Ni, Mo, and Ni x N films on Si wafers using the EMA Sample
Model AirrMeOrMerSiO2rSi
Ni a1 Ni a2 Ni a3 Ni a4 Mo a1 Mo a2 Mo a3 Mo a4 Nix N a1 Nix N a2 Nix N a3 Nix N a4
AirrŽMe q air.rMerSi
AirrMerŽSiO2 q a-Si.rSi
d1
dM
d2
drd0
d1
dM
q
drd0
dM
d2
qU
drd0
0.0 0.0 0.0 0.0 0.00 2.81 0.12 0.30
214 12.2 4.71 16.6 3.32 0.99 16.8 15.1
3.39 1.03 4.59 3.66 6.43 3.32 4.10 3.33
0.27 0.61 0.68 0.67 0.65 0.76 0.28 0.30
1.10 0.0 6.33 3.27 4.75 20.91 0.61 0.92 4.78 8.68 6.20 2.69
21.8 12.4 0.0 14.1 0.91 1.12 16.5 15.1 0.0 0.83 0.09 16.5
0.05 0.0 0.90 0.95 0.70 0.05 0.30 0.20 0.75 0.90 0.70 0.80
0.31 0.63 1.18 0.81 0.86 1.08 0.33 0.34 1.33 1.02 1.4 0.56
21.4 11.9 4.62 16.6 3.27 0.85 16.8 15.2 2.45 7.55 2.76 18.3
2.65 3.42 3.88 3.1 5.5 6.36 4.01 4.58 5.21 4.79 6.55 5.63
0.15 0.75 0.45 0.5 0.35 0.40 0.45 0.50 0.20 0.50 0.35 0.55
0.27 0.41 0.42 0.62 0.51 0.42 0.27 0.26 1.40 0.32 0.4 0.38
d1 is the thickness of the top layer; d 2 is the thickness of the SiO 2 interface layer between Me and Si; d M is the thickness of the Me film; q is the volume content of the Me; qU is the volume content of the a-Si in SiO 2 interface layer.
318
A.A. Tarasenko et al. r Thin Solid Films 313]314 (1998) 314]318
copic, variable angle ellipsometry. Ten optical models have been used to calculate the thicknesses of the layers and determine the quality of the films, i.e. their homogeneity and roughness. It is shown that thick Ž dG 10 nm. films have a homogeneous composition with refractive indices close to the bulk values and roughness less than 1 nm. The thin metal and nickel nitride films Ž dF 10 nm. are probably discontinuous and have an inhomogeneous granular or island structure, which differs substantially from that of the thick films. The best fitting results were obtained for a two-layer model with inhomogeneous interface silicon dioxide layer. The structure of this layer was proposed in w9x. Acknowledgements This work was supported by the Grant Agency of
the Academy of Science. CR under grant No A2010536. References w1x P. ˇ Siroky, ´ J. Sobota, J. Seidl, L. Jastrabık, ´ Thin Solid Films 234 Ž1993. 500. w2x J. Sobota, V. Perina, O. Renner, et al., Acta Phys. Univ. ˇ Comenianae XXXV 1 Ž1994. 123. w3x J.C. Maxwell-Garnett, Philos. Trans. R. Soc. Lond. A 203 Ž1904. 385. w4x J.C. Maxwell-Garnett, Philos. Trans. R. Soc. Lond. A 205 Ž1906. 237. w5x D.A.G. Bruggeman, Ann. Phys. Leipzig 5 Ž1935. 637. w6x Ph.J. Roussel, J. Vanhellemont, H.E. Maes, Thin Solid Films 233 Ž1993. 423. w7x E.D. Palik ŽEd.., Handbook of Optical Constants of Solids, Academic Press, New York, 1985. w8x M.R. Tubbs, Phys. Stat. Sol. Ža. 21 Ž1974. 253. w9x E.A. Irene, Thin Solid Films 233 Ž1993. 96. w10x N. Terao, J. Phys. Soc. Jpn. 17 Ž1962. 238.