- Email: [email protected]
Investigation of elastic and optical properties of electron beam evaporated ZrO2–MgO composite thin films
Thin Solid Films 537 (2013) 163–170
Contents lists available at SciVerse ScienceDirect
Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Investigation of elastic and optical properties of electron beam evaporated ZrO2–MgO composite thin films S. Jena, R.B. Tokas ⁎, N. Kamble, S. Thakur, D. Bhattacharyya, N.K. Sahoo Applied Spectroscopy Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India
a r t i c l e
i n f o
Article history: Received 9 August 2012 Received in revised form 12 April 2013 Accepted 12 April 2013 Available online 25 April 2013 Keywords: ZrO2–MgO composite Atomic force acoustic microscopy Refractive index Grazing incidence X-ray reflectivity Indentation modulus
a b s t r a c t Thin films of composite materials are being progressively explored for achieving tunability in the optical constants for application in multilayer optical devices. In the present study, a set of ZrO2–MgO binary mixed composite thin films have been prepared by reactive electron beam evaporation of solid solution of ZrO2 and MgO at different oxygen partial pressures. Since elastic properties of the thin films are very important for their environmental stability under high power laser application, elastic moduli (indentation moduli) of the films have been measured by atomic force acoustic microscopy measurements. The optical properties especially refractive index of such films has been determined from the optical transmission measurement using an inverse synthesis method, while the density of such films has been measured by grazing incidence X-ray reflectivity. The variation of the elastic moduli of the thin films as a function of oxygen partial pressure used during deposition has been studied and the above variation has been corroborated with the variation of density and refractive index of the thin films. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Design and development of optical thin film multilayer devices are constrained by the optical constants such as refractive index, absorption coefficient, band gap etc. of available coating materials. To achieve design targets, often one has to use very large number of thin dielectric layers using the existing conventional materials that leads to complexity in deposition and often compromises its spectral performance and durability [1,2]. Hence it is necessary to find materials as well as methodologies which can yield desired refractive index values for developing precision optical devices with desired characteristics. In recent years, mixed composite oxide materials like SiO2–Al2O3, ZrO2–Ta2O5, ZrO2–TiO2, ZrO2–Al2O3, TiO2–Al2O3, ZrO2–MgO, ZrO2–SiO2, HfO2–SiO2, Gd2O3–SiO2 etc., which are mixtures of two different materials having different optical and structural properties compared to its constituent material, have been used to fulfill the gap of desired refractive index values [2–7] by using different coating methods such as sol–gel process, reactive electronbeam deposition, laser ablation, ion-beam sputtering and chemical vapor deposition. Such coatings have found in diversified fields of application such as optical interference multilayers, optical wave guides, rugate filters, narrow band filters, broadband antireflection coatings etc. [8]. ZrO2–MgO is one of the specific solid-solution based mixed composite oxide materials, which has been evolved as a promising coating ⁎ Corresponding author. Tel.: +91 22 25590341; fax: +91 22 25505151. E-mail address: [email protected] (R.B. Tokas). 0040-6090/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tsf.2013.04.046
material to develop various types of optical devices such as high reflectivity mirror, edge filters, beam splitters etc., because of its suitable optical properties like transparent spectral range from near-infrared to the ultraviolet, high refractive index and better laser induced damaged threshold [9]. The better optical performance with high stability of the films needs optimization of their mechanical properties (such as low stress and high hardness, scratch, abrasion and wear resistance and better adhesion) also together with their microstructural characteristics and other functional properties for long-term environmental stability [10]. The importance of mechanical properties of thin films is primarily in their relation to coating stability i.e. the extent to which optical thin films coating will continue to behave as they did when removed from the coating chamber, even when subjected to disturbances of an environmental and/or mechanical nature [11]. There are many factors which are responsible for mechanical stability of the optical thin films. One of the important factors is local indentation modulus, which strongly affects the residual stress (thermal stress) generated in thin films. This elastic property of thin films differs significantly from those of the bulk materials due to the interfaces, microstructure, and the underlying substrates and is also affected by the process parameters and the deposition technique like structural and optical properties [12]. Many techniques are being used for the determination of elastic modulus of thin films such as micro- and nano-indentation tests [13], laser induced surface acoustic wave [14], surface Brillouin light scattering measurements [15] and atomic force acoustic microscopy (AFAM) [16]. Out of all the techniques, AFAM technique is capable of giving both quantitative values of elastic modulus (indentation modulus for anisotropic films) like other techniques as well as qualitative picture
164
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
of elastic modulus in terms of acoustic image simultaneously with surface topography of thin film sample; and also capable of giving quantitative mapping of surface elastic modulus by bidimensional reconstruction of the local elastic modulus of sample surface at nanoscale using AFAM two contact resonance frequency imaging technique [17–20]. This makes AFAM, a unique tool for the local investigation of the sample surface elastic properties. So, the main objective of the present study is to determine quantitatively, the indentation modulus (M) of such thin films using this promising technique. The objective also includes the investigation of the dependence of the indentation modulus on the oxygen partial pressure and to establish a correlation between the micro structural, optical and elastic properties of such thin films. 2. Experimental details 2.1. Sample preparation and characterization techniques A several set of such thin films on silicon (111) and quartz substrates were prepared by evaporating ZrO2–MgO solid solution composite material using electron-beam evaporation in a fully automatic vacuum system VERA-902. The total pressure inside the vacuum system and the real-time deposition rate were controlled using MKS mass flow controllers and Inficon's XTC/2 Quartz crystal monitors respectively. The deposition rate of 5 Å/s and the substrate temperature of 350 °C were maintained during deposition of all the samples, while the oxygen pressure was varied from without oxygen pressure to 8 × 10 −4 mbar. The details of the samples prepared along with their thickness as measured by in-situ thickness monitors are shown in Table 1. A commercial Solver P47H, NT-MDT, Russia make atomic force microscopy (AFM) system with AFAM mode is used for the quantitative analysis of elastic modulus/indentation modulus of the thin films. The schematic of AFAM set-up is presented in Fig. 1. The sample is placed on an ultrasonic transducer instead of the sample holder of a standard AFM set-up. The transducer driven by a waveform generator emits longitudinal waves, causing out-of-plane surface vibrations in the sample. These vibrations are coupled to the AFM cantilever by making contact of the AFM tip with the sample surface. The amplitude of the cantilever vibrations is detected by AFM photodiode using a lock-in-amplifier. The cantilever vibration is recorded together with the corresponding ultrasonic frequency to obtain the contact-resonance spectrum. These contact resonance spectra have been used to calculate the indentation modulus of the films. The optical transmission spectra of the films were measured using a UV–VIS-NIR spectrophotometer (UV-3101PC, SHIMADZU) at room temperature in the range 190–1200 nm for determination of refractive index of the films. The relative uncertainty in the transmittance is 0.3%. In the measurement air was used as a reference. Densities of the films have been estimated by grazing incidence X-ray reflectivity (GIXR) measurements carried out in an X-ray reflectometer (SOPRA, France). The measurements have been carried out with Cu Kα (1.54 Å) source with grazing angle of incidence in the range of 0–0.6° and with an angular resolution of 0.01°. Rocking curve measurements have been done prior to each measurement for alignment the sample.
2.2. Determination of elastic modulus of the films The elastic/indentation modulus of the thin films has been determined by modeling the AFM cantilevers tip–film surface interaction in terms of surface-coupled cantilever vibration [21]. Under suitable approximation (assuming linear forces and sufficiently small vibration amplitude of the cantilever ~ 0.1 nm), the tip–film interaction can be approximated by vertical and lateral spring-dashpot systems [22] as shown in Fig. 2(a), where θ0 is the angle between the cantilever and sample surface, while klat⁎, k*, γlat and γ are the lateral and vertical contact stiffness and damping constants, respectively. The total length of the cantilever is L = L1 + L′ and the tip base is located at L1 with L′ = L − L1. It has been found that the k⁎ value depends mostly on the sensor tip position L1 than on the other parameters such as θ0, klat⁎, γlat and γ [23]. Neglecting all these parameters and considering the mass of the tip to be very small compared to the cantilever mass, the tip-sample coupled system reduces to the simplified system as shown in Fig. 2(b). The characteristic equation for the above simplified system is [24,25] 2
3 3 kc ðkn LrÞ ð1 þ coskn L coshkn LÞ 3 fðsinhkn Lr coskn Lr− coshkn Lr sinkn LrÞð1 þ coskn Lð1−r Þ coshk n Lð1−r ÞÞg 4 5 ð coshkn Lð1−rÞ sinkn Lð1−r Þ− sinhkn Lð1−r Þ coskn Lð1−r ÞÞ þ ð1− coskn Lr coshkn LrÞ
k ¼2
ð1Þ with qffiffiffiffiffi kn L ¼ cB L f n
ð2Þ
and cB ¼
rffiffiffiffiffiffi pffiffiffiffiffiffi 4 ρA 2π EI
ð3Þ
where r = L1 / L, cB is a characteristic cantilever constant, ρ is the mass density of the cantilever material, fn is the nth eigenmode mode resonance frequency of the cantilever, kc is the spring constant or stiffness of the rectangular cantilever and k⁎ is the contact stiffness of the tip-sample assembly. The spring constant (kc) of the free cantilever is determined using normal Sader method [26,27]. The evaluation of spring constant is very accurate, as the quality factor of the cantilever is very high (Q > 300). It is worthwhile to note that any uncertainty in kc does not affect the calculated values of reduced Young's modulus as confirmed by the Eq. (7) but only the determination of the normal static load FN by the cantilever on the sample surface [25]. By measuring the free resonant frequency of the cantilever and substituting the measured values in Eq. (2), cBL value for each individual cantilever is determined with high precision and without any knowledge of any additional cantilever data. The knL values for the surface coupled cantilevers are then determined by substituting the value of cBL as determined above and the measured contact resonant frequencies of the cantilever in contact with the film surface in Eq. (2). Experimentally, the value of k* and L1 can be determined by using the fact that, the contact stiffness k⁎ must be the same for all
Table 1 Density and refractive index of ZrO2–MgO thin films. Sample
Oxygen partial pressure (mbar)
Thickness measured in-situ (nm)
Thickness derived from transmission spectra (nm)
Density (g ml−1)
Refractive index @ 550 nm
ZrM-2 ZrM-3 ZrM-4 ZrM-5 ZrM-6
0 0.6x10−4 1x10−4 4x10−4 8x10−4
510 425 511 635 750
529 435 521 680 783
4.6 4.6 4.4 3.7 2.5
1.93 1.96 1.95 1.79 1.76
± ± ± ± ±
5 4 5 6 8
± ± ± ± ±
0.4 0.2 0.3 0.7 1.5
± ± ± ± ±
0.1 0.1 0.1 0.1 0.1
± ± ± ± ±
0.01 0.01 0.01 0.01 0.01
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
165
Fig. 1. Schematic of AFAM set up.
cantilever eigenmode (f1, f2, f3……) at constant applied normal load. This leads to the conditional equation [17,18]
k ðf 1 ; rÞ ¼ k ðf 2 ; r Þ:
ð4Þ
The solution of the Eq. (4) is found numerically by assuming a small range of values for L1, the range being found by using an optical microscope or a scanning electron microscope. First two contact
eigenmode frequencies are measured and the contact stiffness k⁎ obtained from Eq. (1) is plotted as a function of r = L1 / L for the two modes and the point of intersection of the 1st and 2nd resonance curves corresponds to the solution of L1/L and contact stiffness k⁎. The contact stiffness k⁎ obtained from the AFAM measurement can be related to the elastic modulus of the probed material by Hertzian theory of contact mechanics [28]. According to this theory, when a hemispherical tip of radius R (AFM cantilever tip) indents a flat surface with a normal static load FN, then the resulting contact stiffness k⁎can be calculated as
k ¼ 2aE ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 6E2 RF N
ð5Þ
Here a is the contact radius and E⁎ is the reduced Young's modulus, defined as 1 1 1 ¼ þ E M S M t
ð6Þ
Where, MS and Mt are the indentation moduli of the sample and tip, respectively. The left equality in Eq. (5) is true for all geometries while the right equality of the equation can be used only for tips with hemispherical geometry [25,29]. The indentation modulus MS of the sample can only be calculated after determining the contact area or tip geometry, which is very difficult to determine experimentally. Hence this can be avoided only by comparing the value of k⁎obtained for the unknown sample to that of a reference sample with known elastic properties [25,29]:
ES ¼ Eref
Fig. 2. (a): General case for a tip–sample interaction including lateral and vertical tip–sample interaction forces. (b): Simplified case for a tip–sample interaction.
ks kref
n :
ð7Þ
The subscripts s and ref corresponds to the unknown sample and reference sample, respectively. The value of n depends on tip-sample geometry. For a spherical tip, n = 3/2; while for a tip shaped like a flat punch, n = 1. Now the indentation modulus of the sample MS can be calculated from Eqs. (6) and (7). For isotropic samples, Young's modulus (Es) is evaluated from the indentation modulus MS, through Es the relation Ms ¼ 1−ν 2 , where v is the Poisson's ratio. Since the Poisson's ratio of the thin films under present study is unknown and can vary with density of the films, therefore direct indentation modulus of these films is calculated and reported.
166
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
2.3. Determination of refractive index of the films The refractive index of the films has been determined by fitting the measured optical transmission spectra with theoretically generated spectra using a suitable optical dispersion model. The transmission of a single layer film on a substrate can be expressed as follows [30]: T ðλ; n; x; t; no ; xo Þ ¼ P=Q
ð8Þ
where P ¼ ð1 R1 Þ ð1 R2 Þ ð1 R3 Þ xxo
ð8aÞ
2 2 2 2 2 Q ¼ 1 þ R1 R2 x −R1 R3 x xo −R2 R3 xo þ 2r 1 r 2 1−R3 xo x cosφ
8ðbÞ
2
2
2
R 1 ¼ r 1 ; R2 ¼ r 2 ; R3 ¼ r 3
ð8cÞ
1−n n−no n −1 ;r ¼ ;r ¼ o 1 þ n 2 n þ no 3 no þ 1
ð8dÞ
α ¼
0 0 0 4πk 4πko −α t −α o t o ;x ¼ e ; xo ¼ e ;α o ¼ λ λ
ð8eÞ
φ¼
4πnt λ
ð8fÞ
r1 ¼ 0
Where t & to are the thicknesses of the film and substrate respectively. The n, k and no, ko are the refractive indices and the extinction coefficients of the film and substrate respectively. R1, R2 and R3 are the reflectivity for air–film, film–substrate, and substrate–air interface respectively. Using the above mentioned relation and assuming a suitable dispersion model, the fitting has been carried out by minimizing the squared difference (χ 2) between the experimentally measured and calculated values of transmission given by: 2
χ ¼
1 N Exp Cal 2 ∑i¼1 T i −T i ð2N−P Þ
ð9Þ
where TiExp and TiCal are the experimental and theoretical transmittances respectively. N is the number of data points, P is the number of model parameters and the minimization has been done using the Levenberg–Marquardt algorithm. 2.4. Determination of density of the films The densities of such films have been determined by measuring the X-ray reflectivity spectra of the samples at grazing angle of incidence. The complex refractive index (η) of an element in the X-ray region is given by [31]: η ¼ 1−δ−iβ
ð10Þ
where, δ¼
n
o 2 r O λ =2 π N A ðρZ=AW Þ
ð11Þ
and β ¼ ðμλ=4πÞ
ð12Þ
where, ro is the classical electron radius (2.82 x 10–13 cm), NA is the Avogadro number, ρ is the density, Z is the atomic number and Aw is the atomic weight of the element and μ is the linear absorption coefficient of the material at the particular wavelength λ. The quantity, [NA (ρ Z / Aw)], actually gives the number of electrons per cm 3 of the particular element. Since refractive index of all materials in hard X-ray region is less than 1, X-ray suffers total external reflection at an extreme grazing angle of incidence from any surface. However,
as the grazing angle of incidence value (θ) exceeds the critical angle (θc), X-ray starts to penetrate inside the layer and reflectivity starts to fall off rapidly. The critical angle is approximately given by the following expression: θC ¼ √ð2δÞ
ð13Þ
and depends on the electron density of the material apart from the wavelength of X-ray. The reflectivity of X-ray from a thin film i.e., of a plane boundary between two media can be obtained using the well known Fresnel's boundary conditions of continuity of the tangential components of the electric field vector and its derivative at the sharp interface [32]. However, the Fresnel's reflectivity gets modified for a rough surface by a ‘Debye–Waller-like’ factor as follows:
2 2 RO ¼ Rp exp −q σ =2
ð14Þ
where, q is the momentum transfer factor (4π sinθ / λ), RO is the reflectivity of the rough surface and Rp is the reflectivity of an otherwise identical smooth surface and σ is the RMS roughness of the surface. Thus by fitting the X-ray reflectivity spectrum of the surface of a sample near its critical angle, accurate estimation regarding the density ρ and RMS surface roughness σ can be made quite accurately. The theoretical simulation and fitting of the GIXR spectra have been carried out using the “IMD” code under the “XOP” software package [33] and the best fits are achieved by minimizing the χ 2value. It should be noted here that the AFAM measurements have been carried out on films deposited on c-Si substrates while the optical measurements have been carried out on films deposited on quartz substrates prepared in the same run i.e., under identical deposition condition. GIXR measurements have been carried out on all the films deposited on both quartz and c-Si substrate probing mass density of these films. Further, the films considered under present study are amorphous or weakly polycrystalline in nature. For such films, the natures of substrate (i.e., Si or Quartz) are observed not to have any significant influence on the film properties as reflected in the GIXR experiments. 3. Results and discussion Indentation modulus of ZrO2–MgO binary thin films deposited at varying oxygen partial pressure has been estimated by performing AFAM measurements using DLC coated Si cantilever probes. DLC coated Si tips have been chosen for their better hardness and stability in tip geometry with indentation modulus of 590 ± 20 GPa. We have employed two DLC cantilevers because of inability of a single cantilever to perform the measurement over all the samples. The spring constants or force constants of the cantilevers are kc = 6 N/m (tip1) and 6.15 N/m (tip2). Indentation moduli of the samples ZrM-3, ZrM-4 & ZrM-5 prepared at different oxygen partial pressures ranging from 0.6 × 10−4 to 4 × 10−4 mbar have been determined from the contact resonant spectra using tip1, while tip2 has been employed for ZrM-2 and ZrM-6 thin films prepared at two extreme oxygen partial pressure of zero pressure (ambient atmosphere) and 8 × 10−4 mbar, respectively. The contact-resonance spectra for Si (111) reference sample and the samples of such thin films have been measured for the 1st and 2nd flexural modes. For each sample, the contact-resonance frequencies were measured for four different static normal loads FN = 450, 500, 550 and 600 nN. Fig. 3(a) and (b) shows respectively the 1st and 2nd experimental contact-resonant spectra for Si (111) reference sample, while Fig. 4(a) and (b) shows respectively the 1st and 2nd contact-resonant spectra for a representative (ZrM-4) prepared at oxygen pressure of 1 × 10 − 4 mbar. This spectra shows that both the resonance frequencies and the amplitudes increase with
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
Fig. 3. (a): Experimental contact resonance spectrum measured on a Si (111) reference sample at 1st contact resonance with a DLC tip cantilever of stiffness 6.65 N/m at different static loads. (b): Experimental contact resonance spectrum measured on a Si (111) reference sample at 2nd contact resonance with a DLC tip cantilever of stiffness 6.65 N/m at different static loads.
Fig. 4. (a): Experimental contact resonance spectrum measured on a representative Zirconia–Magnesia binary (ZrO2–MgO) thin film prepared at 1x10−4 mbar oxygen partial pressure (ZrM-4) at 1st contact resonance with a DLC tip cantilever of stiffness 6.65 N/m at different static loads. (b): Experimental contact resonance spectrum measured on a representative Zirconia–Magnesia binary (ZrO2–MgO) thin film prepared at 1x10−4 mbar oxygen partial pressure (ZrM-4) at 2nd contact resonance with a DLC tip cantilever of stiffness 6.65 N/m at different static loads.
167
increasing static normal load, as expected from the theory of flexural vibrations [21]. First, the solution of the Eq. (4) is found numerically for Si (111) reference samples by assuming a small range of values for L1, and by plotting the contact stiffness k⁎ obtained from Eq. (1) as a function of L1/L for the two modes as shown in Fig. 5. The ratio L1/L for the point of intersection of the 1st resonance and 2nd resonance curves correspond to the solution of L1/L and contact stiffness k⁎ for the Si (111) reference sample. The calculated relative error Δk⁎/k⁎ is approximately 3%, primarily due to the uncertainties in the cantilever geometry as well as contact resonance frequency. Subsequently, the contact radius “a” or the tip radius “R” has been determined from the contact stiffness using Eq. (8) for the reference Si (111) sample having indentation moduli of 175 GPa. The calculated contact radius “a” of tip-1 and tip-2 are 8 nm and 6 nm, respectively, while the calculated tip radii are 236 nm and 117 nm respectively. The measured thicknesses of all the films shown in Table 1 are more than 400 nm. Since the measured film thickness of the thin films is greater than the “3a” (24 nm for tip-1 and 18 nm for tip-2) value, which is generally accepted as the minimum depth for neglecting stresses produced by the substrate–film interface, hence the effect of mechanical properties of the substrate during AFAM measurements can be safely neglected [17,29]. The contact resonant frequencies for the 1st and 2nd eigenmode for entire thin films have been measured and the contact stiffness k⁎ for the above samples have been calculated using Eq. (1) for a constant static load of 450nN with the L1/L values obtained for the Si (111) reference. Since the exact tip geometry is unknown or due to wear or tip damage, the contact area between the tip and the sample may be somewhere between that of a flat punch and a spherical tip, therefore the indentation modulus MS of the sample has been evaluated by averaging the values obtained in considering n = 1and n = 3/2 in Eq. (7) [25,29,34] i.e. Es⁎ is calculated using Eq. (7), then it is used to calculate MS using Eq. (6) for both spherical as well as flat tip and then average of MS for both spherical as well as flat tip is taken to evaluate the indentation modulus of the sample. The derived contact stiffness (k⁎) values and indentation moduli of the thin films are shown in Table 2 with their contact resonance frequencies. The relative error in measurement of indentation modulus is about 12%, which is due to the error present in indention modulus calculation for tip-sample geometry, error present in determination of contact stiffness, error in indentation modulus of the tip, error present in determination of spring constant of the cantilever due to uncertainty in cantilever geometry etc. The variation of indentation modulus with different deposition oxygen partial pressure has been shown in Fig. 6 and is found to vary from 89 to 161 GPa. For comparison, Wen-Cheng et al. [35] have reported elastic modulus value in the range of 90 to 210 GPa for ZrO2–MgO
Fig. 5. Plot of k⁎vs L1/L for Si (111) reference sample at 1st and 2nd contact resonance.
168
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
Table 2 Resonance frequencies, Contact stiffness and Indentation modulus of various ZrO2–MgO thin films. Sample
1st resonance (kHz)
2nd resonance (kHz)
Contact stiffness k* (N/m)
Indentation modulus M (GPa)
ZrM-2 ZrM-3 ZrM-4 ZrM-5 ZrM-6
745 678 662 678 750
2281 2087 2002 1991 2192
1702 1874 1633 1437 1188
161 ± 20 130 ± 16 106 ± 13 89 ± 11 94 ± 12
films, with 96.4% ZrO2 and 3.6% MgO and measured by ultrasonic velocity method. Fig. 7 shows the experimental transmission spectrum of sample named ZrM-4 prepared at oxygen pressure of 1x10 −4 mbar and measured over the wavelength range of 200–1200 nm along with the best-fit theoretical spectrum, where the fitting has been carried out using the formalism described above using a suitable dispersion model. The Optical properties of materials are best described by the complex frequency-dependent dielectric functions (ε = ε1 + iε2), where the real part ε1 and imaginary part ε2 of the dielectric constants are related to the directly measurable parameters viz., the refractive index (n) and extinction coefficient (k) through the following relations: 2
2
ε 1 ¼ n −k
ð15Þ
ε 2 ¼ 2nk
ð16Þ
There have been developed a number of models to describe the optical properties of amorphous materials for energies around the band gap. One of the most versatile is the Tauc–Lorentz (TL) model proposed by Jellison and Modine [36]. The TL model combines the Tauc expression [37] for the band edge onset with the broadening given by the classic Lorentz oscillator. The imaginary part of the dielectric function given by Jellison and Modine, has the following expression
Fig. 7. Experimental and fitted transmission curves for a representative ZrO2–MgO thin film prepared at 1x10−4 mbar oxygen partial pressure (ZrM-4).
can be described by the five parameters A, Eo, Eg, Г and ε1TL(∞) (appears in real part of dielectric constant). Although this model was derived for amorphous semiconductor, it can be conveniently applied to polycrystalline thin films as well [37]. The TL model discussed above assumed a parabolic density of states with a constant momentum matrix element and hence yields null value of ε2 for energies less than the band gap which does not always agree with experimental evidence. Hence in the above analysis it has been assumed that the imaginary part of the refractive index, i.e., the extinction coefficient (k) of the ZrO2–MgO binary films follow the Urbach model [39] given by 1 1 − k ¼ α exp 12400β λ γ
ð18Þ
where Eg is the band gap, A the amplitude, E0 is the peak transition energy, Г a broadening term. The expression for real part of dielectric constant has subsequently been obtained using the Kramers–Kronig relations [38]. Thus in the TL model, the dispersion of optical constants
The experimental transmission spectrum is fitted using the co-efficient of the dispersion model and the thickness of the film as fitting parameters. Finally these fitting parameters are used to determine the thickness (t) and the refractive index (n) and extinction coefficients (k) spectra of the films. The thickness values of the films obtained as above have been given in Table 1 with the error in thickness determination. The error in refractive index determination form the transmission spectrum using inverse synthesis is negligible and the error of ± 0.01 is only due to the uncertainty in transmission measurement i.e. 0.3%. The refractive index for entire ZrO2–MgO samples is shown in Fig. 8, while the refractive index
Fig. 6. Variation of Indentation modulus of the ZrO2–MgO thin film samples as a function of oxygen partial pressure used for preparation of the samples.
Fig. 8. Dispersive value of refractive index for all the ZrO2–MgO thin film samples.
2 AE0 Γ E−Eg o ε 2TL ðEÞ ¼ n 2 E2 −E0 2 þ Γ 2 E2 E ¼0
E > Eg
ð17Þ
E≤Eg
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
values at 550 nm for the samples prepared at different oxygen partial pressures have been plotted in Fig. 10. The refractive index values of the samples reported here agree with the previously reported values for such thin films [9,40]. Fig. 9 shows the experimental GIXR spectrum of a representative Zirconia–Magnesia thin film sample (ZrM-4) prepared at oxygen pressure of 1x10 −4 mbar, along with the best fit theoretical simulation, carried out as per the formulation given in the previous section. The above exercise has been carried out for all the samples and densities of the films have been estimated and presented in Table 1. The error in density measurement is approximately ±0.1 g ml −1 due to alignment of the sample position to the X-ray beam and angular resolution of the instrument. The thicknesses of the films, derived from the optical transmission spectra, have been kept invariant during GIXR fitting. The densities of the films obtained have been shown in Fig. 10 as a function of oxygen partial pressure. In Fig. 6, the indentation modulus values for entire samples prepared at different oxygen partial pressures are plotted. It has been observed that the indentation modulus or elastic modulus of such films decreases with increase of oxygen partial pressure. As the oxygen partial pressure increases, the mean free path of the evaporated atoms decreases, as a result of which the packing density of the film decreases and porosity increases. The increase in porosity of the films leads to the decrease in indentation modulus or elastic modulus of the films. This type of trend of decreasing elastic modulus with increasing porosity as well as decreasing density is also reported earlier [41,42]. The other possible mechanisms responsible for this effect might be due to the increased grain size of the films with increasing oxygen partial pressure [43]. This can be further explained according to the relation derived from the L–J potential i.e. Elastic modulus (E) is given by E = C (En/h3), where C is a constant depends on the material, En is the bond energy and h is the bond length; when the average bond length expands and the bond energy decreases with increasing grain size, the elastic modulus decreases [44]. It is also known that the elastic modulus within elastic limit of the elastic response curve is strongly correlated to the density of the material. Under the present studies it is observed that the density of the thin films decreases with increase of oxygen pressure consequently leading to the proportionate decrease in the elastic modulus or indentation modulus values. The above result is also corroborated in Fig. 10 in which correlation between the density and refractive index of these films with oxygen partial pressure are presented.
Fig. 9. Experimental and fitted GIXR curves for a representative ZrO2–MgO thin film prepared at 1x10−4 mbar oxygen partial pressure (ZrM-4).
169
Fig. 10. Variation of density and refractive index (@550 nm) of the ZrO2–MgO thin films as a function of oxygen partial pressure depicting an inverse trend.
4. Conclusion A set of ZrO2–MgO thin films has been grown on quartz and Si (111) substrates using reactive electron beam evaporation technique at 350 °C substrate temperature and at various predetermined oxygen partial pressures. Elastic properties of the above films have been investigated using AFAM technique. The AFAM measurements revealed that ZrO2–MgO thin films deposited under ambient deposition condition show highest indentation modulus. The indentation modulus or the elastic modulus of the films observed to decrease monotonically for films deposited at higher oxygen partial pressures. The above observation corroborates with the variation of density of the films probed by GIXR measurement distinctly supplementing this trend. Such a trend may be easily attributed to the higher porosity and less packing density in the films resulted from decrease in the mean free path of the evaporated species under higher oxygen partial pressure. Further, poor density responsible for poor elastic modulus and refractive index values of these films deposited under higher oxygen partial pressure were also evident from the results of optical transmission spectrometry.
References [1] E.N. Firebaugh, D.M. Sanders, J. Vac. Sci. Technol. A 1 (1983) 356. [2] M. Friz, F. Waibel, in: N. Kaiser, H.K. Pulker (Eds.), Optical Interference Coatings, Springer series in optical sciences, vol. 88, Springer-Verlag, 2003, p. 105. [3] N.K. Sahoo, S. Thakur, R.B. Tokas, N.M. Kamble, Appl. Phys. A 89 (2007) 711. [4] N.K. Sahoo, S. Thakur, R.B. Tokas, N.M. Kamble, Appl. Surf. Sci. 253 (2007) 6787. [5] N.M. Kamble, R.B. Tokas, A. Biswas, S. Thakur, D. Bhatacharayya, N.K. Sahoo, Vacuum 86 (2011) 422. [6] N.K. Sahoo, R.B. Tokas, S. Thakur, Appl. Surf. Sci. 253 (2006) 1787. [7] N.K. Sahoo, S. Thakur, R.B. Tokas, A. Biswas, N.M. Kamble, Appl. Surf. Sci. 253 (2007) 3455. [8] Shin-ichi Zaitsu, Takahisa Jitsuno, Masahiro Nakatsuka, Tatsuhiko Yamanaka, Shinji Motokoshi, Appl. Phys. Lett. 80 (2002) 2442. [9] N.K. Sahoo, A.P. Shapiro, Appl. Opt. 37 (1998) 698. [10] Jolanta E. Klemberg-Sapieha, Jo¨ rg Oberste-Berghaus, Ludvik Martinu, Richard Blacker, Ian Stevenson, George Sadkhin, Dale Morton, Scott McEldowney, Robert Klinger, Phil J. Martin, Nadia Court, Svetlana Dligatch, Mark Gross, Roger P. Netterfield, Appl. Opt. 43 (2004) 2670. [11] H.A. Macloed, Thin-Film Optical Filters, CRS Press, New-York NY, 2010. [12] R.P. Vinci, J.J. Vlassak, Annu. Rev. Mater. Sci. 26 (1996) 431. [13] G.M. Pharr, D.L. Callahan, S.D. McAdams, T.Y. Tsui, S. Anders, A. Anders, J.W. Ager, I.G. Brown, C.S. Bhatia, S.R.P. Silva, J. Robertson, Appl. Phys. Lett. 68 (1996) 779. [14] D. Schneider, T. Schwarz, B. Schultrich, Thin Solid Films 219 (1992) 92. [15] A.C. Ferrari, J. Robertson, M.G. Beghi, C.E. Bottani, R. Ferulano, R. Pastorelli, Appl. Phys. Lett. 75 (1999) 1893. [16] U. Rabe, W. Arnold, Appl. Phys. Lett. 64 (1993) 1493. [17] D. Passeri, M. Rossi, A. Alippi, A. Bettucci, D. Manno, A. Serra, E. Filippo, M. Lucci, I. Davoli, Superlattice. Microst. 44 (2008) 641. [18] D. Passeri, A. Bettucci, M. Germano, M. Rossi, A. Alippi, V. Sessa, A. Fiori, E. Tamburri, M.L. Terranova, Appl. Phys. Lett. 88 (2006) 121910. [19] G. Stan, R.F. Cook, Nanotechnology 19 (2008) 235701.
170
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
[20] D.C. Hurley, M. Kopycinska-Muller, A.B. Kos, R.H. Geiss, Meas. Sci. Technol. 16 (2005) 2167. [21] U. Rabe, K. Janser, W. Arnold, Rev. Sci. Instrum. 67 (1996) 3281. [22] S. Amelio, A.V. Goldade, U. Rabe, V. Scherer, B. Bhushan, W. Arnold, Thin Solid Films 392 (2001) 75. [23] E. Kester, U. Rabe, L. Presmanes, Ph. Tailhades, W. Arnold, J. Phys. Chem. Solids 61 (2000) 1275. [24] U. Rabe, S. Amelio, E. Kester, V. Scherer, S. Hirsekorn, W. Arnold, Ultrasonics 38 (2000) 430. [25] D. Passeri, A. Bettucci, M. Germano, M. Rossi, A. Alippi, S. Orlanducci, M.L. Terranova, M. Ciavarella, Rev. Sci. Instrum. 76 (2005) 093904. [26] John E. Sader, James W.M. Chon, Paul Mulvaney, Rev. Sci. Instrum. 70 (1999) 3967. [27] John Elie Sader, J. Appl. Phys. 84 (1998) 64. [28] K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1995. [29] M. Kopycinska-Muller, R.H. Geiss, J. Muller, D.C. Hurley, Nanotechnology 16 (2005) 703. [30] Juan-Maria Gonzalez-Leal, Rafael Prieto-Alcon, Jose-Andres Angel, Dorian A. Minkov, Emilio Marquez, Appl. Opt. 41 (2002) 7300.
[31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43]
I.G. Parrat, Phys. Rev. 95 (1954) 359. D. Bhattacharyya, N.C. Das, A.P. Roy, R. Chitra, S. Basu, J. Opt. 28 (1999) 1. D.L. Windt, IMD Version 4.1.1, http://cletus.phys.columbia.edu/windt/idl2000. A. Caron, W. Arnold, Acta Mater. 57 (2009) 4353. Wen-Cheng J. Wei, Yuh-Pring Lin, J. Eur. Ceram. Soc. 20 (2000) 1159. G.E. Jellison, F.A. Modine, Appl. Phys. Lett. 69 (1996) 361. J. Tauc, R. Grrogorovici, A. Vancu, Phys. Status Solidi 15 (1996) 627. F. Wooten, Optical properties of solids, Academic Press, New York, 1972. J.M. Khosman, M.E. Kordesch, J. Non-Cryst. Solids 351 (2005) 3334. F. Tcheliebou, A. Boyer, L. Martin, Thin Solid Films 249 (1994) 86. A.P. Roberts, E.J. Garboczi, J. Am. Ceram. Soc. 83 (2000) 3041. M. Asmani, C. Kermel, A. Leriche, M. Ourak, J. Eur. Ceram. Soc. 21 (2001) 1081. S. Jena, R.B. Tokas, N.M. Kamble, S. Thakur, N.K. Sahoo, Indian Vacuum Society Symposium on Thin Films: Science and Technology, India, November 09–12, 2011, AIP Conf. Proc, 1451, 2012, p. 292. [44] L.H. Liang, J.C. Li, Q. Jiang, Solid State Commun. 121 (2002) 453.
Contents lists available at SciVerse ScienceDirect
Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Investigation of elastic and optical properties of electron beam evaporated ZrO2–MgO composite thin films S. Jena, R.B. Tokas ⁎, N. Kamble, S. Thakur, D. Bhattacharyya, N.K. Sahoo Applied Spectroscopy Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India
a r t i c l e
i n f o
Article history: Received 9 August 2012 Received in revised form 12 April 2013 Accepted 12 April 2013 Available online 25 April 2013 Keywords: ZrO2–MgO composite Atomic force acoustic microscopy Refractive index Grazing incidence X-ray reflectivity Indentation modulus
a b s t r a c t Thin films of composite materials are being progressively explored for achieving tunability in the optical constants for application in multilayer optical devices. In the present study, a set of ZrO2–MgO binary mixed composite thin films have been prepared by reactive electron beam evaporation of solid solution of ZrO2 and MgO at different oxygen partial pressures. Since elastic properties of the thin films are very important for their environmental stability under high power laser application, elastic moduli (indentation moduli) of the films have been measured by atomic force acoustic microscopy measurements. The optical properties especially refractive index of such films has been determined from the optical transmission measurement using an inverse synthesis method, while the density of such films has been measured by grazing incidence X-ray reflectivity. The variation of the elastic moduli of the thin films as a function of oxygen partial pressure used during deposition has been studied and the above variation has been corroborated with the variation of density and refractive index of the thin films. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Design and development of optical thin film multilayer devices are constrained by the optical constants such as refractive index, absorption coefficient, band gap etc. of available coating materials. To achieve design targets, often one has to use very large number of thin dielectric layers using the existing conventional materials that leads to complexity in deposition and often compromises its spectral performance and durability [1,2]. Hence it is necessary to find materials as well as methodologies which can yield desired refractive index values for developing precision optical devices with desired characteristics. In recent years, mixed composite oxide materials like SiO2–Al2O3, ZrO2–Ta2O5, ZrO2–TiO2, ZrO2–Al2O3, TiO2–Al2O3, ZrO2–MgO, ZrO2–SiO2, HfO2–SiO2, Gd2O3–SiO2 etc., which are mixtures of two different materials having different optical and structural properties compared to its constituent material, have been used to fulfill the gap of desired refractive index values [2–7] by using different coating methods such as sol–gel process, reactive electronbeam deposition, laser ablation, ion-beam sputtering and chemical vapor deposition. Such coatings have found in diversified fields of application such as optical interference multilayers, optical wave guides, rugate filters, narrow band filters, broadband antireflection coatings etc. [8]. ZrO2–MgO is one of the specific solid-solution based mixed composite oxide materials, which has been evolved as a promising coating ⁎ Corresponding author. Tel.: +91 22 25590341; fax: +91 22 25505151. E-mail address: [email protected] (R.B. Tokas). 0040-6090/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tsf.2013.04.046
material to develop various types of optical devices such as high reflectivity mirror, edge filters, beam splitters etc., because of its suitable optical properties like transparent spectral range from near-infrared to the ultraviolet, high refractive index and better laser induced damaged threshold [9]. The better optical performance with high stability of the films needs optimization of their mechanical properties (such as low stress and high hardness, scratch, abrasion and wear resistance and better adhesion) also together with their microstructural characteristics and other functional properties for long-term environmental stability [10]. The importance of mechanical properties of thin films is primarily in their relation to coating stability i.e. the extent to which optical thin films coating will continue to behave as they did when removed from the coating chamber, even when subjected to disturbances of an environmental and/or mechanical nature [11]. There are many factors which are responsible for mechanical stability of the optical thin films. One of the important factors is local indentation modulus, which strongly affects the residual stress (thermal stress) generated in thin films. This elastic property of thin films differs significantly from those of the bulk materials due to the interfaces, microstructure, and the underlying substrates and is also affected by the process parameters and the deposition technique like structural and optical properties [12]. Many techniques are being used for the determination of elastic modulus of thin films such as micro- and nano-indentation tests [13], laser induced surface acoustic wave [14], surface Brillouin light scattering measurements [15] and atomic force acoustic microscopy (AFAM) [16]. Out of all the techniques, AFAM technique is capable of giving both quantitative values of elastic modulus (indentation modulus for anisotropic films) like other techniques as well as qualitative picture
164
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
of elastic modulus in terms of acoustic image simultaneously with surface topography of thin film sample; and also capable of giving quantitative mapping of surface elastic modulus by bidimensional reconstruction of the local elastic modulus of sample surface at nanoscale using AFAM two contact resonance frequency imaging technique [17–20]. This makes AFAM, a unique tool for the local investigation of the sample surface elastic properties. So, the main objective of the present study is to determine quantitatively, the indentation modulus (M) of such thin films using this promising technique. The objective also includes the investigation of the dependence of the indentation modulus on the oxygen partial pressure and to establish a correlation between the micro structural, optical and elastic properties of such thin films. 2. Experimental details 2.1. Sample preparation and characterization techniques A several set of such thin films on silicon (111) and quartz substrates were prepared by evaporating ZrO2–MgO solid solution composite material using electron-beam evaporation in a fully automatic vacuum system VERA-902. The total pressure inside the vacuum system and the real-time deposition rate were controlled using MKS mass flow controllers and Inficon's XTC/2 Quartz crystal monitors respectively. The deposition rate of 5 Å/s and the substrate temperature of 350 °C were maintained during deposition of all the samples, while the oxygen pressure was varied from without oxygen pressure to 8 × 10 −4 mbar. The details of the samples prepared along with their thickness as measured by in-situ thickness monitors are shown in Table 1. A commercial Solver P47H, NT-MDT, Russia make atomic force microscopy (AFM) system with AFAM mode is used for the quantitative analysis of elastic modulus/indentation modulus of the thin films. The schematic of AFAM set-up is presented in Fig. 1. The sample is placed on an ultrasonic transducer instead of the sample holder of a standard AFM set-up. The transducer driven by a waveform generator emits longitudinal waves, causing out-of-plane surface vibrations in the sample. These vibrations are coupled to the AFM cantilever by making contact of the AFM tip with the sample surface. The amplitude of the cantilever vibrations is detected by AFM photodiode using a lock-in-amplifier. The cantilever vibration is recorded together with the corresponding ultrasonic frequency to obtain the contact-resonance spectrum. These contact resonance spectra have been used to calculate the indentation modulus of the films. The optical transmission spectra of the films were measured using a UV–VIS-NIR spectrophotometer (UV-3101PC, SHIMADZU) at room temperature in the range 190–1200 nm for determination of refractive index of the films. The relative uncertainty in the transmittance is 0.3%. In the measurement air was used as a reference. Densities of the films have been estimated by grazing incidence X-ray reflectivity (GIXR) measurements carried out in an X-ray reflectometer (SOPRA, France). The measurements have been carried out with Cu Kα (1.54 Å) source with grazing angle of incidence in the range of 0–0.6° and with an angular resolution of 0.01°. Rocking curve measurements have been done prior to each measurement for alignment the sample.
2.2. Determination of elastic modulus of the films The elastic/indentation modulus of the thin films has been determined by modeling the AFM cantilevers tip–film surface interaction in terms of surface-coupled cantilever vibration [21]. Under suitable approximation (assuming linear forces and sufficiently small vibration amplitude of the cantilever ~ 0.1 nm), the tip–film interaction can be approximated by vertical and lateral spring-dashpot systems [22] as shown in Fig. 2(a), where θ0 is the angle between the cantilever and sample surface, while klat⁎, k*, γlat and γ are the lateral and vertical contact stiffness and damping constants, respectively. The total length of the cantilever is L = L1 + L′ and the tip base is located at L1 with L′ = L − L1. It has been found that the k⁎ value depends mostly on the sensor tip position L1 than on the other parameters such as θ0, klat⁎, γlat and γ [23]. Neglecting all these parameters and considering the mass of the tip to be very small compared to the cantilever mass, the tip-sample coupled system reduces to the simplified system as shown in Fig. 2(b). The characteristic equation for the above simplified system is [24,25] 2
3 3 kc ðkn LrÞ ð1 þ coskn L coshkn LÞ 3 fðsinhkn Lr coskn Lr− coshkn Lr sinkn LrÞð1 þ coskn Lð1−r Þ coshk n Lð1−r ÞÞg 4 5 ð coshkn Lð1−rÞ sinkn Lð1−r Þ− sinhkn Lð1−r Þ coskn Lð1−r ÞÞ þ ð1− coskn Lr coshkn LrÞ
k ¼2
ð1Þ with qffiffiffiffiffi kn L ¼ cB L f n
ð2Þ
and cB ¼
rffiffiffiffiffiffi pffiffiffiffiffiffi 4 ρA 2π EI
ð3Þ
where r = L1 / L, cB is a characteristic cantilever constant, ρ is the mass density of the cantilever material, fn is the nth eigenmode mode resonance frequency of the cantilever, kc is the spring constant or stiffness of the rectangular cantilever and k⁎ is the contact stiffness of the tip-sample assembly. The spring constant (kc) of the free cantilever is determined using normal Sader method [26,27]. The evaluation of spring constant is very accurate, as the quality factor of the cantilever is very high (Q > 300). It is worthwhile to note that any uncertainty in kc does not affect the calculated values of reduced Young's modulus as confirmed by the Eq. (7) but only the determination of the normal static load FN by the cantilever on the sample surface [25]. By measuring the free resonant frequency of the cantilever and substituting the measured values in Eq. (2), cBL value for each individual cantilever is determined with high precision and without any knowledge of any additional cantilever data. The knL values for the surface coupled cantilevers are then determined by substituting the value of cBL as determined above and the measured contact resonant frequencies of the cantilever in contact with the film surface in Eq. (2). Experimentally, the value of k* and L1 can be determined by using the fact that, the contact stiffness k⁎ must be the same for all
Table 1 Density and refractive index of ZrO2–MgO thin films. Sample
Oxygen partial pressure (mbar)
Thickness measured in-situ (nm)
Thickness derived from transmission spectra (nm)
Density (g ml−1)
Refractive index @ 550 nm
ZrM-2 ZrM-3 ZrM-4 ZrM-5 ZrM-6
0 0.6x10−4 1x10−4 4x10−4 8x10−4
510 425 511 635 750
529 435 521 680 783
4.6 4.6 4.4 3.7 2.5
1.93 1.96 1.95 1.79 1.76
± ± ± ± ±
5 4 5 6 8
± ± ± ± ±
0.4 0.2 0.3 0.7 1.5
± ± ± ± ±
0.1 0.1 0.1 0.1 0.1
± ± ± ± ±
0.01 0.01 0.01 0.01 0.01
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
165
Fig. 1. Schematic of AFAM set up.
cantilever eigenmode (f1, f2, f3……) at constant applied normal load. This leads to the conditional equation [17,18]
k ðf 1 ; rÞ ¼ k ðf 2 ; r Þ:
ð4Þ
The solution of the Eq. (4) is found numerically by assuming a small range of values for L1, the range being found by using an optical microscope or a scanning electron microscope. First two contact
eigenmode frequencies are measured and the contact stiffness k⁎ obtained from Eq. (1) is plotted as a function of r = L1 / L for the two modes and the point of intersection of the 1st and 2nd resonance curves corresponds to the solution of L1/L and contact stiffness k⁎. The contact stiffness k⁎ obtained from the AFAM measurement can be related to the elastic modulus of the probed material by Hertzian theory of contact mechanics [28]. According to this theory, when a hemispherical tip of radius R (AFM cantilever tip) indents a flat surface with a normal static load FN, then the resulting contact stiffness k⁎can be calculated as
k ¼ 2aE ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 6E2 RF N
ð5Þ
Here a is the contact radius and E⁎ is the reduced Young's modulus, defined as 1 1 1 ¼ þ E M S M t
ð6Þ
Where, MS and Mt are the indentation moduli of the sample and tip, respectively. The left equality in Eq. (5) is true for all geometries while the right equality of the equation can be used only for tips with hemispherical geometry [25,29]. The indentation modulus MS of the sample can only be calculated after determining the contact area or tip geometry, which is very difficult to determine experimentally. Hence this can be avoided only by comparing the value of k⁎obtained for the unknown sample to that of a reference sample with known elastic properties [25,29]:
ES ¼ Eref
Fig. 2. (a): General case for a tip–sample interaction including lateral and vertical tip–sample interaction forces. (b): Simplified case for a tip–sample interaction.
ks kref
n :
ð7Þ
The subscripts s and ref corresponds to the unknown sample and reference sample, respectively. The value of n depends on tip-sample geometry. For a spherical tip, n = 3/2; while for a tip shaped like a flat punch, n = 1. Now the indentation modulus of the sample MS can be calculated from Eqs. (6) and (7). For isotropic samples, Young's modulus (Es) is evaluated from the indentation modulus MS, through Es the relation Ms ¼ 1−ν 2 , where v is the Poisson's ratio. Since the Poisson's ratio of the thin films under present study is unknown and can vary with density of the films, therefore direct indentation modulus of these films is calculated and reported.
166
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
2.3. Determination of refractive index of the films The refractive index of the films has been determined by fitting the measured optical transmission spectra with theoretically generated spectra using a suitable optical dispersion model. The transmission of a single layer film on a substrate can be expressed as follows [30]: T ðλ; n; x; t; no ; xo Þ ¼ P=Q
ð8Þ
where P ¼ ð1 R1 Þ ð1 R2 Þ ð1 R3 Þ xxo
ð8aÞ
2 2 2 2 2 Q ¼ 1 þ R1 R2 x −R1 R3 x xo −R2 R3 xo þ 2r 1 r 2 1−R3 xo x cosφ
8ðbÞ
2
2
2
R 1 ¼ r 1 ; R2 ¼ r 2 ; R3 ¼ r 3
ð8cÞ
1−n n−no n −1 ;r ¼ ;r ¼ o 1 þ n 2 n þ no 3 no þ 1
ð8dÞ
α ¼
0 0 0 4πk 4πko −α t −α o t o ;x ¼ e ; xo ¼ e ;α o ¼ λ λ
ð8eÞ
φ¼
4πnt λ
ð8fÞ
r1 ¼ 0
Where t & to are the thicknesses of the film and substrate respectively. The n, k and no, ko are the refractive indices and the extinction coefficients of the film and substrate respectively. R1, R2 and R3 are the reflectivity for air–film, film–substrate, and substrate–air interface respectively. Using the above mentioned relation and assuming a suitable dispersion model, the fitting has been carried out by minimizing the squared difference (χ 2) between the experimentally measured and calculated values of transmission given by: 2
χ ¼
1 N Exp Cal 2 ∑i¼1 T i −T i ð2N−P Þ
ð9Þ
where TiExp and TiCal are the experimental and theoretical transmittances respectively. N is the number of data points, P is the number of model parameters and the minimization has been done using the Levenberg–Marquardt algorithm. 2.4. Determination of density of the films The densities of such films have been determined by measuring the X-ray reflectivity spectra of the samples at grazing angle of incidence. The complex refractive index (η) of an element in the X-ray region is given by [31]: η ¼ 1−δ−iβ
ð10Þ
where, δ¼
n
o 2 r O λ =2 π N A ðρZ=AW Þ
ð11Þ
and β ¼ ðμλ=4πÞ
ð12Þ
where, ro is the classical electron radius (2.82 x 10–13 cm), NA is the Avogadro number, ρ is the density, Z is the atomic number and Aw is the atomic weight of the element and μ is the linear absorption coefficient of the material at the particular wavelength λ. The quantity, [NA (ρ Z / Aw)], actually gives the number of electrons per cm 3 of the particular element. Since refractive index of all materials in hard X-ray region is less than 1, X-ray suffers total external reflection at an extreme grazing angle of incidence from any surface. However,
as the grazing angle of incidence value (θ) exceeds the critical angle (θc), X-ray starts to penetrate inside the layer and reflectivity starts to fall off rapidly. The critical angle is approximately given by the following expression: θC ¼ √ð2δÞ
ð13Þ
and depends on the electron density of the material apart from the wavelength of X-ray. The reflectivity of X-ray from a thin film i.e., of a plane boundary between two media can be obtained using the well known Fresnel's boundary conditions of continuity of the tangential components of the electric field vector and its derivative at the sharp interface [32]. However, the Fresnel's reflectivity gets modified for a rough surface by a ‘Debye–Waller-like’ factor as follows:
2 2 RO ¼ Rp exp −q σ =2
ð14Þ
where, q is the momentum transfer factor (4π sinθ / λ), RO is the reflectivity of the rough surface and Rp is the reflectivity of an otherwise identical smooth surface and σ is the RMS roughness of the surface. Thus by fitting the X-ray reflectivity spectrum of the surface of a sample near its critical angle, accurate estimation regarding the density ρ and RMS surface roughness σ can be made quite accurately. The theoretical simulation and fitting of the GIXR spectra have been carried out using the “IMD” code under the “XOP” software package [33] and the best fits are achieved by minimizing the χ 2value. It should be noted here that the AFAM measurements have been carried out on films deposited on c-Si substrates while the optical measurements have been carried out on films deposited on quartz substrates prepared in the same run i.e., under identical deposition condition. GIXR measurements have been carried out on all the films deposited on both quartz and c-Si substrate probing mass density of these films. Further, the films considered under present study are amorphous or weakly polycrystalline in nature. For such films, the natures of substrate (i.e., Si or Quartz) are observed not to have any significant influence on the film properties as reflected in the GIXR experiments. 3. Results and discussion Indentation modulus of ZrO2–MgO binary thin films deposited at varying oxygen partial pressure has been estimated by performing AFAM measurements using DLC coated Si cantilever probes. DLC coated Si tips have been chosen for their better hardness and stability in tip geometry with indentation modulus of 590 ± 20 GPa. We have employed two DLC cantilevers because of inability of a single cantilever to perform the measurement over all the samples. The spring constants or force constants of the cantilevers are kc = 6 N/m (tip1) and 6.15 N/m (tip2). Indentation moduli of the samples ZrM-3, ZrM-4 & ZrM-5 prepared at different oxygen partial pressures ranging from 0.6 × 10−4 to 4 × 10−4 mbar have been determined from the contact resonant spectra using tip1, while tip2 has been employed for ZrM-2 and ZrM-6 thin films prepared at two extreme oxygen partial pressure of zero pressure (ambient atmosphere) and 8 × 10−4 mbar, respectively. The contact-resonance spectra for Si (111) reference sample and the samples of such thin films have been measured for the 1st and 2nd flexural modes. For each sample, the contact-resonance frequencies were measured for four different static normal loads FN = 450, 500, 550 and 600 nN. Fig. 3(a) and (b) shows respectively the 1st and 2nd experimental contact-resonant spectra for Si (111) reference sample, while Fig. 4(a) and (b) shows respectively the 1st and 2nd contact-resonant spectra for a representative (ZrM-4) prepared at oxygen pressure of 1 × 10 − 4 mbar. This spectra shows that both the resonance frequencies and the amplitudes increase with
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
Fig. 3. (a): Experimental contact resonance spectrum measured on a Si (111) reference sample at 1st contact resonance with a DLC tip cantilever of stiffness 6.65 N/m at different static loads. (b): Experimental contact resonance spectrum measured on a Si (111) reference sample at 2nd contact resonance with a DLC tip cantilever of stiffness 6.65 N/m at different static loads.
Fig. 4. (a): Experimental contact resonance spectrum measured on a representative Zirconia–Magnesia binary (ZrO2–MgO) thin film prepared at 1x10−4 mbar oxygen partial pressure (ZrM-4) at 1st contact resonance with a DLC tip cantilever of stiffness 6.65 N/m at different static loads. (b): Experimental contact resonance spectrum measured on a representative Zirconia–Magnesia binary (ZrO2–MgO) thin film prepared at 1x10−4 mbar oxygen partial pressure (ZrM-4) at 2nd contact resonance with a DLC tip cantilever of stiffness 6.65 N/m at different static loads.
167
increasing static normal load, as expected from the theory of flexural vibrations [21]. First, the solution of the Eq. (4) is found numerically for Si (111) reference samples by assuming a small range of values for L1, and by plotting the contact stiffness k⁎ obtained from Eq. (1) as a function of L1/L for the two modes as shown in Fig. 5. The ratio L1/L for the point of intersection of the 1st resonance and 2nd resonance curves correspond to the solution of L1/L and contact stiffness k⁎ for the Si (111) reference sample. The calculated relative error Δk⁎/k⁎ is approximately 3%, primarily due to the uncertainties in the cantilever geometry as well as contact resonance frequency. Subsequently, the contact radius “a” or the tip radius “R” has been determined from the contact stiffness using Eq. (8) for the reference Si (111) sample having indentation moduli of 175 GPa. The calculated contact radius “a” of tip-1 and tip-2 are 8 nm and 6 nm, respectively, while the calculated tip radii are 236 nm and 117 nm respectively. The measured thicknesses of all the films shown in Table 1 are more than 400 nm. Since the measured film thickness of the thin films is greater than the “3a” (24 nm for tip-1 and 18 nm for tip-2) value, which is generally accepted as the minimum depth for neglecting stresses produced by the substrate–film interface, hence the effect of mechanical properties of the substrate during AFAM measurements can be safely neglected [17,29]. The contact resonant frequencies for the 1st and 2nd eigenmode for entire thin films have been measured and the contact stiffness k⁎ for the above samples have been calculated using Eq. (1) for a constant static load of 450nN with the L1/L values obtained for the Si (111) reference. Since the exact tip geometry is unknown or due to wear or tip damage, the contact area between the tip and the sample may be somewhere between that of a flat punch and a spherical tip, therefore the indentation modulus MS of the sample has been evaluated by averaging the values obtained in considering n = 1and n = 3/2 in Eq. (7) [25,29,34] i.e. Es⁎ is calculated using Eq. (7), then it is used to calculate MS using Eq. (6) for both spherical as well as flat tip and then average of MS for both spherical as well as flat tip is taken to evaluate the indentation modulus of the sample. The derived contact stiffness (k⁎) values and indentation moduli of the thin films are shown in Table 2 with their contact resonance frequencies. The relative error in measurement of indentation modulus is about 12%, which is due to the error present in indention modulus calculation for tip-sample geometry, error present in determination of contact stiffness, error in indentation modulus of the tip, error present in determination of spring constant of the cantilever due to uncertainty in cantilever geometry etc. The variation of indentation modulus with different deposition oxygen partial pressure has been shown in Fig. 6 and is found to vary from 89 to 161 GPa. For comparison, Wen-Cheng et al. [35] have reported elastic modulus value in the range of 90 to 210 GPa for ZrO2–MgO
Fig. 5. Plot of k⁎vs L1/L for Si (111) reference sample at 1st and 2nd contact resonance.
168
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
Table 2 Resonance frequencies, Contact stiffness and Indentation modulus of various ZrO2–MgO thin films. Sample
1st resonance (kHz)
2nd resonance (kHz)
Contact stiffness k* (N/m)
Indentation modulus M (GPa)
ZrM-2 ZrM-3 ZrM-4 ZrM-5 ZrM-6
745 678 662 678 750
2281 2087 2002 1991 2192
1702 1874 1633 1437 1188
161 ± 20 130 ± 16 106 ± 13 89 ± 11 94 ± 12
films, with 96.4% ZrO2 and 3.6% MgO and measured by ultrasonic velocity method. Fig. 7 shows the experimental transmission spectrum of sample named ZrM-4 prepared at oxygen pressure of 1x10 −4 mbar and measured over the wavelength range of 200–1200 nm along with the best-fit theoretical spectrum, where the fitting has been carried out using the formalism described above using a suitable dispersion model. The Optical properties of materials are best described by the complex frequency-dependent dielectric functions (ε = ε1 + iε2), where the real part ε1 and imaginary part ε2 of the dielectric constants are related to the directly measurable parameters viz., the refractive index (n) and extinction coefficient (k) through the following relations: 2
2
ε 1 ¼ n −k
ð15Þ
ε 2 ¼ 2nk
ð16Þ
There have been developed a number of models to describe the optical properties of amorphous materials for energies around the band gap. One of the most versatile is the Tauc–Lorentz (TL) model proposed by Jellison and Modine [36]. The TL model combines the Tauc expression [37] for the band edge onset with the broadening given by the classic Lorentz oscillator. The imaginary part of the dielectric function given by Jellison and Modine, has the following expression
Fig. 7. Experimental and fitted transmission curves for a representative ZrO2–MgO thin film prepared at 1x10−4 mbar oxygen partial pressure (ZrM-4).
can be described by the five parameters A, Eo, Eg, Г and ε1TL(∞) (appears in real part of dielectric constant). Although this model was derived for amorphous semiconductor, it can be conveniently applied to polycrystalline thin films as well [37]. The TL model discussed above assumed a parabolic density of states with a constant momentum matrix element and hence yields null value of ε2 for energies less than the band gap which does not always agree with experimental evidence. Hence in the above analysis it has been assumed that the imaginary part of the refractive index, i.e., the extinction coefficient (k) of the ZrO2–MgO binary films follow the Urbach model [39] given by 1 1 − k ¼ α exp 12400β λ γ
ð18Þ
where Eg is the band gap, A the amplitude, E0 is the peak transition energy, Г a broadening term. The expression for real part of dielectric constant has subsequently been obtained using the Kramers–Kronig relations [38]. Thus in the TL model, the dispersion of optical constants
The experimental transmission spectrum is fitted using the co-efficient of the dispersion model and the thickness of the film as fitting parameters. Finally these fitting parameters are used to determine the thickness (t) and the refractive index (n) and extinction coefficients (k) spectra of the films. The thickness values of the films obtained as above have been given in Table 1 with the error in thickness determination. The error in refractive index determination form the transmission spectrum using inverse synthesis is negligible and the error of ± 0.01 is only due to the uncertainty in transmission measurement i.e. 0.3%. The refractive index for entire ZrO2–MgO samples is shown in Fig. 8, while the refractive index
Fig. 6. Variation of Indentation modulus of the ZrO2–MgO thin film samples as a function of oxygen partial pressure used for preparation of the samples.
Fig. 8. Dispersive value of refractive index for all the ZrO2–MgO thin film samples.
2 AE0 Γ E−Eg o ε 2TL ðEÞ ¼ n 2 E2 −E0 2 þ Γ 2 E2 E ¼0
E > Eg
ð17Þ
E≤Eg
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
values at 550 nm for the samples prepared at different oxygen partial pressures have been plotted in Fig. 10. The refractive index values of the samples reported here agree with the previously reported values for such thin films [9,40]. Fig. 9 shows the experimental GIXR spectrum of a representative Zirconia–Magnesia thin film sample (ZrM-4) prepared at oxygen pressure of 1x10 −4 mbar, along with the best fit theoretical simulation, carried out as per the formulation given in the previous section. The above exercise has been carried out for all the samples and densities of the films have been estimated and presented in Table 1. The error in density measurement is approximately ±0.1 g ml −1 due to alignment of the sample position to the X-ray beam and angular resolution of the instrument. The thicknesses of the films, derived from the optical transmission spectra, have been kept invariant during GIXR fitting. The densities of the films obtained have been shown in Fig. 10 as a function of oxygen partial pressure. In Fig. 6, the indentation modulus values for entire samples prepared at different oxygen partial pressures are plotted. It has been observed that the indentation modulus or elastic modulus of such films decreases with increase of oxygen partial pressure. As the oxygen partial pressure increases, the mean free path of the evaporated atoms decreases, as a result of which the packing density of the film decreases and porosity increases. The increase in porosity of the films leads to the decrease in indentation modulus or elastic modulus of the films. This type of trend of decreasing elastic modulus with increasing porosity as well as decreasing density is also reported earlier [41,42]. The other possible mechanisms responsible for this effect might be due to the increased grain size of the films with increasing oxygen partial pressure [43]. This can be further explained according to the relation derived from the L–J potential i.e. Elastic modulus (E) is given by E = C (En/h3), where C is a constant depends on the material, En is the bond energy and h is the bond length; when the average bond length expands and the bond energy decreases with increasing grain size, the elastic modulus decreases [44]. It is also known that the elastic modulus within elastic limit of the elastic response curve is strongly correlated to the density of the material. Under the present studies it is observed that the density of the thin films decreases with increase of oxygen pressure consequently leading to the proportionate decrease in the elastic modulus or indentation modulus values. The above result is also corroborated in Fig. 10 in which correlation between the density and refractive index of these films with oxygen partial pressure are presented.
Fig. 9. Experimental and fitted GIXR curves for a representative ZrO2–MgO thin film prepared at 1x10−4 mbar oxygen partial pressure (ZrM-4).
169
Fig. 10. Variation of density and refractive index (@550 nm) of the ZrO2–MgO thin films as a function of oxygen partial pressure depicting an inverse trend.
4. Conclusion A set of ZrO2–MgO thin films has been grown on quartz and Si (111) substrates using reactive electron beam evaporation technique at 350 °C substrate temperature and at various predetermined oxygen partial pressures. Elastic properties of the above films have been investigated using AFAM technique. The AFAM measurements revealed that ZrO2–MgO thin films deposited under ambient deposition condition show highest indentation modulus. The indentation modulus or the elastic modulus of the films observed to decrease monotonically for films deposited at higher oxygen partial pressures. The above observation corroborates with the variation of density of the films probed by GIXR measurement distinctly supplementing this trend. Such a trend may be easily attributed to the higher porosity and less packing density in the films resulted from decrease in the mean free path of the evaporated species under higher oxygen partial pressure. Further, poor density responsible for poor elastic modulus and refractive index values of these films deposited under higher oxygen partial pressure were also evident from the results of optical transmission spectrometry.
References [1] E.N. Firebaugh, D.M. Sanders, J. Vac. Sci. Technol. A 1 (1983) 356. [2] M. Friz, F. Waibel, in: N. Kaiser, H.K. Pulker (Eds.), Optical Interference Coatings, Springer series in optical sciences, vol. 88, Springer-Verlag, 2003, p. 105. [3] N.K. Sahoo, S. Thakur, R.B. Tokas, N.M. Kamble, Appl. Phys. A 89 (2007) 711. [4] N.K. Sahoo, S. Thakur, R.B. Tokas, N.M. Kamble, Appl. Surf. Sci. 253 (2007) 6787. [5] N.M. Kamble, R.B. Tokas, A. Biswas, S. Thakur, D. Bhatacharayya, N.K. Sahoo, Vacuum 86 (2011) 422. [6] N.K. Sahoo, R.B. Tokas, S. Thakur, Appl. Surf. Sci. 253 (2006) 1787. [7] N.K. Sahoo, S. Thakur, R.B. Tokas, A. Biswas, N.M. Kamble, Appl. Surf. Sci. 253 (2007) 3455. [8] Shin-ichi Zaitsu, Takahisa Jitsuno, Masahiro Nakatsuka, Tatsuhiko Yamanaka, Shinji Motokoshi, Appl. Phys. Lett. 80 (2002) 2442. [9] N.K. Sahoo, A.P. Shapiro, Appl. Opt. 37 (1998) 698. [10] Jolanta E. Klemberg-Sapieha, Jo¨ rg Oberste-Berghaus, Ludvik Martinu, Richard Blacker, Ian Stevenson, George Sadkhin, Dale Morton, Scott McEldowney, Robert Klinger, Phil J. Martin, Nadia Court, Svetlana Dligatch, Mark Gross, Roger P. Netterfield, Appl. Opt. 43 (2004) 2670. [11] H.A. Macloed, Thin-Film Optical Filters, CRS Press, New-York NY, 2010. [12] R.P. Vinci, J.J. Vlassak, Annu. Rev. Mater. Sci. 26 (1996) 431. [13] G.M. Pharr, D.L. Callahan, S.D. McAdams, T.Y. Tsui, S. Anders, A. Anders, J.W. Ager, I.G. Brown, C.S. Bhatia, S.R.P. Silva, J. Robertson, Appl. Phys. Lett. 68 (1996) 779. [14] D. Schneider, T. Schwarz, B. Schultrich, Thin Solid Films 219 (1992) 92. [15] A.C. Ferrari, J. Robertson, M.G. Beghi, C.E. Bottani, R. Ferulano, R. Pastorelli, Appl. Phys. Lett. 75 (1999) 1893. [16] U. Rabe, W. Arnold, Appl. Phys. Lett. 64 (1993) 1493. [17] D. Passeri, M. Rossi, A. Alippi, A. Bettucci, D. Manno, A. Serra, E. Filippo, M. Lucci, I. Davoli, Superlattice. Microst. 44 (2008) 641. [18] D. Passeri, A. Bettucci, M. Germano, M. Rossi, A. Alippi, V. Sessa, A. Fiori, E. Tamburri, M.L. Terranova, Appl. Phys. Lett. 88 (2006) 121910. [19] G. Stan, R.F. Cook, Nanotechnology 19 (2008) 235701.
170
S. Jena et al. / Thin Solid Films 537 (2013) 163–170
[20] D.C. Hurley, M. Kopycinska-Muller, A.B. Kos, R.H. Geiss, Meas. Sci. Technol. 16 (2005) 2167. [21] U. Rabe, K. Janser, W. Arnold, Rev. Sci. Instrum. 67 (1996) 3281. [22] S. Amelio, A.V. Goldade, U. Rabe, V. Scherer, B. Bhushan, W. Arnold, Thin Solid Films 392 (2001) 75. [23] E. Kester, U. Rabe, L. Presmanes, Ph. Tailhades, W. Arnold, J. Phys. Chem. Solids 61 (2000) 1275. [24] U. Rabe, S. Amelio, E. Kester, V. Scherer, S. Hirsekorn, W. Arnold, Ultrasonics 38 (2000) 430. [25] D. Passeri, A. Bettucci, M. Germano, M. Rossi, A. Alippi, S. Orlanducci, M.L. Terranova, M. Ciavarella, Rev. Sci. Instrum. 76 (2005) 093904. [26] John E. Sader, James W.M. Chon, Paul Mulvaney, Rev. Sci. Instrum. 70 (1999) 3967. [27] John Elie Sader, J. Appl. Phys. 84 (1998) 64. [28] K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1995. [29] M. Kopycinska-Muller, R.H. Geiss, J. Muller, D.C. Hurley, Nanotechnology 16 (2005) 703. [30] Juan-Maria Gonzalez-Leal, Rafael Prieto-Alcon, Jose-Andres Angel, Dorian A. Minkov, Emilio Marquez, Appl. Opt. 41 (2002) 7300.
[31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43]
I.G. Parrat, Phys. Rev. 95 (1954) 359. D. Bhattacharyya, N.C. Das, A.P. Roy, R. Chitra, S. Basu, J. Opt. 28 (1999) 1. D.L. Windt, IMD Version 4.1.1, http://cletus.phys.columbia.edu/windt/idl2000. A. Caron, W. Arnold, Acta Mater. 57 (2009) 4353. Wen-Cheng J. Wei, Yuh-Pring Lin, J. Eur. Ceram. Soc. 20 (2000) 1159. G.E. Jellison, F.A. Modine, Appl. Phys. Lett. 69 (1996) 361. J. Tauc, R. Grrogorovici, A. Vancu, Phys. Status Solidi 15 (1996) 627. F. Wooten, Optical properties of solids, Academic Press, New York, 1972. J.M. Khosman, M.E. Kordesch, J. Non-Cryst. Solids 351 (2005) 3334. F. Tcheliebou, A. Boyer, L. Martin, Thin Solid Films 249 (1994) 86. A.P. Roberts, E.J. Garboczi, J. Am. Ceram. Soc. 83 (2000) 3041. M. Asmani, C. Kermel, A. Leriche, M. Ourak, J. Eur. Ceram. Soc. 21 (2001) 1081. S. Jena, R.B. Tokas, N.M. Kamble, S. Thakur, N.K. Sahoo, Indian Vacuum Society Symposium on Thin Films: Science and Technology, India, November 09–12, 2011, AIP Conf. Proc, 1451, 2012, p. 292. [44] L.H. Liang, J.C. Li, Q. Jiang, Solid State Commun. 121 (2002) 453.