ELECTROMIGRATION PROPERTIES OF MULTIGRAIN ALUMINUM THIN FILM CONDUCTORS AS INFLUENCED BY GRAIN BOUNDARY STRUCTURE.

 

O.V. Kononenko, V.N. Matveev,

Institute of Microelectronics technology and High Purity Materials, Russian Academy of Science, Chernogolovka, Moscow District, Russia.

 

D.P. Field

TexSEM Laboratories, Draper, UT, 84020 USA.

 

ABSTRACT

          Electromigration rates in polycrystalline interconnect lines is controlled by grain boundary diffusion.  As such, reliability of such interconnects is a direct function of the grain boundary character distribution in the lines.  In the present work, drift velocity experiments were performed on multi-crystalline lines of pure Al to determine the electromigration activation energy of the lines.  Lines cut from films processed by partially ionized beam deposition techniques were analyzed.  One set of lines was analyzed in the as-deposited condition, while the other film was annealed before etching.  The measured drift velocities varied dramatically between these two types of films, as did the grain boundary character distributions measured by orientation imaging.  The data were analyzed based on Borisov’s equation to obtain mean grain boundary energies.  Grain boundary energy of the film with poor electromigration performance was calculated to be that reported for random boundaries, while that for the more reliable film was calculated to be that reported for twin boundaries in Al.  Percolation theory is used to aid in explaining the results based upon the fraction and connectedness of “special” boundaries in the films. 

 

 

ELECTROMIGRATION PROPERTIES OF MULTIGRAIN ALUMINUM THIN FILM CONDUCTORS AS INFLUENCED BY GRAIN BOUNDARY STRUCTURE.

 

O.V. Kononenko, V.N. Matveev,

Institute of Microelectronics technology and High Purity Materials, Russian Academy of Science, Chernogolovka, Moscow District, Russia.

 

D.P. Field

TexSEM Laboratories, Draper, UT, 84020 USA.

 

I.  INTRODUCTION

 

It is well known that grain boundary self-diffusion controls electromigration behavior in multigrain aluminum thin film conductors [1-6]. Therefore grain boundary structure must influence the measurable electromigration parameters such as electromigration lifetimes, activation energy, drift velocity of ions and so on. The method of film deposition, purity, doping and subsequent treatment influence the grain boundary structure and hence their energy and diffusion characteristics. It is a small wonder then, that current literature on the subject quotes widely varying values of electromigration activation energy for a given alloy [7].

          Recently we have shown that electromigration activation energy can be significantly changed even in the frame of a single deposition technique [8,9]. Using self-ion assisted deposition we have shown that electromigration activation energy in Al lines can be increased by almost a factor of two simply by increasing the bias applied to the substrate holder. In our opinion an increase in the fraction of low energy grain boundaries, such as low angle and low Sigma coincident site lattice (CSL) boundaries, which possess lower diffusivity in comparison with random grain boundaries, is the underlying mechanism for this effect.

          It is unclear what fraction of low energy grain boundaries is required to increase the electromigration resistance. In this paper we attempt to answer this question on the basis of percolation theory and empirical data. Also we make an estimation of the grain boundary energy of those boundaries responsible for electromigration in the structures investigated.  We employ the equation of Borisov et al. [10] and the electromigration activation energy values obtained experimentally to calculate this value.

 

 

II.  THEORY

 

          The assertion that a link exists between diffusivity in polycrystals and grain boundary energy arises from the dependence of both grain boundary energy and the ratio Dgb/Dl on the misorientation angle between neighboring grains. Borisov and co-authors [10] obtained the following expression for grain boundary energy:

 

 

,                                                                       (1)

 

where a= 1 for the interstitial mechanism, and a= 2 for the vacancy mechanism.  a0 is an average interatomic distance, d is the grain boundary width (d=maa0), ma is the number of atomic layers forming the grain boundary, and Dў=Dgb/Dl.  The derivation of this equation relies upon their theoretical expression for Dgb/Dl obtained from studies of the diffusion balance between grain boundaries and the bulk lattice [11].  It also incorporates an expression for the probability that an atom migrates from an equilibrium position to a previously vacant position in a time Dt [12].  The estimations made in work [10] allow one to accept that l»1.

          The further analysis of equation (1) was carried out in reference [13], where the following equation for ggb was obtained:

 

,                               (2)

 

where NA = R/k is Avogadro’s number, DHl is the activation energy for lattice diffusion, and DHgb is that for grain boundary diffusion.

          Considering that grain boundary diffusion occurs by a vacancy mechanism (a=2), and believing that the boundary width is equal to one atomic layer (ma = 1), equation (2) takes the form

 

.                                           (3)

 

          Substituting into this equation the values for electromigration activation energy in a lattice and in grain boundaries, we can estimate the grain boundary energy responsible for electromigration.

 

 

III.  EXPERIMENTAL DETAILS

 

          Titanium nitride films of 250 nm thickness were sputtered onto oxidized (100) silicon wafers. Resistivity of the films was about 60-80 mWmЧcm. Pure aluminum A999 was deposited by the self-ion deposition technique [14]. The fraction of ions in the beam was about 6-10%. Six kV bias was applied to the substrate holder, which accelerated self-ions to the substrate. Irradiation density was about 1015 cm-2. The vacuum pressure during deposition was no worse then 3Ч10-4 Pa. The substrate temperature was not higher than 40°C.

The electromigration test structures [15] were fabricated using a two mask standard photolithographic process. In the first step Al was etched with a mixture of H3PO4; HNO3; CH3COOH; H2O and TiN with a mixture of EDTA and H2O2 to form sandwich stripes 1mm long and 8 mm wide. The Al was then etched to form aluminum free TiN windows in order to split the Al strip from the bonding pads. The length of the strips was 670 mm. Following preparation of the lines, a portion of the structures were annealed in a vacuum of 10-4 Pa for one hour at a temperature of 480°C, while the remaining specimens were maintained in the as-deposited condition.

Electromigration tests were carried out in air at temperatures ranging from 260°C to 370°C. The structures were stressed by a constant current density of 6Ч105 A/cm2. After finishing the tests the films were investigated by optical, scanning and transmission electron microscopy.

The crystallographic texture and grain boundary character distributions of the films were measured by orientation imaging in the SEM [16].  A tungsten filament SEM was used for the measurements that yielded a limiting resolution of about 250 nm so any grains smaller than this could not be resolved with high confidence.  Individual orientation measurements were obtained over a regular hexagonal array covering approximately 50 µm on a side with a grid spacing of 100 nm.  The imaging procedure resulted in reliable measurements of the structure over about 80 percent of the region investigated.  The relatively small region analyzed yielded only a few hundred grain boundary segments.  This sampling size is not statistically significant when compared with the massive space in which grain boundary geometry is defined.  We justify discussion of such data based on the fact that the distribution of misorientation angles approaches that for a spatially random distribution of crystallites (with the exception that a large number of low angle grain boundaries appears in both the annealed and as-deposited films).  In addition, the data herein presented constitute one of the largest sets of such information obtained to date for the investigation of electromigration as a function of grain boundary geometry.

 

 

IV.  RESULTS

 

          Electromigration tests have shown that the drift velocity in annealed films is almost an order of magnitude less than that in as-deposited films at a test temperature of 280°C (0.6 and 4.5 mm/h respectively). The average grain diameters in the films, as determined by both OIM and conventional methods, are each on the order of 0.6 mm.

          In Fig.1 the fits in the Arrhenius plot are represented. The straight lines were obtained by least squares fitting of the experimental data. Electromigration activation energies are indicated on the graph by the slope of these lines.  The axes on the graph are derived from the expression for drift velocity:

 

                  .                                                                         (4),

 

In Eq. 4, V is the average drift velocity of the cathode edge of the line, Dgb is the diffusion constant (Dgb = D0exp (Hgb/kT), k is Boltzmann’s constant, and T is the absolute temperature.  d represents the grain boundary width, d is the average grain size, j is current density, p is the metal resistivity, and z is the effective charge.  It can be seen from the plot, that the electromigration activation energy in annealed films is almost two times higher than that in as-deposited films.

           Assuming that DHl = 1.3 eV as reported in the literature [17], and referring to Eq. 3, we can estimate the grain boundary energy responsible for electromigration in annealed and as-deposited films. In our case we have obtained values of 125 erg/cm2 and 314 erg/cm2 for the annealed and as-deposited films respectively. This difference is substantial considering that there are no differences in alloy or processing other than annealing of the patterned lines. The value for the annealed lines is close to that of twin grain boundaries in pure aluminum [18,19], and that for the as-deposited lines is near the value cited for the energy of a random grain boundary [20].

           The misorientation angle histogram of grain boundaries in annealed and as-deposited films are shown in Fig. 2. Both of these structures contain a much larger fraction of low angle grain boundaries than would be estimated from bulk texture measurements.  This is consistent with other results from Al thin film structures.  Fig.3 contains the relative proportions of CSL boundaries up to S29 for each specimen. The annealed film contains approximately 64 % of low angle boundaries (up to 15°) and about 4% of S3 boundaries. The as-deposited film contains about 37% of low angle boundaries and about 1% of S3 boundaries.

 

 

V.  DISCUSSION

 

           The results suggest that in annealed Al films the process of electromigration is controlled by low energy grain boundaries. It is consistent with current research in the field to assume that the low angle and low S CSL-type boundaries control electromigration behavior in multi-crystalline Al lines. The fraction of such boundaries in our annealed films was about 68%. In as-deposited films the microstructure is dominated by high energy boundaries. The percentage of such boundaries in our films was about 62%. It appears that a structure with 38% of the boundaries classified as low energy boundaries exhibits a relatively low electromigration activation energy, while a similar structure with 68% low energy boundaries possesses a remarkably high activation energy.  In our view, an explanation of such behavior can be made on the basis of percolation theory.

          It is known that the percolation threshold for bond percolation in a honeycomb lattice is equal to 0.65 [21].  In our opinion, the honeycomb lattice best approximates the structure applicable to grain boundary diffusion controlled electromigration in multi-crystalline lines.  For directed percolation, the threshold should not be less than 0.65. Thus in the annealed films, where the fraction of low energy boundaries is more than the percolation threshold, the so-called "infinite cluster" from such boundaries exists. In other words there is a continuous network of low energy boundaries in the film.  These control the electromigration behavior. The high-energy boundaries are in the film as separate boundaries or small clusters that practically do not significantly influence electromigration performance. In our case the percolation threshold for the infinite cluster is much less than 0.65 due to geometric restrictions imposed by the sides of the lines. 

A simple numerical approach to determining the percolation threshold for our specific geometry was taken by creating an idealized honeycomb lattice over a rectangular region having 13 grains across the width and 1600 along the length.  Boundary segments were pseudo-randomly assigned a special or non-special character, and a simulation was performed to determine whether or not a contiguous path of non-special boundaries existed.  This calculation was repeated for approximately 20,000 iterations with the fraction of special boundaries varying between 30 and 55 percent.  The maximum value of special boundaries for which a contiguous path of non-special segments existed was 0.425.  When 35 percent of the boundaries were special, a contiguous path was achieved on approximately 60 percent of the trials.  This simulation does not necessarily represent the actual structures tested because there was significant clustering of the low angle boundaries that was not enforced in the simulation.  In addition, because of the numerical approach to a statistical problem, the actual percolation threshold is somewhat higher than the value obtained in the simulation, but likely less than 0.45.

For the as-deposited films, there was apparently a percolative path of grain boundaries susceptible to electromigration processes in the test structures. We suspect that high-energy boundaries (random, high angle boundaries) play the key role, and that low energy boundaries are slow diffusion paths that retard electromigration processes.

          Thus, the increase in the fraction of low energy boundaries in multigrain conductors, up to values exceeding the percolation threshold, results in an essential increase in the electromigration resistance of conductors. It is interesting to note, that the doping of aluminum by Mg, which increases electromigration resistance even more than doping by Cu [22-24], reduces the grain boundary energy in aluminum down to values near 127 erg/cm2 (234 erg/cm2 for Cu) [20]. But the resistivity of the films is strongly increased by doping. In our case, when the fraction of low energy grain boundaries exceeds a percolation threshold, we achieve the same effect of electromigration resistance increase. The film resistivity remains virtually equivalent to that of the bulk material.

 

 

VI.  CONCLUSIONS

 

          A strong correlation between electromigration activation energy and grain boundary structure was demonstrated for multi-crystalline Al conductor lines. Using Borisov’s equation and the results of drift velocity experiments, grain boundary energies approaching those reported for twin boundaries in Al were calculated for the material containing a high fraction of low angle and low Sigma boundaries.  The value of grain boundary energy obtained from a film containing less than 40 percent low angle and low Sigma boundaries approached that of a random boundary in Al.  This suggests that for optimum reliability of a multi-crystalline Al interconnect line, the processing should proceed such that there exists a high fraction of low angle and low Sigma boundaries in the final structure. Because pure metals have generally lower diffusivities than alloyed materials it is intuitively apparent that pure structures could feasibly perform on par or better than the alloyed metals currently in use.  The reliability of multi-crystalline IC interconnect lines fabricated from pure metals will be directly dependent upon the grain boundary character distribution in the films. 

 

 

ACKNOWLEDGMENT

 

The work is supported in part by the government of the Russian Federation and the Russian Foundation of Basic Research, grant No. 97-02-16753.

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Figure 1 – Results of drift velocity experiments in determining the electromigration activation energies (E) for the as-deposited and annealed lines. 

 

 

 

 

 

 

Figure 2 – Misorientation angle histogram for the as-deposited and annealed films.

 

 

 

 

 

 

Figure 3 – Coincident site lattice boundary histogram for the as-deposited and annealed films. 

 

 

List of Figures

 

Figure 1 – Results of drift velocity experiments in determining the electromigration activation energies (E) for the as-deposited and annealed lines. 

 

Figure 2 – Misorientation angle histogram for the as-deposited and annealed films.

 

Figure 3 – Coincident site lattice boundary histogram for the as-deposited and annealed films.