Nanoindentation creep behaviors of amorphous, tetragonal, and bcc Ta films

Materials Science and Engineering A 516 (2009) 253–258

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Nanoindentation creep behaviors of amorphous, tetragonal, and bcc Ta films Z.H. Cao, P.Y. Li, X.K. Meng ∗ National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 16 December 2008 Received in revised form 8 March 2009 Accepted 9 March 2009 Keywords: Nanoindentation Creep Ta Nanocrystalline Amorphous

a b s t r a c t Nanoindentation creep tests were carried out at the maximum indentation load from 500 to 9000 ␮N to study the indentation size effect (ISE) on the creep behavior of amorphous, nanocrystalline (NC) bcc and NC tetragonal Ta films. For NC bcc and tetragonal Ta films, the creep strain rate ε˙ decreases and stress exponent n increases with enhanced peak loads or indent depth, and are therefore both indentation size dependent. However, an inverse ISE on ε˙ and n is found for amorphous Ta films. The difference of the ISE is attributed to the distinct creep deformation process. Several creep mechanisms including self-diffusion along the indenter/specimen interface, grain boundary diffusion and sliding, and dislocation climb have been introduced to interpret the ISE for NC Ta films. The inverse ISE on amorphous Ta films is explained by the shear transformation zone theory. © 2009 Elsevier B.V. All rights reserved.

1. Introduction The creep behavior of nanocrystalline (NC) materials has been extensively studied over the past decade, since they will strongly influence the working reliability in engineering applications [1–4]. Even at room temperature, significant creep through grain boundary (GB) diffusion and sliding has been found for NC materials [5–8]. For example, it was found that the creep deformation of NC Cu films with average grain size (d) of 5 nm was controlled by GB sliding [9]. Similarly, NC Ni films with d < 20 nm also exhibit GB mediated creep deformation at room temperature [10]. However, other reports indicate that the creep behavior of NC materials is dominated by dislocation climb [11,12]. Consequently, it is necessary to investigate the intrinsic creep mechanisms of NC materials further. Nanoindentation is a popular way to study the creep behavior of materials [13,14], especially for metal films [15]. Besides hardness, the creep strain rate ε˙ and stress exponent n can be obtained in this way. Recently, the indentation size effects (ISE) on the creep behavior of NC materials during nanoindentation test have been extensively investigated. For example, the creep behavior of NC metal, such as Cu, Al and Ni, indicate that hardness and creep strain rate both have a remarkable ISE [16–19]. Furthermore, a similar ISE on n was also found in single crystal and amorphous materials during nanoindentation testing [20]. In addition to experimental results, ISE on the mechanical properties are also observed during atomistic simulations [21] and in analytic models [22].

∗ Corresponding author. Fax: +86 25 8359 5535. E-mail address: [email protected] (X.K. Meng). 0921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2009.03.019

Pure Ta, as most of the refractory metals, is generally present in the form of amorphous, tetragonal (␤ phase) and bcc (␣ phase) phase structure [23,24]. The flow stress and modulus of NC Ta have been widely investigated through experimental tests [25–27] and molecular dynamics simulations [28]. It was found that the mechanical properties of Ta strongly depend on the phase structure and grain size. Moreover, the creep behavior of coarse-grained Ta were studied amply by compress and tensile creep tests at temperatures above 1000 ◦ C, and the dislocation climb is the dominant creep mechanism [29,30]. Most investigations of creep in NC metal are usually performed at room temperature because grains tend to grow at higher temperature. However, the creep behavior of amorphous and NC Ta have not been studied in detail. In a previous work [8], we studied the creep behavior of NC tetragonal Ta films by nanoindentation tests. It was found that the GB mediated mechanism is the dominant deformation process for NC tetragonal Ta films. However, the room temperature creep behavior and deformation mechanism of amorphous and NC bcc Ta films is still unexplored. The present paper mainly focuses on the nanoindentation creep behavior of amorphous and NC bcc Ta films under different indentation loads at room temperature, and on comparing with results from NC tetragonal Ta films. Our aim is to explore the ISE on the creep behavior of Ta films with three different phase structures and the corresponding deformation mechanisms.

2. Experimental Ta films were deposited on Si (1 1 1) substrates in pure argon gas by DC magnetron sputtering at room temperature using a 99.95% purity Ta target. The base pressure in the sputtering chamber was

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Fig. 1. XRD spectrum of amorphous, NC tetragonal and bcc Ta films.

kept at 6.2 × 10−5 Pa, while the working pressure was 1.4 Pa. The sputtering power was about 150 W for amorphous Ta films and 280 W for tetragonal and bcc ones. While the substrate temperature was room temperature for amorphous and tetragonal Ta films,

it was about 500 ◦ C for bcc Ta. The deposition rate was about 20 nm/min for amorphous Ta and 50 nm/min for tetragonal and bcc Ta. The different Ta films were also prepared by Narayan et al. [31], who suggested that the lower deposition rate can result in an amorphous Ta since it can increase the oxygen content in the films [32]. Amorphous Ta films with 60 nm thickness on Si (1 0 0) were also prepared by pulsed laser deposition (PLD) at a base pressure of 1.3 × 10−5 Pa [31] with a relatively low deposition rate of about 3 nm/min. In the present study, we used DC magnetron sputtering at 6.5 × 10−5 Pa base pressure to prepare the amorphous Ta films with a comparatively high deposition rate of about 20 nm/min that decreases oxygen content. On the other hand, the higher base pressure of 6.5 × 10−5 Pa in the present study compared with that in the literature [31] can increase the oxygen content. The main impurity contents in the present amorphous Ta films, such as oxygen (∼1.2 ± 0.1 at.%), nitrogen (∼1.2 ± 0.1 at.%) and Argon (∼0.6 ± 0.1 at.%), were detected, which is slightly higher than that in tetragonal Ta films. The formation of amorphous Ta is believed to partly result from oxygen impurities, which reduce the mobility of Ta atoms on the Si substrate. The decrease in mobility prohibits the formation of long-range order needed for crystallization of Ta films [31,32]. The thickness of the Ta films was kept at about 2 ␮m through controlling the total deposited time. Then, the microstructure of as-deposited Ta films was characterized by Xray diffraction (XRD; Rigaku, Ultima-lll) and transmission electron microscope (TEM; JEM-2100).

Fig. 2. Plan-view TEM images and selected area electron diffraction pattern of (a) tetragonal, (c) bcc and (d) amorphous Ta; and (b) lattice image of tetragonal Ta film.

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P˙ = 5000 ␮N/s. The drift measurement is performed immediately prior to testing. Then, the drift rate is calculated by fitting a line to the displacement versus time during the Drift Analysis Time. The rate will be used to correct the acquired data from the real indentation testing. In order to ensure the credibility of measurement results, the holding time for the creep and hardness measurements was 40 and 5 s, respectively. Then the samples were unloaded to 10% of the maximum load and held at that constant load for the thermal drift correction. Finally, the indenter was withdrawn to zero load. Indentation at each load value was repeated at least 10 times, and the results are consistent. 3. Results 3.1. Microstructural characterization Fig. 3. Experimental and fitted creep curve of NC tetragonal Ta films at 9000 ␮N. The obtained fitting parameters are hi = 180.1, a = 7.1, ti = 1.8, b = 0.248 and k = 0.001.

The nanoindentation tests were carried out at room temperature using a TriboIndenter from Hysitron Inc. with a Berkovich diamond indenter where the nominal tip radius of curvature R was about 150 nm. Consequently, the minimum depth for self-similar indentation is estimated to be about 9 nm, which is calculated from the equation R(1 − sin 70.3◦ ) = 0.06R [20]. The displacement and load resolutions of the instrument were 0.1 nm and 100 nN, respectively. To avoid the substrate effect, the indentation depth was controlled below 1/10 of the film thickness. Ta films were tested via changing the maximum loads from 500 to 9000 ␮N at a constant loading rate

Fig. 1 shows the XRD spectra of the three Ta films. The XRD results clearly indicate that no crystalline peak is found in amorphous Ta films. For as-deposited NC tetragonal Ta films, we find the (0 0 2) and (0 0 4) ␤ phase peaks at 33.6◦ and 70.8◦ ; the ␤ phase is the only phase. For NC bcc Ta films, the two main peaks positioned at 38.7◦ and 82.4◦ are the (1 1 0) and (2 2 0) peaks of ␣ Ta. A small amount of ␤ phase is also found at 33.6◦ corresponding to (0 0 2) the peak of ␤ Ta. It is not expected that the little amount of ␤ phase has a significant effect on the creep behavior of bcc Ta. The average grain size of the tetragonal and bcc Ta films is about 10 and 40 nm respectively, determined using the Scherrer method. A typical plan-view TEM image of a tetragonal Ta film is shown in Fig. 2a, where the corresponding selected area electron diffraction (SAED) pattern is presented in the bottom right corner. It is found that the tetragonal Ta film is composed of equiaxial NC grain. A detailed lattice image is shown in Fig. 2b, from which the grain size distribution is determined to be from 3 to 8 nm. The grain size determined by TEM should be more accurate compared to that of XRD. A plan-view TEM of bcc Ta film also composed of equiaxial NC grain and the corresponding SAED are shown in Fig. 2c. The grain sizes range from 20 to 60 nm. Fig. 2d shows a typical TEM image of amorphous Ta film. The SAED presented in the bottom right corner indicates that the Ta film is indeed amorphous. 3.2. Equations for the theoretical analysis For a self-similar indenter, the indentation strain rate ε˙ and the stress  in depth-sensing indentation technique obey the following relations [33,34] ε˙ =

Fig. 4. (a) Creep responses of NC tetragonal Ta films at 500, 5000 and 9000 ␮N peak loads. (b) Variation of creep depth hc with different peak loads at room temperature.

1 dh , h dt

=

P Ac

(1)

Fig. 5. Variation of the hardness with different peak loads at room temperature.

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lowest hc at the same peak loads and the hc increases from 3.1 to 6.9 nm with enhanced peak loads from 500 to 9000 ␮N. Additionally, a moderate hc is present for amorphous Ta films. On the other hand, the hardness was determined by means of the Oliver–Pharr method [35]. The effect of creep on the hardness is avoided since the load holding time is just 5 s during the hardness measurement. Consequently, the resultant hardness is believed to be the intrinsic strength of Ta films. Fig. 5 shows the hardness of all Ta films as a function of peak load. The hardness of amorphous Ta films is higher than that of NC Ta films. However, the creep depth of amorphous Ta film is also larger than that of NC bcc Ta film, as shown in Fig. 4b. It should be noted that this phenomenon was also found for NC metals. Creep is apparent in NC Cu even at room temperature [5], although NC Cu often exhibits higher strength compared with that of the corresponding coarse-grain Cu [36]. Hence, it is reasonable that the metastable amorphous Ta films exhibit a high hardness and poor stability simultaneously. Furthermore, a more obvious ISE on the hardness is found for bcc and amorphous Ta films compared to that of NC tetragonal ones. This is attributed to the different deformation responses. The creep stain rate ε˙ of NC bcc Ta films shown in Fig. 6a was calculated by Eqs. (1) and (2). For all peak loads, ε˙ decreases within the holding time to a stable value in the steady-state creep stage. As is shown in the magnified curve in the left top corner of Fig. 6a, the steady ε˙ decreases from 3.6 × 10−4 to 1.4 × 10−4 s−1 when the peak load increases from 500 to 9000 ␮N and exhibits a strong ISE. Moreover, the NC tetragonal Ta films exhibit a similar ISE on the steady-state ε˙ which decreases from 1.5 × 10−3 to 5.0 × 10−4 s−1

Fig. 6. Variation of creep strain rate with holding time at peak loads from 500 to 9000 ␮N for (a) bcc and tetragonal, and (b) amorphous Ta films.

where P is the indentation load, h is the instantaneous indenter displacement, t is time, and Ac is the contact area. To calculate the displacement rate h˙ = dh/dt, the indenter displacement versus time curve at constant indentation load can be fitted by the following empirical law [20] h(t) = hi + a(t − ti )b + kt,

(2)

where hi , a, ti , b and k are fitting constants. The function in Eq. (2) is found to fit the creep curves at all indentation loads accurately. An example of an experimental result (Pmax = 9000 ␮N) and fitting curve is shown in Fig. 3. 3.3. Nanoindentation creep behavior Fig. 4a shows the variation of creep depth hc of NC tetragonal Ta films with holding time at peak loads of 500, 5000 and 9000 ␮N. It is evident that the hc is larger at higher peak loads. The curves also show that there is an initial abrupt increase in hc , followed by a stage with a smaller rate of increase for each load. The initial stage is known as transient creep and the latter corresponds to steadystate creep. The amorphous and NC bcc Ta films show similar creep indentation response to the tetragonal Ta films. The creep curves of the three kinds of Ta films have different hc at the same peak loads. As shown in Fig. 4b, the NC tetragonal Ta films exhibit the highest hc at same indentation loads in the three kinds of Ta films. Its hc increases from 6.3 to 16.3 nm with increasing peak loads from 500 to 9000 ␮N. Moreover, it is found that NC bcc Ta films have the

Fig. 7. The plots of ln(strain rate) versus ln(stress) at different peak loads for (a) bcc and (b) amorphous Ta films.

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Fig. 8. Variation of stress exponent n with different peak loads.

with enhanced peak loads, as shown in the right insert in Fig. 6a. A similar behavior was also found in the nanoindentation creep study of NC Ni films [37]. It is expected that the creep behavior is dominated by different deformation mechanisms at different peak loads or indent depths. For amorphous Ta films, however, an inverse ISE on the steady ε˙ is found from strain rate versus time curves as shown in Fig. 6b, where the ε˙ increases from 4.2 × 10−5 to 2.9 × 10−4 s−1 as peak load increase from 500 to 9000 ␮N. Note that the inverse ISE has not been found for other amorphous materials, such as fused quartz and silicon oxide films [20,38]. The reason responsible for the inverse ISE will be discussed in a latter section. To investigate the stress exponent n of Ta films, the relation of ln(strain rate) versus ln(stress) has been plotted in Fig. 7a and b. Thus, n can be determined through the slope of the curves. In the case of each curve under different peak loads, the n decreases to a steady-state value with prolonged holding time. As shown in Fig. 7a, the n of bcc Ta films at the beginning of the load hold is about 68.6, but it decreases toward a steady-state value of about 34.9 at 500 ␮N. The value 34.9 in the steady-state creep stage can be taken as the n of the whole creep process. Similarly, the value 4.3 and 78.7 can be taken as the n for tetragonal and amorphous Ta films respectively, which is shown Fig. 7b and Fig. 8. Fig. 8 shows the variations of n as a function of peak load. It is found that n increases with enhanced peak loads for NC bcc and tetragonal Ta films, which both exhibit a strong ISE. On the contrary, an inverse ISE on n is revealed for amorphous Ta films, and n decreases quickly with enhanced peak loads. This behavior has not been reported in previous research. 4. Discussion 4.1. Creep mechanisms of NC bcc and tetragonal Ta films To reveal which mechanism is responsible for the ISE on nanoindentation creep behavior, the change of ε˙ and n with peak load or

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indent depth will be considered. Fig. 6a shows the change of ε˙ with peak load for NC bcc Ta films, where the ε˙ decreases with increasing peak loads. The ISE are present during nanoindentation creep tests. We find lower ε˙ and higher n for NC bcc Ta films. Firstly, GB diffusion and sliding can be excluded by the high n ranging from 34.9 to 86. Instead, dislocation climb may be the dominant creep mechanism for most indent depths. As shown in Fig. 5, an obvious ISE on the hardness indicates that the plastic deformation is dominated by dislocation activation. It is noted that the present hardness of NC bcc Ta films is higher than that of NC bcc Ta with grain size of 76.5 nm in Ref. [26]. This also suggests that the dislocation mediated mechanism is still dominant for NC bcc Ta with d as small as about 40 nm. Moreover, at lower peak loads and shallower indent depths, especially for 500 ␮N and about 30 nm depth, the self-diffusion along indenter/specimen interface will be responsible for the creep behavior [39,40]. A similar ISE on creep behavior is present for NC tetragonal Ta films. The change of ε˙ with peak load for NC tetragonal Ta films is shown in the right insert of Fig. 6a, where ε˙ decreases with increasing peak load. Moreover, the high ε˙ ranging from 1.5 × 10−3 to 5.0 × 10−4 s−1 can come up to that of NC Cu films with about 5 nm grain size which is dominated by GB diffusion and sliding deformation [9]. On the other hand, an obvious ISE on n is found from Fig. 8, where n increases from 4.3 to 24 with increasing peak loads from 500 to 9000 ␮N. The high ε˙ and low n indicate that GB diffusion and sliding is the dominant deformation mechanism for all peak loads. Creep controlled by GB diffusion and sliding has been found for other NC metals through experiments [11,12] and molecular dynamics simulation [41,42]. Note that other mechanism may be effective at lower peak load or shallower indent depth. For example, the small indent penetration depth is below 28 nm and is very close to the surface of the sample at 500 ␮N. Thus, the self-diffusion along the indenter/specimen interface and along the free surface of the specimen will play an important role during the creep [39,40]. The critical indentation depth for self-diffusion along the indenter/specimen interface is about 30 nm for ultrafine grained Cu [43]. As indent depth increases to about 80 nm at 3000 ␮N peak load, the diffusion length l from the area beneath the indenter to the free surface will become much longer. Therefore, the indenter/specimen interface diffusion mechanism is weakened. Then, n increases to be about 17.9, and the ε˙ decreases to about 6.1 × 10−4 s−1 . This indicates the transition from self-diffusion along indenter/specimen interface to GB diffusion and sliding. The hardness in the present work is much lower than that of tetragonal Ta film with an average grain size of 32.3 nm in Ref. [25]. We suggest that the inverse Hall-Petch relation takes over as the average grain size of Ta film decreases to below 10 nm. Consequently, the dislocation pile-up is excluded by the softening hardness behavior. Finally, the n slightly increases to be about 24 at about 200 nm indent depth under 9000 ␮N. 4.2. Creep mechanism of amorphous Ta films The creep behavior of amorphous Ta films is different from that of NC bcc and tetragonal Ta films. There occurs an inverse ISE on the creep behavior during nanoindentation creep tests. As shown in Fig. 6b, ε˙ increases with enhanced peak loads or indent depth. Moreover, Fig. 8 shows that n decreases from 469.9 to 78.7 with enhanced peak loads or indent depth. This is also different from the ISE of other amorphous materials, such as fused quartz and silicon oxide films where n increases with enhanced peak load or indent depth [20,38]. In general, amorphous metal is deformed by a local rearrangement of atoms to accommodate shear strain, as explained by shear transformation zone (STZ) theory [44,45]. It can be seen from Fig. 7b and Fig. 8 that the present creep process starts out to be almost ideally plastic with high n and rate-insensitivity at high

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stress level. Under the applied stress above the yield stress, a local dilatation of the nearby free volume will be induced by the movement of STZ, which will create the shear bands of the STZ [46,47]. Finally, this will cause a local softening of the amorphous Ta films and the applied strain relaxing. Moreover, at room temperature and high stress level, n exhibits an inverse ISE. Argon [47] systematically predicted the change of the strain rate sensitivity m (m = 1/n [34]) from the equation, m=

f (/0 ) × 0 f kT

(3)

where  is the applied shear stress,  0 is ideal shear strength, and f is the shear volume. f(/ 0 ) and m are symmetrical about their maximum at / 0 = 0.5. The  0 of Ta single crystal is ∼11 GPa [27], and the present stress regime of amorphous Ta under the indenter determined by Eq. (1) is about 7.8–10.6 GPa. It is suggested that / 0 > 0.5. Moreover, the stress, like hardness, also decreases with the increasing indentation load. Thus, m increases and n decreases with increasing indentation load for the present amorphous Ta films. Therefore, the inverse ISE on n can be explained by the decreasing stress with increasing indent depth. Moreover, the change of f during nanoindentation creep should be considered. Generally, f increases along with indent depth. This also can decrease n. Note that amorphous materials, such as Si and Ge, can undergo crystallization under the indenter [48,49]. Moreover, the metastable tetragonal Ta was also found to undergo phase transformation from tetragonal to bcc phase underneath the indenter [50]. It is thus in the present work possible that Ta transformed from the metastable amorphous phase to bcc Ta during nanoindentation creep testing. Especially, at the highest indentation load of 9000 ␮N, it is found that the n of amorphous Ta film is very close to that of bcc Ta film. The phase transformation during nanoindentation testing may be partly responsible for the inverse ISE on n of amorphous Ta film. 5. Conclusions The creep behavior of amorphous, NC bcc and NC tetragonal Ta films were characterized by nanoindentation tests at different peak loads ranging from 500 to 9000 ␮N. The NC Ta films exhibit a normal ISE on ε˙ and n during creep. For NC tetragonal Ta films, ε˙ decreases from 1.5 × 10−3 to 5.0 × 10−4 s−1 and n increases from 4.3 to 24 with increasing peak loads or indent depth. The high ε˙ and low n indicate that GB diffusion and sliding is the dominant creep mechanism at all indent depths. It is noticed that the self-diffusion along the indenter/specimen interface may take effect for shallow indent depth under low peak loads, such as 500 ␮N. Similarly, n of NC bcc Ta increases from 34.9 to 86 with increasing peak loads. The high n can be attributed to the dislocation climb creep mechanism. However, the amorphous Ta films exhibit an inverse ISE on the creep behavior. The n decreases from 469.9 to 78.7 with enhanced peak loads, which is well explained by the shear transformation zone theory.

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