- Email: [email protected]
Grain boundary contributions to transport
SURFACE
SCIENCE
GRAIN
31(1972)
BOUNDARY
566-585
CONTRIBUTIONS
R. ROSENBERG, IBM
Watson
Research
0 North-Holland
A. F. MAYADAS
Center.
Yorktown
Heights,
Publishing
Co.
TO TRANSPORT
and New
D. GUPTA York 10598,
U.S.A.
Several important features of grain boundaries, as related to thin metallic film properties, will be discussed. Boundaries are particularly important in films where diffusional processes occur mainly at low temperatures and grain sizes are of the order of 1 urn or less. One phenomenon of interest is electromigration where a high dc current density causes a net atom drift in the direction of electron flow, mainly along boundaries. Non-uniformities in the boundary network lead to a divergence in the diffusion flux, with resultant mass depletion and void formation. A related discussion will be presented on radioactive tracer self-diffusion in gold films at temperatures below 200°C where dislocations and grain boundaries are controlling. Relationships to electromigration will be illustrated. Also to be discussed will be measurements of grain boundary contributions to electrical resistivity in terms of specific grain boundary models. Analytical expressions will be presented to allow extraction of the boundary contributions.
1. Introduction Initial interest in the structure and properties of grain boundaries in the electronics industry was stimulated by a reliability problem associated with electromigrationr). At the relatively low temperatures of operation of integrated circuit devices, where lattice diffusivity is negligible, the high current densities typically used can cause atom migration only along high diffusivity paths such as boundaries. This migration ultimately leads to sufficient mass depletion to cause an open circuit and short device lifetimes. Restriction of the electromigration to boundaries makes analysis of the details of the process difficult. Very little quantitative information is available for such important parameters as thermal diffusion constants, effective charge of the diffusing species with respect to the electron flow, boundary diffusion mechanisms, boundary structure and defects, and impurity adsorption effects on diffusion. Thus, to try to gain an understanding of basic electromigration behavior in thin films it is necessary to pursue a broad range of boundary properties. In this paper, the important aspects of electromigration behavior in films will be presented specifically to illustrate the implications of the various properties of grain boundaries. Also included will be discussions on two of the boundary-related studies presently being pursued in our laboratory, 566
GRAIN
BOUNDARY
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namely, radioactive tracer diffusion and low temperature should provide important insight into the electromigration other film phenomena which are dependent upon boundary
567
resistivity, which process as well as behaviour.
2. Electromigration A typical depleted region resulting from a dc current in an aluminum thin film stripe is shown in fig. 1 2). The average temperature of the stripe was 125°C and the current density 2 x lo6 A/cm’. Of importance are the inter-
Fig. 1. Electron micrograph of a typical open in an aluminum conductor stripe caused by electromigration-induced local mass depletion. Note the grain boundary nature of the damage area (see ref. 2).
568
R.ROSENBERG,
A.F.MAYADAS
AND D.GUPTA
granular nature of the voids and the non-uniformity of the depletion with respect to the stripe geometry. These observations point to the reasons behind the difficulty in studying electromigration in films; damage is confined to certain boundaries and, because of this, methods for measuring atomic flux rates used in bulk samples, for example marker motion, which depend on uniform motion of atoms across any cross-section, are not applicable. Clearly, in films, local flux divergences are prevalent and the problem becomes one of characterizing the various causes of such divergences. Extracting physical constants from experiment becomes a formidable task. 2.1. DAMAGE MECHANISMS Flux divergences during electromigration have been shown to be associated with the presence of temperature gradients3) and structural irregularities 4-7). This is illustrated schematically in fig. 2. Migration through an increasing MECHANISMS TEMPERATURE
T
1
FOR FLUX DIVERGENCE GRADIENT
Jout
:VJ a $)
Jin>l
X 1
I
tb
00
0
Holes STRUCTURAL
-e
Growths NONUNIFORMITIES:
VJ a! d N = Grain Size
, AH = Act. Energy
Fig. 2. Schematic diagrams of mechanisms by which electromigration flux becomes nonuniform. Temperature gradients lead to cathodic opens. Structural irregularities are shown to be of two types, local and area, the former being a triple point problem, and the latter a mixed grain size problem.
GRAIN
temperature
BOQNDARY
leads to accumulation
CONTRIBUTIONS
TO TRANSPORT
of vacancies,
depletion,
569
and void forma-
tion, while migration through a decreasing temperature leads to mass buildup in the form of surface growths. This is a direct consequence of the temperature dependence of the diffusivity. Structural damage sites are of two basic types, local and area. Local damage is typified by the triple point (three grain junction) in fig. 2, where the flux of atoms leading out of the junction must be balanced with the &IX coming in 4%~7). An imbalance can occur because of the inherent difference in diffusion characteristics of each grain boundary, and the relative angles between boundary normals and the direction of the applied field; that is, DIFr #D2F, #D,F,, where Fis the force component in the direction of atom motion, and D is the diffusivity. The large area problem is a result of the normal spread in grain size encountered during film growth. If, by chance, a single grain spans the width of a stripe, then a depletion is to
(4 Fig. 3. Scanning electron micrograph of progression of local damage in an aluminum stripe. Both holes and growths appear in the same cross-section, thus minimizing temperature gradient effects (see ref. 4).
570
R. ROSENBERG,
A. F. MAYADAS
AND D. GUPTA
be expected at the line of intersection between the single grain and the adjacent area containing many grains per width. Mass carried away through the boundaries cannot be replaced. In most instances, the structural damage occurs earlier and superimposes onto the slower temperature gradient effects 4). Examples of structural damage are illustrated in figs. 3 and 4. In fig. 3 the progression of damage in an alumininum film is shown by scanning electron microscopy4). Both peaks and holes are formed simultaneously in the same cross-section showing the accumulation and depletion characteristic of triple point interactions, and the relative unimportance of the temperature profile. Fig. 4 shows a transmission micrograph of depletion at a location having mixed grain sizes). Note the equilibrium void shape, bounded by dihedral angles with the grain boundaries and a planar surface in the single crystal.
Fig. 4. Transmission electron micrograph of mass depletion caused by a mixed grain size. In this case a single crystal spanned the stripe and was bounded by grains about one-quarter of the stripe width. Boundary diffusion was not replaceable.
Calculations of depletion rates based on these models is difficult because it is required to know z* and D, the effective charge and diffusivity of the diffusing species, respectively. The activation energy for electro-migration has been approximated by various meanss,“,s) but the factors D, and z* on the basis of remain elusive. The multiple D,z * has been estimatedg) measurements involving void5, 8, or peak”) growth to be about 3 f0.5 x 10m2
GRAIN
BOUNDARY
CONTRIBUTIONS
TO TRANSPORT
571
cm2 set-’ for aluminum, facilitating the calculations. Estimation of vacancy supersaturations have been made under various conditionssps) and have been found to be < 1. At this level of supersaturation it is doubtful in films that spontaneous void formation can occur in boundaries without the presence of heterogeneous nucleating centers. In the absence of void formation, excess vacancies diffuse to the surface where accelerated grain boundary grooving can take places). The grooving mechanism, which causes general thinning, requires surface as well as boundary transport. This was illustrated by the electromigration behavior of silver filmslo) where surface atoms are highly active. Fig. 5 shows the general rippling of the silver surface during
Fig. 5.
Scanning electron micrograph of a silver stripe after powering. Surface roughening of a previously smooth surface indicates significant surface activity.
Fig. 6. Scanning electron micrograph of a silver stripe after powering whose top surface was coated with a thin layer of chromium. Damage was confined to uncoated edges.
572
R.ROSENBERG.
A. F. MAYADAS
AND
D. GUPTA
test, which is indicative of a grooving process. Conclusive evidence of the surface effect is shown in fig. 6. The stripe used in this test had a thin (- lOOA> diffusion resistant chromium layer on the top surface but the edges were bare. Note the restriction of damage to the uncoated edges while the top surface is unaffected. Calculation of the time required for grooves to reach the substrate are within an order of magnitude of the time it takes to observe a hole in a test stripe. 2.2. EFFECTS OF DIFFUSIVITY Independent of the particular mechanisms by which electromigration damage takes place, the underlying rate determining factor is the diffusion behavior of the individual boundaries. Control of this behavior is the key to higher performance and longer lifetimes for film stripes and device circuitry. Examples of this can be found from the results of introducing the concepts of preferred orientation and addition of certain solute species, each of which were effective in prolonging lifetime. In the former case, it was postulated5) that preferred orientation would produce two effects, reduction of damage sites by normalization of boundary diffusivities and lowering of diffusivity by orienting boundary line defects perpendicular to the applied field. The triple point problem should be less severe in the case where all boundaries are tilt boundaries with the tilt axis and diffusion channels normal to the plane of the film. These ideas were borne out in (111) oriented aluminum films by the increased activation energy observed (from -0.6 to -0.7 eV), longer lifetimes, and decreased G, the standard deviation in the log normal distribution of failure times. The CJparameter is dependent on the number of contributing mechanisms, which in this case was reduced to just mixed grain size effects. The solute effect has been illustrated for the case of copper in aluminumrl) in which the lifetime was shown to be increased. This result can be attributed to interactions between the solute and boundary defects through which the matrix atoms are diffusing102 la). For example, a schematic is shown in fig. 7 of the partitioning of solute to ledge sites. By assuming the existence of bonding energies between the solute and boundary defect and between solute at the defect and the diffusing species, a reduction in electromigration flux can be calculated. It should be kept in mind that there is no obvious connection between the effects of solute on diffusion in the lattice and diffusion in the boundary. Copper in aluminum is an example of this; increased lifetime is observed but it has been reportedra) that copper has no influence on the lattice diffusivity. Fig. 8 is a plot of the reduction in flux of the matrix atoms as a function of the solute concentration in the boundary. It is apparent that boundary concentrations of greater than 1% would produce effective
GRAIN
BOUNDARY
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TO TRANSPORT
573
(a
Solute Segregation
(b) Fig. 7.
Schematic of grain boundary ledge defects. Solute atoms segregate to defects with a binding energy, BNS. Solute complexes also form to reduce their mobility in the defects.
inhibition of migration. This effect can best be illustrated by the type of test shown in fig. 9, in which magnesium was diffused into the central region of an aluminum stripe. From the above analysis, the migration rate of aluminum in the magnesium-diffused region should be less than in the adjacent pure region; thus, passage of electrons through the stripe should cause a net transport away from the diffused region. The open in fig. 9 is the result of such a depletion. Microprobe analysis of the magnesium content, shown in fig. 10, indicates the critical concentration at the open to be about 0.5% which agrees generally with prediction. The concentration profile in fig. 10 points out the most serious problem when using solute to inhibit diffusion; that is, a shift in concentration in the direction of electron flow. Because of the large resistivity characteristic of solute atoms, they are rapidly transported in the field and eventually can be depleted from areas of the stripe. From fig. 8 it is inevitable that this will lead to rapid deterioration by accelerated transport of the matrix atoms. This
574
R. ROSENBERG,
A. F. MAYADAS
AND
D. GUPTA
0.8
0.6
-5.0
-4.5
-4.0
-3.5 LOG
Fig. 8. Reduction Concentrations of
-3.0
-2.5
Co (boundary
solute)
-2.0
-1.5
of electromigration flux produced by solute in the boundary to be sufficient to cause an order of magnitude
1% appear
defects. change.
solute depletion has been observed in the Al-Cu systeml4,15) and is believed to be responsible for lower than expected lifetimes. Much of the present work in the area of electromigration in films is concerned with prevention of the solute depletion by providing a uniform distribution of precipitates which, by dissolving, can replace thedepleting solute. This is not a cure and only prolongs the lifetime by the time it takes to dissolve the precipitates. What is needed is a method to immobilize the solute, to keep it in the boundary defect where it can be effective; for example, addition of a second solute species which can form a stable complex with the first in the boundary. 3. Radioactive
tracer diffusion in films
From the previous discussion, it is apparent that direct methods of analyzing boundary diffusivities are a necessity. Lifetime measurements are complicated by phenomena other than simple boundary diffusion and thus cannot give dependable values for diffusion constants. The example of solute effects is obvious, as lifetime is a measure more of the depletion rate of solute than of the effect of solute on the migration of the matrix atoms. Poly-
GRAIN
BOUNDARY
CONTRIBUTIONS
TO TRANSPORT
57.5
Fig. 9. Effect of magnesium on electromigration flux of aluminum. On the left hand side of the electron micrograph the stripe has been treated with magnesium. Electrons passing from left to right cause depletion in the untreated portion because of reduced flux in the treated region.
Fig. 10. Electron microprobe scan of stripe of fig. 9. The location of the damage occurs where the magnesium content is less than 1% or about in the range predicted in fig. 9. Note drift of magnesium in direction of electron flow.
576
R. ROSENBERG,
A. F. MAYADAS
AND D. GUPTA
crystalline thin films are very attractive for measuring grain boundary selfdiffusion using radioactive tracers and serial sectioning procedures. The inherent advantage in using thin films are (1) very large grain boundary to grain volume ratios, and (2) the grain boundaries are ordinarily normal to the plane of the film. The former should result in high resolution between lattice and the grain boundary diffusion processes, particularly at low temperatures and the latter should make the handling of the tracer penetration profiles analytically simpler. Also the absorption of the nuclear emission may be totally absent in the films which is also a very desirable feature in some cases. 3.1. SECTIONING Any meaningful radioactive work in thin films necessarily involves submicron sectioning since films themselves are typically only microns thick and diffusion depths are shallow at the temperatures of interest. Also, the sectioning operation should be uniform over the grain and the grain boundary. Any mechanical method of material removal can hardly be considered for metallic films since substrates are usually very fragile and section thicknesses would be too great. The electrochemical technique used earlier for profiling Au radiotracer in Au single crystal diffusion workr6) does not appear to be adequate for polycrystalline films since we find grain boundaries to be preferentially attacked. We have developed a novel sectioning technique using an RF sputter-etching procedure for thin films which fulfills the criteria given above. For a complete account of the RF sputter-etching technique as applied to diffusion measurements, the interested reader is referred to our earlier publicationl7). 3.2. DIFFUSION PROCEDURES Au films were chosen for the work in view of the large bulk of valuable information available in the published literature including diffusion and quenched-in defect data which could be useful for comparison purposes. Au’ 95 (180 day, 0.067 MeV 7) radioactive isotope was employed as the tracer. $in. x 2um thick polycrystalline Au films were deposited onto fused quartz substrates coated with an adhesive MO layer by the electron-gun evaporation technique in an ultra-high vacuum system. The starting metal had 99.999 + % purity. The substrate temperature during Au deposition was maintained at 500 “C to obtain about a 1urn grain size in the films. Standard procedures were used for tagging of the isotope (0.1 PC) and radiocounting of Au 195 for 0.067 MeV yl*) with the difference that no surface preparation prior to diffusion was considered necessary for the thin film specimens. Annealing to achieve diffusion of the tracer was carried out
GRAIN
BOUNDARY
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TO TRANSPORT
577
in a silicon oil bath controlled to f 0.5 “C; the specimens were immersed into the bath up to temperatures of 210°C to eliminate transient temperatures during warmup and cooling stages of the annealing. Annealing times were typically a few minutes and were dictated by the temperature of the diffusion run and the condition that tracer be allowed to penetrate to only a fraction of the film thickness (< 50%). RF sputter-etching of the diffused specimens was carried out in an argon glow discharge with a peak to peak voltage of 1000 V at 13.56 MHz applied at the cathode (specimen), resulting in a power density of about 0.7 W cmm2 of the and an etch rate of about 3 A set- ‘. Prior to the actual application technique to diffusion measurements in Au polycrystalline films, it was considered important to test the technique for its precision. For this purpose, one bulk Au specimen (for comparison) and two (100) single crystal Au film specimens (2 urn thick) grown epitaxially on MgO were used. The diffusion anneals were made at 500, 352 and 3OO”C, respectively, in an ultra-high vacuum furnace. The penetration distance was calculated on the basis of the cumulative weight loss of the specimen between successive sectioning cycles, diameter of the specimen and the density of Au. The diffusivities were computed from the slope of the penetration profiles, plots of log specific activity versus penetration distance squared according to the solution for an instantaneous planar source, C = [C,/(rcDt)+]
exp (-
x2/4Dt),
where C is the concentration of tracer at a distance the tracer concentration at x = 0 and t = 0.
(1)
x and at time t, and C,
In fig. 11 an Arrhenius plot of the published self-diffusion coefficients in Au over some nine orders of magnitude is shownrs-2s). The three diffusivities measured by the RF sputter-etching technique, covering 200°C temperature range and spanning 4 orders of magnitude change in the diffusivities, fall precisely on this plot well within the scatter found among the various investigations. This excellent agreement is strong evidence that the sputteretching technique is sound for diffusion work and free from artifacts such as perturbations due to surface damage by Au ions (energy < 500 eV) and possible heating by the plasma. In fig. 12 is shown a penetration profile plot of log specific activity of Au lg5 tracer versus the penetration distance in a polycrystalline Au film having a grain size of - 1 urn. The diffusion annealing was carried out at 137 “C (410°K) for 10 min. The profile has two distinct regions: the initial region of very high specific activity over the first -500 A depth which is followed by a gradual decrease of activity over a large penetration distance in the film. The former is most probably attributable to the dislocations in the
578
R.ROSENBERG,
A.F.MAYADAS
AND
D.GUPTA
MAKIN,ROWE8.LECLAIRE (LATHESECTIONING) x OKKERSE (LATHE SECTIONING) o GAlNOTTl8ZECCHlNA(ABSORPTION) l RUPP,ERMERTb SIZMANN (ELECTROCHEMICAL PEELING) a PRESENT WORK (SPUTTERETCHING1
q
Fig. 11. Au19” penetration 1 pm grain size (columnar).
profile in a polycrystalline Au film of 2 pm thickness and A molybdenum film (N 600 8, thick) was used for adhesion to the fused quartz substrate.
film and “pipe” diffusion of the tracer. The second region which is unmistakably linear is attributable to the grain boundary contribution; since grain boundaries are normally the highest diffusivity paths, the tracer penetration would persist to large depths of the film. The linearity of the penetration profile in this region suggests that Fisher’s s4) analysis may be carried out for computing D,, the grain boundary diffusivity. The slope S is then given as \I2
d lnc s =
dj
where y is the tracer penetration
= - (rcD;t)* (SD&)+ distance
normal
(2)
to the film surface, D, the
GRAIN
BOUNDARY
I
I
CONTRIBUTIONS
I
I
I
I
TO TRANSPORT
I
J
579
I
10 20 30 40 50 60 70 00 90 100 TRACER PENETRATION DISTANCE x IO-%m
Fig. 12. Arrhenius plot of self-diffusion coefficients in Au. diffusivity which may be obtained from fig. 11 and equal to 5.1 x 10mz4 cm2 set at 137”C, and 6 the width of the grain boundary commonly taken as 10 x lOmE cm. From eq. (2), the grain boundary diffusivity D, is thus comdependputed at 8.0 x 10-l 5 cm* sec. Attempts to measure the temperature ence of the diffusivity have provided preliminary values for the activation energy of about 1 - 1.2 eV. More accurate values for activation energy and pre-exponential factors will be forthcoming. Once having established the diffusion constants characteristic of the films, effects of certain solute species on self-diffusion will be explored in hopes of quantifying correlary electromigration studies. 4. Resistivity
in thin films
In bulk metals, a theoretical analysis of electron-atom interactions by Huntington and Grone 2s) provides an expression for average velocity which is thus quite well understood in samples where lattice diffusion dominates. An equivalent analysis of electron-atom interactions does not exist for the case where grain-boundary diffusion dominates, as described earlier. In order to develop a model for electromigration in grain boundaries, it is essential that the atomic structure in the boundary be known and that atom positions be mathematically describable. This knowledge could then be used to define saddle-point configurations and to compute quantities such as the resistivity of a grain boundary, and the excess resistivity of a grain boundary due to the presence of activated complexes. Unfortunately experimental and theoretical knowledge of grain boundary structure and resistivity is currently at a rather rudimentary stage, although the recent activity discussed below has resulted in some progress. The first attempt to quantitatively measure grain boundary resistivity appears to be
580
R.ROSENBERG,
A.F.MAYADAS
AND
D.GUPTA
due to Andrews26), who studied Cu wires having different grain sizes and arrived at a specific grain boundary resistivity (resistivity per boundary surface area). Subsequently, measurements have been reported of grain boundary resistivity by Arajs et a1.27) in Fe, Andrews et al.28) in Cu and AI and Kasen2g) in Al. These authors studied bulk samples in which grain boundary contributions to sample resistance were small even in high purity samples measured at 4.2”K. This is because the mean free path, Z,, due to scatterers other than grain boundaries (mainly impurities) was approximately equal to average grain diameter d; thus, even though a single boundary may be a strong scatterer, the overall effect is small. In all these cases, n~easurements were reported as resistivity per boundary surface area and provided little insight into the nature of the boundary. At approximately the same time, our laboratory reported measurements in evaporated AI films3*) which indicated that grain boundaries contribute significantly to the total film resistivity at 4.2 OK; this simply because in evaporated films the condition for large grain boundary contribution, I,$=d, is easy to satisfy due to the generally fine-grained structure. The data was interpreted in terms of a three-parameter phenomenoIogi~a1 model describing resistivity in a polycrystalline film. The model assumes three scattering mechanisms in a film: scattering at external surfaces [Fuchs size-effect”“)], scattering at grain boundaries (described by the reflection coefficient R of a single boundary) and isotropic scattering due to all other defects (described by a mean free path lo). For bulk samples or very thick films in which the Fuchs size-effect can be neglected, the model simplifies to :=3{f--
&+cr2--a31n(l
-t-i))...,
(3)
with
pp is the total resistivity and pO is the resistivity in the absence of grain boundaries. For thinner films in which the total resistivity includes surface scattering, a simple algebraic expression cannot be written down and numerical integration is required. Grain boundary reflection coefficients obtained from this model contain some uncertainty since the Fuchs size-effect parameter p (the fraction of electrons specularly reflected at external surfaces) and I, are seldom known with a high degree of precision. Nevertheless useful estimates of R can be made. For the Al films discussed here, a value of R=O. 15 was obtained, indicating a rather strong interaction between grain boundaries and electrons,
GRAIN
This result compares
BOUNDARY
rather
CONTRIBUTIONS
favorably
TO TRANSPORT
with the data of Andrews
581
et a1.28) on
bulk Al which was processed through eq. (3) to give R= 0.17. Kasen 2g) found a smaller grain boundary resistivity in higher purity Al which, from eq. (3), gives R = 0.10. Values for R,which can then be related to the scattering potential, appear to be about the most information a phenomenological model can provide. To go further, the atomic structure of the boundary must be considered. A general derivation of resistivity for a crystal containing a distribution of arbitrary boundaries would be enormously complex, for all atom positions in the crystal cannot be mathematically described. The problem is more tractable in the case of coincident boundaries since a superlattice. continuous throughout the crystal, can be used as a coordinate system in which all other atom positions are describable. Fortunately many polycrystalline film samples of reasonable thickness (several thousand angstroms) contain coincident boundaries so that the mathematical simplification corresponds to a physical reality as well. It has recently been demonstrated that the superlattice concept can be very effectively employed to calculate the geometric structure factor of a crystal containing coincident boundariesss). Once the structure factor is known the method of pseudopotentials can be used obtain resistivity3a). The resistivity
Fig. 13. Resistivity of Ag with twin boundaries. Here pp is the total resistivity, po and are the resistivity and mean free path without twins, and d is the average distance between boundaries.
lo
for twin boundaries in Ag has in fact been calculated by Shatzkes et al.34). (fig. 13) who also prepared epitaxial Ag thin films in which the only planar defects were twins. Unfortunately the usual uncertainty in the film data caused by the Fuchs size effect was compounded by the fact that a high dislocation density existed in samples with high twin density and tended to ob-
582
R. ROSENBERG,
scure the grain boundary
A. F. MAYADAS
effects. At present,
AND
D. GUPTA
measurements
in this material
indicate
that the twin reflectivity is about a factor of 4 higher than the value R=0.03 predicted by the pseudopotential calculation. Although this is respectable agreement, it should be considerably improved if better numbers were made available for the resistivity per dislocation in Ag. It is anticipated that better, more conclusive data on low dislocation content material will be available shortly which will allow a more valid test of theory. Eventually, pseudo-potential calculations based on models of more complex boundaries will be available for comparison against experiment and will contribute to a theoretical understanding of electromigration in grain boundaries.
Appl. Phys. Letters 11 (1967) 263; W. A. Mutter, The Electrochem. Sot. Meeting, Dallas, Texas, May, 1967; J. R. Black, Trans. IEEE ED-16 (1969) 338. R. Rosenberg and L. Berenbaum, Appl. Phys. Letters 12 (1968) 201. D. Chaabra, N. Ainslie and D. Jepsen, The Electrochem. Sot. Meeting, Dallas, Texas, May, 1967. L. Berenbaum and R. Rosenberg, Thin Solid Films 4 (1969) 187. M. J. Attardo and R. Rosenberg, J. Appl. Phys. 41 (1970) 2381. R. Rosenberg and M. Ohring, J. Appl. Phys. to be published. L. Berenbaum, J. Appt. Phys. 42 (1971) 880. F. A. Blech and E. S. Meieran, J. Appt. Phys. 40 (1969) 485. R. Rosenberg, Appl. Phys. Letters 16 (1970) 27. R. Rosenberg and L. Berenbaum, in: Pvoc. of Europhys. Conj: on Atomic Transport, Marstrand, Sweden, June, 1970 (pub]. Z. Naturforsch, Germany). I. Ames, F. d’Heurle and R. E. Horstmann, IBM J. Res. Develop. 14 (1970) 461. R. Rosenberg, in: Puoc. Fifth Intern. Vacuum Congrrss. Boston, Mass., October, 1971, in J. Vacuum Sci. Technol. T. R. Anthony, Phys. Rev. B 2 (1970) 264. F. M. d’Heurle, Metal Trans. 2 (1971) 683. L. Berenbaum and R. Rosenberg, in: Proc. IEEE Reliability Phys. Symp., Las Vegas, Nevada, April, 1971. T. S. Lundy and R. A. Padgett, Trans. Met. Sot. AlME 242 (1968) 1963. D. Gupta and R. T. C. Tsui, Appt. Phys. Letters 17 (1970) 294. See for example, D. Gupta, D. Lazarus and D. S. Lieberman, Phys. Rev. 153 (1967) 863. W. Rupp, U. Ermert and R. Sizmann, Phys. Status Sohdi 33 (1969) 509. A. Gainotti and L. Zecchina, Nuovo Cimento 40B (1965) 295. S. M. Makin, A. H. Rowe, and A. D. LeClaire, Proc. Phys. Sot. (London) 70 (1957) 545. A. Seeger and H. Mehrer, Phys. Status Solidi 29 (1968) 231. B. Okkerse, Phys. Rev. 103 (1956) 1246. J. C. Fisher, J. Appl. Phys. 22 (1951) 74. H. B. Huntington and A. R. Grone, J. Phys. Chem. Solids 20 (1961) 76. P. V. Andrews, Phys. Letters 19 (1965) 558. S. Arajs, B. F. Oliver and 3. T. Michalak, J. Appt. Phys. 38 (1967) 1676. P. V. Andrews, M. B. West and C. R. Robeson, Phil. Mag. 19 (1969) 887. M. B. Kasen, Phil. Mag. 21 (1970) 599.
1) See, for example, I. A. Blech and E. S. Meieran,
2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29)
GRAINBOUNDARY CONTRIBUTIONS TOTRANSPORT
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30) A. F. Mayadas and M. Shatzkes, Phys. Rev. B 1 (1970) 1382. 31) See for example, E. H. Sondheimer, Advan. Phys. 1 (1952) 1. 32) P. Chaudhari, M. Shatzkes and A. F. Mayadas, to be published. 33) W. A. Harrison, Pseudopotentials in the Theory of Metals (Benjamin, New York, 1966) p. 156. 34) M. Shatzkes, P. Chaudhari, A. A. Levi and A. F. Mayadas, to be published.
Discussion M. E. GLICKSMAN (Naval Fuchs-Sondheimer of electrons
theory
Research of thin
Laboratory, film
in thin films. The deviations
resistivity from
D.C.):
Washington, describes
that, I suspect,
the
The
transport
do not necessar-
ily give a unique value for the surface reflection coefficient. Dr. Ehrlich in our laboratory has studied certain refinements of that theory. In a material like aluminum, where you would expect the occurrence of multiband conduction processes, are there other deviations that, perhaps, a refined theory would bring to the typical spherical one-band model? In the material that you are looking at, this suggests that conduction from several bands could give effects not simply describable by a surface reflection coefficient. R. ROSENBERG: I think that Frank Mayadas would like to answer that. He is sitting on the edge of his chair. A. F. MAYADAS (IBM Watson Research Center, Yorktown Heights, New York): I think I know the work to which you are referring and I just want to make two comments. I talked with Ehrlich at the Physical Society Meeting in Dallas last year and it turns out that the effects he has been calculating are in the phonon resistivity, and not in the defect region. Secondly, the effect we have observed, namely that a Fuchs theory fit to data is impossible if a single mean free path and a single value of the surface scattering coefficient are used, is too large to be explained in terms of these multi-band processes. This is especially true in aluminum for which the free electron theory with isotropic scattering is a good approximation, and for which previous measurements in thin rolled foils have previously shown excellent agreement with the Fuchs therory. H. B. HUNTINGTON: (Rensselaer Polytechnical Institute, Troy, New York): What is your picture as to the distribution of copper atoms in the aluminum grain boundary? Suppose you are looking down a short circuit channel, how many copper atoms would you see? One every five planes? ROSENBERG: Well, I think that is a little difficult to calculate. I think the best you can do is to consider that you have a certain number of solute atoms in the boundary and predict the percentage that are in the defect sites. Since one does not know the exact density of defect sites or number of solute atoms in a boundary one can only make an approximation as to the solute distri-
584
R. ROSENBERG,
A. F. MAYADAS
AND D. GUPTA
bution. The calculation presented was done strictly on the assumption that you have a boundary defect containing a solute atom, whose effectiveness lies in its interaction with matrix atoms diffusing within the defect. As the diffusing species contacts the solute atom it can only break away after overcoming an additional binding energy. All I am saying is that if you change the activation energy for migration by an amount proportional to the binding energy then you get a change in the flux. What you are suggesting in terms of the number of such interactions may be a possible pre-exponential effect. HUN~~NCTON: I see, one impurity is sufficient to block any channel and the energy for the vacancy to pass it determines the transport rate. ROSENBERG: Yes, any di~using boundary atom will eventualiy see the solute. D. KUHLMANN-WILSDORF (University of Virginia, Charlottesville, Virginia): The assumption that there is no dependence of defect density on film thickness may need some checking. Dr. Raghavan [K. S. Raghavan, Ph. D. thesis, Univ. of Pennsylvania, 1963; K. S. Raghavan and D. KuhlmannWilsdorf, Mater. Sci. Eng. 1 (1966) 1951 made some investigations in this direction several years ago on electrolytically deposited gold films, finding a very strong decrease in defect density as film thickness increased. You can use two criteria in order to check this up. One is the curling of films once they have been taken off the substrate. The amount of strain could be deduced from the curling indicated that the defect concentration and the strain in the films diminished as the films got thicker, at quite a rapid rate. Secondly, the tensile strengths of the films depended very much on thickness, and decreased strongly with film thickness. So both of these observations suggested that there was a strong dependence of defect density on film thickness. ROSENBERG: Yes, the question is what the defects are. In some cases I agree with you that stress changes with thickness, but generally I am not sure I do because we have done a great deal of stress measurements and we find that the stress is not changing with film thickness. The force is increasing but the stress - the built-in residual stress - seems to be constant in the film. I agree that if we had a large negative change in dislocation density with thickness, for example, then we would see precisely what we have seen, namely, that the mean free path will go up as you increase the film thickness. We have transmission micrographs of the aluminum films used in our resistivity studies and do not see a very high density of dislocations. We are in the range of lo6 or 10’ (per cm’), and this is not high enough to greatly effect the resistivity in the aluminum samples. The silver work represented a different situation. We had about 10” dislocations per cm’, and in this case the resistivity provided by the dislocations is comparable to the resistivity of the grain boundaries. Now we are in a lot of trouble. We cannot differentiate
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TO TRANSPORT
585
boundary scattering from dislocation scattering. More than that I really cannot say because we have not done that much work on the dislocation density. KUHLMANN-WILSDORF: I probably phrased my comments a bit loosely. I just wanted to suggest that in certain cases there is such a strong thickness dependence and that this needs checking. ROSENBERG: Yes. We are checking that on single crystals. We have been running single crystals of different thickness, trying to determine whether or not the Fuchs-Sondheimer relationship for a single mean free path holds in single crystals. Based on only a few data, it seems that in single crystal silver films, the change in resistivity with thickness can be explained by only the Fuchs effect with partially specular scattering. Here, the dislocation density does not seem to be a factor. M. E. GLICKSMAN (Naval Research Laboratory, Washington, D.C.): With regard to the solute-vacancy binding model that you see, Burke has put some upper bounds on solute-vacancy binding energies, ROSENBERG: In a lattice? GLICKSMAN: Well, yes. ROSENBERG: Lattice results are no good. GLICKSMAN: Why no good? ROSENBERG: I do not know what goes on in a grain boundary. There is much data on lattice diffusion, but there is no apparent correlation at all with results we get. For example, Tom Anthony, [T. R. Anthony, Phys. Rev. B 2 (1970) 2641 (G.E.), did a lot of work on etch pitting by vacancy condensation in Al with Cu additions. He found that copper had zero effect on the selfdiffusion of aluminum, and yet we find copper to be very effective for inhibiting electromigration. GIJCKSMAN: Burke’s results, incidentally, bracket binding energy between zero and something like l/l0 eV so that, since those two results tend to agree, it would be interesting to see whether you can get the right effect within those limits of (say) zero and l/lOth eV. ROSENBERG: You are discussing the problem we have. We do not know how to measure these energy parameters in grain boundaries directly, so we have to learn how to obtain this type of data. That is why we entered into the radio tracer work.
SCIENCE
GRAIN
31(1972)
BOUNDARY
566-585
CONTRIBUTIONS
R. ROSENBERG, IBM
Watson
Research
0 North-Holland
A. F. MAYADAS
Center.
Yorktown
Heights,
Publishing
Co.
TO TRANSPORT
and New
D. GUPTA York 10598,
U.S.A.
Several important features of grain boundaries, as related to thin metallic film properties, will be discussed. Boundaries are particularly important in films where diffusional processes occur mainly at low temperatures and grain sizes are of the order of 1 urn or less. One phenomenon of interest is electromigration where a high dc current density causes a net atom drift in the direction of electron flow, mainly along boundaries. Non-uniformities in the boundary network lead to a divergence in the diffusion flux, with resultant mass depletion and void formation. A related discussion will be presented on radioactive tracer self-diffusion in gold films at temperatures below 200°C where dislocations and grain boundaries are controlling. Relationships to electromigration will be illustrated. Also to be discussed will be measurements of grain boundary contributions to electrical resistivity in terms of specific grain boundary models. Analytical expressions will be presented to allow extraction of the boundary contributions.
1. Introduction Initial interest in the structure and properties of grain boundaries in the electronics industry was stimulated by a reliability problem associated with electromigrationr). At the relatively low temperatures of operation of integrated circuit devices, where lattice diffusivity is negligible, the high current densities typically used can cause atom migration only along high diffusivity paths such as boundaries. This migration ultimately leads to sufficient mass depletion to cause an open circuit and short device lifetimes. Restriction of the electromigration to boundaries makes analysis of the details of the process difficult. Very little quantitative information is available for such important parameters as thermal diffusion constants, effective charge of the diffusing species with respect to the electron flow, boundary diffusion mechanisms, boundary structure and defects, and impurity adsorption effects on diffusion. Thus, to try to gain an understanding of basic electromigration behavior in thin films it is necessary to pursue a broad range of boundary properties. In this paper, the important aspects of electromigration behavior in films will be presented specifically to illustrate the implications of the various properties of grain boundaries. Also included will be discussions on two of the boundary-related studies presently being pursued in our laboratory, 566
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namely, radioactive tracer diffusion and low temperature should provide important insight into the electromigration other film phenomena which are dependent upon boundary
567
resistivity, which process as well as behaviour.
2. Electromigration A typical depleted region resulting from a dc current in an aluminum thin film stripe is shown in fig. 1 2). The average temperature of the stripe was 125°C and the current density 2 x lo6 A/cm’. Of importance are the inter-
Fig. 1. Electron micrograph of a typical open in an aluminum conductor stripe caused by electromigration-induced local mass depletion. Note the grain boundary nature of the damage area (see ref. 2).
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R.ROSENBERG,
A.F.MAYADAS
AND D.GUPTA
granular nature of the voids and the non-uniformity of the depletion with respect to the stripe geometry. These observations point to the reasons behind the difficulty in studying electromigration in films; damage is confined to certain boundaries and, because of this, methods for measuring atomic flux rates used in bulk samples, for example marker motion, which depend on uniform motion of atoms across any cross-section, are not applicable. Clearly, in films, local flux divergences are prevalent and the problem becomes one of characterizing the various causes of such divergences. Extracting physical constants from experiment becomes a formidable task. 2.1. DAMAGE MECHANISMS Flux divergences during electromigration have been shown to be associated with the presence of temperature gradients3) and structural irregularities 4-7). This is illustrated schematically in fig. 2. Migration through an increasing MECHANISMS TEMPERATURE
T
1
FOR FLUX DIVERGENCE GRADIENT
Jout
:VJ a $)
Jin>l
X 1
I
tb
00
0
Holes STRUCTURAL
-e
Growths NONUNIFORMITIES:
VJ a! d N = Grain Size
, AH = Act. Energy
Fig. 2. Schematic diagrams of mechanisms by which electromigration flux becomes nonuniform. Temperature gradients lead to cathodic opens. Structural irregularities are shown to be of two types, local and area, the former being a triple point problem, and the latter a mixed grain size problem.
GRAIN
temperature
BOQNDARY
leads to accumulation
CONTRIBUTIONS
TO TRANSPORT
of vacancies,
depletion,
569
and void forma-
tion, while migration through a decreasing temperature leads to mass buildup in the form of surface growths. This is a direct consequence of the temperature dependence of the diffusivity. Structural damage sites are of two basic types, local and area. Local damage is typified by the triple point (three grain junction) in fig. 2, where the flux of atoms leading out of the junction must be balanced with the &IX coming in 4%~7). An imbalance can occur because of the inherent difference in diffusion characteristics of each grain boundary, and the relative angles between boundary normals and the direction of the applied field; that is, DIFr #D2F, #D,F,, where Fis the force component in the direction of atom motion, and D is the diffusivity. The large area problem is a result of the normal spread in grain size encountered during film growth. If, by chance, a single grain spans the width of a stripe, then a depletion is to
(4 Fig. 3. Scanning electron micrograph of progression of local damage in an aluminum stripe. Both holes and growths appear in the same cross-section, thus minimizing temperature gradient effects (see ref. 4).
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R. ROSENBERG,
A. F. MAYADAS
AND D. GUPTA
be expected at the line of intersection between the single grain and the adjacent area containing many grains per width. Mass carried away through the boundaries cannot be replaced. In most instances, the structural damage occurs earlier and superimposes onto the slower temperature gradient effects 4). Examples of structural damage are illustrated in figs. 3 and 4. In fig. 3 the progression of damage in an alumininum film is shown by scanning electron microscopy4). Both peaks and holes are formed simultaneously in the same cross-section showing the accumulation and depletion characteristic of triple point interactions, and the relative unimportance of the temperature profile. Fig. 4 shows a transmission micrograph of depletion at a location having mixed grain sizes). Note the equilibrium void shape, bounded by dihedral angles with the grain boundaries and a planar surface in the single crystal.
Fig. 4. Transmission electron micrograph of mass depletion caused by a mixed grain size. In this case a single crystal spanned the stripe and was bounded by grains about one-quarter of the stripe width. Boundary diffusion was not replaceable.
Calculations of depletion rates based on these models is difficult because it is required to know z* and D, the effective charge and diffusivity of the diffusing species, respectively. The activation energy for electro-migration has been approximated by various meanss,“,s) but the factors D, and z* on the basis of remain elusive. The multiple D,z * has been estimatedg) measurements involving void5, 8, or peak”) growth to be about 3 f0.5 x 10m2
GRAIN
BOUNDARY
CONTRIBUTIONS
TO TRANSPORT
571
cm2 set-’ for aluminum, facilitating the calculations. Estimation of vacancy supersaturations have been made under various conditionssps) and have been found to be < 1. At this level of supersaturation it is doubtful in films that spontaneous void formation can occur in boundaries without the presence of heterogeneous nucleating centers. In the absence of void formation, excess vacancies diffuse to the surface where accelerated grain boundary grooving can take places). The grooving mechanism, which causes general thinning, requires surface as well as boundary transport. This was illustrated by the electromigration behavior of silver filmslo) where surface atoms are highly active. Fig. 5 shows the general rippling of the silver surface during
Fig. 5.
Scanning electron micrograph of a silver stripe after powering. Surface roughening of a previously smooth surface indicates significant surface activity.
Fig. 6. Scanning electron micrograph of a silver stripe after powering whose top surface was coated with a thin layer of chromium. Damage was confined to uncoated edges.
572
R.ROSENBERG.
A. F. MAYADAS
AND
D. GUPTA
test, which is indicative of a grooving process. Conclusive evidence of the surface effect is shown in fig. 6. The stripe used in this test had a thin (- lOOA> diffusion resistant chromium layer on the top surface but the edges were bare. Note the restriction of damage to the uncoated edges while the top surface is unaffected. Calculation of the time required for grooves to reach the substrate are within an order of magnitude of the time it takes to observe a hole in a test stripe. 2.2. EFFECTS OF DIFFUSIVITY Independent of the particular mechanisms by which electromigration damage takes place, the underlying rate determining factor is the diffusion behavior of the individual boundaries. Control of this behavior is the key to higher performance and longer lifetimes for film stripes and device circuitry. Examples of this can be found from the results of introducing the concepts of preferred orientation and addition of certain solute species, each of which were effective in prolonging lifetime. In the former case, it was postulated5) that preferred orientation would produce two effects, reduction of damage sites by normalization of boundary diffusivities and lowering of diffusivity by orienting boundary line defects perpendicular to the applied field. The triple point problem should be less severe in the case where all boundaries are tilt boundaries with the tilt axis and diffusion channels normal to the plane of the film. These ideas were borne out in (111) oriented aluminum films by the increased activation energy observed (from -0.6 to -0.7 eV), longer lifetimes, and decreased G, the standard deviation in the log normal distribution of failure times. The CJparameter is dependent on the number of contributing mechanisms, which in this case was reduced to just mixed grain size effects. The solute effect has been illustrated for the case of copper in aluminumrl) in which the lifetime was shown to be increased. This result can be attributed to interactions between the solute and boundary defects through which the matrix atoms are diffusing102 la). For example, a schematic is shown in fig. 7 of the partitioning of solute to ledge sites. By assuming the existence of bonding energies between the solute and boundary defect and between solute at the defect and the diffusing species, a reduction in electromigration flux can be calculated. It should be kept in mind that there is no obvious connection between the effects of solute on diffusion in the lattice and diffusion in the boundary. Copper in aluminum is an example of this; increased lifetime is observed but it has been reportedra) that copper has no influence on the lattice diffusivity. Fig. 8 is a plot of the reduction in flux of the matrix atoms as a function of the solute concentration in the boundary. It is apparent that boundary concentrations of greater than 1% would produce effective
GRAIN
BOUNDARY
CONTRIBUTIONS
TO TRANSPORT
573
(a
Solute Segregation
(b) Fig. 7.
Schematic of grain boundary ledge defects. Solute atoms segregate to defects with a binding energy, BNS. Solute complexes also form to reduce their mobility in the defects.
inhibition of migration. This effect can best be illustrated by the type of test shown in fig. 9, in which magnesium was diffused into the central region of an aluminum stripe. From the above analysis, the migration rate of aluminum in the magnesium-diffused region should be less than in the adjacent pure region; thus, passage of electrons through the stripe should cause a net transport away from the diffused region. The open in fig. 9 is the result of such a depletion. Microprobe analysis of the magnesium content, shown in fig. 10, indicates the critical concentration at the open to be about 0.5% which agrees generally with prediction. The concentration profile in fig. 10 points out the most serious problem when using solute to inhibit diffusion; that is, a shift in concentration in the direction of electron flow. Because of the large resistivity characteristic of solute atoms, they are rapidly transported in the field and eventually can be depleted from areas of the stripe. From fig. 8 it is inevitable that this will lead to rapid deterioration by accelerated transport of the matrix atoms. This
574
R. ROSENBERG,
A. F. MAYADAS
AND
D. GUPTA
0.8
0.6
-5.0
-4.5
-4.0
-3.5 LOG
Fig. 8. Reduction Concentrations of
-3.0
-2.5
Co (boundary
solute)
-2.0
-1.5
of electromigration flux produced by solute in the boundary to be sufficient to cause an order of magnitude
1% appear
defects. change.
solute depletion has been observed in the Al-Cu systeml4,15) and is believed to be responsible for lower than expected lifetimes. Much of the present work in the area of electromigration in films is concerned with prevention of the solute depletion by providing a uniform distribution of precipitates which, by dissolving, can replace thedepleting solute. This is not a cure and only prolongs the lifetime by the time it takes to dissolve the precipitates. What is needed is a method to immobilize the solute, to keep it in the boundary defect where it can be effective; for example, addition of a second solute species which can form a stable complex with the first in the boundary. 3. Radioactive
tracer diffusion in films
From the previous discussion, it is apparent that direct methods of analyzing boundary diffusivities are a necessity. Lifetime measurements are complicated by phenomena other than simple boundary diffusion and thus cannot give dependable values for diffusion constants. The example of solute effects is obvious, as lifetime is a measure more of the depletion rate of solute than of the effect of solute on the migration of the matrix atoms. Poly-
GRAIN
BOUNDARY
CONTRIBUTIONS
TO TRANSPORT
57.5
Fig. 9. Effect of magnesium on electromigration flux of aluminum. On the left hand side of the electron micrograph the stripe has been treated with magnesium. Electrons passing from left to right cause depletion in the untreated portion because of reduced flux in the treated region.
Fig. 10. Electron microprobe scan of stripe of fig. 9. The location of the damage occurs where the magnesium content is less than 1% or about in the range predicted in fig. 9. Note drift of magnesium in direction of electron flow.
576
R. ROSENBERG,
A. F. MAYADAS
AND D. GUPTA
crystalline thin films are very attractive for measuring grain boundary selfdiffusion using radioactive tracers and serial sectioning procedures. The inherent advantage in using thin films are (1) very large grain boundary to grain volume ratios, and (2) the grain boundaries are ordinarily normal to the plane of the film. The former should result in high resolution between lattice and the grain boundary diffusion processes, particularly at low temperatures and the latter should make the handling of the tracer penetration profiles analytically simpler. Also the absorption of the nuclear emission may be totally absent in the films which is also a very desirable feature in some cases. 3.1. SECTIONING Any meaningful radioactive work in thin films necessarily involves submicron sectioning since films themselves are typically only microns thick and diffusion depths are shallow at the temperatures of interest. Also, the sectioning operation should be uniform over the grain and the grain boundary. Any mechanical method of material removal can hardly be considered for metallic films since substrates are usually very fragile and section thicknesses would be too great. The electrochemical technique used earlier for profiling Au radiotracer in Au single crystal diffusion workr6) does not appear to be adequate for polycrystalline films since we find grain boundaries to be preferentially attacked. We have developed a novel sectioning technique using an RF sputter-etching procedure for thin films which fulfills the criteria given above. For a complete account of the RF sputter-etching technique as applied to diffusion measurements, the interested reader is referred to our earlier publicationl7). 3.2. DIFFUSION PROCEDURES Au films were chosen for the work in view of the large bulk of valuable information available in the published literature including diffusion and quenched-in defect data which could be useful for comparison purposes. Au’ 95 (180 day, 0.067 MeV 7) radioactive isotope was employed as the tracer. $in. x 2um thick polycrystalline Au films were deposited onto fused quartz substrates coated with an adhesive MO layer by the electron-gun evaporation technique in an ultra-high vacuum system. The starting metal had 99.999 + % purity. The substrate temperature during Au deposition was maintained at 500 “C to obtain about a 1urn grain size in the films. Standard procedures were used for tagging of the isotope (0.1 PC) and radiocounting of Au 195 for 0.067 MeV yl*) with the difference that no surface preparation prior to diffusion was considered necessary for the thin film specimens. Annealing to achieve diffusion of the tracer was carried out
GRAIN
BOUNDARY
CONTRIBUTIONS
TO TRANSPORT
577
in a silicon oil bath controlled to f 0.5 “C; the specimens were immersed into the bath up to temperatures of 210°C to eliminate transient temperatures during warmup and cooling stages of the annealing. Annealing times were typically a few minutes and were dictated by the temperature of the diffusion run and the condition that tracer be allowed to penetrate to only a fraction of the film thickness (< 50%). RF sputter-etching of the diffused specimens was carried out in an argon glow discharge with a peak to peak voltage of 1000 V at 13.56 MHz applied at the cathode (specimen), resulting in a power density of about 0.7 W cmm2 of the and an etch rate of about 3 A set- ‘. Prior to the actual application technique to diffusion measurements in Au polycrystalline films, it was considered important to test the technique for its precision. For this purpose, one bulk Au specimen (for comparison) and two (100) single crystal Au film specimens (2 urn thick) grown epitaxially on MgO were used. The diffusion anneals were made at 500, 352 and 3OO”C, respectively, in an ultra-high vacuum furnace. The penetration distance was calculated on the basis of the cumulative weight loss of the specimen between successive sectioning cycles, diameter of the specimen and the density of Au. The diffusivities were computed from the slope of the penetration profiles, plots of log specific activity versus penetration distance squared according to the solution for an instantaneous planar source, C = [C,/(rcDt)+]
exp (-
x2/4Dt),
where C is the concentration of tracer at a distance the tracer concentration at x = 0 and t = 0.
(1)
x and at time t, and C,
In fig. 11 an Arrhenius plot of the published self-diffusion coefficients in Au over some nine orders of magnitude is shownrs-2s). The three diffusivities measured by the RF sputter-etching technique, covering 200°C temperature range and spanning 4 orders of magnitude change in the diffusivities, fall precisely on this plot well within the scatter found among the various investigations. This excellent agreement is strong evidence that the sputteretching technique is sound for diffusion work and free from artifacts such as perturbations due to surface damage by Au ions (energy < 500 eV) and possible heating by the plasma. In fig. 12 is shown a penetration profile plot of log specific activity of Au lg5 tracer versus the penetration distance in a polycrystalline Au film having a grain size of - 1 urn. The diffusion annealing was carried out at 137 “C (410°K) for 10 min. The profile has two distinct regions: the initial region of very high specific activity over the first -500 A depth which is followed by a gradual decrease of activity over a large penetration distance in the film. The former is most probably attributable to the dislocations in the
578
R.ROSENBERG,
A.F.MAYADAS
AND
D.GUPTA
MAKIN,ROWE8.LECLAIRE (LATHESECTIONING) x OKKERSE (LATHE SECTIONING) o GAlNOTTl8ZECCHlNA(ABSORPTION) l RUPP,ERMERTb SIZMANN (ELECTROCHEMICAL PEELING) a PRESENT WORK (SPUTTERETCHING1
q
Fig. 11. Au19” penetration 1 pm grain size (columnar).
profile in a polycrystalline Au film of 2 pm thickness and A molybdenum film (N 600 8, thick) was used for adhesion to the fused quartz substrate.
film and “pipe” diffusion of the tracer. The second region which is unmistakably linear is attributable to the grain boundary contribution; since grain boundaries are normally the highest diffusivity paths, the tracer penetration would persist to large depths of the film. The linearity of the penetration profile in this region suggests that Fisher’s s4) analysis may be carried out for computing D,, the grain boundary diffusivity. The slope S is then given as \I2
d lnc s =
dj
where y is the tracer penetration
= - (rcD;t)* (SD&)+ distance
normal
(2)
to the film surface, D, the
GRAIN
BOUNDARY
I
I
CONTRIBUTIONS
I
I
I
I
TO TRANSPORT
I
J
579
I
10 20 30 40 50 60 70 00 90 100 TRACER PENETRATION DISTANCE x IO-%m
Fig. 12. Arrhenius plot of self-diffusion coefficients in Au. diffusivity which may be obtained from fig. 11 and equal to 5.1 x 10mz4 cm2 set at 137”C, and 6 the width of the grain boundary commonly taken as 10 x lOmE cm. From eq. (2), the grain boundary diffusivity D, is thus comdependputed at 8.0 x 10-l 5 cm* sec. Attempts to measure the temperature ence of the diffusivity have provided preliminary values for the activation energy of about 1 - 1.2 eV. More accurate values for activation energy and pre-exponential factors will be forthcoming. Once having established the diffusion constants characteristic of the films, effects of certain solute species on self-diffusion will be explored in hopes of quantifying correlary electromigration studies. 4. Resistivity
in thin films
In bulk metals, a theoretical analysis of electron-atom interactions by Huntington and Grone 2s) provides an expression for average velocity which is thus quite well understood in samples where lattice diffusion dominates. An equivalent analysis of electron-atom interactions does not exist for the case where grain-boundary diffusion dominates, as described earlier. In order to develop a model for electromigration in grain boundaries, it is essential that the atomic structure in the boundary be known and that atom positions be mathematically describable. This knowledge could then be used to define saddle-point configurations and to compute quantities such as the resistivity of a grain boundary, and the excess resistivity of a grain boundary due to the presence of activated complexes. Unfortunately experimental and theoretical knowledge of grain boundary structure and resistivity is currently at a rather rudimentary stage, although the recent activity discussed below has resulted in some progress. The first attempt to quantitatively measure grain boundary resistivity appears to be
580
R.ROSENBERG,
A.F.MAYADAS
AND
D.GUPTA
due to Andrews26), who studied Cu wires having different grain sizes and arrived at a specific grain boundary resistivity (resistivity per boundary surface area). Subsequently, measurements have been reported of grain boundary resistivity by Arajs et a1.27) in Fe, Andrews et al.28) in Cu and AI and Kasen2g) in Al. These authors studied bulk samples in which grain boundary contributions to sample resistance were small even in high purity samples measured at 4.2”K. This is because the mean free path, Z,, due to scatterers other than grain boundaries (mainly impurities) was approximately equal to average grain diameter d; thus, even though a single boundary may be a strong scatterer, the overall effect is small. In all these cases, n~easurements were reported as resistivity per boundary surface area and provided little insight into the nature of the boundary. At approximately the same time, our laboratory reported measurements in evaporated AI films3*) which indicated that grain boundaries contribute significantly to the total film resistivity at 4.2 OK; this simply because in evaporated films the condition for large grain boundary contribution, I,$=d, is easy to satisfy due to the generally fine-grained structure. The data was interpreted in terms of a three-parameter phenomenoIogi~a1 model describing resistivity in a polycrystalline film. The model assumes three scattering mechanisms in a film: scattering at external surfaces [Fuchs size-effect”“)], scattering at grain boundaries (described by the reflection coefficient R of a single boundary) and isotropic scattering due to all other defects (described by a mean free path lo). For bulk samples or very thick films in which the Fuchs size-effect can be neglected, the model simplifies to :=3{f--
&+cr2--a31n(l
-t-i))...,
(3)
with
pp is the total resistivity and pO is the resistivity in the absence of grain boundaries. For thinner films in which the total resistivity includes surface scattering, a simple algebraic expression cannot be written down and numerical integration is required. Grain boundary reflection coefficients obtained from this model contain some uncertainty since the Fuchs size-effect parameter p (the fraction of electrons specularly reflected at external surfaces) and I, are seldom known with a high degree of precision. Nevertheless useful estimates of R can be made. For the Al films discussed here, a value of R=O. 15 was obtained, indicating a rather strong interaction between grain boundaries and electrons,
GRAIN
This result compares
BOUNDARY
rather
CONTRIBUTIONS
favorably
TO TRANSPORT
with the data of Andrews
581
et a1.28) on
bulk Al which was processed through eq. (3) to give R= 0.17. Kasen 2g) found a smaller grain boundary resistivity in higher purity Al which, from eq. (3), gives R = 0.10. Values for R,which can then be related to the scattering potential, appear to be about the most information a phenomenological model can provide. To go further, the atomic structure of the boundary must be considered. A general derivation of resistivity for a crystal containing a distribution of arbitrary boundaries would be enormously complex, for all atom positions in the crystal cannot be mathematically described. The problem is more tractable in the case of coincident boundaries since a superlattice. continuous throughout the crystal, can be used as a coordinate system in which all other atom positions are describable. Fortunately many polycrystalline film samples of reasonable thickness (several thousand angstroms) contain coincident boundaries so that the mathematical simplification corresponds to a physical reality as well. It has recently been demonstrated that the superlattice concept can be very effectively employed to calculate the geometric structure factor of a crystal containing coincident boundariesss). Once the structure factor is known the method of pseudopotentials can be used obtain resistivity3a). The resistivity
Fig. 13. Resistivity of Ag with twin boundaries. Here pp is the total resistivity, po and are the resistivity and mean free path without twins, and d is the average distance between boundaries.
lo
for twin boundaries in Ag has in fact been calculated by Shatzkes et al.34). (fig. 13) who also prepared epitaxial Ag thin films in which the only planar defects were twins. Unfortunately the usual uncertainty in the film data caused by the Fuchs size effect was compounded by the fact that a high dislocation density existed in samples with high twin density and tended to ob-
582
R. ROSENBERG,
scure the grain boundary
A. F. MAYADAS
effects. At present,
AND
D. GUPTA
measurements
in this material
indicate
that the twin reflectivity is about a factor of 4 higher than the value R=0.03 predicted by the pseudopotential calculation. Although this is respectable agreement, it should be considerably improved if better numbers were made available for the resistivity per dislocation in Ag. It is anticipated that better, more conclusive data on low dislocation content material will be available shortly which will allow a more valid test of theory. Eventually, pseudo-potential calculations based on models of more complex boundaries will be available for comparison against experiment and will contribute to a theoretical understanding of electromigration in grain boundaries.
Appl. Phys. Letters 11 (1967) 263; W. A. Mutter, The Electrochem. Sot. Meeting, Dallas, Texas, May, 1967; J. R. Black, Trans. IEEE ED-16 (1969) 338. R. Rosenberg and L. Berenbaum, Appl. Phys. Letters 12 (1968) 201. D. Chaabra, N. Ainslie and D. Jepsen, The Electrochem. Sot. Meeting, Dallas, Texas, May, 1967. L. Berenbaum and R. Rosenberg, Thin Solid Films 4 (1969) 187. M. J. Attardo and R. Rosenberg, J. Appl. Phys. 41 (1970) 2381. R. Rosenberg and M. Ohring, J. Appl. Phys. to be published. L. Berenbaum, J. Appt. Phys. 42 (1971) 880. F. A. Blech and E. S. Meieran, J. Appt. Phys. 40 (1969) 485. R. Rosenberg, Appl. Phys. Letters 16 (1970) 27. R. Rosenberg and L. Berenbaum, in: Pvoc. of Europhys. Conj: on Atomic Transport, Marstrand, Sweden, June, 1970 (pub]. Z. Naturforsch, Germany). I. Ames, F. d’Heurle and R. E. Horstmann, IBM J. Res. Develop. 14 (1970) 461. R. Rosenberg, in: Puoc. Fifth Intern. Vacuum Congrrss. Boston, Mass., October, 1971, in J. Vacuum Sci. Technol. T. R. Anthony, Phys. Rev. B 2 (1970) 264. F. M. d’Heurle, Metal Trans. 2 (1971) 683. L. Berenbaum and R. Rosenberg, in: Proc. IEEE Reliability Phys. Symp., Las Vegas, Nevada, April, 1971. T. S. Lundy and R. A. Padgett, Trans. Met. Sot. AlME 242 (1968) 1963. D. Gupta and R. T. C. Tsui, Appt. Phys. Letters 17 (1970) 294. See for example, D. Gupta, D. Lazarus and D. S. Lieberman, Phys. Rev. 153 (1967) 863. W. Rupp, U. Ermert and R. Sizmann, Phys. Status Sohdi 33 (1969) 509. A. Gainotti and L. Zecchina, Nuovo Cimento 40B (1965) 295. S. M. Makin, A. H. Rowe, and A. D. LeClaire, Proc. Phys. Sot. (London) 70 (1957) 545. A. Seeger and H. Mehrer, Phys. Status Solidi 29 (1968) 231. B. Okkerse, Phys. Rev. 103 (1956) 1246. J. C. Fisher, J. Appl. Phys. 22 (1951) 74. H. B. Huntington and A. R. Grone, J. Phys. Chem. Solids 20 (1961) 76. P. V. Andrews, Phys. Letters 19 (1965) 558. S. Arajs, B. F. Oliver and 3. T. Michalak, J. Appt. Phys. 38 (1967) 1676. P. V. Andrews, M. B. West and C. R. Robeson, Phil. Mag. 19 (1969) 887. M. B. Kasen, Phil. Mag. 21 (1970) 599.
1) See, for example, I. A. Blech and E. S. Meieran,
2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29)
GRAINBOUNDARY CONTRIBUTIONS TOTRANSPORT
583
30) A. F. Mayadas and M. Shatzkes, Phys. Rev. B 1 (1970) 1382. 31) See for example, E. H. Sondheimer, Advan. Phys. 1 (1952) 1. 32) P. Chaudhari, M. Shatzkes and A. F. Mayadas, to be published. 33) W. A. Harrison, Pseudopotentials in the Theory of Metals (Benjamin, New York, 1966) p. 156. 34) M. Shatzkes, P. Chaudhari, A. A. Levi and A. F. Mayadas, to be published.
Discussion M. E. GLICKSMAN (Naval Fuchs-Sondheimer of electrons
theory
Research of thin
Laboratory, film
in thin films. The deviations
resistivity from
D.C.):
Washington, describes
that, I suspect,
the
The
transport
do not necessar-
ily give a unique value for the surface reflection coefficient. Dr. Ehrlich in our laboratory has studied certain refinements of that theory. In a material like aluminum, where you would expect the occurrence of multiband conduction processes, are there other deviations that, perhaps, a refined theory would bring to the typical spherical one-band model? In the material that you are looking at, this suggests that conduction from several bands could give effects not simply describable by a surface reflection coefficient. R. ROSENBERG: I think that Frank Mayadas would like to answer that. He is sitting on the edge of his chair. A. F. MAYADAS (IBM Watson Research Center, Yorktown Heights, New York): I think I know the work to which you are referring and I just want to make two comments. I talked with Ehrlich at the Physical Society Meeting in Dallas last year and it turns out that the effects he has been calculating are in the phonon resistivity, and not in the defect region. Secondly, the effect we have observed, namely that a Fuchs theory fit to data is impossible if a single mean free path and a single value of the surface scattering coefficient are used, is too large to be explained in terms of these multi-band processes. This is especially true in aluminum for which the free electron theory with isotropic scattering is a good approximation, and for which previous measurements in thin rolled foils have previously shown excellent agreement with the Fuchs therory. H. B. HUNTINGTON: (Rensselaer Polytechnical Institute, Troy, New York): What is your picture as to the distribution of copper atoms in the aluminum grain boundary? Suppose you are looking down a short circuit channel, how many copper atoms would you see? One every five planes? ROSENBERG: Well, I think that is a little difficult to calculate. I think the best you can do is to consider that you have a certain number of solute atoms in the boundary and predict the percentage that are in the defect sites. Since one does not know the exact density of defect sites or number of solute atoms in a boundary one can only make an approximation as to the solute distri-
584
R. ROSENBERG,
A. F. MAYADAS
AND D. GUPTA
bution. The calculation presented was done strictly on the assumption that you have a boundary defect containing a solute atom, whose effectiveness lies in its interaction with matrix atoms diffusing within the defect. As the diffusing species contacts the solute atom it can only break away after overcoming an additional binding energy. All I am saying is that if you change the activation energy for migration by an amount proportional to the binding energy then you get a change in the flux. What you are suggesting in terms of the number of such interactions may be a possible pre-exponential effect. HUN~~NCTON: I see, one impurity is sufficient to block any channel and the energy for the vacancy to pass it determines the transport rate. ROSENBERG: Yes, any di~using boundary atom will eventualiy see the solute. D. KUHLMANN-WILSDORF (University of Virginia, Charlottesville, Virginia): The assumption that there is no dependence of defect density on film thickness may need some checking. Dr. Raghavan [K. S. Raghavan, Ph. D. thesis, Univ. of Pennsylvania, 1963; K. S. Raghavan and D. KuhlmannWilsdorf, Mater. Sci. Eng. 1 (1966) 1951 made some investigations in this direction several years ago on electrolytically deposited gold films, finding a very strong decrease in defect density as film thickness increased. You can use two criteria in order to check this up. One is the curling of films once they have been taken off the substrate. The amount of strain could be deduced from the curling indicated that the defect concentration and the strain in the films diminished as the films got thicker, at quite a rapid rate. Secondly, the tensile strengths of the films depended very much on thickness, and decreased strongly with film thickness. So both of these observations suggested that there was a strong dependence of defect density on film thickness. ROSENBERG: Yes, the question is what the defects are. In some cases I agree with you that stress changes with thickness, but generally I am not sure I do because we have done a great deal of stress measurements and we find that the stress is not changing with film thickness. The force is increasing but the stress - the built-in residual stress - seems to be constant in the film. I agree that if we had a large negative change in dislocation density with thickness, for example, then we would see precisely what we have seen, namely, that the mean free path will go up as you increase the film thickness. We have transmission micrographs of the aluminum films used in our resistivity studies and do not see a very high density of dislocations. We are in the range of lo6 or 10’ (per cm’), and this is not high enough to greatly effect the resistivity in the aluminum samples. The silver work represented a different situation. We had about 10” dislocations per cm’, and in this case the resistivity provided by the dislocations is comparable to the resistivity of the grain boundaries. Now we are in a lot of trouble. We cannot differentiate
GRAIN
BOUNDARY
CONT’RIBUTlONS
TO TRANSPORT
585
boundary scattering from dislocation scattering. More than that I really cannot say because we have not done that much work on the dislocation density. KUHLMANN-WILSDORF: I probably phrased my comments a bit loosely. I just wanted to suggest that in certain cases there is such a strong thickness dependence and that this needs checking. ROSENBERG: Yes. We are checking that on single crystals. We have been running single crystals of different thickness, trying to determine whether or not the Fuchs-Sondheimer relationship for a single mean free path holds in single crystals. Based on only a few data, it seems that in single crystal silver films, the change in resistivity with thickness can be explained by only the Fuchs effect with partially specular scattering. Here, the dislocation density does not seem to be a factor. M. E. GLICKSMAN (Naval Research Laboratory, Washington, D.C.): With regard to the solute-vacancy binding model that you see, Burke has put some upper bounds on solute-vacancy binding energies, ROSENBERG: In a lattice? GLICKSMAN: Well, yes. ROSENBERG: Lattice results are no good. GLICKSMAN: Why no good? ROSENBERG: I do not know what goes on in a grain boundary. There is much data on lattice diffusion, but there is no apparent correlation at all with results we get. For example, Tom Anthony, [T. R. Anthony, Phys. Rev. B 2 (1970) 2641 (G.E.), did a lot of work on etch pitting by vacancy condensation in Al with Cu additions. He found that copper had zero effect on the selfdiffusion of aluminum, and yet we find copper to be very effective for inhibiting electromigration. GIJCKSMAN: Burke’s results, incidentally, bracket binding energy between zero and something like l/l0 eV so that, since those two results tend to agree, it would be interesting to see whether you can get the right effect within those limits of (say) zero and l/lOth eV. ROSENBERG: You are discussing the problem we have. We do not know how to measure these energy parameters in grain boundaries directly, so we have to learn how to obtain this type of data. That is why we entered into the radio tracer work.