- Email: [email protected]
Quantitative correlation between intrinsic stress and microstructure of thin films
Thin Solid Films 604 (2016) 90–93
Contents lists available at ScienceDirect
Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Critical review
Quantitative correlation between intrinsic stress and microstructure of thin films D. Depla, B.R. Braeckman Department of Solid State Sciences, Ghent University, Krijgslaan 281/S1, 9000 Ghent, Belgium
a r t i c l e
i n f o
a b s t r a c t A critical review of the available literature on thin film intrinsic stress has generated a database with 111 entries representing 19 different metals deposited by evaporation. Although there is a wide range of experimental conditions, the data can be presented in a comprehensible way based on the surface mean free path of diffusing adatoms. This characteristic length L is calculated based on the deposition temperature, the melting temperature of the evaporant, and the deposition flux. The calculated strain as a function of L not only shows the trends in a quantitative way, but also allows one to connect the data with the thin-film microstructure as represented in structure-zone models. The proposed procedure appears to also be applicable to amorphous metallic glass thin films (4 alloy systems, 29 entries) as well. © 2016 Elsevier B.V. All rights reserved.
Available online 23 March 2016
Contents 1. Introduction . . . . . 2. Method . . . . . . . 3. Results and discussion . 4. Conclusions. . . . . . References. . . . . . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
1. Introduction Intrinsic stress evolution during thin film deposition by evaporation is a research topic that has been studied for decades and has been reviewed in several papers [1–9]. The intrinsic stress is strongly material-dependent, and for continuous, non-epitaxial thin films can be divided into two groups. For materials deposited under conditions leading to low adatom surface mobility, a tensile stress state is observed, while a compressive stress state is usually obtained for high-adatom-mobility materials. For metals deposited at the same substrate temperature Ts, the evaporant melting temperature Tm is a good measure to distinguish between these two classes since diffusion processes for metals scale inversely with Tm. The Arrhenius behavior of these processes explains the importance of the deposition (or substrate) temperature Ts, and hence experimental trends are often presented in terms of the homologous temperature, i.e. the ratio between the deposition temperature and the melting temperature, both expressed in Kelvin (Ts/Tm). The homologous temperature is also used to classify the microstructure of evaporated thin films in structure-zone models (SZM). A relationship between the microstructure and the intrinsic stress of thin films can therefore be expected. Despite this apparent connection, no
http://dx.doi.org/10.1016/j.tsf.2016.03.039 0040-6090/© 2016 Elsevier B.V. All rights reserved.
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
90 90 91 92 92
quantitative proof has been given in the literature. Here this quantitative link is made and this allows one to predict the stress state of evaporated thin films. 2. Method Kinetic models used to describe thin-film nucleation [11] predict scaling laws for the mean free path of the diffusing adatoms before they form a nucleus or are captured by an existing island, also known as the characteristic nucleation length L. When the critical nucleus size is one atom, which is a quite common situation during thermal evaporation, L is related to the incident flux of atoms F [11–13] sffiffiffi !1=6 1 Da2s L¼ η F
ð1Þ
with D the adatom surface diffusion rate, as the lattice parameter of the surface unit cell, and η a dimensionless parameter with a maximum value of 0.25.
Fig. 1. Strain, measured at different film thicknesses, as a function of the characteristic length L (lower horizontal axis). The symbols refer to the references while the color code is used to identify the material. The upper horizontal axis converts the characteristic length L to the homologous temperature via Eqs. (1) and (2) in the text, using a deposition flux F averaged over all references. To calculate the average strain (solid line), the data was ordered according to the characteristic length L with a bin size of ΔlnL = 0.35. The maximum and minimum of the average strain correspond approximately to a homologous temperature of 0.1 and 0.3 respectively, which are also the demarcation temperatures between zone I and zone T, and zone T and zone II, in the structure zone model of Sanders [10]. A linear correlation was obtained between the strain and the natural logarithm of the characteristic length for thin films in a tensile stressed state within zone T. This correlation is indicated with a dashed line. The symbols refer to pure metals while numbers are used to identify amorphous metallic glasses. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
D. Depla, B.R. Braeckman / Thin Solid Films 604 (2016) 90–93
91
The surface diffusion rate depends on the homologous temperature, and can be written as
D ¼ D0 e−CTm =Ts
ð2Þ
according to Flynn [14]. D0 and C are 2 × 10− 4 cm2 s− 1 and 1.5 respectively for closest-packed metal surfaces. With these equations, it is possible to evaluate the impact of the deposition flux on the characteristic length. A decrease in the deposition rate by a factor of 10, results at Ts/Tm = 0.2, in an increase in L by approximately 50%. This increase in L can also be achieved by increasing the homologous temperature from 0.200 to 0.288, or stated differently with a substrate temperature increase of 44%. Some papers on intrinsic stress during thin-film deposition explore the material dependency without considering the difference in F, although it plays a pivotal role in thin-film microstructural evolution. This could be one of the reasons for the missing quantitative relationship between microstructure and intrinsic stress. Eqs. (1) and (2) enable one to compare experiments performed with different metals, at several deposition temperatures, and with different deposition rates. The following procedure was used. Intrinsic stress measurements are in most cases presented as graphs of force per unit width (N/m) vs. film thickness (nm) [8,9,15–31]. Here, the graphs have been digitalized, and the first derivative, or the film stress, was determined at three different film thicknesses (30, 50 and 90 nm), where available, by a linear fit through five data points. From the obtained stress values, the strain was calculated using the biaxial modulus (E / (1 − ν), with E the Young's modulus and ν Poisson's ratio. As Eq. (2) is only valid for closest-packed surfaces, it was assumed that the films have a fiber texture with the closest-packed lattice planes ((111) for fcc metals, (110) for bcc metals and (0001) for hcp metals) parallel to the substrate surface [32–34]. As the closest-packed surfaces typically have the lowest surface energy [35], this assumption seems reasonable. The anisotropy of the biaxial modulus [34,36] was taken into account to calculate the strain. The surface lattice parameter was calculated from the metal's unit cell parameters, and used together with the deposition flux and the diffusion rate to obtain the characteristic length L from Eq. (1). 3. Results and discussion Fig. 1 presents literature film strain results as a function of the characteristic length L (note that L is plotted on a log scale) for the three film thicknesses noted above. To show the overall trend, the data was binned according to the natural logarithm of the characteristic length with a bin size of ΔlnL = 0.35, and the average strain was calculated per bin. The results are plotted as a solid line in Fig. 1. A slight increase in the tensile stress is observed at low L values, reaching a maximum at L ≃ 5 nm. At higher values of L, the tensile stress decreases to become zero at L ≃ 14 nm. Films with L ≥ 14 nm are in compressive stress reaching a minimum (for 30-nm- and 50-nm-thick films) at approximately 28 nm. Above this latter value, the films again become somewhat more tensile, or at least less compressive. To link this trend with the microstructure, the SZM of Sanders [10], which is a refinement of the initial SZM of Movchan and Demchishin [37], has been used. Sanders defines three important zones. Zone I is the low-adatom-mobility zone, often called the hit-and-stick regime, which is characterized by a porous microstructure. The transition zone T is defined as Ts/Tm between 0.1 and 0.3. The out-of-plane growth competition between grains with different crystallographic orientations results in a V-shaped columnar microstructure. At Ts/Tm N 0.3, grain boundaries become mobile [38], and the microstructure changes to a thin film composed of domed, straight columns with larger width. An overview of this, and other, SZMs is given by Mahieu et al. [38].
92
D. Depla, B.R. Braeckman / Thin Solid Films 604 (2016) 90–93
To compare the entire data set, the characteristic length was converted back to Ts/Tm, via Eqs. (1) and (2). To use common values for the surface lattice parameter, and the deposition flux, these parameters were averaged over the entire data set yielding values of a2s = 7.27 × 10−16 cm2 and F = 7.59 x 1015 at cm−2 s−1. In this way, the calculated Ts/Tm values can be used as a normalized values. The output of this normalization procedure is given as the upper horizontal axis of Fig. 1. The observed maximum and minimum in the average strain vs. L plot correspond nicely to the limits defined by the SZM of Sanders. Thus, Fig. 1 links the intrinsic stress during deposition with the microstructure in a quantitative way. It also provides insights into which diffusion processes are dominant in the stress evolution. In zone T, surface mobility is the key process. A higher surface mobility leads to a larger value of L, and as shown in Fig. 1, this results in a lower tensile, or a higher compressive, stress. Several models proposed in the literature explain this trend indeed by an increase of the surface mobility. In the Nix–Clemens [39] model, larger islands lead to a reduction of the tensile stress contribution due to island coalescence. In the model of Chason et al. [8], increased surface mobility is used to explain the mechanisms of compressive stress generation. Insertion of surface adatoms into grain boundaries or triple junctions results in, according to these authors, a compressive stress contribution if the surface mobility is high and the grain boundary mobility low (Ts/Tm b 0.3). In the model presented by Yu et al. [27], a similar reasoning is followed which results in a continuous compressive stress contribution at sufficiently high adatom surface mobility. When the grain boundary density is decreased, this contribution overrules the tensile contribution. We would expect that upon further increase in the mobility, or at larger values of L, the films would become strongly compressive. However, in zone II (Ts/Tm N 0.3), the grain boundary mobility affects the microstructure. Fig. 1 shows that this change in microstructure is connected with a change in trend from compressive back to tensile stress. In both the models proposed by Chason et al. [8] and Yu et al. [27], a larger grain size will result in less compressive stress because the separation distance between the grain boundaries increases. In Fig. 1, a linear correlation between the positive strain and the natural logarithm of L in zone T (see linear fit in Fig. 1) is indicated. The deviation from this line at high values of L within zone T can be explained by the onset of grain growth which reduces the compressive stress. The onset of the deviation starts at Ts/Tm ≃ 0.2 which agrees well with the model proposed by Yu et al. [27]. Decreasing growth stress was mentioned already in the 1968 paper of Klokholm [15] to occur at Ts/ Tm = 0.22. As grain growth can occur in the bulk of the thin film during deposition, one can expect an influence of the film thickness. This behavior can explain the significant decrease of the slope of the fitted line as a function of the film thickness. At lnL = 2.78 (Ts/Tm = 0.22), the strain changes from compressive to tensile (strain at a film thickness of 30 nm = −3.29 × 10−4; strain at 50 nm = −5.97 × 10−5; strain at 90 nm = 3.76 × 10−4). Some intrinsic stress measurements have been published for amorphous metallic alloys [18,40,41]. It is therefore interesting to investigate whether the above procedure can also be applied to these alloys. To convert the deposition rate into a deposition flux (F), the density was estimated from X i ρ¼ X
f i mi f i Vi
ð3Þ
i
with fi, mi, and Vi the fraction, atomic mass and atomic volume of the constituent elements. The elastic properties (Young's modulus and Poisson's ratio) were averaged according to the method proposed by Wang et al. [42] for bulk metallic glasses. For pure (crystalline) metals, the reference temperature for Eq. (2) is the melting point. Indeed, the melting point can be connected to several
mechanical and thermal properties of metals [43]. For metallic glasses, similar correlations are obtained using the glass transition temperature Tg as a reference [44]; this indicates that Tg for these materials is correlated to the bond strength [42] in a similar way as the melting temperature for pure metals. Therefore, we purpose to use the glass transition temperature in this study as a reference temperature for the amorphous alloys. The same assumption was made in the study of Moske et al. [18] on the intrinsic stress development of amorphous Zr–Cu and Zr–Co alloys. The glass transition temperature was calculated based on the model of Lu et al. [45] which links the average melting temperature to the glass transition temperature. Due to the lack of information on the activation energy for adatom diffusion on amorphous alloy surfaces, we assume that Eq. (2) with the same constants used for metals, can be applied. A deviation of this latter assumption would lead to a horizontal shift of the obtained data for amorphous alloys in Fig. 1 (the amorphous alloys are coded by numbers). However the assumption allows us to compare the observed trend which is surprisingly similar to the crystalline metal films. The metallic glasses indeed exhibit a tensile behavior at low homologous temperature, and a compressive state at higher deposition temperature which, under the given assumptions, is the same trend as for the crystalline materials. This leads to the conclusion that the surface mobility for these amorphous alloys is much higher than for their crystalline counterparts because Ts/Tg is approximately 2.6 times larger than Ts/Tm. This conclusion is consistent with the high surface mobility reported by Cao et al. [46] and theoretical studies on the influence of amorphization on atomic diffusion [47].
4. Conclusions The presented results indicate that the proposed theories for the stress evolution appear to be applicable for a wide range of materials and phases. Using only the melting (or glass transition) temperature of the deposited material together with the deposition flux, one can predict the stress state of polycrystalline and amorphous thin films. Indeed, based on Fig. 1, the determined strain can be converted into a stress based on the biaxial modulus. When the films are deposited in the lnL interval 1.37–2.78, the linear fits make the prediction more quantitative as the error of the calculated value is only 0.2 GPa (for a biaxial modulus of 250 GPa). In summary, this compilation of data opens the possibility to calculate/predict the stress state of thin films as a function of deposition parameters.
References [1] M.F. Doerner, W.D. Nix, Stresses and deformation processes in thin-films on substrates, Crc Crit. Rev. Solid State Mater. Sci. 14 (3) (1988) 225–268. [2] F. Spaepen, Interfaces and stresses in thin films, Acta Mater. 48 (1) (2000) 31–42. [3] C.V. Thompson, R. Carel, Stress and grain growth in thin films, J. Mech. Phys. Solids 44 (5) (1996) 657–673. [4] R. Koch, The intrinsic stress of polycrystalline and epitaxial thin metal-films, J. Phys. Condens. Matter 6 (45) (1994) 9519–9550. [5] J.A. Floro, E. Chason, R.C. Cammarata, D.J. Srolovitz, Physical origins of intrinsic stresses in Volmer-Weber thin films, MRS Bull. 27 (1) (2002) 19–25. [6] R. Abermann, Measurements of the intrinsic stress in thin metal-films, Vacuum 41 (4–6) (1990) 1279–1282. [7] G. Janssen, Stress and strain in polycrystalline thin films, Thin Solid Films 515 (17) (2007) 6654–6664. [8] E. Chason, A kinetic analysis of residual stress evolution in polycrystalline thin films, Thin Solid Films 526 (2012) 1–14. [9] R. Koch, Stress in evaporated and sputtered thin films — a comparison, Surf. Coat. Technol. 204 (12–13) (2010) 1973–1982. [10] J.V. Sanders, Chemisorption and Reaction on Metallic Films, vol. 1Academic Press Inc. LTD, London, 1971. [11] T. Michely, in: J. Krug (Ed.), Islands, Mounds and Atoms: Patterns and Processes in Crystal Growth Far From Equilibrium, Springer, Berlin etc., 2003 (ISBN: 3540407286). [12] J. Villain, A. Pimpinelli, L. Tang, D. Wolf, Terrace sizes in molecular-beam epitaxy, J. Phys. I 2 (11) (1992) 2107–2121. [13] H. Brune, Microscopic view of epitaxial metal growth: nucleation and aggregation, Surf. Sci. Rep. 31 (4–6) (1998) 121–229.
D. Depla, B.R. Braeckman / Thin Solid Films 604 (2016) 90–93 [14] C.P. Flynn, Point defect reactions at surfaces and in bulk metals, Phys. Rev. B 71 (8) (2005) 085422. [15] E. Klokholm, B.S. Berry, Intrinsic stress in evaporated metal films, J. Electrochem. Soc. 115 (8) (1968) 823–826. [16] R. Abermann, R. Koch, R. Kramer, Electron-microscope structure and internal-stress in thin silver and gold-films deposited onto MGF2 and SiO substrates, Thin Solid Films 58 (2) (1979) 365–370. [17] R. Abermann, R. Koch, The internal-stress in thin silver, copper and gold-films, Thin Solid Films 129 (1–2) (1985) 71–78. [18] M. Moske, K. Samwer, The origin of internal-stresses in amorphous transition-metal alloy-films, Z. Phys. B Condens. Matter 77 (1) (1989) 3–9. [19] G. Thurner, R. Abermann, Internal-stress and structure of ultrahigh-vacuum evaporated chromium and iron films and their dependence on substrate-temperature and oxygen partial-pressure during deposition, Thin Solid Films 192 (2) (1990) 277–285. [20] R. Koch, D. Winau, A. Fuhrmann, K.H. Rieder, Growth-mode-specific intrinsic stress of thin silver films, Phys. Rev. B 44 (7) (1991) 3369–3372. [21] H.J. Schneeweiss, R. Abermann, Ultra-high vacuum measurements of the internalstress of PVD titanium films as a function of thickness and its dependence on substrate-temperature, Vacuum 43 (5–7) (1992) 463–465. [22] A.L. Shull, F. Spaepen, Measurements of stress during vapor deposition of copper and silver thin films and multilayers, J. Appl. Phys. 80 (11) (1996) 6243–6256. [23] S.C. Seel, C.V. Thompson, S.J. Hearne, J.A. Floro, Tensile stress evolution during deposition of Volmer-Weber thin films, J. Appl. Phys. 88 (12) (2000) 7079–7088. [24] J.A. Floro, S.J. Hearne, J.A. Hunter, P. Kotula, E. Chason, S.C. Seel, C.V. Thompson, The dynamic competition between stress generation and relaxation mechanisms during coalescence of Volmer-Weber thin films, J. Appl. Phys. 89 (9) (2001) 4886–4897. [25] A.L. Del Vecchio, F. Spaepen, The effect of deposition rate on the intrinsic stress in copper and silver thin films, J. Appl. Phys. 101 (6) (2007) 063518. [26] A. Proszynski, D. Chocyk, G. Gladyszewski, Stress modification in gold metal thin films during thermal annealing, Opt. Appl. 39 (4) (2009) 705–710. [27] H.Z. Yu, C.V. Thompson, Grain growth and complex stress evolution during VolmerWeber growth of polycrystalline thin films, Acta Mater. 67 (2014) 189–198. [28] D. Floetotto, Z.M. Wang, L.P.H. Jeurgens, E.J. Mittemeijer, Kinetics and magnitude of the reversible stress evolution during polycrystalline film growth interruptions, J. Appl. Phys. 118 (5) (2015) 055305. [29] S.C. Seel, C.V. Thompson, Piezoresistive microcantilevers for in situ stress measurements during thin film deposition, Rev. Sci. Instrum. 76 (7) (2005) 075103. [30] D. Chocyk, T. Zientarski, A. Proszynski, T. Pienkos, L. Gladyszewski, G. Gladyszewski, Evolution of stress and structure in Cu thin films, Cryst. Res. Technol. 40 (4–5) (2005) 509–516.
93
[31] J. Yu, Y. Kim, Stress shift to tensile side by the interruption of deposition during Al and Cr film processing, Mater. Trans. 55 (11) (2014) 1777–1780. [32] H.-M. Zhang, Y. Zhang, K.-W. Xu, V. Ji, General compliance transformation relation and applications for anisotropic cubic metals, Mater. Lett. 62 (8–9) (2008) 1328–1332. [33] D. Tromans, Elastic anisotropy of HCP metal crystals and polycrystals, IJRRAS 6 (4) (2011) 462–483. [34] L.B. Freund, S. Suresh, Thin Film Materials: Stress, Defect Formation and Surface Evolution, Cambridge University Press, 2004 (ISBN: 9781139449823). [35] H. Ibach, Physics of Surfaces and Interfaces, Springer-Verlag, 2006 (ISBN 9783540347095). [36] D. Tromans, Elastic anisotropy of HCP metals crystals and polycrystals, IJRRAS 6 (4) (2011) 462–483. [37] B.A. Movchan, A.V. Demchishin, Investigation of the structure and properties of thick vacuum- deposited films of nickel, titanium, tungsten, alumina and zirconium dioxide, Fiz. Met. Metalloved. 28 (4) (1969) 653–660. [38] S. Mahieu, P. Ghekiere, D. Depla, R. De Gryse, Biaxial alignment in sputter deposited thin films, Thin Solid Films 515 (4) (2006) 1229–1249. [39] W.D. Nix, B.M. Clemens, Crystallite coalescence: a mechanism for intrinsic tensile stresses in thin films, J. Mater. Res. 14 (8) (1999) 3467–3473. [40] S. Dina, U. Geyer, G. Vonminnigerode, Investigations on macroscopic intrinsic stress in amorphous binary-alloy films, Ann. Phys. 1 (3) (1992) 164–171. [41] U. Geyer, U. von Hulsen, H. Kopf, Internal interfaces and intrinsic stress in thin amorphous Cu-Ti and Co-Tb films, J. Appl. Phys. 83 (6) (1998) 3065–3070. [42] W.H. Wang, The elastic properties, elastic models and elastic perspectives of metallic glasses, Prog. Mater. Sci. 57 (3) (2012) 487–656. [43] G. Grimvall, S. Sjodin, Correlation of properties of materials to debye and melting temperatures, Phys. Scr. 10 (6) (1974) 340–352. [44] R.T. Qu, Z.Q. Liu, R.F. Wang, Z.F. Zhang, Yield strength and yield strain of metallic glasses and their correlations with glass transition temperature, J. Alloys Compd. 637 (2015) 44–54. [45] Z. Lu, J. Li, Correlation between average melting temperature and glass transition temperature in metallic glasses, Appl. Phys. Lett. 94 (6) (2009) 061913. [46] C.R. Cao, Y.M. Lu, H.Y. Bai, W.H. Wang, High surface mobility and fast surface enhanced crystallization of metallic glass, Appl. Phys. Lett. 107 (14) (2015) 141606. [47] A. Milchev, I. Avramov, On the influence of amorphization on atomic diffusion in condensed systems, Phys. Status Solidi B 120 (1) (1983) 123–130.
Contents lists available at ScienceDirect
Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Critical review
Quantitative correlation between intrinsic stress and microstructure of thin films D. Depla, B.R. Braeckman Department of Solid State Sciences, Ghent University, Krijgslaan 281/S1, 9000 Ghent, Belgium
a r t i c l e
i n f o
a b s t r a c t A critical review of the available literature on thin film intrinsic stress has generated a database with 111 entries representing 19 different metals deposited by evaporation. Although there is a wide range of experimental conditions, the data can be presented in a comprehensible way based on the surface mean free path of diffusing adatoms. This characteristic length L is calculated based on the deposition temperature, the melting temperature of the evaporant, and the deposition flux. The calculated strain as a function of L not only shows the trends in a quantitative way, but also allows one to connect the data with the thin-film microstructure as represented in structure-zone models. The proposed procedure appears to also be applicable to amorphous metallic glass thin films (4 alloy systems, 29 entries) as well. © 2016 Elsevier B.V. All rights reserved.
Available online 23 March 2016
Contents 1. Introduction . . . . . 2. Method . . . . . . . 3. Results and discussion . 4. Conclusions. . . . . . References. . . . . . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
1. Introduction Intrinsic stress evolution during thin film deposition by evaporation is a research topic that has been studied for decades and has been reviewed in several papers [1–9]. The intrinsic stress is strongly material-dependent, and for continuous, non-epitaxial thin films can be divided into two groups. For materials deposited under conditions leading to low adatom surface mobility, a tensile stress state is observed, while a compressive stress state is usually obtained for high-adatom-mobility materials. For metals deposited at the same substrate temperature Ts, the evaporant melting temperature Tm is a good measure to distinguish between these two classes since diffusion processes for metals scale inversely with Tm. The Arrhenius behavior of these processes explains the importance of the deposition (or substrate) temperature Ts, and hence experimental trends are often presented in terms of the homologous temperature, i.e. the ratio between the deposition temperature and the melting temperature, both expressed in Kelvin (Ts/Tm). The homologous temperature is also used to classify the microstructure of evaporated thin films in structure-zone models (SZM). A relationship between the microstructure and the intrinsic stress of thin films can therefore be expected. Despite this apparent connection, no
http://dx.doi.org/10.1016/j.tsf.2016.03.039 0040-6090/© 2016 Elsevier B.V. All rights reserved.
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
90 90 91 92 92
quantitative proof has been given in the literature. Here this quantitative link is made and this allows one to predict the stress state of evaporated thin films. 2. Method Kinetic models used to describe thin-film nucleation [11] predict scaling laws for the mean free path of the diffusing adatoms before they form a nucleus or are captured by an existing island, also known as the characteristic nucleation length L. When the critical nucleus size is one atom, which is a quite common situation during thermal evaporation, L is related to the incident flux of atoms F [11–13] sffiffiffi !1=6 1 Da2s L¼ η F
ð1Þ
with D the adatom surface diffusion rate, as the lattice parameter of the surface unit cell, and η a dimensionless parameter with a maximum value of 0.25.
Fig. 1. Strain, measured at different film thicknesses, as a function of the characteristic length L (lower horizontal axis). The symbols refer to the references while the color code is used to identify the material. The upper horizontal axis converts the characteristic length L to the homologous temperature via Eqs. (1) and (2) in the text, using a deposition flux F averaged over all references. To calculate the average strain (solid line), the data was ordered according to the characteristic length L with a bin size of ΔlnL = 0.35. The maximum and minimum of the average strain correspond approximately to a homologous temperature of 0.1 and 0.3 respectively, which are also the demarcation temperatures between zone I and zone T, and zone T and zone II, in the structure zone model of Sanders [10]. A linear correlation was obtained between the strain and the natural logarithm of the characteristic length for thin films in a tensile stressed state within zone T. This correlation is indicated with a dashed line. The symbols refer to pure metals while numbers are used to identify amorphous metallic glasses. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
D. Depla, B.R. Braeckman / Thin Solid Films 604 (2016) 90–93
91
The surface diffusion rate depends on the homologous temperature, and can be written as
D ¼ D0 e−CTm =Ts
ð2Þ
according to Flynn [14]. D0 and C are 2 × 10− 4 cm2 s− 1 and 1.5 respectively for closest-packed metal surfaces. With these equations, it is possible to evaluate the impact of the deposition flux on the characteristic length. A decrease in the deposition rate by a factor of 10, results at Ts/Tm = 0.2, in an increase in L by approximately 50%. This increase in L can also be achieved by increasing the homologous temperature from 0.200 to 0.288, or stated differently with a substrate temperature increase of 44%. Some papers on intrinsic stress during thin-film deposition explore the material dependency without considering the difference in F, although it plays a pivotal role in thin-film microstructural evolution. This could be one of the reasons for the missing quantitative relationship between microstructure and intrinsic stress. Eqs. (1) and (2) enable one to compare experiments performed with different metals, at several deposition temperatures, and with different deposition rates. The following procedure was used. Intrinsic stress measurements are in most cases presented as graphs of force per unit width (N/m) vs. film thickness (nm) [8,9,15–31]. Here, the graphs have been digitalized, and the first derivative, or the film stress, was determined at three different film thicknesses (30, 50 and 90 nm), where available, by a linear fit through five data points. From the obtained stress values, the strain was calculated using the biaxial modulus (E / (1 − ν), with E the Young's modulus and ν Poisson's ratio. As Eq. (2) is only valid for closest-packed surfaces, it was assumed that the films have a fiber texture with the closest-packed lattice planes ((111) for fcc metals, (110) for bcc metals and (0001) for hcp metals) parallel to the substrate surface [32–34]. As the closest-packed surfaces typically have the lowest surface energy [35], this assumption seems reasonable. The anisotropy of the biaxial modulus [34,36] was taken into account to calculate the strain. The surface lattice parameter was calculated from the metal's unit cell parameters, and used together with the deposition flux and the diffusion rate to obtain the characteristic length L from Eq. (1). 3. Results and discussion Fig. 1 presents literature film strain results as a function of the characteristic length L (note that L is plotted on a log scale) for the three film thicknesses noted above. To show the overall trend, the data was binned according to the natural logarithm of the characteristic length with a bin size of ΔlnL = 0.35, and the average strain was calculated per bin. The results are plotted as a solid line in Fig. 1. A slight increase in the tensile stress is observed at low L values, reaching a maximum at L ≃ 5 nm. At higher values of L, the tensile stress decreases to become zero at L ≃ 14 nm. Films with L ≥ 14 nm are in compressive stress reaching a minimum (for 30-nm- and 50-nm-thick films) at approximately 28 nm. Above this latter value, the films again become somewhat more tensile, or at least less compressive. To link this trend with the microstructure, the SZM of Sanders [10], which is a refinement of the initial SZM of Movchan and Demchishin [37], has been used. Sanders defines three important zones. Zone I is the low-adatom-mobility zone, often called the hit-and-stick regime, which is characterized by a porous microstructure. The transition zone T is defined as Ts/Tm between 0.1 and 0.3. The out-of-plane growth competition between grains with different crystallographic orientations results in a V-shaped columnar microstructure. At Ts/Tm N 0.3, grain boundaries become mobile [38], and the microstructure changes to a thin film composed of domed, straight columns with larger width. An overview of this, and other, SZMs is given by Mahieu et al. [38].
92
D. Depla, B.R. Braeckman / Thin Solid Films 604 (2016) 90–93
To compare the entire data set, the characteristic length was converted back to Ts/Tm, via Eqs. (1) and (2). To use common values for the surface lattice parameter, and the deposition flux, these parameters were averaged over the entire data set yielding values of a2s = 7.27 × 10−16 cm2 and F = 7.59 x 1015 at cm−2 s−1. In this way, the calculated Ts/Tm values can be used as a normalized values. The output of this normalization procedure is given as the upper horizontal axis of Fig. 1. The observed maximum and minimum in the average strain vs. L plot correspond nicely to the limits defined by the SZM of Sanders. Thus, Fig. 1 links the intrinsic stress during deposition with the microstructure in a quantitative way. It also provides insights into which diffusion processes are dominant in the stress evolution. In zone T, surface mobility is the key process. A higher surface mobility leads to a larger value of L, and as shown in Fig. 1, this results in a lower tensile, or a higher compressive, stress. Several models proposed in the literature explain this trend indeed by an increase of the surface mobility. In the Nix–Clemens [39] model, larger islands lead to a reduction of the tensile stress contribution due to island coalescence. In the model of Chason et al. [8], increased surface mobility is used to explain the mechanisms of compressive stress generation. Insertion of surface adatoms into grain boundaries or triple junctions results in, according to these authors, a compressive stress contribution if the surface mobility is high and the grain boundary mobility low (Ts/Tm b 0.3). In the model presented by Yu et al. [27], a similar reasoning is followed which results in a continuous compressive stress contribution at sufficiently high adatom surface mobility. When the grain boundary density is decreased, this contribution overrules the tensile contribution. We would expect that upon further increase in the mobility, or at larger values of L, the films would become strongly compressive. However, in zone II (Ts/Tm N 0.3), the grain boundary mobility affects the microstructure. Fig. 1 shows that this change in microstructure is connected with a change in trend from compressive back to tensile stress. In both the models proposed by Chason et al. [8] and Yu et al. [27], a larger grain size will result in less compressive stress because the separation distance between the grain boundaries increases. In Fig. 1, a linear correlation between the positive strain and the natural logarithm of L in zone T (see linear fit in Fig. 1) is indicated. The deviation from this line at high values of L within zone T can be explained by the onset of grain growth which reduces the compressive stress. The onset of the deviation starts at Ts/Tm ≃ 0.2 which agrees well with the model proposed by Yu et al. [27]. Decreasing growth stress was mentioned already in the 1968 paper of Klokholm [15] to occur at Ts/ Tm = 0.22. As grain growth can occur in the bulk of the thin film during deposition, one can expect an influence of the film thickness. This behavior can explain the significant decrease of the slope of the fitted line as a function of the film thickness. At lnL = 2.78 (Ts/Tm = 0.22), the strain changes from compressive to tensile (strain at a film thickness of 30 nm = −3.29 × 10−4; strain at 50 nm = −5.97 × 10−5; strain at 90 nm = 3.76 × 10−4). Some intrinsic stress measurements have been published for amorphous metallic alloys [18,40,41]. It is therefore interesting to investigate whether the above procedure can also be applied to these alloys. To convert the deposition rate into a deposition flux (F), the density was estimated from X i ρ¼ X
f i mi f i Vi
ð3Þ
i
with fi, mi, and Vi the fraction, atomic mass and atomic volume of the constituent elements. The elastic properties (Young's modulus and Poisson's ratio) were averaged according to the method proposed by Wang et al. [42] for bulk metallic glasses. For pure (crystalline) metals, the reference temperature for Eq. (2) is the melting point. Indeed, the melting point can be connected to several
mechanical and thermal properties of metals [43]. For metallic glasses, similar correlations are obtained using the glass transition temperature Tg as a reference [44]; this indicates that Tg for these materials is correlated to the bond strength [42] in a similar way as the melting temperature for pure metals. Therefore, we purpose to use the glass transition temperature in this study as a reference temperature for the amorphous alloys. The same assumption was made in the study of Moske et al. [18] on the intrinsic stress development of amorphous Zr–Cu and Zr–Co alloys. The glass transition temperature was calculated based on the model of Lu et al. [45] which links the average melting temperature to the glass transition temperature. Due to the lack of information on the activation energy for adatom diffusion on amorphous alloy surfaces, we assume that Eq. (2) with the same constants used for metals, can be applied. A deviation of this latter assumption would lead to a horizontal shift of the obtained data for amorphous alloys in Fig. 1 (the amorphous alloys are coded by numbers). However the assumption allows us to compare the observed trend which is surprisingly similar to the crystalline metal films. The metallic glasses indeed exhibit a tensile behavior at low homologous temperature, and a compressive state at higher deposition temperature which, under the given assumptions, is the same trend as for the crystalline materials. This leads to the conclusion that the surface mobility for these amorphous alloys is much higher than for their crystalline counterparts because Ts/Tg is approximately 2.6 times larger than Ts/Tm. This conclusion is consistent with the high surface mobility reported by Cao et al. [46] and theoretical studies on the influence of amorphization on atomic diffusion [47].
4. Conclusions The presented results indicate that the proposed theories for the stress evolution appear to be applicable for a wide range of materials and phases. Using only the melting (or glass transition) temperature of the deposited material together with the deposition flux, one can predict the stress state of polycrystalline and amorphous thin films. Indeed, based on Fig. 1, the determined strain can be converted into a stress based on the biaxial modulus. When the films are deposited in the lnL interval 1.37–2.78, the linear fits make the prediction more quantitative as the error of the calculated value is only 0.2 GPa (for a biaxial modulus of 250 GPa). In summary, this compilation of data opens the possibility to calculate/predict the stress state of thin films as a function of deposition parameters.
References [1] M.F. Doerner, W.D. Nix, Stresses and deformation processes in thin-films on substrates, Crc Crit. Rev. Solid State Mater. Sci. 14 (3) (1988) 225–268. [2] F. Spaepen, Interfaces and stresses in thin films, Acta Mater. 48 (1) (2000) 31–42. [3] C.V. Thompson, R. Carel, Stress and grain growth in thin films, J. Mech. Phys. Solids 44 (5) (1996) 657–673. [4] R. Koch, The intrinsic stress of polycrystalline and epitaxial thin metal-films, J. Phys. Condens. Matter 6 (45) (1994) 9519–9550. [5] J.A. Floro, E. Chason, R.C. Cammarata, D.J. Srolovitz, Physical origins of intrinsic stresses in Volmer-Weber thin films, MRS Bull. 27 (1) (2002) 19–25. [6] R. Abermann, Measurements of the intrinsic stress in thin metal-films, Vacuum 41 (4–6) (1990) 1279–1282. [7] G. Janssen, Stress and strain in polycrystalline thin films, Thin Solid Films 515 (17) (2007) 6654–6664. [8] E. Chason, A kinetic analysis of residual stress evolution in polycrystalline thin films, Thin Solid Films 526 (2012) 1–14. [9] R. Koch, Stress in evaporated and sputtered thin films — a comparison, Surf. Coat. Technol. 204 (12–13) (2010) 1973–1982. [10] J.V. Sanders, Chemisorption and Reaction on Metallic Films, vol. 1Academic Press Inc. LTD, London, 1971. [11] T. Michely, in: J. Krug (Ed.), Islands, Mounds and Atoms: Patterns and Processes in Crystal Growth Far From Equilibrium, Springer, Berlin etc., 2003 (ISBN: 3540407286). [12] J. Villain, A. Pimpinelli, L. Tang, D. Wolf, Terrace sizes in molecular-beam epitaxy, J. Phys. I 2 (11) (1992) 2107–2121. [13] H. Brune, Microscopic view of epitaxial metal growth: nucleation and aggregation, Surf. Sci. Rep. 31 (4–6) (1998) 121–229.
D. Depla, B.R. Braeckman / Thin Solid Films 604 (2016) 90–93 [14] C.P. Flynn, Point defect reactions at surfaces and in bulk metals, Phys. Rev. B 71 (8) (2005) 085422. [15] E. Klokholm, B.S. Berry, Intrinsic stress in evaporated metal films, J. Electrochem. Soc. 115 (8) (1968) 823–826. [16] R. Abermann, R. Koch, R. Kramer, Electron-microscope structure and internal-stress in thin silver and gold-films deposited onto MGF2 and SiO substrates, Thin Solid Films 58 (2) (1979) 365–370. [17] R. Abermann, R. Koch, The internal-stress in thin silver, copper and gold-films, Thin Solid Films 129 (1–2) (1985) 71–78. [18] M. Moske, K. Samwer, The origin of internal-stresses in amorphous transition-metal alloy-films, Z. Phys. B Condens. Matter 77 (1) (1989) 3–9. [19] G. Thurner, R. Abermann, Internal-stress and structure of ultrahigh-vacuum evaporated chromium and iron films and their dependence on substrate-temperature and oxygen partial-pressure during deposition, Thin Solid Films 192 (2) (1990) 277–285. [20] R. Koch, D. Winau, A. Fuhrmann, K.H. Rieder, Growth-mode-specific intrinsic stress of thin silver films, Phys. Rev. B 44 (7) (1991) 3369–3372. [21] H.J. Schneeweiss, R. Abermann, Ultra-high vacuum measurements of the internalstress of PVD titanium films as a function of thickness and its dependence on substrate-temperature, Vacuum 43 (5–7) (1992) 463–465. [22] A.L. Shull, F. Spaepen, Measurements of stress during vapor deposition of copper and silver thin films and multilayers, J. Appl. Phys. 80 (11) (1996) 6243–6256. [23] S.C. Seel, C.V. Thompson, S.J. Hearne, J.A. Floro, Tensile stress evolution during deposition of Volmer-Weber thin films, J. Appl. Phys. 88 (12) (2000) 7079–7088. [24] J.A. Floro, S.J. Hearne, J.A. Hunter, P. Kotula, E. Chason, S.C. Seel, C.V. Thompson, The dynamic competition between stress generation and relaxation mechanisms during coalescence of Volmer-Weber thin films, J. Appl. Phys. 89 (9) (2001) 4886–4897. [25] A.L. Del Vecchio, F. Spaepen, The effect of deposition rate on the intrinsic stress in copper and silver thin films, J. Appl. Phys. 101 (6) (2007) 063518. [26] A. Proszynski, D. Chocyk, G. Gladyszewski, Stress modification in gold metal thin films during thermal annealing, Opt. Appl. 39 (4) (2009) 705–710. [27] H.Z. Yu, C.V. Thompson, Grain growth and complex stress evolution during VolmerWeber growth of polycrystalline thin films, Acta Mater. 67 (2014) 189–198. [28] D. Floetotto, Z.M. Wang, L.P.H. Jeurgens, E.J. Mittemeijer, Kinetics and magnitude of the reversible stress evolution during polycrystalline film growth interruptions, J. Appl. Phys. 118 (5) (2015) 055305. [29] S.C. Seel, C.V. Thompson, Piezoresistive microcantilevers for in situ stress measurements during thin film deposition, Rev. Sci. Instrum. 76 (7) (2005) 075103. [30] D. Chocyk, T. Zientarski, A. Proszynski, T. Pienkos, L. Gladyszewski, G. Gladyszewski, Evolution of stress and structure in Cu thin films, Cryst. Res. Technol. 40 (4–5) (2005) 509–516.
93
[31] J. Yu, Y. Kim, Stress shift to tensile side by the interruption of deposition during Al and Cr film processing, Mater. Trans. 55 (11) (2014) 1777–1780. [32] H.-M. Zhang, Y. Zhang, K.-W. Xu, V. Ji, General compliance transformation relation and applications for anisotropic cubic metals, Mater. Lett. 62 (8–9) (2008) 1328–1332. [33] D. Tromans, Elastic anisotropy of HCP metal crystals and polycrystals, IJRRAS 6 (4) (2011) 462–483. [34] L.B. Freund, S. Suresh, Thin Film Materials: Stress, Defect Formation and Surface Evolution, Cambridge University Press, 2004 (ISBN: 9781139449823). [35] H. Ibach, Physics of Surfaces and Interfaces, Springer-Verlag, 2006 (ISBN 9783540347095). [36] D. Tromans, Elastic anisotropy of HCP metals crystals and polycrystals, IJRRAS 6 (4) (2011) 462–483. [37] B.A. Movchan, A.V. Demchishin, Investigation of the structure and properties of thick vacuum- deposited films of nickel, titanium, tungsten, alumina and zirconium dioxide, Fiz. Met. Metalloved. 28 (4) (1969) 653–660. [38] S. Mahieu, P. Ghekiere, D. Depla, R. De Gryse, Biaxial alignment in sputter deposited thin films, Thin Solid Films 515 (4) (2006) 1229–1249. [39] W.D. Nix, B.M. Clemens, Crystallite coalescence: a mechanism for intrinsic tensile stresses in thin films, J. Mater. Res. 14 (8) (1999) 3467–3473. [40] S. Dina, U. Geyer, G. Vonminnigerode, Investigations on macroscopic intrinsic stress in amorphous binary-alloy films, Ann. Phys. 1 (3) (1992) 164–171. [41] U. Geyer, U. von Hulsen, H. Kopf, Internal interfaces and intrinsic stress in thin amorphous Cu-Ti and Co-Tb films, J. Appl. Phys. 83 (6) (1998) 3065–3070. [42] W.H. Wang, The elastic properties, elastic models and elastic perspectives of metallic glasses, Prog. Mater. Sci. 57 (3) (2012) 487–656. [43] G. Grimvall, S. Sjodin, Correlation of properties of materials to debye and melting temperatures, Phys. Scr. 10 (6) (1974) 340–352. [44] R.T. Qu, Z.Q. Liu, R.F. Wang, Z.F. Zhang, Yield strength and yield strain of metallic glasses and their correlations with glass transition temperature, J. Alloys Compd. 637 (2015) 44–54. [45] Z. Lu, J. Li, Correlation between average melting temperature and glass transition temperature in metallic glasses, Appl. Phys. Lett. 94 (6) (2009) 061913. [46] C.R. Cao, Y.M. Lu, H.Y. Bai, W.H. Wang, High surface mobility and fast surface enhanced crystallization of metallic glass, Appl. Phys. Lett. 107 (14) (2015) 141606. [47] A. Milchev, I. Avramov, On the influence of amorphization on atomic diffusion in condensed systems, Phys. Status Solidi B 120 (1) (1983) 123–130.