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Effects of oblique-angle deposition on intrinsic stress evolution during polycrystalline film growth
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ScienceDirect Acta Materialia 77 (2014) 284–293 www.elsevier.com/locate/actamat
Effects of oblique-angle deposition on intrinsic stress evolution during polycrystalline film growth Hang Z. Yu, Carl V. Thompson ⇑ Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Received 16 March 2014; received in revised form 27 May 2014; accepted 29 May 2014
Abstract Precise control of the residual stress in polycrystalline films, which remains a central but difficult task in a variety of emerging technologies, requires synergistic manipulation of multiple processing parameters. In addition to the substrate temperature and the rate of deposition, the angle of incidence of the deposition flux is known to affect structure evolution processes during film formation. However, its role in influencing the evolution of the intrinsic stress has not been determined. In this work, we investigate the effects of oblique-angle deposition on intrinsic stress evolution in polycrystalline gold and nickel films, using in situ stress measurements as well as ex situ surface and microstructure characterization. We find that as the angle between the surface normal and the direction of the deposition flux increases, the thickness at which film coalescence occurs increases and the post-coalescence stress shifts toward the tensile direction. We suggest that the first trend is associated with the effects of shadowing on the nucleation density in the pre-coalescence regime, and we attribute the second trend to an increase in surface roughness and shadowing effects associated with the dome-shaped surfaces of individual grains. According to this view, oblique-angle deposition on a mesoscopically rough surface eliminates or reduces condensation at and near grain boundaries, and therefore lowers the rate of adatom–grain boundary attachment, resulting in reduction in the compressive component of the intrinsic stress. The stress evolution map built from this work suggests routes to achieve specific stress levels in polycrystalline films. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Intrinsic stress; Thin films; Shadowing; In situ measurement; Surface roughness
1. Introduction The use of polycrystalline thin films is ubiquitous in emerging fields of science and technology, from microelectronics and flexible electronics to micro- and nanomanufacturing [1–5]. For many applications, control of the residual stress in the films remains a central but difficult task [6]. Residual stress includes extrinsic factors, such as thermal stress due to differential thermal expansion, and intrinsic factors, such as intrinsic stress caused by structure evolution during film deposition [7]. Intrinsic stresses can ⇑ Corresponding author. Tel.: +1 617 253 7652; fax: +1 617 258 6749.
E-mail address: [email protected] (C.V. Thompson).
dominate in determining the residual stress in a film [1,7]. For films grown from the vapor phase, for example, intrinsic stresses of the order of 100 MPa or 1 GPa can be generated during the film formation processes [8,9]. Such high levels of stress can cause formation of voids and hillocks, cracking, buckling, delamination and other reliability problems [1,2,7]. The intrinsic stresses can also have profound effects on the properties and performance of films released from their substrates to perform mechanical functions as in nano- and micro-electromechanical devices such as nanobeam-based sensors and actuators [10,11]. The intrinsic stress in polycrystalline films is often correlated with surface and microstructure evolution processes during film formation [12–21]. Polycrystalline films form
http://dx.doi.org/10.1016/j.actamat.2014.05.060 1359-6454/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
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through nucleation of islands that grow to impinge and coalesce to form a continuous film. This is known as the Volmer–Weber mode of film formation [22]. Three types of intrinsic stress evolution behaviors have been identified during evaporative deposition of polycrystalline films [8,9,23]. In all three types of behaviors, a tensile stress develops during island coalescence due to an elastic deformation that occurs when islands meet and grain boundaries form through a “zipping” process [24,25]. After the film becomes continuous, the intrinsic stress continues to evolve in a tensile state under conditions of low atomic mobility (Type I behavior) or evolves toward or into a compressive state under conditions of high atomic mobility (Type II). Under conditions of intermediate atomic mobility, the evolution of post-coalescence stress involves a turnaround from a compressive state to a tensile state (intermediate behavior type) [23]. These stress evolution behaviors are controlled by a number of kinetic processes during film deposition, including adatom diffusion on the grain surface, adatom attachment to grain boundaries and grain growth during film thickening [16,23,26,27]. The homologous temperature Th (defined as the substrate temperature divided by the melting temperature in K, i.e. Th = T/Tm) and the rate of deposition are known to strongly influence these behaviors [8,9,16,23,28]. Precise control of the residual stress in thin films requires simultaneous manipulation of multiple processing parameters during deposition. In addition to the substrate temperature and deposition rate, the angle of the incident deposition flux is known to influence the surface morphology and grain structure of polycrystalline films through self-shadowing effects that lead to roughening of the film surface and vacancy formation in the bulk of the film [29–34]. However, the effects of the deposition angle on intrinsic stress evolution in thin films have not been investigated. As the first report of in situ stress measurements for oblique-angle deposition, we show here that the angle of the incident flux significantly affects the evolution of the intrinsic stress during growth of polycrystalline gold and nickel films. Specifically, a higher incidence angle leads to
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(i) an increase of the nominal thickness at which islands coalesce to form a continuous film (i.e. the coalescence thickness), and (ii) an overall less compressive or a more tensile post-coalescence stress in the film. We explain the first trend by self-shadowing in the pre-coalescence stage, and attribute the second trend to an increase in surface roughness and the shadowing effects associated with the dome-shaped surfaces of the grains in the post-coalescence stage. These findings lead to a stress evolution map in which the three types of stress evolution behaviors (i.e. Type I, intermediate type and Type II) are categorized as a function of the homologous temperature and the incidence angle. 2. Experimental methods Gold and nickel films were deposited in an ultra-highvacuum e-beam evaporation system, with a base pressure of 5.0 109 Torr. The deposition rate measured using a quartz crystal microbalance was adjusted to ensure that the real deposition flux (number of incident atoms per unit area of substrate surface per time) was the same for depositions carried out at different incident flux angles. All the films were deposited at a deposition rate normal to the ˚ s1, as confirmed plane of the substrate surface of 0.5 A using atomic force microscopy (AFM) measurements. The surface and grain structures of the films were characterized using a Veeco Nanoscope IV AFM in tapping mode and a JEOL 2010 transmission electron microscope. Intrinsic stress evolution during film growth was measured in situ using the cantilever deflection method. The details of this method can be found elsewhere [23,35,36]. To enable in situ measurements during oblique-angle deposition, we designed and fabricated a tiltable stress sensor platform, with which the inclination of the cantilever could be varied from 0° to 90°, as shown in the schematic illustration in Fig. 1a, where a refers to the angle of the incident flux relative to the direction normal to the substrate surface. A picture of our tiltable stress sensor setup is shown in Fig. 1b. It is important to note that the deflection of
Fig. 1. (a) Illustration of the configuration used for in situ stress measurements during oblique angle-deposition and (b) a picture of the tiltable stress sensor.
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the cantilever was of the order of 10 nm, while the length of the cantilever was of the order of 1 cm. Therefore, deflection of the cantilevers led to negligible changes (106 rad) in the incidence angle during film growth. This work focuses on oblique-angle deposition with a of low and intermediate values (a = 0–60° for Au, a = 0–45° for Ni); the resultant films were continuous and consisted of columnar grains with boundaries generally parallel with the substrate surface normal. Stress evolution during glancing angle deposition that leads to tilted isolated nanocolumnar structures [37–41] is beyond the scope of this work.
The intrinsic stress in a film results in a force exerted at the interface between the film and the substrate [12]. In situ stress measurements give the force per unit width, F/w, at the interface as a function of the film thickness h [7–9,12]. Due to a force balance, F/w is equal to the product of the average stress in the film and the film thickness h. Typical shapes of the stress curves of Type I, intermediate type and Type II behavior observed during normal angle deposition (a = 0°) are schematically shown in Fig. 2a.
In situ stress measurements for oblique-angle deposition are summarized in Fig. 2b, in which we show stress evolution curves for gold films deposited with incidence angles a = 0°, 30°, 52°, 60° and for nickel films with a = 0°, 30°, 45°. Considering the rough surface of the films deposited at high incidence angles (as will be discussed in Section 4), the horizontal axis in this figure and Figs. 4 and 5 is labeled “nominal film thickness” rather than “film thickness”. All these depositions and measurements were carried out at room temperature. Under these conditions, nickel films display the intermediate type and Type I stress behaviors; gold films display the intermediate type and Type II stress behaviors. As a signature of the intermediate type of stress behavior, the post-coalescence stress turnarounds [23] observed in nickel and gold films have been marked with red arrows. The film thicknesses at which the peak tensile stress occurred (hpeak) have been marked with black arrows. Two trends are noted from the in situ measurement results. First, the peak thickness hpeak increases with the incidence angle a for both gold and nickel films. This trend is highlighted in Fig. 3a in which the peak thickness hpeak is plotted as a function of the incidence angle a. Second, the overall post-coalescence stress evolution shifts toward the
Fig. 2. (a) Schematic stress evolution curves for Type I, intermediate type and Type II stress behaviors and (b) in situ stress measurement during oblique-angle deposition of gold and nickel films. The tensile peaks corresponding to film coalescence are marked with black arrows. The post-coalescence thickness at which the stress turns to evolve in the tensile direction is marked with red arrows. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. (a) Plot of the film thickness at which the tensile peak occurs, hpeak, as a function of the incidence angle a and (b) plot of the value of F/w as a function of the incidence angle a, for Au and Ni at h = 20 nm and h = 40 nm.
3. Effects of incidence angle on intrinsic stress evolution in gold and nickel films
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tensile direction as a is increased. This trend is further illustrated in Fig. 3b by plotting the value of F/w at given film thicknesses as a function of the incidence angle a. It is widely agreed that grain boundary formation during island coalescence leads to the development of a tensile stress observed early in the film formation process, and that the film thickness at which the stress is at its maximum value (hpeak) corresponds to the end of the coalescence process [8,9,25]. The first trend noted above, an increase in hpeak with increasing a, thus indicates that the thickness at which the films became fully continuous (i.e. the coalescence thickness) increases with increasing incidence angle. We explain this finding as to be due to geometrical effects in oblique-angle deposition as follows. During the initial stage of Volmer–Weber film growth, when isolated islands nucleate and grow independently, the incident beam arrives from an oblique angle and the atoms are preferentially captured by pre-existing islands due to self-shadowing [30,42], and possibly steering [43,44]. This lowers the rate of island nucleation and therefore increases the island size and the nominal film thickness at which coalescence occurs, resulting in the trends shown in Fig. 3a. The second trend, that the post-coalescence stress evolution shifts toward the tensile direction as a is increased, is clear from the in situ stress measurements in Fig. 2b and the plots in Fig. 3b. Gold films display typical Type II stress behavior at a = 0° and a = 30°, but as the incidence angle is further increased, the post-coalescence stress becomes much less compressive. At a = 60°, the compressive stress level remains low after coalescence. Moreover, a stress turnaround from a compressive to a tensile state, which is a signature of the intermediate type of stress behavior, is seen at a thickness of 40 nm, as indicated by the red arrow. On the other hand, at room temperature the nickel films display the intermediate type of stress behavior up to a = 30°, with the turnaround thickness reducing from 37 nm at a = 0°, to 15 nm at a = 30°. At a = 45° the stress turnaround disappears. Instead, the instantaneous stress (i.e. the slope of the stress evolution curve [18,23]) of the nickel film is in a tensile state in all growth stages, which is typical for Type I stress behavior. Overall, the intrinsic stress in gold and nickel films becomes less compressive or more tensile as the incidence angle increases, during which the stress behavior changes from Type II to the intermediate type and then to Type I. The origin of this trend will be analyzed in the following section. 4. Origin of the stress shift toward the tensile direction at higher incidence angles It has been discovered that in the intermediate type and Type II stress behaviors, the intrinsic stress evolution is governed by a compressive component controlled by adatom diffusion [16,23,26,27] and a tensile component controlled by grain growth during deposition [23]. The instantaneous stress during film growth, rin, can be thus
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comp expressed as rin ¼ rcomp þ rgg and rgg in in , where rin in refer to the compressive component of the instantaneous stress and the instantaneous stress caused by grain growth, respectively. Therefore, the second trend noted above, i.e. a stress shift toward the tensile direction with increasing incidence angles, has two possible origins: (i) strengthening of the grain growth component ðrgg in Þ, and (ii) weakening of the compressive component ðrcomp in Þ, at a higher value of a.
4.1. Effects of incidence angle on the grain growth component of intrinsic stress To investigate the possibility of origin (i) above, we characterized the microstructures of the films using planview and cross-sectional TEM imaging. Under the experimental conditions in this work (a = 0–60° for Au and a = 0–45°for Ni), we did not observe the tilted isolated nanocolumnar structures that are sometimes observed to result in refractory metals deposited at a glancing angle (a 80° or more) [37–41]. Instead, the films were continuous and consisted of columnar, transverse grains. Fig. 4a–c shows plan-view TEM images of Ni films grown at an a of 45°, with film thicknesses of 7, 14 and 28 nm, respectively. Under conditions of high [45] and intermediate atomic mobility [23], the grain size is known to increase with the film thickness for films grown by normal angle deposition. The same trend is clearly seen here for the Ni films grown by oblique-angle deposition. In Fig. 4d, the measured inplane grain size is plotted as a function of the film thickness for films deposited at a = 0°, 30° and 45°. The average grain size was determined by tracing the boundaries of hundreds of grains on transparencies, followed by image analysis of the transparencies. For all the cases, the grain size is seen to increase linearly with the film thickness, as observed for films deposited at normal incidence [23,45]. In addition, an increase of the incidence angle a from 0° to 30° to 45° leads to only a small decrease in the average grain size in Ni films, at the same film thickness. This suggests that the influence of incidence angle a on the grain growth component ðrgg in Þ of the intrinsic stress should be weak. Moreover, the decrease in grain size in films deposited at a = 30° and a = 45° should lead to weakening, rather than strengthening, of the grain growth component. Consequently, the possibility of origin (i) can be excluded. In Fig. 5, we quantify the effects of grain growth during deposition on intrinsic stress evolution in Ni films, and compare the effects for the cases of a = 0°, a = 30° and a = 45°. We first plot the instantaneous stress rin at various film thicknesses for the three cases. Here the instantaneous stress is given by the slope of the stress evolution curves in Fig. 2b, i.e. rin ¼ DðFDh=wÞ. In a recently developed model, we have shown that when the grain size d increases linearly with film thickness h, the instantaneous stress caused by grain growth during deposition can be calculated using 1 Da rgg [23,36], where M is the in ðdÞ ¼ M d ð1 þ MDa=ry dÞ biaxial modulus of Ni (290 GPa [46]), Da is the grain
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Fig. 4. Plan-view TEM images of Ni films deposited at an incidence angle of 45° with film tn can be calculated uhickness (a) 7 nm, (b) 14 nm and (c) 28 nm. (d) The grain size–thickness relationships in Ni films deposited at incidence angles of 0° [23], 30° and 45°.
Fig. 5. Comparison of the in situ instantaneous stress measurements as well as the stress components caused by grain growth and the compressive mechanism, for Ni films deposited at a = 0°, 30° and 45°.
˚ [47,48]) and ry is the tensile yield boundary width (1.0 A stress. Using the grain size data in Fig. 4, we calculated the grain growth component of the instantaneous stress 1 ðrgg in Þ at a = 0°, a = 30° and a = 45°, as shown by the blue solid, black dash-dotted and red dashed lines in Fig. 5. It 1 For interpretation of color in Fig. 5, the reader is referred to the web version of this article.
can be seen that the magnitude of rgg in is slightly lower at a = 30° and a = 45° than at a = 0°, but the difference is extremely small. It should be noted that depending on the average grain size, film thickness and processing method, different values of tensile yield stress have been reported for nanocrystalline Ni [23,49–52]. For the calculation of the grain growth component of the intrinsic stress we use ry = 600 MPa [23]. It can be shown that the conclusion, that rgg in changes little as a changes from 0° to 30° to 45°, is not affected for ry values ranging from a few hundred MPa to 1 GPa. The compressive component of the instantaneous stress ¼ rin rgg can be then determined as rcomp in in . As shown in Fig. 5, the compressive instantaneous stress is 300–500 MPa at a = 0° and is 150–300 MPa at a = 30°, whereas at a = 45° this stress is in the range of 0–90 MPa. Clearly, the compressive component is substantially influenced by the angle of the incident flux a. Therefore, the differences in the stress behavior at different incidence angles are dominated by changes in the compressive component of the intrinsic stress ðrcomp in Þ, rather than by the changes in the grain growth component ðrgg in Þ. To summarize, based on a qualitative discussion on grain growth during deposition in Fig. 4 and a quantitative analysis of different stress components in Fig. 5, we conclude that the stress shift toward the tensile direction
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does not originate from the strengthening of the grain growth component. Instead, it originates from the weakening of the compressive component at higher incidence angles (i.e. origin (ii)). 4.2. Effects of oblique-angle deposition on the compressive component of intrinsic stress Chason and co-workers [16,26,27] proposed that the post-coalescence compressive stress observed in Type II behavior is caused by diffusion of adatoms from the surface of the film into grain boundaries. In this model, excess atoms are incorporated into the grain boundaries during deposition because there is a non-equilibrium excess of adatoms on the surface during deposition. These extra atoms at grain boundaries are then seen to cause the compressive component of the intrinsic stress ðrcomp in Þ. This view is supported by a number of experiments and simulations [13,20,21,23]. The decrease in rcomp in , which is seen as a is increased, should therefore correlate with a change in the adatom–grain boundary interaction. 4.2.1. Characterization of surface roughness Adatom diffusion and adatom–grain boundary interaction occur on the film surface during deposition, and therefore are influenced by the surface morphology. In this work, the surface topography was characterized using AFM for films deposited at different incidence angles. Fig. 6 shows AFM images for 115 nm thick gold films deposited at (a) a = 0° and (b) a = 60°, and 60 nm thick nickel films deposited at (c) a = 0° and (d) a = 45°. These images show no evidence of strong in-plane anisotropy, as observed in the films deposited by glancing angle deposition [37–41]. Typical 1-D surface profiles are compared in Fig. 6e for gold films deposited at a = 0° and a = 60°, and in Fig. 6f for nickel films deposited at a = 0° and a = 45°. In both cases, as the incidence angle a is increased, the peaks in the surface height profile become sharper and higher, indicating an increase in the local surface steepness. In surface analysis, the degree of steepness of a local surface can be described by the inclination angle H [53], which is defined as the angle between the normal of a local surface and the normal of the horizontal surface. A higher value of the inclination angle H means a steeper local surface. The distribution of the inclination angles of a film surface can be determined by processing the AFM images as discussed elsewhere [36,53]. Fig. 7a and b shows the distribution of inclination angles (H) (i.e. distribution of steepness) on the surfaces of gold and nickel films deposited at different oblique angles. For gold films, as shown in Fig. 7a, the steepness distribution curves are similar for a = 0° and a = 30°. However, as the incidence angle a is further increased, the distribution curves move toward larger H values, indicating an increase in the area of steep regions. Interestingly, the stress evolution curves in Fig. 2b show that at a = 0° and a = 30°, the gold films develop
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compressive stress after coalescence, which is typical for Type II stress behavior. As the incidence angle a is further increased, the post-coalescence stress shifts toward the tensile direction. Therefore, there appears to be a correlation between the increase in surface roughness and the tensile shift of the post-coalescence stress in gold films. This correlation can also be seen in nickel films by comparing Fig. 7b with the stress evolution curves in Fig. 2b. The results in Figs. 6 and 7 clearly show that the surface of a polycrystalline film formed by oblique-angle deposition is rough, and that the surface roughness increases as the incidence angle a is increased. This can be explained by the self-shadowing effect, for which the atom flux is preferentially captured by the higher surface sites of the film [29–34]. In addition, due to the short-range attraction between the substrate and the atom flux, the atomic trajectory can deviate significantly from the original one as the atoms approach a surface from an oblique angle. This is known as the steering effect [43,44], and gives rise to a redistribution of the incident atoms according to their morphology-dependent trajectories. Both the shadowing effect and the steering effect lead to an enhancement of the surface roughness during deposition. Comparing the steepness distribution curves with the stress evolution curves suggests a correlation between the surface roughness and adatom– grain boundary interaction. The origin of this correlation will be discussed next. 4.2.2. Influence of surface roughness on the adatom–grain boundary interaction For rough surfaces, the terraces and step edges on an individual grain surface should be taken into account, and the grain surface can no longer be treated as flat, as in the models in Refs. [16,23]. The surface roughness significantly influences the adatom–grain boundary attachment process. Specifically, an increase in the surface roughness will lower the rate of adatom–grain boundary attachment. This is because downhill diffusion from higher terraces leads to substantially reduced adatom attachment to grain boundaries (as will be shown in detail in the next paragraph) so that the rate of adatom–grain boundary attachment is limited by the number of adatoms condensing on the terraces adjacent to a grain boundary. On a rougher surface, more step edges are present and the terrace length is shorter. As a result, fewer atoms condense on the two terraces adjacent to a grain boundary, and therefore the rate of adatom–grain boundary attachment is lower. The corresponding compressive component of the intrinsic stress ðrcomp in Þ is thus lower too. The influence of surface roughness and terrace length on adatom–grain boundary interaction is illustrated in Fig. 8. 4.2.3. The dome-shadowing effect For a sufficiently rough surface, oblique-angle deposition can lead to zero condensation on the terraces adjacent to the grain boundaries due to shadowing of dome-shaped
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Fig. 6. AFM images (1 lm 1 lm) of 115 nm thick gold films deposited at incidence angles of (a) 0° and (b) 60° and 60 nm thick nickel films deposited at (c) 0° and (d) 45°. Comparison of the 1-D surface profiles (e) in Au films deposited at a = 0° and 60°, and (f) in Ni films deposited at a = 0° and 45°.
grain surfaces. This effect is illustrated in Fig. 9, where the region without adatom condensation has been highlighted in red. In this scenario, adatom attachment to grain boundaries requires downhill diffusion of adatoms to cross the step edges, as illustrated in the atomic-scale schematic in Fig. 9. The rate for crossing a step edge can be written as m ¼ m0 eðEs þDEÞ=kT , compared to m ¼ m0 eEs =kT for diffusion on a terrace, where Es is the activation energy for terrace diffusion and DE is the additional thermal energy needed to overcome the Ehrlich–Schwoebel (ES) barrier, which has been estimated to be 0.1 eV for face-centered cubic metals [54,55]. It is important to note that m0 < m0 , because m0 is the attempt frequency for a random walk irrespective of direction, whereas m0 is the attempt frequency for a jump in a specific direction. For example, field ion microscopy experiments show that mm00 102 for homoepitaxial growth
of Pt films [56]. Consequently, the rate for step edge crossing is much lower than that for terrace diffusion; for DE = 0.1 eV and mm00 ¼ 102 , we have mm ¼ 2 104 at room temperature. Moreover, as an adatom crosses a step, it has a probability pE of being incorporated into the edge of the step. If the probability of an atom diffusing from a high terrace to a grain boundary is p, p ¼ 1 ny pE , where ny is the number of step edges in the diffusion path. As a result, the rate of adatom–grain boundary incorporation is further reduced with an increase in the number of step edges necessary for the adatoms to cross. Because of above reasons, the need for downhill diffusion over significant distances will severely limit the number of excess adatoms on terraces adjacent to the grain boundaries and will reduce the incorporation of excess atoms in the boundaries. In the scenario illustrated in
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Fig. 7. Distribution of the inclination angles of (a) the gold film surfaces and (b) the nickel film surfaces.
Fig. 9, therefore, the adatom–grain boundary attachment process is substantially suppressed, and the resultant compressive component of the intrinsic stress is much lower than in the case when condensation occurs on the two terraces adjacent to a grain boundary. As the incidence angle increases, the shadowed area increases, and this domeshadowing effect is stronger. To summarize, an increase in the incidence angle a leads to an increase in the surface roughness and a stronger dome-shadowing effect. These effects result in reduction in the adatom–grain boundary interaction and therefore a reduction in the compressive component of the intrinsic stress. This explains the shift of the intrinsic stress toward the tensile direction when the films are deposited at higher incidence angles, as indicated by the in situ stress measurements. 5. Stress evolution map Based on the above discussion, we conclude that an increase in the incidence angle leads to reduced incorporation of excess atoms at grain boundaries and therefore a weaker compressive component of the intrinsic stress. As the homologous temperature decreases, adatom diffusivities
Fig. 8. Illustration of adatom–grain boundary attachment on (a) a relatively flat surface with more atoms condensing on the terrace adjacent to a grain boundary and (b) a rougher surface with fewer atoms condensing on the terrace adjacent to a grain boundary.
are reduced; as the incidence angle increases, the distance that adatoms must diffuse and the number of ledges they must cross, increases. As a consequence of both of these effects, the intrinsic stress shifts toward the tensile direction, and the stress evolution behavior changes from Type II to the intermediate type and then to Type I. A stress evolution map summarizing this behavior is shown in Fig. 10, in which the experimental data for Au, Ni, Ag [16], Cu [18], Pt [23], Pd [23], Cr [57], Ti [58] and Al [59] are plotted. In this map, the horizontal axis represents the atomic mobility, with the mobility decreasing from left to right, and the vertical axis represents the required diffusion distance for adatom–grain boundary incorporation, with the diffusion distance decreasing from the top to the bottom. In moving from the lower-left to
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temperature and the deposition rate has been developed in Ref. [23]. The two stress evolution maps together suggest routes to synergistic control of deposition conditions to achieve specific residual stress levels required for optimal performance and reliability of films to be used in different applications. 6. Conclusions Using in situ stress measurements, ex situ surface and microstructure characterization, and analytical modeling, we have studied the influence of the angle of the incident atomic flux on the evolution of intrinsic stress during vapor-phase growth of polycrystalline films. Key results from this work can be summarized as follows:
Fig. 9. Illustration of the dome-shadowing model. The shadowed region has been highlighted in red. Downhill diffusion of adatoms to cross the step edges is illustrated in the atomic-scale schematic. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 10. Stress evolution map summarizing the effects of the homologous deposition temperature for the film (Th) and the angle of incidence of the deposition flux (a) on the mode of stress evolution during film deposition. Here the same type of stress behavior is plotted using the same shape symbols, and the same material is in the same color. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the upper-right of the map, therefore, the adatom–grain boundary incorporation process is reduced, and the type of stress evolution changes from Type II to the intermediate type and to Type I. The boundaries of the regions associated with different stress types were determined empirically. A similar stress evolution map that categorizes the stress types as a function of the film’s homologous
The intrinsic stress evolution is significantly influenced by the angle of the incident atomic flux during vaporphase growth. Due to self-shadowing, a higher incidence angle leads to an increase in the film thickness at which the peak tensile stress occurs, hpeak. After the film becomes continuous, a higher incidence angle leads to a shift of the intrinsic stress toward the tensile direction. Grain structure characterization shows that the incidence angle only weakly affects the grain growth process during film growth in these studies. The shift of the intrinsic stress toward the tensile direction, therefore, originates from the weakening of the compressive component caused by a reduction of the adatom–grain boundary interaction. We suggest that the decrease of the compressive stress is associated with the increase in surface roughness and the shadowing effects caused by the dome-like shapes of the surfaces of individual grains. When the surface is sufficiently rough, the dome-shadowing effect during oblique-angle deposition leads to little condensation on the terraces adjacent to grain boundaries, and therefore a very small compressive stress associated with incorporation of excess atoms at the boundaries. Conditions under which Type I, the intermediate type and Type II stress behaviors are observed can be categorized as a function of the homologous deposition temperature of the film and the incidence angle of the flux in a stress map. The residual stress in polycrystalline films can be controlled and optimized for specific applications through synergistic control of various processing parameters including the substrate temperature, the deposition rate and the angle of the incidence of the deposition flux.
Acknowledgment This work was supported by the US National Science Foundation through Grant No. DMR-1104610. The authors would also like to thank Reiner Mo¨nig for help with design of the tiltable stress sensor.
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References [1] Ohring M. The materials science of thin films. Boston, MA: Academic Press; 1992. [2] Ohring M. Reliability and failure of electronic materials and devices. San Diego, CA: Academic Press; 1998. [3] Kim DH, Ahn JH, Choi WM, Kim HS, Kim TH, Song JZ, et al. Science 2008;320:507. [4] Spearing SM. Acta Mater 2000;48:179. [5] Jackson MJ. Micro and nanomanufacturing. New York: Springer; 2007. [6] Withers PJ. Rep Prog Phys 2007;70:2211. [7] Nix WD. Metall Trans A – Phys Metall Mater Sci 1989;20:2217. [8] Koch R. J Phys-Condens Matter 1994;6:9519. [9] Floro JA, Chason E, Cammarata RC, Srolovitz DJ. MRS Bull 2002;27:19. [10] Leondes CT. MEMS/NEMS: handbook techniques and applications. New York: Springer; 2006. [11] Li M, Tang HX, Roukes ML. Nat Nanotechnol 2007;2:114. [12] Spaepen F. Acta Mater 2000;48:31. [13] Leib J, Monig R, Thompson CV. Phys Rev Lett 2009;102. [14] Gonzalez-Gonzalez A, Polop C, Vasco E. Phys Rev Lett 2013;110. [15] Floro JA, Hearne SJ, Hunter JA, Kotula P, Chason E, Seel SC, et al. J Appl Phys 2001;89:4886. [16] Chason E, Sheldon BW, Freund LB, Floro JA, Hearne SJ. Phys Rev Lett 2002;88. [17] Koch R, Hu DZ, Das AK. Phys Rev Lett 2005;94. [18] Friesen C, Thompson CV. Phys Rev Lett 2002;89. [19] Friesen C, Seel SC, Thompson CV. J Appl Phys 2004;95:1011. [20] Pao CW, Foiles SM, Webb EB, Srolovitz DJ, Floro JA. Phys Rev Lett 2007;99. [21] Pao CW, Foiles SM, Webb EB, Srolovitz DJ, Floro JA. Phys Rev B 2009;79. [22] Thompson CV. Annu Rev Mater Sci 2000;30:159. [23] Yu HZ, Thompson CV. Acta Mater 2014;67:189. [24] Hoffman RW. Thin Solid Films 1976;34:185. [25] Nix WD, Clemens BM. J Mater Res 1999;14:3467. [26] Tello JS, Bower AF, Chason E, Sheldon BW. Phys Rev Lett 2007;98. [27] Chason E, Shin JW, Hearne SJ, Freund LB. J Appl Phys 2012;111. [28] Del Vecchio AL, Spaepen F. J Appl Phys 2007;101. [29] Shim Y, Borovikov V, Amar JG. Phys Rev B 2008;77.
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Effects of oblique-angle deposition on intrinsic stress evolution during polycrystalline film growth Hang Z. Yu, Carl V. Thompson ⇑ Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Received 16 March 2014; received in revised form 27 May 2014; accepted 29 May 2014
Abstract Precise control of the residual stress in polycrystalline films, which remains a central but difficult task in a variety of emerging technologies, requires synergistic manipulation of multiple processing parameters. In addition to the substrate temperature and the rate of deposition, the angle of incidence of the deposition flux is known to affect structure evolution processes during film formation. However, its role in influencing the evolution of the intrinsic stress has not been determined. In this work, we investigate the effects of oblique-angle deposition on intrinsic stress evolution in polycrystalline gold and nickel films, using in situ stress measurements as well as ex situ surface and microstructure characterization. We find that as the angle between the surface normal and the direction of the deposition flux increases, the thickness at which film coalescence occurs increases and the post-coalescence stress shifts toward the tensile direction. We suggest that the first trend is associated with the effects of shadowing on the nucleation density in the pre-coalescence regime, and we attribute the second trend to an increase in surface roughness and shadowing effects associated with the dome-shaped surfaces of individual grains. According to this view, oblique-angle deposition on a mesoscopically rough surface eliminates or reduces condensation at and near grain boundaries, and therefore lowers the rate of adatom–grain boundary attachment, resulting in reduction in the compressive component of the intrinsic stress. The stress evolution map built from this work suggests routes to achieve specific stress levels in polycrystalline films. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Intrinsic stress; Thin films; Shadowing; In situ measurement; Surface roughness
1. Introduction The use of polycrystalline thin films is ubiquitous in emerging fields of science and technology, from microelectronics and flexible electronics to micro- and nanomanufacturing [1–5]. For many applications, control of the residual stress in the films remains a central but difficult task [6]. Residual stress includes extrinsic factors, such as thermal stress due to differential thermal expansion, and intrinsic factors, such as intrinsic stress caused by structure evolution during film deposition [7]. Intrinsic stresses can ⇑ Corresponding author. Tel.: +1 617 253 7652; fax: +1 617 258 6749.
E-mail address: [email protected] (C.V. Thompson).
dominate in determining the residual stress in a film [1,7]. For films grown from the vapor phase, for example, intrinsic stresses of the order of 100 MPa or 1 GPa can be generated during the film formation processes [8,9]. Such high levels of stress can cause formation of voids and hillocks, cracking, buckling, delamination and other reliability problems [1,2,7]. The intrinsic stresses can also have profound effects on the properties and performance of films released from their substrates to perform mechanical functions as in nano- and micro-electromechanical devices such as nanobeam-based sensors and actuators [10,11]. The intrinsic stress in polycrystalline films is often correlated with surface and microstructure evolution processes during film formation [12–21]. Polycrystalline films form
http://dx.doi.org/10.1016/j.actamat.2014.05.060 1359-6454/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
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through nucleation of islands that grow to impinge and coalesce to form a continuous film. This is known as the Volmer–Weber mode of film formation [22]. Three types of intrinsic stress evolution behaviors have been identified during evaporative deposition of polycrystalline films [8,9,23]. In all three types of behaviors, a tensile stress develops during island coalescence due to an elastic deformation that occurs when islands meet and grain boundaries form through a “zipping” process [24,25]. After the film becomes continuous, the intrinsic stress continues to evolve in a tensile state under conditions of low atomic mobility (Type I behavior) or evolves toward or into a compressive state under conditions of high atomic mobility (Type II). Under conditions of intermediate atomic mobility, the evolution of post-coalescence stress involves a turnaround from a compressive state to a tensile state (intermediate behavior type) [23]. These stress evolution behaviors are controlled by a number of kinetic processes during film deposition, including adatom diffusion on the grain surface, adatom attachment to grain boundaries and grain growth during film thickening [16,23,26,27]. The homologous temperature Th (defined as the substrate temperature divided by the melting temperature in K, i.e. Th = T/Tm) and the rate of deposition are known to strongly influence these behaviors [8,9,16,23,28]. Precise control of the residual stress in thin films requires simultaneous manipulation of multiple processing parameters during deposition. In addition to the substrate temperature and deposition rate, the angle of the incident deposition flux is known to influence the surface morphology and grain structure of polycrystalline films through self-shadowing effects that lead to roughening of the film surface and vacancy formation in the bulk of the film [29–34]. However, the effects of the deposition angle on intrinsic stress evolution in thin films have not been investigated. As the first report of in situ stress measurements for oblique-angle deposition, we show here that the angle of the incident flux significantly affects the evolution of the intrinsic stress during growth of polycrystalline gold and nickel films. Specifically, a higher incidence angle leads to
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(i) an increase of the nominal thickness at which islands coalesce to form a continuous film (i.e. the coalescence thickness), and (ii) an overall less compressive or a more tensile post-coalescence stress in the film. We explain the first trend by self-shadowing in the pre-coalescence stage, and attribute the second trend to an increase in surface roughness and the shadowing effects associated with the dome-shaped surfaces of the grains in the post-coalescence stage. These findings lead to a stress evolution map in which the three types of stress evolution behaviors (i.e. Type I, intermediate type and Type II) are categorized as a function of the homologous temperature and the incidence angle. 2. Experimental methods Gold and nickel films were deposited in an ultra-highvacuum e-beam evaporation system, with a base pressure of 5.0 109 Torr. The deposition rate measured using a quartz crystal microbalance was adjusted to ensure that the real deposition flux (number of incident atoms per unit area of substrate surface per time) was the same for depositions carried out at different incident flux angles. All the films were deposited at a deposition rate normal to the ˚ s1, as confirmed plane of the substrate surface of 0.5 A using atomic force microscopy (AFM) measurements. The surface and grain structures of the films were characterized using a Veeco Nanoscope IV AFM in tapping mode and a JEOL 2010 transmission electron microscope. Intrinsic stress evolution during film growth was measured in situ using the cantilever deflection method. The details of this method can be found elsewhere [23,35,36]. To enable in situ measurements during oblique-angle deposition, we designed and fabricated a tiltable stress sensor platform, with which the inclination of the cantilever could be varied from 0° to 90°, as shown in the schematic illustration in Fig. 1a, where a refers to the angle of the incident flux relative to the direction normal to the substrate surface. A picture of our tiltable stress sensor setup is shown in Fig. 1b. It is important to note that the deflection of
Fig. 1. (a) Illustration of the configuration used for in situ stress measurements during oblique angle-deposition and (b) a picture of the tiltable stress sensor.
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the cantilever was of the order of 10 nm, while the length of the cantilever was of the order of 1 cm. Therefore, deflection of the cantilevers led to negligible changes (106 rad) in the incidence angle during film growth. This work focuses on oblique-angle deposition with a of low and intermediate values (a = 0–60° for Au, a = 0–45° for Ni); the resultant films were continuous and consisted of columnar grains with boundaries generally parallel with the substrate surface normal. Stress evolution during glancing angle deposition that leads to tilted isolated nanocolumnar structures [37–41] is beyond the scope of this work.
The intrinsic stress in a film results in a force exerted at the interface between the film and the substrate [12]. In situ stress measurements give the force per unit width, F/w, at the interface as a function of the film thickness h [7–9,12]. Due to a force balance, F/w is equal to the product of the average stress in the film and the film thickness h. Typical shapes of the stress curves of Type I, intermediate type and Type II behavior observed during normal angle deposition (a = 0°) are schematically shown in Fig. 2a.
In situ stress measurements for oblique-angle deposition are summarized in Fig. 2b, in which we show stress evolution curves for gold films deposited with incidence angles a = 0°, 30°, 52°, 60° and for nickel films with a = 0°, 30°, 45°. Considering the rough surface of the films deposited at high incidence angles (as will be discussed in Section 4), the horizontal axis in this figure and Figs. 4 and 5 is labeled “nominal film thickness” rather than “film thickness”. All these depositions and measurements were carried out at room temperature. Under these conditions, nickel films display the intermediate type and Type I stress behaviors; gold films display the intermediate type and Type II stress behaviors. As a signature of the intermediate type of stress behavior, the post-coalescence stress turnarounds [23] observed in nickel and gold films have been marked with red arrows. The film thicknesses at which the peak tensile stress occurred (hpeak) have been marked with black arrows. Two trends are noted from the in situ measurement results. First, the peak thickness hpeak increases with the incidence angle a for both gold and nickel films. This trend is highlighted in Fig. 3a in which the peak thickness hpeak is plotted as a function of the incidence angle a. Second, the overall post-coalescence stress evolution shifts toward the
Fig. 2. (a) Schematic stress evolution curves for Type I, intermediate type and Type II stress behaviors and (b) in situ stress measurement during oblique-angle deposition of gold and nickel films. The tensile peaks corresponding to film coalescence are marked with black arrows. The post-coalescence thickness at which the stress turns to evolve in the tensile direction is marked with red arrows. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. (a) Plot of the film thickness at which the tensile peak occurs, hpeak, as a function of the incidence angle a and (b) plot of the value of F/w as a function of the incidence angle a, for Au and Ni at h = 20 nm and h = 40 nm.
3. Effects of incidence angle on intrinsic stress evolution in gold and nickel films
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tensile direction as a is increased. This trend is further illustrated in Fig. 3b by plotting the value of F/w at given film thicknesses as a function of the incidence angle a. It is widely agreed that grain boundary formation during island coalescence leads to the development of a tensile stress observed early in the film formation process, and that the film thickness at which the stress is at its maximum value (hpeak) corresponds to the end of the coalescence process [8,9,25]. The first trend noted above, an increase in hpeak with increasing a, thus indicates that the thickness at which the films became fully continuous (i.e. the coalescence thickness) increases with increasing incidence angle. We explain this finding as to be due to geometrical effects in oblique-angle deposition as follows. During the initial stage of Volmer–Weber film growth, when isolated islands nucleate and grow independently, the incident beam arrives from an oblique angle and the atoms are preferentially captured by pre-existing islands due to self-shadowing [30,42], and possibly steering [43,44]. This lowers the rate of island nucleation and therefore increases the island size and the nominal film thickness at which coalescence occurs, resulting in the trends shown in Fig. 3a. The second trend, that the post-coalescence stress evolution shifts toward the tensile direction as a is increased, is clear from the in situ stress measurements in Fig. 2b and the plots in Fig. 3b. Gold films display typical Type II stress behavior at a = 0° and a = 30°, but as the incidence angle is further increased, the post-coalescence stress becomes much less compressive. At a = 60°, the compressive stress level remains low after coalescence. Moreover, a stress turnaround from a compressive to a tensile state, which is a signature of the intermediate type of stress behavior, is seen at a thickness of 40 nm, as indicated by the red arrow. On the other hand, at room temperature the nickel films display the intermediate type of stress behavior up to a = 30°, with the turnaround thickness reducing from 37 nm at a = 0°, to 15 nm at a = 30°. At a = 45° the stress turnaround disappears. Instead, the instantaneous stress (i.e. the slope of the stress evolution curve [18,23]) of the nickel film is in a tensile state in all growth stages, which is typical for Type I stress behavior. Overall, the intrinsic stress in gold and nickel films becomes less compressive or more tensile as the incidence angle increases, during which the stress behavior changes from Type II to the intermediate type and then to Type I. The origin of this trend will be analyzed in the following section. 4. Origin of the stress shift toward the tensile direction at higher incidence angles It has been discovered that in the intermediate type and Type II stress behaviors, the intrinsic stress evolution is governed by a compressive component controlled by adatom diffusion [16,23,26,27] and a tensile component controlled by grain growth during deposition [23]. The instantaneous stress during film growth, rin, can be thus
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comp expressed as rin ¼ rcomp þ rgg and rgg in in , where rin in refer to the compressive component of the instantaneous stress and the instantaneous stress caused by grain growth, respectively. Therefore, the second trend noted above, i.e. a stress shift toward the tensile direction with increasing incidence angles, has two possible origins: (i) strengthening of the grain growth component ðrgg in Þ, and (ii) weakening of the compressive component ðrcomp in Þ, at a higher value of a.
4.1. Effects of incidence angle on the grain growth component of intrinsic stress To investigate the possibility of origin (i) above, we characterized the microstructures of the films using planview and cross-sectional TEM imaging. Under the experimental conditions in this work (a = 0–60° for Au and a = 0–45°for Ni), we did not observe the tilted isolated nanocolumnar structures that are sometimes observed to result in refractory metals deposited at a glancing angle (a 80° or more) [37–41]. Instead, the films were continuous and consisted of columnar, transverse grains. Fig. 4a–c shows plan-view TEM images of Ni films grown at an a of 45°, with film thicknesses of 7, 14 and 28 nm, respectively. Under conditions of high [45] and intermediate atomic mobility [23], the grain size is known to increase with the film thickness for films grown by normal angle deposition. The same trend is clearly seen here for the Ni films grown by oblique-angle deposition. In Fig. 4d, the measured inplane grain size is plotted as a function of the film thickness for films deposited at a = 0°, 30° and 45°. The average grain size was determined by tracing the boundaries of hundreds of grains on transparencies, followed by image analysis of the transparencies. For all the cases, the grain size is seen to increase linearly with the film thickness, as observed for films deposited at normal incidence [23,45]. In addition, an increase of the incidence angle a from 0° to 30° to 45° leads to only a small decrease in the average grain size in Ni films, at the same film thickness. This suggests that the influence of incidence angle a on the grain growth component ðrgg in Þ of the intrinsic stress should be weak. Moreover, the decrease in grain size in films deposited at a = 30° and a = 45° should lead to weakening, rather than strengthening, of the grain growth component. Consequently, the possibility of origin (i) can be excluded. In Fig. 5, we quantify the effects of grain growth during deposition on intrinsic stress evolution in Ni films, and compare the effects for the cases of a = 0°, a = 30° and a = 45°. We first plot the instantaneous stress rin at various film thicknesses for the three cases. Here the instantaneous stress is given by the slope of the stress evolution curves in Fig. 2b, i.e. rin ¼ DðFDh=wÞ. In a recently developed model, we have shown that when the grain size d increases linearly with film thickness h, the instantaneous stress caused by grain growth during deposition can be calculated using 1 Da rgg [23,36], where M is the in ðdÞ ¼ M d ð1 þ MDa=ry dÞ biaxial modulus of Ni (290 GPa [46]), Da is the grain
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Fig. 4. Plan-view TEM images of Ni films deposited at an incidence angle of 45° with film tn can be calculated uhickness (a) 7 nm, (b) 14 nm and (c) 28 nm. (d) The grain size–thickness relationships in Ni films deposited at incidence angles of 0° [23], 30° and 45°.
Fig. 5. Comparison of the in situ instantaneous stress measurements as well as the stress components caused by grain growth and the compressive mechanism, for Ni films deposited at a = 0°, 30° and 45°.
˚ [47,48]) and ry is the tensile yield boundary width (1.0 A stress. Using the grain size data in Fig. 4, we calculated the grain growth component of the instantaneous stress 1 ðrgg in Þ at a = 0°, a = 30° and a = 45°, as shown by the blue solid, black dash-dotted and red dashed lines in Fig. 5. It 1 For interpretation of color in Fig. 5, the reader is referred to the web version of this article.
can be seen that the magnitude of rgg in is slightly lower at a = 30° and a = 45° than at a = 0°, but the difference is extremely small. It should be noted that depending on the average grain size, film thickness and processing method, different values of tensile yield stress have been reported for nanocrystalline Ni [23,49–52]. For the calculation of the grain growth component of the intrinsic stress we use ry = 600 MPa [23]. It can be shown that the conclusion, that rgg in changes little as a changes from 0° to 30° to 45°, is not affected for ry values ranging from a few hundred MPa to 1 GPa. The compressive component of the instantaneous stress ¼ rin rgg can be then determined as rcomp in in . As shown in Fig. 5, the compressive instantaneous stress is 300–500 MPa at a = 0° and is 150–300 MPa at a = 30°, whereas at a = 45° this stress is in the range of 0–90 MPa. Clearly, the compressive component is substantially influenced by the angle of the incident flux a. Therefore, the differences in the stress behavior at different incidence angles are dominated by changes in the compressive component of the intrinsic stress ðrcomp in Þ, rather than by the changes in the grain growth component ðrgg in Þ. To summarize, based on a qualitative discussion on grain growth during deposition in Fig. 4 and a quantitative analysis of different stress components in Fig. 5, we conclude that the stress shift toward the tensile direction
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does not originate from the strengthening of the grain growth component. Instead, it originates from the weakening of the compressive component at higher incidence angles (i.e. origin (ii)). 4.2. Effects of oblique-angle deposition on the compressive component of intrinsic stress Chason and co-workers [16,26,27] proposed that the post-coalescence compressive stress observed in Type II behavior is caused by diffusion of adatoms from the surface of the film into grain boundaries. In this model, excess atoms are incorporated into the grain boundaries during deposition because there is a non-equilibrium excess of adatoms on the surface during deposition. These extra atoms at grain boundaries are then seen to cause the compressive component of the intrinsic stress ðrcomp in Þ. This view is supported by a number of experiments and simulations [13,20,21,23]. The decrease in rcomp in , which is seen as a is increased, should therefore correlate with a change in the adatom–grain boundary interaction. 4.2.1. Characterization of surface roughness Adatom diffusion and adatom–grain boundary interaction occur on the film surface during deposition, and therefore are influenced by the surface morphology. In this work, the surface topography was characterized using AFM for films deposited at different incidence angles. Fig. 6 shows AFM images for 115 nm thick gold films deposited at (a) a = 0° and (b) a = 60°, and 60 nm thick nickel films deposited at (c) a = 0° and (d) a = 45°. These images show no evidence of strong in-plane anisotropy, as observed in the films deposited by glancing angle deposition [37–41]. Typical 1-D surface profiles are compared in Fig. 6e for gold films deposited at a = 0° and a = 60°, and in Fig. 6f for nickel films deposited at a = 0° and a = 45°. In both cases, as the incidence angle a is increased, the peaks in the surface height profile become sharper and higher, indicating an increase in the local surface steepness. In surface analysis, the degree of steepness of a local surface can be described by the inclination angle H [53], which is defined as the angle between the normal of a local surface and the normal of the horizontal surface. A higher value of the inclination angle H means a steeper local surface. The distribution of the inclination angles of a film surface can be determined by processing the AFM images as discussed elsewhere [36,53]. Fig. 7a and b shows the distribution of inclination angles (H) (i.e. distribution of steepness) on the surfaces of gold and nickel films deposited at different oblique angles. For gold films, as shown in Fig. 7a, the steepness distribution curves are similar for a = 0° and a = 30°. However, as the incidence angle a is further increased, the distribution curves move toward larger H values, indicating an increase in the area of steep regions. Interestingly, the stress evolution curves in Fig. 2b show that at a = 0° and a = 30°, the gold films develop
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compressive stress after coalescence, which is typical for Type II stress behavior. As the incidence angle a is further increased, the post-coalescence stress shifts toward the tensile direction. Therefore, there appears to be a correlation between the increase in surface roughness and the tensile shift of the post-coalescence stress in gold films. This correlation can also be seen in nickel films by comparing Fig. 7b with the stress evolution curves in Fig. 2b. The results in Figs. 6 and 7 clearly show that the surface of a polycrystalline film formed by oblique-angle deposition is rough, and that the surface roughness increases as the incidence angle a is increased. This can be explained by the self-shadowing effect, for which the atom flux is preferentially captured by the higher surface sites of the film [29–34]. In addition, due to the short-range attraction between the substrate and the atom flux, the atomic trajectory can deviate significantly from the original one as the atoms approach a surface from an oblique angle. This is known as the steering effect [43,44], and gives rise to a redistribution of the incident atoms according to their morphology-dependent trajectories. Both the shadowing effect and the steering effect lead to an enhancement of the surface roughness during deposition. Comparing the steepness distribution curves with the stress evolution curves suggests a correlation between the surface roughness and adatom– grain boundary interaction. The origin of this correlation will be discussed next. 4.2.2. Influence of surface roughness on the adatom–grain boundary interaction For rough surfaces, the terraces and step edges on an individual grain surface should be taken into account, and the grain surface can no longer be treated as flat, as in the models in Refs. [16,23]. The surface roughness significantly influences the adatom–grain boundary attachment process. Specifically, an increase in the surface roughness will lower the rate of adatom–grain boundary attachment. This is because downhill diffusion from higher terraces leads to substantially reduced adatom attachment to grain boundaries (as will be shown in detail in the next paragraph) so that the rate of adatom–grain boundary attachment is limited by the number of adatoms condensing on the terraces adjacent to a grain boundary. On a rougher surface, more step edges are present and the terrace length is shorter. As a result, fewer atoms condense on the two terraces adjacent to a grain boundary, and therefore the rate of adatom–grain boundary attachment is lower. The corresponding compressive component of the intrinsic stress ðrcomp in Þ is thus lower too. The influence of surface roughness and terrace length on adatom–grain boundary interaction is illustrated in Fig. 8. 4.2.3. The dome-shadowing effect For a sufficiently rough surface, oblique-angle deposition can lead to zero condensation on the terraces adjacent to the grain boundaries due to shadowing of dome-shaped
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Fig. 6. AFM images (1 lm 1 lm) of 115 nm thick gold films deposited at incidence angles of (a) 0° and (b) 60° and 60 nm thick nickel films deposited at (c) 0° and (d) 45°. Comparison of the 1-D surface profiles (e) in Au films deposited at a = 0° and 60°, and (f) in Ni films deposited at a = 0° and 45°.
grain surfaces. This effect is illustrated in Fig. 9, where the region without adatom condensation has been highlighted in red. In this scenario, adatom attachment to grain boundaries requires downhill diffusion of adatoms to cross the step edges, as illustrated in the atomic-scale schematic in Fig. 9. The rate for crossing a step edge can be written as m ¼ m0 eðEs þDEÞ=kT , compared to m ¼ m0 eEs =kT for diffusion on a terrace, where Es is the activation energy for terrace diffusion and DE is the additional thermal energy needed to overcome the Ehrlich–Schwoebel (ES) barrier, which has been estimated to be 0.1 eV for face-centered cubic metals [54,55]. It is important to note that m0 < m0 , because m0 is the attempt frequency for a random walk irrespective of direction, whereas m0 is the attempt frequency for a jump in a specific direction. For example, field ion microscopy experiments show that mm00 102 for homoepitaxial growth
of Pt films [56]. Consequently, the rate for step edge crossing is much lower than that for terrace diffusion; for DE = 0.1 eV and mm00 ¼ 102 , we have mm ¼ 2 104 at room temperature. Moreover, as an adatom crosses a step, it has a probability pE of being incorporated into the edge of the step. If the probability of an atom diffusing from a high terrace to a grain boundary is p, p ¼ 1 ny pE , where ny is the number of step edges in the diffusion path. As a result, the rate of adatom–grain boundary incorporation is further reduced with an increase in the number of step edges necessary for the adatoms to cross. Because of above reasons, the need for downhill diffusion over significant distances will severely limit the number of excess adatoms on terraces adjacent to the grain boundaries and will reduce the incorporation of excess atoms in the boundaries. In the scenario illustrated in
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Fig. 7. Distribution of the inclination angles of (a) the gold film surfaces and (b) the nickel film surfaces.
Fig. 9, therefore, the adatom–grain boundary attachment process is substantially suppressed, and the resultant compressive component of the intrinsic stress is much lower than in the case when condensation occurs on the two terraces adjacent to a grain boundary. As the incidence angle increases, the shadowed area increases, and this domeshadowing effect is stronger. To summarize, an increase in the incidence angle a leads to an increase in the surface roughness and a stronger dome-shadowing effect. These effects result in reduction in the adatom–grain boundary interaction and therefore a reduction in the compressive component of the intrinsic stress. This explains the shift of the intrinsic stress toward the tensile direction when the films are deposited at higher incidence angles, as indicated by the in situ stress measurements. 5. Stress evolution map Based on the above discussion, we conclude that an increase in the incidence angle leads to reduced incorporation of excess atoms at grain boundaries and therefore a weaker compressive component of the intrinsic stress. As the homologous temperature decreases, adatom diffusivities
Fig. 8. Illustration of adatom–grain boundary attachment on (a) a relatively flat surface with more atoms condensing on the terrace adjacent to a grain boundary and (b) a rougher surface with fewer atoms condensing on the terrace adjacent to a grain boundary.
are reduced; as the incidence angle increases, the distance that adatoms must diffuse and the number of ledges they must cross, increases. As a consequence of both of these effects, the intrinsic stress shifts toward the tensile direction, and the stress evolution behavior changes from Type II to the intermediate type and then to Type I. A stress evolution map summarizing this behavior is shown in Fig. 10, in which the experimental data for Au, Ni, Ag [16], Cu [18], Pt [23], Pd [23], Cr [57], Ti [58] and Al [59] are plotted. In this map, the horizontal axis represents the atomic mobility, with the mobility decreasing from left to right, and the vertical axis represents the required diffusion distance for adatom–grain boundary incorporation, with the diffusion distance decreasing from the top to the bottom. In moving from the lower-left to
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temperature and the deposition rate has been developed in Ref. [23]. The two stress evolution maps together suggest routes to synergistic control of deposition conditions to achieve specific residual stress levels required for optimal performance and reliability of films to be used in different applications. 6. Conclusions Using in situ stress measurements, ex situ surface and microstructure characterization, and analytical modeling, we have studied the influence of the angle of the incident atomic flux on the evolution of intrinsic stress during vapor-phase growth of polycrystalline films. Key results from this work can be summarized as follows:
Fig. 9. Illustration of the dome-shadowing model. The shadowed region has been highlighted in red. Downhill diffusion of adatoms to cross the step edges is illustrated in the atomic-scale schematic. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 10. Stress evolution map summarizing the effects of the homologous deposition temperature for the film (Th) and the angle of incidence of the deposition flux (a) on the mode of stress evolution during film deposition. Here the same type of stress behavior is plotted using the same shape symbols, and the same material is in the same color. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the upper-right of the map, therefore, the adatom–grain boundary incorporation process is reduced, and the type of stress evolution changes from Type II to the intermediate type and to Type I. The boundaries of the regions associated with different stress types were determined empirically. A similar stress evolution map that categorizes the stress types as a function of the film’s homologous
The intrinsic stress evolution is significantly influenced by the angle of the incident atomic flux during vaporphase growth. Due to self-shadowing, a higher incidence angle leads to an increase in the film thickness at which the peak tensile stress occurs, hpeak. After the film becomes continuous, a higher incidence angle leads to a shift of the intrinsic stress toward the tensile direction. Grain structure characterization shows that the incidence angle only weakly affects the grain growth process during film growth in these studies. The shift of the intrinsic stress toward the tensile direction, therefore, originates from the weakening of the compressive component caused by a reduction of the adatom–grain boundary interaction. We suggest that the decrease of the compressive stress is associated with the increase in surface roughness and the shadowing effects caused by the dome-like shapes of the surfaces of individual grains. When the surface is sufficiently rough, the dome-shadowing effect during oblique-angle deposition leads to little condensation on the terraces adjacent to grain boundaries, and therefore a very small compressive stress associated with incorporation of excess atoms at the boundaries. Conditions under which Type I, the intermediate type and Type II stress behaviors are observed can be categorized as a function of the homologous deposition temperature of the film and the incidence angle of the flux in a stress map. The residual stress in polycrystalline films can be controlled and optimized for specific applications through synergistic control of various processing parameters including the substrate temperature, the deposition rate and the angle of the incidence of the deposition flux.
Acknowledgment This work was supported by the US National Science Foundation through Grant No. DMR-1104610. The authors would also like to thank Reiner Mo¨nig for help with design of the tiltable stress sensor.
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