Constrained Grain Boundary diffusion in thin copper films

Constrained Grain Boundary diffusion in thin copper films

(Parte 4 de 6)

In films thinner than 10 nm, image stresses on climb dislocations can be as large as 1 GPa (see Section 2.3). This can severely hinder climb-mediated diffusional creepand indicates that the behavior of discrete dislocations needs to be considered in nanoscale thin films. This is supported by the atomistic results showing that stress cannot be completely relaxed in extremely thin films. These results are in qualitative agreement with experimental results that often show large residual stresses in extremely thin films [2].

The diffusion wedge has properties similar to a crack, but it requires a larger SIF to nucleate a dislocation. The reason for this is that in the case of a diffusion wedge, a dislocation dipole needs to be formed, and the dipole interaction force is twice as strong as the image force on an emergent dislocation near a crack tip. We have studied common and distinct properties observed in atomistic simulations of the two kinds of defects (crack versus diffusion wedge) along the grain boundary at elevated temperatures. For a crack, the following was observed: as the applied stress 0 is increased, the normal stress x along the grain boundary remains zero throughout the film thickness, consistent with the traction- free condition along the crack faces; the loading rate can be much higher than in the case of diffusional creep(there is no rate-limiting factor on dislocation nucleation); dislocation nucleation occurs at a relatively small stress intensity factor; and dislocation nucleation starts with an incipient dislocation close to the crack tip.

In contrast, for a diffusion wedge the following can be summarized: the loading rate must be slow enough for diffusion to remain as the dominant relaxation mechanism—at high loading rates, dislocation activities on inclined planes are observed instead of grain boundary diffusion; to nucleate a parallel glide dislocation, dislocation climb in the grain boundary must occur to annihilate part of an incipient dipole (on atomistic timescales, this is an extremely slow process—(for a crack, dislocation nucleation is fast); dislocation nucleation starts when the stress intensity factor reaches a critical value required to create a dislocation dipole near the diffusion wedge; and there exists a minimal thickness for parallel glide dislocation nucleation: If the film is very thin, the applied stress reaches the cohesive strength of the material before the critical stress intensity factor KPG for dislocation nucleation is reached.

Constrained Grain Boundary Diffusion in Thin Copper Films 21

The two types of defects have significantly different timescales associated with dislocation nucleation. A crack is a ready source for dislocations, whereas a diffusion wedge has an intrinsic characteristic time associated with the dislocation climb. No essential difference in the mechanism of parallel glide dislocation nucleation from a diffusion wedge has been


Since its proposal in 1999, the model for constrained diffusional creep [12] has been further developed in light of experimental results [7, 35]. Weiss et al. [25] invoked the constrained diffusional creepmodel to explain the occurrence of a stress dropobserved during the first heating cycle of thin copper films. They also used constrained diffusional creep to model the stress–temperature curves measured during thermal cycling of several films and found good agreement for a 500 nm copper film, albeit by assuming a very large grain size. Later, the discovery of parallel glide dislocations [45] provided experimental support for the constrained diffusional creepmodel. In turn, constrained diffusional creepfur nished the basis for the interpretation of certain experimental results, especially in regard to the mechanisms for the creation and emission of parallel glide dislocations. In the following sections, we present key experimental results and their connection to the model of constrained diffusional creep.

4.1. Thermomechanical Behavior of Thin Copper Films

A series of thin copper films, ranging in thickness from 2 m down to 35 nm, was produced by magnetron sputtering under ultrahigh vacuum. All films were annealed immediately thereafter in the deposition chamber, without breaking vacuum, yielding oxide-free unpassivated copper films. The substrates used for the films were (001)-oriented single crystalline silicon that had been coated with 50 nm amorphous silicon oxide and 50 nm amorphous silicon nitride before copper deposition. Thus, the interface between film and substrate is crystalline/amorphous. The average grain size, as determined from focused ion beam (FIB) and transmission electron microscopy (TEM) measurements, ranged from 1.5 times the film thickness (for the 2- m film) to 2.5 times the film thickness (for the 100-nm film). X-ray diffraction measurements revealed that all films had a strong [1] fiber texture, albeit with a small population of [100]-oriented grains for films thicker than 200 nm. Thus, the vast majority of grains within each film, including the grains imaged using TEM and presented below, are oriented with a (1) plane parallel to the substrate.

The thermomechanical behavior of each film was determined by subjecting it to a thermal cycle between room temperature and 500 C. Because copper possesses a higher coefficient of thermal expansion than silicon, an equibiaxial compressive stress evolves in the film during heating, and a tensile stress evolves during cooling. This coupling of stress and temperature in the film/substrate system enables the thermomechanical loading of thin films, and a variety of thermal paths can be employed to generate compressive and tensile stresses of varying magnitude. In the examples presented below, simple thermal cycles starting at room temperature, progressing up to 500 C and then returning to 50 C were performed. Heating and cooling rates were 6 K/min, except for final cooling below 100 C, which proceeded at 4 K/min because of the limited cooling capacity of the oven.

An example of the thermomechanical behavior of an ultrathin copper film is presented in Fig. 17. The stress within this 100-nm film was initially 360 MPa. During heating, the tensile stress decreased and a compressive stress was achieved by 210 C. The compressive stress rose in magnitude with further heating but then dropped after reaching a maximum at 260 C. The stress level decreased slightly during heating to 320 C and then became more compressive during heating to 500 C. From this point on, the stress evolution was monotonic with temperature: cooling produced a tensile stress and subsequent heating in the second cycle produced a compressive stress again. No stress drops were observed in the second cycle or later.

The stress dropthat occurs above 250 C in the 100-nm film, as well as in all thicker films measured in this study, appears to be the result of constrained diffusional creep, as previously

2 Constrained Grain Boundary Diffusion in Thin Copper Films 800

Temperature (°C)

Stress (MPa)

Cycle 1 Cycle 2

Figure 17. The first two thermal cycles of a 100-nm copper film. During the first heating segment, a stress drop is observed at 260 C, which is attributed to constrained diffusional creep. Subsequent thermal cycles are highly repeatable, with no stress drop.

explained by Weiss et al. [25]. The temperature of 250 C, which represents a homologous temperature of 0.4, is apparently sufficient to activate surface and grain boundary diffusion and lead to the formation of diffusion wedges during heating. Only when the relaxation of stress at the grain boundaries is saturated, in this case at a temperature well above 300 C, does stress increase again. The lack of the stress dropduring the second and later thermal cycles is explained by the stress level: at 250 C in the second cycle, film stress is only −26 MPa, which may be insufficient to cause outward diffusion of copper atoms from the grain boundaries, and therefore no stress relaxation occurs.

The second cycle in Fig. 17 deviates from the first cycle during the final stages of cooling (below ∼200 C), perhaps because of the thermal drift of the sample. This, however, is an inherent error in the experimental technique and gives a good measure of the error one should assign to the absolute stress values that are reported. The film strength is typically taken to be the flow stress measured at the end of a thermal cycle. Thus, in this case, the strength of the 100-nm film would simply be given by the average of the two stresses measured at 50 C at the end of cooling: 676 ± 39 MPa.

Although film strength generally increases with decreasing film thickness [2, 25, 46], unpassivated copper films deviate from this trend below 400 nm [7]. Instead of rising continuously, the film strength exhibits a plateau between 650 and 700 MPa for films 400 nm and thinner. This is apparent in Fig. 18, which shows the second thermal cycle for a 200-nm copper film, along with the second cycle for the 100-nm film from Fig. 17. The two films exhibit virtually identical thermomechanical behavior, with the film strengths at 50 C (695 ± 9 MPa for the 200-nm film) and the flow stresses at 500 C matching very closely. Although the 500 C flow stress does become slightly more compressive in thinner films, the plateau in 50 C film strength persists down to a thickness of 35 nm.

To explore whether the stress–temperature cycles, such as those shown in Figs. 17 and 18, represent steady-state behavior, a 50-nm copper film was thermally cycled at two different rates. In addition to the standard 6 K/min rate, a complete cycle was performed at 1 K/min; both are portrayed in Fig. 19. Because of the extremely small film thickness, this comparison allows us to investigate whether grain boundary diffusion and constrained diffusional creep are able to proceed to completion within the time frame of these experiments. The heating segments of each cycle are somewhat different, but they yield roughly the same 500 C

Constrained Grain Boundary Diffusion in Thin Copper Films 23 800

Temperature (°C)

Stress (MPa)

100 nm Cu 200 nm Cu

Figure 18. The second thermal cycle of a 200-nm copper film, along with the second cycle of the 100-nm film from Fig. 18. Both films exhibit the same thermomechanical behavior, with the same stress levels at 500 and 50 C.

flow stress; namely, 322 ± 14 MPa. However, there is a large discrepancy in stress evolution during cooling, especially between 350 and 200 C. Within this temperature range, the lower cooling rate permits significantly more stress relaxation. This indicates that the standard 6 K/min used throughout this study is too fast to allow constrained diffusional creep to reach steady state and that grain boundary diffusion may be the rate-limiting stepin this

Temperature (°C)

Stress (MPa)

1 K/min cooling

6 K/min heating 6 K/min cooling

1 K/min heating

Figure 19. Two thermal cycles of a 50 nm copper film, conducted at different heating and cooling rates. Although the same 500 C flow stress is reached in both cases, the stress evolution during cooling is seen to depend strongly on cooling rate, indicating that the standard rate of 6 K/min is too fast to allow constrained diffusional creepto proceed to completion.

24 Constrained Grain Boundary Diffusion in Thin Copper Films temperature regime. The final cooling curves below 200 C appear to be offset by approximately 200 MPa, but they exhibit the same slope, indicating that constrained diffusional creepis equally slow in both cases, or that constrained diffusional creepis no longer able to provide stress relaxation below 200 C.

4.2. Transmission Electron Microscopy Observations of Dislocation Behavior

Thermal cycling experiments were also conducted in-situ in the TEM to elucidate the deformation mechanisms underlying the thermomechanical behavior illustrated in Figs. 17–19. These figures clearly showed that films in this thickness range (≤200 nm) exhibit a plateau in strength, which indicates that the Mathews–Freund–Nix mechanism involving threading dislocations is saturated or has been replaced. As discussed below, in-situ observations of dislocation motion revealed that a new, alternative deformation mechanism does indeed dominate in ultrathin, unpassivated copper films.

Figure 20 shows an example of parallel glide dislocations in a small grain within a 200-nm copper film. There are four dislocations oriented roughly perpendicular to the diffraction vector g in the TEM micrograph. During subsequent heating, these dislocations moved in the direction of g and underwent glide across the entire width of the grain. In this image of the [1]-oriented grain, the projected width of all inclined 213 planes is 70 nm. On the basis of their length and the extent of their motion (upto 300 nm), the dislocations must therefore have moved on the (1) plane parallel to the film/substrate interface. Because of this, the observed motion was termed “parallel glide” [7].

An important consequence of glide occurring parallel to the film/substrate interface is that the Burgers vector of the dislocations, which must lie within the (1) glide plane, is parallel to the plane of the film. However, the biaxial film stress that evolves in the film during thermal cycling does not produce a resolved shear stress on this plane, and it therefore cannot be directly responsible for the motion of parallel glide dislocations. Both of these points, however, are addressed by the constrained diffusional creep model [12], which aids the interpretation of these experimental results. As predicted by the theoretical simulations and discussed further below, parallel glide is a consequence of constrained diffusional creep.

Additional experimental observations have clarified several details of this deformation mechanism. Figure 21 shows another example of parallel glide dislocations, extending from g = [220]

50 nm

Figure 20. Transmission electron micrograph of parallel glide dislocations in a 200-nm copper film. These edgeoriented dislocations underwent glide in the direction of the diffraction vector g. On the basis of the extent of their motion, the only possible glide plane is the (1) plane parallel to the film–substrate interface.

Constrained Grain Boundary Diffusion in Thin Copper Films 25

g = [1]200 nm g = [220]

200 nm

(a) (b)

Figure 21. (a) Three parallel glide dislocations are visible in this transmission electron (TEM) micrograph of a 200-nm copper film. Their (1) glide plane, which is also the plane of this image, contains the Burgers vector b. (b) TEM of the same location, but with a different diffraction vector. The three parallel glide dislocations are invisible here, indicating that b is perpendicular to ,1-. On the basis of these images, b must be parallel to ,220-, and the dislocations thus have predominantly edge character.

the twin in the middle of the micrographs to the grain boundary at the right. In Fig. 21(a), three dislocations are visible, but in Fig. 21(b), they are invisible, indicating that the Burgers vector is perpendicular to the ,1- direction. Moreover, the Burgers vector lies within the (1) plane and must therefore be parallel to the ,220- diffraction vector in Fig. 21(a). The dislocations thus have predominantly edge character, as they are oriented roughly perpendicular to b and g in Fig. 21(a). This is a general feature of parallel glide dislocations, which are always emitted with edge character. During subsequent glide, which can involve interaction with other dislocations and with obstacles such as twins and grain boundaries, the parallel glide dislocations may bow into a curved shape and attain mixed character.

(Parte 4 de 6)