Large Discrete Resistance Jump at Grain Boundary in Copper

pubs.acs.org/NanoLett

Large Discrete Resistance Jump at Grain Boundary in Copper Nanowire Tae-Hwan Kim,† X.-G. Zhang,† Don M. Nicholson,† Boyd M. Evans,† Nagraj S. Kulkarni,‡ B. Radhakrishnan,† Edward A. Kenik,† and An-Ping Li*,† †

Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 and ‡ University of Tennessee, Knoxville, Tennessee 37996 ABSTRACT Copper is the current interconnect metal of choice in integrated circuits. As interconnect dimensions decrease, the resistivity of copper increases dramatically because of electron scattering from surfaces, impurities, and grain boundaries (GBs) and threatens to stymie continued device scaling. Lacking direct measurements of individual scattering sources, understanding of the relative importance of these scattering mechanisms has largely relied on semiempirical modeling. Here we present the first ever attempt to measure and calculate individual GB resistances in copper nanowires with a one-to-one correspondence to the GB structure. Large resistance jumps are directly measured at the random GBs with a value far greater than at coincidence GBs and first-principles calculations. The high resistivity of the random GB appears to be intrinsic, arising from the scaling of electron mean free path with the size of the lattice relaxation region. The striking impact of random GB scattering adds vital information for understanding nanoscale conductors. KEYWORDS Grain boundary, resistance, copper, interconnect, four-probe measurement, scanning tunneling microscope

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lectron transport across defect planes such as grain boundary (GB) is a great concern for electronic materials.1-5 In nanowire in particular, electric currents have nowhere to escape but to go through where GBs are present, making the understanding of GB effect all the more relevant to nanotechnology. For instance, the GB effect has been extensively studied in copper nanowires, the current interconnect of choice in integrated circuits. As the interconnect line width narrows, and especially when the wire width approaches the electron mean free path in copper, the resistivity increase becomes the major contributor to the resistance beyond the geometrical factor. This increase in resistivity is due to the increasing dominance of the electron scattering from defect planes (either GB or copper/barrier interfaces).3-7 Greater interconnect resistance will result in higher energy use, more heat generation, reduced electromigration resistance, and slower switching speeds. There is a growing concern that as line widths become comparable to the electron mean free path in copper, a hard limit will be reached and progress along the International Technology Roadmap for Semiconductors (ITRS) will halt.1 To keep pace with the increase in the projected planar transistor density, a critical challenge is to identify the dominant factors that contribute to the high interconnect resistance. Furthermore, since the grain size tends to scale linearly with the geometric dimensions (thickness and width) of a metal wire, the value of the specific resistivity, defined as the resistance of a single grain boundary with a unit area,

may become the dominant factor in determining the size scaling of the wire resistance on the nanoscale. Over four decades, the Fuchs-Sondheimer8,9 and Mayadas-Shatzkes formalisms10 formed the foundation for interpretation of the vast majority of experiments performed on polycrystalline films.3,5,6 Unfortunately, ubiquitous fitting parameters in these models make their application semiempirical at best. The relative importance of the various scattering mechanisms remains an issue of debate.6,11-14 Direct measurements of the resistance of individual GBs and interfaces in polycrystalline nanowires have been surprisingly rare due largely to the dimension constraints related to a single GB in a nanosized wire that renders detection beyond the reach of conventional methods. In measurements on unconfined bulk crystals or thin films that are larger than their grain sizes, current may bypass high resistance GBs in favor of paths with lower resistance. Only in a nanowire with a line width and thickness smaller than the grain size, can the contributions from various resistive GBs be probed separately. Recently, Kitaoka et al. has observed a resistance change along a damascene copper interconnect wire and attributed this change to GB scattering.7 But due to the lack of a correlation of the resistance change with the corresponding GB, it does not help in reconciling the wide range of GB resistance values in the literature. Here we present direct measurement and theoretical calculation of the resistance of individual GBs in copper nanowires with results indicating that the GB scattering effect can differ by orders of magnitude depending on the level of structural symmetry. Grain boundaries have been classified as either coincidence boundaries with high symmetry or “random boundaries” with low symmetry.15 Co-

* To whom correspondence should be addressed. E-mail: [email protected]. Received for review: 05/17/2010 Published on Web: 07/07/2010 © 2010 American Chemical Society

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FIGURE 1. Microstructures of copper nanowires. (a) The inverse pole figure of EBSD map showing the crystallographic orientations of grains in the copper sample, where the color gives the crystallographic direction of the local surface normal; darker means poorer quality or no pattern in the trenches between the nanowires. Three nanowires are separated by four trenches in copper film. The arrows and labels indicate the locations and the types of grain boundaries respectively, corresponding to those boundaries measured by four-probe STM. Scale bar is 1 µm. (b) SEM image showing four-probe STM contacted onto the same copper nanowire (wire 2 in Figure 1a). Scale bar is 5 µm. (c) A schematic illustrating the sample structure and the resistance measurement procedure with probes P1, P2, and P4 fixed, and P3 moving along the nanowire.

incidence boundaries are formed between grains that hold a number of lattice sites in common.15 The simplest coincidence boundary is the twin boundary, where the reciprocal density of common lattice points in the two grains (Σ) is 3. A GB with misorientation beyond Brandon’s criterion15 is defined as a random boundary. We measure the specific resistivities of particular GBs using four-probe scanning tunneling microscopy (STM)16 to establish a direct link between GB structure and the resistance. The measurement uncovers a critical role of random GB scattering on the increased resistivity of copper nanowires. Surprisingly, a nearly universal resistance jump is observed for high-angle random GBs, while the resistance of coincidence GBs is negligibly small. We present a model in terms of a universal specific resistivity which may be an intrinsic characteristic of random GBs arising from the scaling of the electron mean free path with the size of the lattice relaxation region, independent of wire size and GB orientation. The nanowires (Cu lines) were fabricated by using focused ion beam (FIB) from an electroplated blanket film on a silicon substrate. The substrate was a 12 in. Si wafer with 100 nm of thermal oxide on the surface. A TaN/Ta film (20 nm thick) was deposited as a barrier layer. A conventional © 2010 American Chemical Society

copper electroplating process, involving copper seed deposition followed by a 2000 nm of Cu film electrochemical plating, was used to form a thick layer. The sample was subsequently annealed at 400 °C for 4 h to allow grains growth and then chemical-mechanically polished to the designed thickness (∼200 nm). During FIB milling, a layer of photoresist was applied to protect the surface from redeposition of copper and it was removed before introducing the sample to STM chamber. The depths of the trenches were approximately 200 nm to mill through the copper layer. Because most of the grains were larger than 500 nm, the grain boundaries were expected to penetrate the entire wire thickness and width, which was confirmed by scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) images. A series of wires 25 µm long and 300 - 600 nm in width were fabricated. The crystallographic orientations of grains on the copper sample were analyzed by the EBSD technique. The inverse pole figure EBSD image is shown in Figure 1a. The colors give the crystallographic direction of the local surface normal. The trenches between copper nanowires appear black as a result of the nonexistent or poor quality EBSD patterns that are misindexed as high density of “dislocations”. It can 3097

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be seen that the Cu lines contain high fraction of coincidence GBs (white for Σ3 and red for Σ9) with a few high-angle random GBs, typical for electroplated Cu films.17 The misorientations of some GBs (marked in Figure 1a) are given below in the Bunge axis/angle notation: Random GB: GB1 - 〈753〉 45.89°; GB2 - 〈321〉 48.669°; GB3 - 〈321〉 50.72°; GB4 - 〈952〉 48.681° and 〈654〉 46.496°. Coincidence GB: Σ3 - 〈111〉 60°; Σ9 - 〈110〉 38.9° Figure 1b shows the SEM image of the Cu sample with four STM probes located on the same Cu line (corresponding to wire 2 in Figure 1a). The four-probe STM measurement procedure is shown schematically in Figure 1c, where multiple measurements are carried out along the same nanowire with variable probe spacing. For a uniform onedimensional classical conductor, the resistance (R) increases linearly with probe spacing (L), and the gradient dR/dL provides an accurate measure of the linear resistivity of the conductor. In the presence of GBs, the GB scattering may lead to a local resistance change as analyzed in the Supporting Information (SI1). To carry out four-probe resistivity measurements, the probes were monitored and located on a nanowire using a SEM and STM. In order to make contact, first the tunneling current was achieved by adjusting the heights of the STM probes with the STM feedback loops on. Then, the gain of current preamplifier was changed from high to low in order to detect a dramatically increased current when the probe made physical contact with the surface. The lateral spacing between probes was controlled with nanometer precision by the piezo-driven motors. The minimal spacing is limited only by the radius of the probes (∼50 nm). When all four probes were located on the surface, current was sourced through the outer two probes using a Keithley 2400 source meter (current source) and the voltage drop was measured through the inner two probes using a Keithley 6430 source meter (voltage meter). The resistance measurements were carried out with electrochemically etched tungsten tips at a controlled temperature between 10-400 K. The measured four-probe resistance is shown in Figure 2 as a function of probe spacing for the regions that contain different types of GB as analyzed above. On both wires (wire 1 and wire 2), the R(L) curve is essentially linear, confirming the one-dimensional diffusive transport. However, as shown in the inset of Figure 2a, we see some abrupt increases in resistance along both wires. These resistance jumps occur at precisely the locations of high-angle random GBs. The large discrete resistance jumps can be more clearly seen after subtracting the bulk resistance contributions from the grains. As shown in Figure 2b, the size of discrete resistance jumps is 0.061 to 0.075 Ω. However, at the locations of coincidence boundaries such as Σ3 and Σ9, no resistance jumps are observed within the detection limit (∼0.005 Ω). The cross-sectional areas of individual grains can be obtained by measuring the temperature-dependent grain © 2010 American Chemical Society

FIGURE 2. Discrete resistance jumps near random grain boundaries. (a) Measured nanowire resistances as a function of probe spacing at room temperature (300 K). Insets: zoom-in views of abrupt change in resistance near random grain boundaries. Solid line: linear leastsquares fitting. (b) Resistance jumps near random grain boundary on a nanowire obtained by subtracting the bulk resistance contributions from grains. TABLE 1. Grain Resistivity and Specific Grain Boundary Resistivity Measured on Two Copper Nanowires grain resistivity Fgrain (10-6 Ω cm) specific GB resistivity γGB (10-12 Ω cm2)

wire 1

wire 2

Fgrain1 ) 1.795 Fgrain2 ) 1.796 Fgrain3 ) 1.779 γGB1 ) 23.3 γGB3 ) 19.0

Fgrain4 ) 1.712 Fgrain5 ) 1.708 Fgrain6 ) 1.710 γGB2 ) 25.9 γGB4 ) 39.0

resistance13 as explained in the Supporting Information (SI2). Using the gradient of the fitted Rline(L) lines, the resistance jumps, and the cross-section of the individual grains, the grain resistivity (excluding the GB contributions) and the specific GB resistivity at room temperature (300 K) are obtained and displayed in Table 1. The grain resistivities are (1.710-1.796) × 10-6 Ωcm, in comparison to 1.723 × 10-6 Ωcm for the pure bulk copper.18 Random boundaries of GB1, GB2, and GB3 all have similar specific resistivity (γGB) values of (19.0-25.9) × 10-12 Ωcm2, though they have different misorientation axis/angle pairs. GB4 has a higher γGB of 39.0 × 10-12 Ωcm2, which actually results from two high-angle random boundaries that are at a distance less than the measurement probe spacing. We now turn to the theoretical calculation of the specific resistivity for different types of GBs. The specific GB resistivity values γGB for several coincidence GBs were calculated 3098

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For copper we use a Fermi wavelength λF ) 0.46 nm to find γGB ) 13 × 10-12 Ωcm2, which is close to the experimentally measured values for random GBs. Note, if we use λF ) 0.36 nm for aluminum, the calculated random boundary specific resistivity of aluminum is 8 × 10-12 Ωcm2, which is lower than that of copper. We now discuss the role of impurities. The grain resistivities measured in Table 1 are very close to the value of pure bulk copper, indicating little impurity incorporation in the bulk grains. Indeed, unintentional impurities (e.g., C, S, and Cl) in the ppm level in electroplated Cu should not significantly affect the bulk resistivity.11 On the other hand, some impurities in copper may segregate at GBs and lead to a higher GB resistivity.26 In our first-principles calculations for the coincidence GB resistances, we examined the specific resistivity due to a monatomic layer of Ga and found that the increase in specific resistivity (2.11 × 10-12 Ωcm2 for Σ3 twin) was an order of magnitude smaller than the measured value for random boundaries. Moreover, in a recent experimental report,17 the resistivity of an electroplated Cu film was found to be very high due to the presence of a large fraction of random GBs; however, after replacing most of the random GBs with coincidence GBs by thermal annealing but without changing the impurity concentration, the resistivity was reduced significantly,17 which clearly proves that the structure of GB, rather than impurity segregation, is the dominant contributor to the high resistance of random boundaries. In addition, Kitaoka et al. have detected resistance jumps in the range of (0.12-0.17) Ω along copper damascene nanowires,7 fabricated with a different method from ours. Despite the much higher resistance jumps, from the dimension of their wires,7 we calculate the corresponding γGB value to be (20-29) × 10-12 Ωcm2, surprisingly close to our measurement. All these experimental measurements and theoretical calculations indicate that the high specific resistivity of random GBs is an intrinsic effect of GB scattering. In summary, we have shown that the GB scattering effect can differ by orders of magnitude depending on the level of structural symmetry, which clarifies the role of different GBs on the electrical conductance. High-angle random GBs contribute to a specific resistivity of about 25 × 10-12 Ωcm2 (13 × 10-12 Ωcm2 from FERPS model) for each boundary, while coincidence boundaries are significantly less-resistive than random boundaries. Thus, replacing random boundaries with coincidence ones would be a route to suppress the GB impact to the resistivity of polycrystalline conductors. The intrinsic nature of the specific resistivity of random GBs, if confirmed by further studies, can have a profound impact on our understanding of how resistance scales with geometry on the nanoscale.

TABLE 2. Calculated Specific Grain Boundary Resistivity for a Number of Different Types of Coincidence Grain boundaries type of GB Σ3 (twin) Σ5 Σ7 Σ13

specific GB resistivity γGB (10-12 Ω cm2) 0.202 0.807 1.885 0.532 0.863

relaxed or unrelaxed structure relaxed unrelaxed relaxed unrelaxed unrelaxed

using a first-principles electronic structure method. This approach differs from the dislocation model introduced by Brown which neglects the effect of planar stacking faults between line defects.19 The first-principles calculation is done in three steps. In the first step, the lattice structure of the coincidence GB is relaxed using the Projector Augmented Wave method implemented within the Vienna Ab-initio Simulation Package.20 Periodic boundary conditions were used for a system that included ten atomic layers. The eight layers nearest the GB were allowed to relax completely. The two distant layers were relaxed only in the direction normal to the GB while their lattice constant parallel to the GB was held fixed at 6.8165 Bohr (3.607 Å). In the second step with the relaxed structure, the electron wave vectors and group velocities in the bulk solid, and the transmission and reflection matrices across the GB for all states at the Fermi energy are calculated using the layer-Korringa-Kohn-Rostoker (layer-KKR) method.21,22 In the third step, using the wave vectors, group velocities, and the transmission and reflection matrices as inputs, the Boltzmann transport equation23 is solved to obtain the specific GB resistivity. The results for coincidence GBs using first-principles layer-KKR method combined with the Boltzmann transport equation23 are listed in Table 2. The result for twin boundary (Σ3) is close to a previous calculation of unrelaxed boundary24 and experimental value of 1.7 × 10-13 Ωcm2 for bulk copper crystal.25 We see that the γGB of these coincidence boundaries are one or 2 orders of magnitude smaller than the measured specific resistivity for random boundaries and are currently beyond the measurement sensitivity of our four-probe STM technique. High-angle random GBs are beyond the capabilities of today’s first-principles electronic structure codes. But these GBs have much higher resistances than the coincidence boundaries due to the existence of a high density of defects and the potential segregations of impurities.19,26 Here we use a simple model of free electron with random point scatterers (FERPS)27 to describe such boundaries. Because of the scaling of electron mean free path with the size of lattice relaxation region at the random GB (details in the Supporting Information SI3), a universal specific resistivity is obtained for random GBs as

γGB )

2 h 3λF 2e2 2π

© 2010 American Chemical Society

Acknowledgment. The authors thank Boyan Boyanov (Intel Corporation) for providing electroplated copper wafers. This research was sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National

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Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy (T.-H.K., B.M.E., N.S.K., and B.R.) and the Division of Scientific User Facilities (X.-G.Z., E.A.K., and A.-P.L.) and the Division of Materials Sciences and Engineering (D.M.N.), U.S. Department of Energy. Sample preparation was performed at the Nanoscale Science and Technology Lab at ORNL.

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Supporting Information Available. Analysis on resistance change in four-probe measurements, description on nanowire cross-sectional area measurement, and details on freeelectron-with-random-point-scatterer (FERPS) model. This material is available free of charge via the Internet at http:// pubs.acs.org. REFERENCES AND NOTES (1) (2)

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