X-Ray Microdiffraction for VLSI

Award Recipient: P.C. Wang

X-ray diffraction has been used to measure the thermal strains along the length, width and thickness of interconnect lines [2,4-6]. Since, to the first order, the thermal strains can be treated as spatially uniform, these measurements were done with large beams, and the strains measured were averages over millimeter-size areas. However, micron-scale spatial resolution is necessary in order to quantify the strain variation caused by electromigration. Microdiffraction with micronscale x-ray beams has sometimes been used for strain [7] and strain distribution [8] measurements, although there have been no previous published reports of real time diffraction studies of electromigration. Spatially resolved studies of electromigration-related stresses have been reported from experiments using local pressure sensors [9] and micro-Reman scattering [10].

Figure 1. Schematic Diagram of x-ray microdiffraction system.

The synchrotron-based microdiffraction system described here has been developed for measurements of strain in thin film materials with micron-scale spatial resolution [11,12]. As shown in Fig. 1, this system consists of a tapered borosilicate glass capillary as a white x-ray concentrator, a liquid nitrogen cooled, energy-dispersive intrinsic silicon solid state detector (SSD), and an x-y-z sample stage. The SSD is mounted on a detector arm attached to a goniometer and has two angular motions, and . The detector can be moved over a range of angles. Apertures between the detector and the sample define the range of scattering angles accepted by the detector for a chosen position , . Different parts of the sample can be positioned in the x-ray beam by x and y translations of the sample stage. A novel feature of the system is that the samples need not be rotated to measure strains along different directions. This allows polycrystalline samples to be studied with spatial resolution limited only by the x-ray beam size, since it avoids the uncertain translations which inevitably accompany rotations in imperfect mechanical systems.

Figure 2. Plane and cross-section views of aluminum interconnect line sample.

The sample used for the diffraction measurements was a silicon strip with the conductor line parallel to the long dimension of the strip and centered on it. The silicon strip was mounted on a chip carrier to facilitate wire-bonding for four-point resistance measurements, and the chip carrier was mounted on a heating stage. The orientation of the chip carrier on the heating stage was such that the conductor line was vertical, and its long dimension was therefore always perpendicular to the incident x-ray beam.

Diffraction geometry:
X-ray microdiffraction experiments were performed at NSLS on the X26C bending magnet beamline using unfocused white radiation and on the X25 wiggler beamline using white radiation doubly focused by an upstream mirror. Tapered borosilicate glass capillaries with 100µm entrance diameter and Am exit diameter were used to confine and concentrate the x- rays.

Figure 3. Diffraction geometry for microdiffraction.

The diffraction geometry is shown in Fig. 3, where the scattering angle 2(, ) was determined by the two angles and which define the SSD position,

2 (, ) = cos^-1(cos·cos), (1)

and ' is the angle between the sample surface and the incident beam. The angle between the film normal n and the scattering vector k can thus be determined from 2(,) and '.

In this study, ' was set at 13° and diffraction measurements were made at several chosen SSD positions 2(, ) for the Al conductor lines, the W pads, and the Si substrate. Si substrate diffraction measurements on three different reflections, (400), (311) and (511), were used to provide a more accurate calibration of the diffraction angles, which were affected by any alignment and sample position errors which remain after the procedures described above. Whenever the sample temperature was changed by more than a few degrees, the sample stage alignment had to be repeated to correct for displacements caused by thermal expansion.

For the measurements described in this paper, the exit of the capillary was positioned about 1.5mm from the sample surface. This configuration gave a projected x-ray beam on the sample which was 30µm wide and 10µm high. Because the Al line and W pads were narrower than the 30µm beam width, the irradiated areas for the lines and pads were determined by the 10µm line widths.

Grain orientation distribution measurements: [12]
In examining the distribution along the Al lines of grains oriented in a particular direction, the SSD positions and were adjusted so that grains with the chosen orientation would diffract into the SSD. Energies E_hkl(2) of the corresponding Al(hkl) reflections were calculated with Bragg's law as

E_hkl(2)=(keV), (2)

where the scattering angle 2 was calculated with Eq.(1). Energy windows, with resolutions E_hkl(2)/E_hkl(2)=0.03, were then opened in the multichannel analyzer (MCA), and the scattered intensities I_hkl were monitored by summing the counts within the corresponding energy windows. In this way, the distribution of the Al(hkl) grains with orientations along a particular direction were mapped out by translating the sample to scan the x-ray beam along the interconnect line.

Strain measurements:
If the thermal stress state in the sample is equi-biaxial, it is necessary to measure plane spacings from only two reflections with different angles in order to determine the stress state with the Sin² technique [13] and the strain-free plane spacing with the Hauk's formula [13,14]. In the present work, plane spacings d_hkl were measured at two different angles. These plane spacings were converted to effective lattice constants, a_eff=d_hkl(h²+k²+l²)^1/2, for comparing among different (hkl) planes. The values of a_eff for Al and for W along the film normal (=0°) were measured from the Al (111) reflections and W (110) reflections, which are the fiber textures observed in the Al line and W pad.

Al(200) reflections were measured to determine off-normal values of a_eff along the Al line. Because of the strong Al<111> fiber texture and the limited number of Al grains within the irradiated area, the probability of having an Al grain with its (200) plane diffracting into an arbitrarily-positioned SSD receiving aperture was very small. To overcome this difficulty, we took advantage of the <111> fiber texture in the Al film. For a cubic system the angle between (111) and (200) planes is 54.7° [15], so that for an Al film with a strong <111> fiber texture most of the (200) planes can be represented in the {111} pole figure by dots uniformly distributed over a ring of 54.7° radius. and values were chosen to position the receiving aperture on this ring.

In measuring the thermal strains in the 10µm-wide Al conductor line before electromigration, the grain orientation distribution along the line was first measured with the proper diffraction geometry for a particular (hkl) plane, (111) for (=0°) and (200) for =55°. In the distribution profiles, positions of several local maxima were located. An energy dispersive diffraction pattern was collected for 50 seconds at each position where the (hkl) planes of a single grain or a cluster of grains diffracted into the SSD . The (hkl) peak in the energy dispersive diffraction pattern was fitted by a Gaussian function, with a linear background, to determine its mean energy E_hkl from which the plane spacings d_hkl and thus the values of a_eff were calculated.

In measuring the normal plane spacing a symmetric reflection geometry was used, with and set to 26° and 0°, respectively. With this configuration where 2(, )=26° and =0°, the energies of the Al(111) and W(110) reflections were about 11.8keV and 12.3keV. The measurements of the off-normal plane spacings were performed in an asymmetric reflection geometry, where and were set to 19° and 25°. In this case, where 2 (, )= 31° and =55°, and the Al(200) and W(211) reflections were at about 11.4keV and 17.9keV.

Values of a_eff =0° were measured at three different temperatures, in the order of room temperature, 139° and 267°. Sample stage realignment and plane spacing measurements were performed approximately one hour after the temperature of the heating stage reached the set points.

In-situ plane spacing measurements during electromigration:
An electromigration test was performed at 267° by passing 0.6x10⁶ A/cm² current through the passivated 10µm-wide Al interconnect line for about 69 hours. The resistance of the conductor line was monitored during electromigration. The measurements were automated so that the normal plane spacings at nine positions along the Al line and at positions on each of the two W pads were determined during electromigration. Each value is the average of measurements made during three scans along the line. During each scan, an energy dispersive diffraction pattern was collected for 50 seconds at every chosen position. With these procedures each set of measurements took about 50 minutes, and measurements were continuously repeated during the 69 hours of electromigration test.

Figures 4(a) and 4(b). aeff versus Sin2 plot for (a) the W pad and (b) the Al line.

For the Al line, measurements of a_eff were made at five positions along the line for =0° and at seven positions for =55°. These values of a_eff are shown by open squares ()in Fig.4(b). Averaged values of a_eff, shown by solid squares (), were obtained from these individual measurements. The resulting uncertainties, calculated from the distributions of individual values, at 90% confidence level, are shown by the error bars in Fig.4(b).

The =55° measurements are from grains with their [200] directions oriented along the chosen =55° off-normal direction. From grain orientation distribution measurements, these grains were observed to be well separated. Therefore, we believe that each of these individual measurements involved only a single grain, or a small number of grains. In contrast, the individual measurements of a_eff for =0°, from Al(111) reflections, involved large number of grains, because of the strong <111> fiber texture of the Al line.

As shown in Fig.4(b), the off-normal values of a_eff, Sin²=0.67, show a much wider distribution than the normal values of a_eff Sin²=0. This difference may be due to instrumental effects like beam divergence, since the effects of divergence for the off-normal values of a_eff are expected to be larger than for the normal ones. Another possible reason is strain variations between grains, as the sampling volume is much smaller in measurements of the off-normal values of a_eff. Further measurements and calculations are needed in order to better understand this observation. Nevertheless, the average values provide reasonable evaluations of the strain-free lattice constants a₀ and the in-plane stresses , as discussed below.

Because of the small thickness-to-width ratios, which are 0.02 for the W pad and 0.05 for the Al line, the stress states were treated as equi-biaxial. This approximation is supported by results from analytical modeling [16,17]. Based on the equi-biaxial stress assumption, the strain-free lattice constants a₀ were obtained using the biaxial Hauk formula [13,14], and the average inplane stresses were evaluated for W and Al [18].

Table 1. Strain free lattice parameters a0 and in-plane stresses from strain measurements for the W pad and the Al line at room temperature. The uncertainties of W values were estimated from three identical measurements, and those of Al values were estimated from measurements at different positions along the Al line.
	W	Al
a0(Å)	3.1681±0.0005	4.053±0.008
(MPa)	-2100±100	280±180

Table 1 lists the strain-free lattice constants and the in-plane stresses determined for the W pad and the Al line. The uncertainties of W results were estimated from three different measurements at the same position, and those of Al results were estimated from single measurements at different positions along the interconnect line. A highly compressive in- plane stress was found for the W pad, as has been reported previously for sputtered W films [20]. The strain-free lattice constant agrees reasonably well with expected value for W blanket films [21]. The observed thermal stress in the 10µm-wide Al line was lower than the value calculated based on cooling without relaxation from the 350°C passivation temperature, 770MPa. Possible reasons include yielding during cooling from this processing temperature, and relaxation during storage at room temperature for several months before these measurements.

We note that the normal value of a_eff determined for the Al line in these measurements on the focused wiggler beam line X25 is 0.005Å larger than the value measured with the 100-times lower intensity x-ray beam of the unfocused bending magnet beamline X26C. This suggests that there may be ~20° localized x-ray heating during the "room temperature" measurements on beamline X25.

Effect of temperature on strains:
Figure 5 shows the measured normal values of a_eff for the 10µm-wide Al line investigated at room temperature and two elevated temperatures on beamline X26C. In Fig.5(a) values of a_eff(=0°C) are plotted versus positions along the line. The error bars represent one standard deviation for four measurements at the same position, and the dashed lines show the mean values of a_eff averaged over measurements along the entire interconnect line. The fluctuations of a_eff seen along the line may result from having a small number of irradiated grains catching slightly different parts of the incident beam divergence at different positions along the line.

Figure 5. (a) The measured aeff values for positions along the passivated 10µm-wide Al line at different temperatures, and (b) the measured aeff values versus temperature (data points) and the calculated dependence of aeff on temperature for a laterally confined film with equi-biaxial stress (dashed line).

The dependence of the mean normal values of a_eff on temperature is shown in Fig.5(b), in which the one standard deviation error bars were determined from the fluctuations of a_eff along the line. The difference in the mean normal values of a_eff at different temperatures could be explained by treating the Al line as a laterally confined film in an equi-biaxial stress state. Assuming no yielding on heating from room temperature and no significant normal confinement by the passivation, the normal values of a_eff in the Al line at the elevated temperature T can be calculated from

, (3)

where a_eff(RT) is the normal value of a_eff measured at room temperature, T is the temperature difference from room temperature, V_Al is the Poisson coefficient of Al, and _Al and _Si are the thermal expansion coefficients of Al and Si. The second term in the square brackets on the right hand side of Eq.(3) is the free thermal expansion along the film normal, and the third term is the Poisson expansion caused by the biaxial confinement. The predictions of this model, as shown by the dashed line in Fig.5(b), agree satisfactorily with the experimental measurements. The elastic behavior observed up to 267°C, at which an equi-biaxial thermal stress of 230MPa is expected, indicates that the yield point of the confined metal line is higher than that for blanket films. This result is in agreement with other studies [5,22].

Effects of electromigration on strains:
Figure 6 shows the change of the sample resistance during electromigration. The resistance started to increase after about 10 hours, when the Al had migrated off the W pad and the higher resistance Ti/TiN underlayer began carrying the current [23]. The increase in resistance remained essentially linear with time during the rest of the test. Figure 7 shows an optical micrograph of the Al interconnect line after 69 hours of electromigration. The depletion region at the cathode end is about 30µm long. Modulations on the passivation surface were observed in interference micrographs near the anode end, where the electromigrated Al atoms accumulated.

Figure 6. Change of sample resistance during electromigration.

Figure 7. Optical micrograph of the Al line after electromigration.

The normal values of a_eff measured at the chosen positions along the conductor line at T=267°C, before electromigration and after 15 hours and 69 hours of electromigration are shown in Fig.8. The values of a_eff at the first three positions (no. 7, 8 and 9) from the cathode end decreased, except at the first position (no. 9), between 15 hours and 69 hours of electromigration. The values of a_eff at the rest of the positions near the anode end (no. 1-6) showed increases during the first 15 hours, and then dropped during the rest of the electromigration test. The strain-free value, a₀, is also indicated in Fig.8.

Figure 8. Measured normal values of aeff along the interconnect line before electromigration, and after 15 hours and 69 hours of electromigration. The arrow indicates the strain-free value of aeff.

The evolution of the values of a_eff at each position during electromigration is shown in Fig. 9, with the expected strain-free value indicated by dashed lines. The value at the first position from the cathode end (no. 9) dropped slightly below the strain-free value within the first eight hours, and stayed roughly at the strain-free value for 60 hours of electromigration. The values of a_eff rose above the strain-free value during the last ten hours. The values at the second and third positions from the cathode end (no. 8 and 9) showed gradual decreases during the test. The values of a_eff at the rest of the positions near the anode end (no. 1-6) showed increases at the beginning of electromigration, followed by abrupt drops after about 15 hours of electromigration.

Figure 9. Measured normal values of aeff at chosen positions along the interconnect line during electromigration. The dashed lines indicate the strain-free value of aeff.

The results of the time-dependent electromigration strain measurements can be explained qualitatively by electromigration within grain-boundaries as follows. As described in the previous section, the Al line was under biaxial compressive stresses at 267°C before electromigration. The stresses resulted in Poisson expansion along the film normal, so the normal values of a_eff were larger than the strain-free value. Electromigration caused mass transfer from the cathode end to the anode end. The grain boundaries served as paths for fast diffusion. Al atoms were removed from the grain boundaries near the cathode end, and they were accumulated in the grain boundaries near the cathode end. Since the grains in the Al line extended through the line thickness, almost all of the grain boundaries were nearly parallel to the film normal. As a result, the atom depletion from the grain boundaries tended to reduce the in-plane compressive stress, causing the relaxation of the Poisson expansion along the film normal and reducing the normal values of a_eff near the cathode end. After the in-plane compressive stresses were completely relaxed, further mass depletion caused growth of voids and did not create large tensile stresses at the cathode end.

The in-plane compressive stresses near the anode end were increased as a result of mass accumulation of electromigrated atoms in the grain boundaries there. The normal values of a_eff increased due to the Poisson expansion along the film normal. After the stresses built up to certain levels, relaxations occurred by yielding of the Al deformation of the passivation, which reduced the in-plane stresses to lower levels. These relaxations of the in-plane stresses caused the abrupt decreases in the normal values of a_eff observed in Fig.9. The build-ups and relaxations of the in-plane compressive stresses continued during the rest of the electromigration test. Since only the normal values of a_eff were measured, the full stress state in the interconnect could not be determined. However, assuming the effect of electromigration on the stress state is equi-biaxial, it is interesting to note that the yielding occurred at about 300MPa.

Since the atom flux during electromigration is stress-gradient dependent, the change of stress at a particular position is expected to alter the flux nearby, which in turn affects the stresses at neighboring positions. Therefore the stress evolution is coupled at different positions along the line, and the stress behavior becomes more complicated when the relaxation processes begins.

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