- Email: [email protected]
Optical and electronic properties of magnetron sputtered ZrNx thin films
Thin Solid Films 447 – 448 (2004) 316–321
Optical and electronic properties of magnetron sputtered ZrNx thin films ´ P.E. Schmid, F. Levy ´ R. Lamni*, E. Martinez, S.G. Springer, R. Sanjines, ` Complexe, FSB-EPFL, Lausanne CH-1015, Switzerland Institut de Physique de la Matiere
Abstract The optical properties of sputtered ZrNx films with 0.81FxF1.35 have been investigated and interpreted in terms of stoichiometry-related defects and crystal structure. The optical properties were determined by optical reflectivity, transmission and spectroscopic ellipsometry. As x increases from 0.81 to 1.35, the optical properties continuously change from metallic to semiconducting behavior. The experimental results have been fitted with a model dielectric function based on a set of Drude– Lorentz oscillators in order to separate the contributions due to free carriers and interband transitions. The effective density N* of conduction electrons decreases from N*s4.9=1022 cmy3 to N*s2.9=1021 cmy3 as x is increased from 0.81 to 1.29. The charge carrier scattering time increases from 4.9=10y16 to 2.6=10y15 s for 0.81-xF0.98, and decreases from 2.6=10y15 to 3.3=10y16 s for 0.98-xF1.29. The ZrNx films with x)1.3 are poorly crystallized. In this composition range, the compounds exhibit a crystal structure close to orthorhombic Zr3 N4 ; they are insulating with optical absorption coefficients in the range of 2=104 cmy1 below 2 eV and an optical absorption onset at 2.3 eV. 䊚 2003 Elsevier B.V. All rights reserved. Keywords: ZrNx films; Optical properties; Magnetron sputtering
1. Introduction Transition metal nitride coatings, mainly based on titanium, chromium and zirconium, are used as protective coatings against wear and corrosion w1x. Furthermore, they are widely used as optical and decorative coatings w2x. Zirconium nitrides exhibit very interesting properties such as high hardness, high melting point, high corrosion resistance w3x. Their optical and mechanical properties intensively depend on the nitrogen composition w4–6x. The stoichiometric nitride ZrN is metallic-like with a gold, yellow color; it is the thermodynamically stable phase. On the contrary, the Zr3N4 compound is a metastable phase; it is insulating and almost transparent w6x. In this article, we present an experimental study of the optical properties of sputtered ZrNx films. The ZrNx films were deposited by reactive magnetron sputtering in a wide range of chemical composition (0.81xF1.35). The dielectric function obtained from spectroscopic ellipsometry and normal reflectivity measurements were modeled as the response of a set of *Corresponding author. Tel.: q41-21-693-4144; fax: q41-21-6934666. E-mail address: [email protected] (R. Lamni).
adjustable Drude–Lorentz oscillators. In the present study the free carrier response and the free-carrier relaxation time have been determined with a minimum of assumptions. The variations of the optical parameters are discussed with the help of band structure calculations reported for fcc ZrN, and related defects such as nitrogen vacancies andyor interstitials and zirconium vacancies. 2. Experimental ZrNx films, approximately 1000 nm in thickness, have been deposited by reactive r.f. magnetron sputtering in an high vacuum reactor. The residual pressure was approximately 10y5 Pa before the introduction of the sputtering gases, namely argon and nitrogen. Discs (50 mm in diameter) of 99.99% pure zirconium were used as target material. The r.f. discharge power was kept constant at 100 W, and the target–substrate distance fixed at 100 mm. In order to ensure a uniform deposit, the substrate was rotated. The total pressure was kept constant at 0.4 Pa. The nitrogen partial pressure was adjusted in the range 3 to 75% of the total pressure, in order to deposit films with different nitrogen compositions. The substrate temperature was kept constant at 373"20 K during the deposition. Different substrates
0040-6090/04/$ - see front matter 䊚 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0040-6090Ž03.01109-X
R. Lamni et al. / Thin Solid Films 447 – 448 (2004) 316–321
317
such as silicon and quartz wafers have been used. The layer thickness was measured by profilometry. The crystallographic phases were analyzed by X-ray diffraction (XRD) using monochromatized Cu Ka radiation at a grazing incidence of 48. The sin2C method was applied to determine the stress and the stress-free lattice parameters. Electron probe microanalysis (EPMA) was used to determine the chemical composition. The measurements were performed at 8 kV (accelerating voltage) and 100 nA (beam current) for typical 1000 nm thick films, limiting the penetration depth of the electron beam to less than 35% of the film thickness. A RuO2 single crystal, and CrN and Zr thin films served as standards. The precision of the results is within "1% at. The optical constant of the films were investigated by spectroscopic ellipsometry in the 1.5–5.0 eV photon energy range. The optical reflectivity was measured at near normal incidence from 200 to 2700 nm with a Cary 2400 spectrophotometer. An evaporated aluminum mirror film was used as a reference. 3. Results and discussion 3.1. Structure and morphology The X-ray diffraction patterns of selected ZrNx films are shown in Fig. 1. In the 0.81FxF1.19 chemical composition range, all the films are well crystallized in the fcc ZrN structure. In contrast, for 1.20FxF1.35 the X-ray diffraction patterns change significantly. With increasing x the (200) reflection broadens and decreases in intensity; new broad reflection peaks appear near the (111) and (311) reflections. These trends indicate that an important modification of the fcc NaCl-type structure occurs when the N content is increased beyond xs1.2. For x)1.3, the broad reflection peaks lay close to the positions of the (320) and (042) peaks reported for the orthorhombic Zr3N4 phase w7,8x indicating that the structure of these films is a poorly crystallized, distorted structure of the Zr3N4 phase. Fig. 2 shows the lattice parameter a111 calculated from the (111) reflection, as well as the stress-free lattice parameter a0 obtained from the (200) reflection, as a function of the nitrogen content. Below xs1.2, both a111 and a0 increase monotonously with increasing x, above xs1.2 a111 increases rapidly. The a0 increases from a0s0.457 nm for xs0.92 to a0s0.459 nm for xs1.09. Stoichiometric ZrN has not been obtained in the present work, however, the interpolated lattice parameter for xs1 is a0s0.458 nm, which compares well with the reported bulk value of aB0 s0.4577 nm. While nitrogen vacancies are generally accepted to be dominant defect in substoichiometric ZrNx films, the exact crystal structure of the overstoichiometric ZrNx films is not well known yet, in particular in films with x values higher than 1.2. As pointed out by Johansson
Fig. 1. X-Ray diffraction patterns of ZrNx films at different x. The Xray diffraction was performed in a 48 grazing incidence geometry.
et al. w5x, at low nitrogen content (x-1.2) the excess nitrogen can preferentially occupy interstitial positions leading to a monotonous increase of the lattice parameter. In the compositional range 1.20FxF1.30, the increase of the a111 parameter is steeper, nevertheless Zr vacancies may possibly be created, leading to a highly defective and poorly crystallized fcc structure. In addition, as the XRD data for xs1.27 suggest (Fig. 1), the ZrNx films should consist of a mixture of defect-rich, fcc ZrN and poorly crystallized Zr3N4. 3.2. Optical properties The reflectivity spectra of a selected set of films are shown in Fig. 3. The highest reflectivity at low photon energy is achieved by the nearly stoichiometric ZrN0.99 sample. Note that this sample exhibits a minimum reflectivity value of 0.10 located at "vmins3.5 eV. The minimum ZrN0.84 reflectivity is 0.18, and occurs at "vs3.94 eV, while that of ZrN1.16 is 0.2 and is shifted to lower energies: "vs2.67 eV. These results agree well with previously reported Rmin values ranging from 0.10 to 0.16 at photon energies between 3.5 and 4.0 eV
318
R. Lamni et al. / Thin Solid Films 447 – 448 (2004) 316–321
Fig. 2. Relative lattice expansion in ZrNx thin films. The stress-free lattice parameters are calculated using the sin2C method.
w9,10x. The reflectivity spectrum of the ZrN1.34 film exhibits no metallic reflectivity and the interference fringes indicate transparency up to approximately 2.6 eV. The inset in Fig. 3 is a plot of the transmittance spectra of two ZrNx films with x)1.30, they exhibit optical absorption edges at approximately 2.7–3 eV with a transmittance decrease of 20–60% from the visible to the near infrared spectrum region. In the case of ZrNx films with 0.81FxF1.29, which are opaque, the reflectivity measurements were complemented by ellipsometry measurements in the energy range extending from 1.5 to 5.0 eV. These films behaved as semi-infinite samples for ellipsometry, providing directly the complex dielectric function ´(v)s´1q i´2(v) of the bulk film without any contribution from the Si substrate. The real part ´1 of the dielectric function is represented in Fig. 4 as a function of the photon energy for various ZrNx compounds. Following the analysis procedure described in Ref. w11x, the optical properties of the ZrNx films have been examined as a function of chemical composition under the assumption that the films consist of a single, though defective, fcc phase. The dielectric function and reflectivity spectra were fitted simultaneously considering the contributions of intraband and interband transitions described by a Drude term and Lorentz oscillators, respectively:
´Žv.s´`y
v2p v2k q v2qiGp 8 v2kyv2qiGkv k
Fig. 3. Optical reflectivity of ZrNx films with xs0.84, 0.99, 1.16, and 1.33. The inset shows the transmittance spectra of ZrNx with x)1.3.
´` is a background dielectric constant larger than unity approximating the contributions of the higher-energy transitions that are not taken into account in the Lorentz
(1) Fig. 4. The real part of the dielectric function ´1 of typical ZrNx thin films as a function of photon energy.
R. Lamni et al. / Thin Solid Films 447 – 448 (2004) 316–321
319
The variations of the optical properties as a function of the chemical composition of ZrNx can be understood by tracking the changes of the band structure. The band structure of ZrN is similar to the band structure of the equi-electronic compound TiN. Therefore, one will assume that like in TiN the band structure comprises three bands, located between 3 and 8 eV below the Fermi level, which are derived essentially from two 2p nitrogen orbitals and from one d zirconium orbital with e.g. symmetry w12x. This implies a charge transfer of roughly one more p electron to the nitrogen ion. One can then predict that when a nitrogen ion is removed from the stoichiometric ZrN crystal, the charge transfer no longer takes place and the corresponding electron is returned to the Fermi level. Conversely, if a nitrogen
Fig. 5. Typical real part of the dielectric function ´1 and reflectivity R spectra, fitted with the Drude–Lorentz model, for a ZrN0.99 thin film.
terms. The Drude term is characterized by the plasma frequency vp and the damping factor Gp. The plasma frequency vp is related to the effective optical free electron density N* and is given by the expression
N *s
´0mevp2 e2
(2)
where me is the mass of the electron and e is the electron charge. Gp is related to the charge carrier scattering time t by Gps"y t. A typical fit of the real part of the dielectric function ´1("v) and reflectivity R("v) data obtained in the case of nearly ZrN0.99 stoichiometric film is illustrated in Fig. 5. The solid lines are obtained from the Drude– Lorentz approximation over the photon energy range interval 0.5–6.5 eV, while the squares and circles correspond to measured reflectivity and dielectric function data, respectively. Similar good agreement as obtained for the others ZrNx films. The results from the Drude– Lorentz fits are the effective free electron density N*s me N * , determined from the plasma frequency vp (Eq. m (2)), and the free electron relaxation time (Fig. 6). In Fig. 6a one notes that the effective free electron concentration in stoichiometric ZrN is N*s3.70=1022 cmy3 which is close to its cation density, 4.17=1022 cmy3. With increasing x from 1 to 1.19 N* decreases to 2.9=1021 cmy3, while in substoichiometric films, N* increases up to 4.88=1022 cmy3 for ZrN0.81.
Fig. 6. (a) Effective electron density N*, (b) Charge carrier scattering t obtained from optical analyses and grain size determined by XRD for ZrNx thin films as a function of nitrogen content.
320
R. Lamni et al. / Thin Solid Films 447 – 448 (2004) 316–321
metal in which the mean free path of the charge carriers is of the order of the interatomic spacing w13x. 4. Conclusions
Fig. 7. Optical resistivity obtained from optical analyses of ZrNx thin films as a function of nitrogen content.
atom is inserted in an interstitial position, it is likely to bind an extra electron, thereby removing it from the Fermi surface. By a similar reasoning one expects that a zirconium vacancy would deprive the conduction band of two electrons, and that a zirconium interstitial would contribute two more electrons. Accordingly, the carrier concentration N at the Fermi level should vary like N0g(1-x) in ZrNx, where is N0 the free carrier concentration in the stoichiometric compound. For xF1, it can be inferred from the variation of N* (Fig. 6a) that gf1 with m*ymef1, i.e. stoichiometry variations are accommodated by nitrogen vacancies, and for xG1, it can be inferred that gf2 with m*ymef1, i.e. stoichiometry variations are accommodated by zirconium vacancies. The charge carrier scattering time t shown as a function of the concentration x in Fig. 6b also depends strongly on the composition, in particular in the vicinity of xs1. In this composition range a strong correlation is noted between the charge carrier scattering time t and the grain size deduced from the width of the X-ray diffraction lines. It appears that the ZrN crystalline structure does not tolerate more than approximately 3% of vacancies. This strong correlation indicates that lattice defects are responsible for the short scattering time. The d.c.-resistivity which can be extracted from the optical properties as roptsme y(N*t e 2) is rapidly larger than 100 mV=cm (See Fig. 7), indicating that non-stoichiometric ZrNx can be described as a dirty metal, i.e. a
The optical properties of zirconium nitride ZrNx films have been investigated as a function of the nitrogen content in a wide chemical composition range (0.81FxF1.35). The dielectric function, deduced from spectroscopic ellipsometry, and the optical reflectivity are characterized by a composition–dependent screened plasma energy "vsp and reflectivity minimum "vmin energy at photons energies proportional to the corresponding plasma energies "vp. In order to separate contributions due to free carriers and to interband transitions, the dielectric function, obtained from spectroscopic ellipsometry and the near normal reflectivity measurements were modeled by a set of Drude–Lorentz oscillators. The free carrier concentration decreases steadily with increasing nitrogen content The linear relationships between x and N* or v2p observed in the range of 0.8FxF1 and 1F1.3 can be used as an estimate of the chemical composition of these films. Using a defect model based on the band structure we show that two different regimes are associated to the stoichiometry-related defects, namely nitrogen vacancies in substoichiometric samples, and metal vacancies in Nrich ZrNx compounds. Acknowledgments This work was supported by the Fonds National Suisse de la Recherche Scientifique. Particular thanks are due to Dr Francois Bussy at the Universite´ de ¸ Lausanne for the electron probe microanalysis measurements and to H. Jotterand for his technical help. References w1x J.-E. Sundgren, et al., Thin Solid Films 105 (1983) 367. w2x U. Beck, G. Reiners, I. Urban, H.A. Jehn, U. Kopacz, H. Schack, Surf. Coat. Technol. 61 (1993) 215. w3x L.E. Toth, Transition Metal Carbides and Nitrides, Academic Press, New York, 1971. w4x L. Pichon, T. Girardeau, A. Straboni, F. Lignou, J. Perriere, ´ ´ J.M. Frigerio, Nucl. Instr. Meth. Phys. Res. B 147 (1999) 378–382. w5x B.O. Johansson, H.T.G. Hentzell, J.M.E. Harper, J.J. Cuomo, J. Mater. Res. 1 (1986) 442. w6x M. Yoshitake, T. Yotsuya, S. Ogawa, Jpn. J. Appl. Phys. 31 (1992) 4002. w7x M. Lerch, E. Fuglein, J. Wrba, Z. Anorg, Allg. Chem. 622 (1996) 972. w8x L. Pichon, T. Girardeau, A. Straboni, F. Lignou, Ph. Gerin, ´ J. ` Appl. Surf. Sci. 150 (1999) 115. Perriere, w9x M. Veszeilei, K. Andersson, C.G. Ribbing, K. Jarrendahl, ¨ h. Arwin, Appl. Opt. 33 (1994) 1993–2001.
R. Lamni et al. / Thin Solid Films 447 – 448 (2004) 316–321 w10x H.M. Benia, M. Guemmaz, G. Schmerber, A. Mosser, J.-C. Parlebas, Appl. Surf. Sci. 200 (2002) 231. w11x P.E. Schimd, M.S. Sunaga, F. Levy, ´ J. Vac. Sci. Technol. A 16 (5) (1998) 2870.
321
w12x A. Delin, O. Eriksson, R. Ahuja, B. Johansson, Phys. Rev. B 54 (1996) 1673. w13x J.H. Mooij, Phys. Status Solidi A17 (1973) 521.
Optical and electronic properties of magnetron sputtered ZrNx thin films ´ P.E. Schmid, F. Levy ´ R. Lamni*, E. Martinez, S.G. Springer, R. Sanjines, ` Complexe, FSB-EPFL, Lausanne CH-1015, Switzerland Institut de Physique de la Matiere
Abstract The optical properties of sputtered ZrNx films with 0.81FxF1.35 have been investigated and interpreted in terms of stoichiometry-related defects and crystal structure. The optical properties were determined by optical reflectivity, transmission and spectroscopic ellipsometry. As x increases from 0.81 to 1.35, the optical properties continuously change from metallic to semiconducting behavior. The experimental results have been fitted with a model dielectric function based on a set of Drude– Lorentz oscillators in order to separate the contributions due to free carriers and interband transitions. The effective density N* of conduction electrons decreases from N*s4.9=1022 cmy3 to N*s2.9=1021 cmy3 as x is increased from 0.81 to 1.29. The charge carrier scattering time increases from 4.9=10y16 to 2.6=10y15 s for 0.81-xF0.98, and decreases from 2.6=10y15 to 3.3=10y16 s for 0.98-xF1.29. The ZrNx films with x)1.3 are poorly crystallized. In this composition range, the compounds exhibit a crystal structure close to orthorhombic Zr3 N4 ; they are insulating with optical absorption coefficients in the range of 2=104 cmy1 below 2 eV and an optical absorption onset at 2.3 eV. 䊚 2003 Elsevier B.V. All rights reserved. Keywords: ZrNx films; Optical properties; Magnetron sputtering
1. Introduction Transition metal nitride coatings, mainly based on titanium, chromium and zirconium, are used as protective coatings against wear and corrosion w1x. Furthermore, they are widely used as optical and decorative coatings w2x. Zirconium nitrides exhibit very interesting properties such as high hardness, high melting point, high corrosion resistance w3x. Their optical and mechanical properties intensively depend on the nitrogen composition w4–6x. The stoichiometric nitride ZrN is metallic-like with a gold, yellow color; it is the thermodynamically stable phase. On the contrary, the Zr3N4 compound is a metastable phase; it is insulating and almost transparent w6x. In this article, we present an experimental study of the optical properties of sputtered ZrNx films. The ZrNx films were deposited by reactive magnetron sputtering in a wide range of chemical composition (0.81xF1.35). The dielectric function obtained from spectroscopic ellipsometry and normal reflectivity measurements were modeled as the response of a set of *Corresponding author. Tel.: q41-21-693-4144; fax: q41-21-6934666. E-mail address: [email protected] (R. Lamni).
adjustable Drude–Lorentz oscillators. In the present study the free carrier response and the free-carrier relaxation time have been determined with a minimum of assumptions. The variations of the optical parameters are discussed with the help of band structure calculations reported for fcc ZrN, and related defects such as nitrogen vacancies andyor interstitials and zirconium vacancies. 2. Experimental ZrNx films, approximately 1000 nm in thickness, have been deposited by reactive r.f. magnetron sputtering in an high vacuum reactor. The residual pressure was approximately 10y5 Pa before the introduction of the sputtering gases, namely argon and nitrogen. Discs (50 mm in diameter) of 99.99% pure zirconium were used as target material. The r.f. discharge power was kept constant at 100 W, and the target–substrate distance fixed at 100 mm. In order to ensure a uniform deposit, the substrate was rotated. The total pressure was kept constant at 0.4 Pa. The nitrogen partial pressure was adjusted in the range 3 to 75% of the total pressure, in order to deposit films with different nitrogen compositions. The substrate temperature was kept constant at 373"20 K during the deposition. Different substrates
0040-6090/04/$ - see front matter 䊚 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0040-6090Ž03.01109-X
R. Lamni et al. / Thin Solid Films 447 – 448 (2004) 316–321
317
such as silicon and quartz wafers have been used. The layer thickness was measured by profilometry. The crystallographic phases were analyzed by X-ray diffraction (XRD) using monochromatized Cu Ka radiation at a grazing incidence of 48. The sin2C method was applied to determine the stress and the stress-free lattice parameters. Electron probe microanalysis (EPMA) was used to determine the chemical composition. The measurements were performed at 8 kV (accelerating voltage) and 100 nA (beam current) for typical 1000 nm thick films, limiting the penetration depth of the electron beam to less than 35% of the film thickness. A RuO2 single crystal, and CrN and Zr thin films served as standards. The precision of the results is within "1% at. The optical constant of the films were investigated by spectroscopic ellipsometry in the 1.5–5.0 eV photon energy range. The optical reflectivity was measured at near normal incidence from 200 to 2700 nm with a Cary 2400 spectrophotometer. An evaporated aluminum mirror film was used as a reference. 3. Results and discussion 3.1. Structure and morphology The X-ray diffraction patterns of selected ZrNx films are shown in Fig. 1. In the 0.81FxF1.19 chemical composition range, all the films are well crystallized in the fcc ZrN structure. In contrast, for 1.20FxF1.35 the X-ray diffraction patterns change significantly. With increasing x the (200) reflection broadens and decreases in intensity; new broad reflection peaks appear near the (111) and (311) reflections. These trends indicate that an important modification of the fcc NaCl-type structure occurs when the N content is increased beyond xs1.2. For x)1.3, the broad reflection peaks lay close to the positions of the (320) and (042) peaks reported for the orthorhombic Zr3N4 phase w7,8x indicating that the structure of these films is a poorly crystallized, distorted structure of the Zr3N4 phase. Fig. 2 shows the lattice parameter a111 calculated from the (111) reflection, as well as the stress-free lattice parameter a0 obtained from the (200) reflection, as a function of the nitrogen content. Below xs1.2, both a111 and a0 increase monotonously with increasing x, above xs1.2 a111 increases rapidly. The a0 increases from a0s0.457 nm for xs0.92 to a0s0.459 nm for xs1.09. Stoichiometric ZrN has not been obtained in the present work, however, the interpolated lattice parameter for xs1 is a0s0.458 nm, which compares well with the reported bulk value of aB0 s0.4577 nm. While nitrogen vacancies are generally accepted to be dominant defect in substoichiometric ZrNx films, the exact crystal structure of the overstoichiometric ZrNx films is not well known yet, in particular in films with x values higher than 1.2. As pointed out by Johansson
Fig. 1. X-Ray diffraction patterns of ZrNx films at different x. The Xray diffraction was performed in a 48 grazing incidence geometry.
et al. w5x, at low nitrogen content (x-1.2) the excess nitrogen can preferentially occupy interstitial positions leading to a monotonous increase of the lattice parameter. In the compositional range 1.20FxF1.30, the increase of the a111 parameter is steeper, nevertheless Zr vacancies may possibly be created, leading to a highly defective and poorly crystallized fcc structure. In addition, as the XRD data for xs1.27 suggest (Fig. 1), the ZrNx films should consist of a mixture of defect-rich, fcc ZrN and poorly crystallized Zr3N4. 3.2. Optical properties The reflectivity spectra of a selected set of films are shown in Fig. 3. The highest reflectivity at low photon energy is achieved by the nearly stoichiometric ZrN0.99 sample. Note that this sample exhibits a minimum reflectivity value of 0.10 located at "vmins3.5 eV. The minimum ZrN0.84 reflectivity is 0.18, and occurs at "vs3.94 eV, while that of ZrN1.16 is 0.2 and is shifted to lower energies: "vs2.67 eV. These results agree well with previously reported Rmin values ranging from 0.10 to 0.16 at photon energies between 3.5 and 4.0 eV
318
R. Lamni et al. / Thin Solid Films 447 – 448 (2004) 316–321
Fig. 2. Relative lattice expansion in ZrNx thin films. The stress-free lattice parameters are calculated using the sin2C method.
w9,10x. The reflectivity spectrum of the ZrN1.34 film exhibits no metallic reflectivity and the interference fringes indicate transparency up to approximately 2.6 eV. The inset in Fig. 3 is a plot of the transmittance spectra of two ZrNx films with x)1.30, they exhibit optical absorption edges at approximately 2.7–3 eV with a transmittance decrease of 20–60% from the visible to the near infrared spectrum region. In the case of ZrNx films with 0.81FxF1.29, which are opaque, the reflectivity measurements were complemented by ellipsometry measurements in the energy range extending from 1.5 to 5.0 eV. These films behaved as semi-infinite samples for ellipsometry, providing directly the complex dielectric function ´(v)s´1q i´2(v) of the bulk film without any contribution from the Si substrate. The real part ´1 of the dielectric function is represented in Fig. 4 as a function of the photon energy for various ZrNx compounds. Following the analysis procedure described in Ref. w11x, the optical properties of the ZrNx films have been examined as a function of chemical composition under the assumption that the films consist of a single, though defective, fcc phase. The dielectric function and reflectivity spectra were fitted simultaneously considering the contributions of intraband and interband transitions described by a Drude term and Lorentz oscillators, respectively:
´Žv.s´`y
v2p v2k q v2qiGp 8 v2kyv2qiGkv k
Fig. 3. Optical reflectivity of ZrNx films with xs0.84, 0.99, 1.16, and 1.33. The inset shows the transmittance spectra of ZrNx with x)1.3.
´` is a background dielectric constant larger than unity approximating the contributions of the higher-energy transitions that are not taken into account in the Lorentz
(1) Fig. 4. The real part of the dielectric function ´1 of typical ZrNx thin films as a function of photon energy.
R. Lamni et al. / Thin Solid Films 447 – 448 (2004) 316–321
319
The variations of the optical properties as a function of the chemical composition of ZrNx can be understood by tracking the changes of the band structure. The band structure of ZrN is similar to the band structure of the equi-electronic compound TiN. Therefore, one will assume that like in TiN the band structure comprises three bands, located between 3 and 8 eV below the Fermi level, which are derived essentially from two 2p nitrogen orbitals and from one d zirconium orbital with e.g. symmetry w12x. This implies a charge transfer of roughly one more p electron to the nitrogen ion. One can then predict that when a nitrogen ion is removed from the stoichiometric ZrN crystal, the charge transfer no longer takes place and the corresponding electron is returned to the Fermi level. Conversely, if a nitrogen
Fig. 5. Typical real part of the dielectric function ´1 and reflectivity R spectra, fitted with the Drude–Lorentz model, for a ZrN0.99 thin film.
terms. The Drude term is characterized by the plasma frequency vp and the damping factor Gp. The plasma frequency vp is related to the effective optical free electron density N* and is given by the expression
N *s
´0mevp2 e2
(2)
where me is the mass of the electron and e is the electron charge. Gp is related to the charge carrier scattering time t by Gps"y t. A typical fit of the real part of the dielectric function ´1("v) and reflectivity R("v) data obtained in the case of nearly ZrN0.99 stoichiometric film is illustrated in Fig. 5. The solid lines are obtained from the Drude– Lorentz approximation over the photon energy range interval 0.5–6.5 eV, while the squares and circles correspond to measured reflectivity and dielectric function data, respectively. Similar good agreement as obtained for the others ZrNx films. The results from the Drude– Lorentz fits are the effective free electron density N*s me N * , determined from the plasma frequency vp (Eq. m (2)), and the free electron relaxation time (Fig. 6). In Fig. 6a one notes that the effective free electron concentration in stoichiometric ZrN is N*s3.70=1022 cmy3 which is close to its cation density, 4.17=1022 cmy3. With increasing x from 1 to 1.19 N* decreases to 2.9=1021 cmy3, while in substoichiometric films, N* increases up to 4.88=1022 cmy3 for ZrN0.81.
Fig. 6. (a) Effective electron density N*, (b) Charge carrier scattering t obtained from optical analyses and grain size determined by XRD for ZrNx thin films as a function of nitrogen content.
320
R. Lamni et al. / Thin Solid Films 447 – 448 (2004) 316–321
metal in which the mean free path of the charge carriers is of the order of the interatomic spacing w13x. 4. Conclusions
Fig. 7. Optical resistivity obtained from optical analyses of ZrNx thin films as a function of nitrogen content.
atom is inserted in an interstitial position, it is likely to bind an extra electron, thereby removing it from the Fermi surface. By a similar reasoning one expects that a zirconium vacancy would deprive the conduction band of two electrons, and that a zirconium interstitial would contribute two more electrons. Accordingly, the carrier concentration N at the Fermi level should vary like N0g(1-x) in ZrNx, where is N0 the free carrier concentration in the stoichiometric compound. For xF1, it can be inferred from the variation of N* (Fig. 6a) that gf1 with m*ymef1, i.e. stoichiometry variations are accommodated by nitrogen vacancies, and for xG1, it can be inferred that gf2 with m*ymef1, i.e. stoichiometry variations are accommodated by zirconium vacancies. The charge carrier scattering time t shown as a function of the concentration x in Fig. 6b also depends strongly on the composition, in particular in the vicinity of xs1. In this composition range a strong correlation is noted between the charge carrier scattering time t and the grain size deduced from the width of the X-ray diffraction lines. It appears that the ZrN crystalline structure does not tolerate more than approximately 3% of vacancies. This strong correlation indicates that lattice defects are responsible for the short scattering time. The d.c.-resistivity which can be extracted from the optical properties as roptsme y(N*t e 2) is rapidly larger than 100 mV=cm (See Fig. 7), indicating that non-stoichiometric ZrNx can be described as a dirty metal, i.e. a
The optical properties of zirconium nitride ZrNx films have been investigated as a function of the nitrogen content in a wide chemical composition range (0.81FxF1.35). The dielectric function, deduced from spectroscopic ellipsometry, and the optical reflectivity are characterized by a composition–dependent screened plasma energy "vsp and reflectivity minimum "vmin energy at photons energies proportional to the corresponding plasma energies "vp. In order to separate contributions due to free carriers and to interband transitions, the dielectric function, obtained from spectroscopic ellipsometry and the near normal reflectivity measurements were modeled by a set of Drude–Lorentz oscillators. The free carrier concentration decreases steadily with increasing nitrogen content The linear relationships between x and N* or v2p observed in the range of 0.8FxF1 and 1F1.3 can be used as an estimate of the chemical composition of these films. Using a defect model based on the band structure we show that two different regimes are associated to the stoichiometry-related defects, namely nitrogen vacancies in substoichiometric samples, and metal vacancies in Nrich ZrNx compounds. Acknowledgments This work was supported by the Fonds National Suisse de la Recherche Scientifique. Particular thanks are due to Dr Francois Bussy at the Universite´ de ¸ Lausanne for the electron probe microanalysis measurements and to H. Jotterand for his technical help. References w1x J.-E. Sundgren, et al., Thin Solid Films 105 (1983) 367. w2x U. Beck, G. Reiners, I. Urban, H.A. Jehn, U. Kopacz, H. Schack, Surf. Coat. Technol. 61 (1993) 215. w3x L.E. Toth, Transition Metal Carbides and Nitrides, Academic Press, New York, 1971. w4x L. Pichon, T. Girardeau, A. Straboni, F. Lignou, J. Perriere, ´ ´ J.M. Frigerio, Nucl. Instr. Meth. Phys. Res. B 147 (1999) 378–382. w5x B.O. Johansson, H.T.G. Hentzell, J.M.E. Harper, J.J. Cuomo, J. Mater. Res. 1 (1986) 442. w6x M. Yoshitake, T. Yotsuya, S. Ogawa, Jpn. J. Appl. Phys. 31 (1992) 4002. w7x M. Lerch, E. Fuglein, J. Wrba, Z. Anorg, Allg. Chem. 622 (1996) 972. w8x L. Pichon, T. Girardeau, A. Straboni, F. Lignou, Ph. Gerin, ´ J. ` Appl. Surf. Sci. 150 (1999) 115. Perriere, w9x M. Veszeilei, K. Andersson, C.G. Ribbing, K. Jarrendahl, ¨ h. Arwin, Appl. Opt. 33 (1994) 1993–2001.
R. Lamni et al. / Thin Solid Films 447 – 448 (2004) 316–321 w10x H.M. Benia, M. Guemmaz, G. Schmerber, A. Mosser, J.-C. Parlebas, Appl. Surf. Sci. 200 (2002) 231. w11x P.E. Schimd, M.S. Sunaga, F. Levy, ´ J. Vac. Sci. Technol. A 16 (5) (1998) 2870.
321
w12x A. Delin, O. Eriksson, R. Ahuja, B. Johansson, Phys. Rev. B 54 (1996) 1673. w13x J.H. Mooij, Phys. Status Solidi A17 (1973) 521.