Diffusion processes in thin films

Diffusion processes in thin films

Thin Solid Films, 72 (1980) 399-418 © Elsevier Sequoia S.A., Lausanne--Printed in the Netherlands 399 S DIFFUSION PROCESSES IN THIN FILMS * D. GUPT...

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Thin Solid Films, 72 (1980) 399-418 © Elsevier Sequoia S.A., Lausanne--Printed in the Netherlands

399

S

DIFFUSION PROCESSES IN THIN FILMS * D. GUPTA AND P. S. HO I B M Thomas J. Watson Research Center, Yorktown Heights, N. Y. 10598 (U.S.A.)

(Received April 21, 1980; accepted May 20, 1980)

A knowledge of the diffusion processes operating in thin films for applications such as microelectronic devices is important for the design, fabrication and reliability of the thin film package. The integrity of the package is determined by the kinetics of the mass transport between the various levels of metallurgy at the temperatures of fabrication and of use. The mass transport may manifest itself in the development of undesirable characteristics, such as a decrease in electrical conductivity, shorting of devices, precipitation of phases in layers, generation of stresses etc., and in the eventual disintegration of the device. To prevent intermixing, diffusion barriers are sometimes used; their efficiencyis also determined by material transport through the diffusion paths present. In the packaging as well, which utilizes such technologies as flip-chip-solder interconnection and alternate wire bonding, an understanding of diffusion is important since oxide-forming metals may be transported to the surface, making the interconnection difficult. Diffusion is not, however, always detrimental and is commonly used for making homogeneous alloy films from successive evaporations. The reliability problems in thin film stripes also involve diffusion driven by electron or phonon currents rather than by chemical gradients. Thin films contain a high density of defects, namely grain boundaries and dislocations in addition to vacancies present within the grains. Reliable data on the diffusion paths in thin films have become available over the last decade or so, largely through the use of in-depth profiling of the diffusant using ion backsputtering and radiotracers and of surface analytical techniques, notably Auger electron spectroscopy. Some illustrative data on thin films and foils will be discussed to show that a hierarchy of the diffusion rates along grain boundaries, dislocations and vacancies exists. By incorporating the actual grain size and dislocation densities present in thin films, it is possible to delineate temperature regimes where any particular process or a combination of processes may be expected to be dominant. Finally, the role of solutes added to the films in altering the diffusion kinetics of the solvent species along the respective paths will be discussed and illustrated by some beneficial observations in applications, notably the electromigration lifetimes.

* Paper presented at the International Conference on Metallurgical Coatings, San Diego, California, U.S.A., April 21-25, 1980.

400

D. GUPTA, P. S. HO

| . INTRODUCTION

Thin film packages used in integrated circuits, solar energy conversion devices and metallurgical coatings may have poor thermal stability owing to the discrete layers of metals used which have a natural tendency to diffuse and to react chemically. This tendency is enhanced by the presence of a high density of defects in thin films such as grain boundaries and dislocations which provide fast and efficient paths for mass transport 1. In thin films these defects are in close proximity or directly connected to surfaces and interfaces, so the interactions between them need to be considered. In addition, thin film devices also experience strong electrical and temperature gradients which promote directed mass transport known as electromigration and thermomigration. Any divergence of flux at the thin film defects, notably the grain boundaries, may cause sufficiently large mass depletion, leading to open circuits 2' a. The thermal damage to the thin film package caused by various diffusion processes manifests itself in the formation of undesirable layered phases and the generation of porosity and stresses by the Kirkendall effect which is schematically shown in Fig. I and which eventually leads to the disintegration of the structure. The materials reactions are accompanied by the development of undesirable performance characteristics such as a decrease in electrical conductivity, shorting and breaks in the circuits and the loss of ohmic contacts.

~

IRKENOALL VOIDS

SUBSTRATE

Fig. 1. Interdiffusion and reaction processes in a polycrystalline thin film package shown schematically. The film couple A/B diffuses leaving Kirkendall voids in B since JA < ,/~, whereas the couple B/C interacts partially to form the hypothetical compound BxC.

It is appropriate to consider diffusion-related phenomena in thin films by examining the two fundamental parameters describing the mass transport: the diffusivity and the driving force. For thin films these factors not only are instrinsic properties of the material but also depend on the film microstructure. The structural sensitivity of these parameters is an important characteristic of diffusion in thin films. Indeed, it is this characteristic which distinguishes the nature of the kinetic reactions in thin films from that in bulk materials. The driving force arises from the gradient of the total free energy which can originate from thermal, chemical, electrical, mechanical and other potentials. The main structural defects are dislocations, grain boundaries, surfaces and interfaces. The various combinations of potential gradients and structural defects are numerous. This leads to the complex nature of diffusion-related problems in thin films. In general, it is best to consider each problem individually. Thus it is not our intention to discuss fully in this paper the combined effects of diffusion and driving forces. We shall limit the discussion to the structural aspects of diffusion with particular emphasis on grain boundaries. For some specific applications the reader can refer to other references ~-7.

DIFFUSION PROCESSES IN THIN FILMS

401

The rapid nature of mass transport along grain boundaries and dislocations in bulk polycrystalline materials has been recognized and reviewed in the literature 4-6. However, owing to the complexity discussed above, available data are not readily applicable to thin films. The special aspects of thin film diffusion have recently been reviewed by us comprehensively with respect to experimental techniques, the mathematical analysis needed for interpretation of the results and the influence of chemical and physical variables. As the scope of this paper is limited, it is intended to provide guidelines to workers in thin film technology so that the integrity and characteristics of a given thin package may be assessed during its design, fabrication and actual service. Our discussions center around the diffusion kinetics along the individual defects in thin films and a framework is presented for assessing their collective contributions in thin films of known structure and dimensions. Chemical effects, such as the effect of added solutes on diffusion kinetics and complications caused by the formation of layered compounds, are discussed. Finally, these concepts are used to explain some thin film reliability problems such as electromigration and thermomigration effects. 2.

SPECIAL ASPECTS OF DIFFUSION IN THIN FILMS

Solid state diffusion in single-crystal metals and alloys has been widely discussed in the literature. In this paper we discuss only the important features of diffusion processes which are likely to occur in polycrystalline solids. The temperature dependence of the diffusion coefficient D is described by the Arrhenius equation

o O°exp( ) where D ° is the temperature-independent "frequency factor", Q is the activation energy, R is the gas constant and T is the temperature in kelvins. In real materials surfaces, grain boundaries and dislocations are present and these are known as short-circuit paths for diffusion, because diffusion along them is orders of magnitude faster than in the lattice. We distinguish between the various diffusion processes by using the following subscripts in eqn. (1): 1 for lattice diffusion, s for surface diffusion, b for grain boundary diffusion and d for dislocation pipe diffusion. Diffusion kinetics along these individual paths have been reviewed by many authors 1-7. The activation energies for diffusion along the individual paths are found to correlate well with the absolute melting temperature. Consequently, the homologous temperature T / T m is a convenient measure for discussion of the diffusion parameters along the various paths in the polycrystalline metal and alloy thin films. There is a hierarchy of diffusion rates along these paths, the fastest being along the surfaces and the slowest being within the lattice. The activation energies for surface, grain boundary, dissociated dislocations and lattice are described respectively by 13Tm, 17Tn~, 25Tm and 34Tm and the corresponding values 4 for the pre-exponential terms are 0.014, 0.3, 2.1 and 0.5 cm 2 s -1. These parameters in practice lead to measurable contributions from structural defects such as grain boundaries and dislocations at temperatures less than 0.5Tm. Dislocations, in fact, become the dominant diffusion processes in thin films and metallurgical coatings. In

402

D. GUPTA, P. S. HO

addition, two or more processes may be active simultaneously which may not be in general additive but in effect interactive. The extent to which the lattice diffusion influences the material transport along grain boundaries or dislocations is best described by the three kinetic re~mes A, B and C of Harrison a which are shown in Fig. 2. Figure 2(a) demonstrates A-type kinetics which involves extensive lattice diffusion, together with grain boundary diffusion and mixing across the grains. In B-type kinetics, however, each boundary is assumed to be isolated and diffusion along the grain boundaries results in leakage into the grains because lattice diffusion in the x direction (Fig. 2(b)) approaches zero. In the C-type kinetics shown in Fig. 2(c) the lattice diffusion distance is considered to be negligible in relation to 6, the grain boundary width, so that atomic transport occurs only within the boundaries by the grain boundary diffusion process alone. Diffusion measurements in bulk polycrystalline materials invariably involve B-type kinetics because they cannot sustain fine enough grains. In this respect, thin films are both unique and challenging for diffusion studies because the inherent high density of structural defects makes them suitable for observation of the three diffusion regimes. For example, self-diffusion along dislocations could be studied very conveniently in epitaxial gold films 9 rather than in the bulk material.

(a)

T

y~.,/~

l

/a

tc) Fig. 2. Schematic representation of (a) A-type, (b) B-type and (c) C-type kinetics in polycrystalline thin films. The vertical lines indicate the grain boundaries; the curves are the isoconccntration contours. The diffusion source coincides with the top horizontal lines.

The three diffusion regimes possible in thin fills are shown in Fig. 3 with respect to the grain size L (gin), the time (s), the diffusion coefficients (cm 2 s- 1) in the lattice and grain boundaries and the homologous temperatures. The values for lattice diffusivities were computed from the expression D! ~ 0.5 exp(-- 34Tm/RT) cra2,S-1 which is valid for most metals andalloys as discussed before and the grain boundary diffusivities from D b ,~ 0.3exp(-17Tm/RT). The temperature dependence of the two diffusion processes together is shown by the line on the far left

DIFFUSION PROCESSES IN THIN FILMS

403

computed for an annealing time of 1 s. The region left of this line does not have any physical significance. The progress of diffusion with time is shown by the three parallel lines on the left for periods of 1 h, 1 d and 1 month. The dimensionless parameter fl = 6Db/2D~(D~t)1/2 is a convenient measure of the grain boundary diffusion and B-type kinetics are characterized by a fl value greater than unity for semi-infinite specimens. On the right-hand side of Fig. 3, parallel lines are drawn to indicate fl values of 1, 10 and 100 and higher values can be obtained by drawing more lines in the same manner. In thin films and foils, however, their finite thickness and grain size must also be considered, together with the total diffusion lengths in the lattice and the grain boundaries. In thin films held on substrates the thickness and grain size are generally of the same dimension as the quantity denoted by L in Fig. 3. The films and foils with 0.01 ttm ~< L ~< 100 Ixm shown in the shaded region diffuse in the B regime at temperatures below 0.5 Tn,even with long annealing times. At higher temperatures they are likely to diffuse in the A regime if sufficient time is allowed and would in fact homogenize. The C regime is shown to the left of the broken line, indicating 6 = 5 A, and can be realized only at temperatures below approximately 0.35Tmor at very short times below 0.5Tm. Since 2(Dlt) < 6 = 5 A, the thickness and grain size of the specimens are of little consequence at temperatures below 0.35 Tm. LOG Db/DI

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Fig. 3. Master curve for diffusion processes for metallic polycrystaUine thinfilms showingthe role of the temperature, the grain size L and # (# = 6D/2DI(Dlt) 1/2) in determining the various kinetic regimes.

3. EXPERIMENTAL TECHNIQUES There are three basic types of diffusion measurements in thin films: in the first type, lateral spreading of the diffusant is observed on the film plane using either the microprobe or the tracer scanning technique; in the second type, the in-depth concentration of the diffusant is profiled directly by the tracer technique or by employing surface analytical techniques, notably Auger electron spectroscopy (AES); in the third type of study the diffusion flux through the film is determined by measuring the material accumulation on the exit surface. Owing to the limited length of this paper, it is not possible to discuss these techniques individually in any detail. The interested reader is referred to our recent review paper 7 for detailed

404

D. GUPTA, P.S. HO

discussions. Here we discuss the implications of the grain size, the grain structure, the finite film thickness and the annealing conditions which dictate the choice of experimental techniques and the subsequent analytical procedures. 3.1. A-type kinetics in the film plane When the lattice diffusion distance 2(Dlt) 1/2 is comparable with or larger than L, the half-intergranular-spacing, the diffusing atoms sample the lattice and the grain boundary sites alike and the diffusion front becomes planar, as shown in Fig. 2(a). In this situation, diffusant profiling in the film plane employing either a microprobe or a tracer scanning technique is very useful. The non-destructive nature of these techniques is a very attractive feature, particularly when fast diffusion rates are involved. A microprobe technique was used in the cross- stripe configuration for electromigration studies in aluminum films using copper as the diffusant 1°. Tracer scanning was also used by Tai et al. ~t and by Sun and Ohring 12 for electromigration studies in gold films using ~95Au and ~19Sn isotopes. However, the lateral diffusion geometry causes considerable complications to the analysis of the data because of the contributions from the film surface and the film-substrate interface. In the absence of any analysis which takes into account fully the coupling between surface, interface, grain boundary and lattice mechanisms, these experiments are not widely used. Analytically the development of A-type kinetics in the above experiments results when the normalized grain size A is not more than 0.1 (A = L/(D1t)I/2). As A continues to decrease below 0.1, lateral spreading away from grain boundaries is so extensive that the lattice diffusion no longer poses any limitation in penetration to further depths. In this situation the concentration profile is simple gaussian of the form M [ x2 / C = (rcDbt--~exp[--4--~bt} (2)

where C is the concentration of the diffusant at distance x in the film plane, t is the time, M is the amount of diffusant at the source at x = 0, t = 0, and Db is the grain boundary diffusivity. These techniques therefore measure directly the grain boundary diffusivity instead of the usual product of the diffusivity and the width of the grain boundary which will be seen later. 3.2. B-type kinetics normal to film plane Since most thin film structures are planar, mass transport into the adjoining materials normal to the film plane is the usual problem when considering the thermal stability of the structure. In this situation there are two regions to be considered: (1) the lattice exterior to the grain boundaries where the diffusivity D~ prevails; (2) the region within the grain boundaries themselves of width ~ and diffusivity Db. In general, neither of these two diffusivities is negligible and consequently B-type diffusion kinetics (Fig. 2(b)) are a good description of the situation. Diffusion experiments employing serial sectioning of the specimen parallel to the diffusion plane in this kinetic regime have been found to be the most relevant and illustrative for mass transport problems in thin film packages 7. Serial sectioning for diffusant profiling in thin films, typically a few microns thick, requires

DIFFUSION PROCESSES IN THIN FILMS

405

the capability of removing thin layers of materials down to a few tens of fingstr6ms. To achieve this, ion sputtering has emerged as the principal method. It has two variations. In one it is coupled with the use of radioactive tracers and standard counting techniques la and is generally used for self-diffusion measurements. In the other, various surface analytical techniques such as AES, X-ray photoemission spectroscopy, secondary ion mass spectrometry etc. are used for material analysis14. ~5. Significant progress has also been made on the mathematical analysis of the diffusion profiles obtained in these experiments. For mathematical analysis the film thickness I in relation to the diffusion length in the grain boundaries is an important consideration so that when l >>2(Dbt)1/2 it may be considered semi-infinite or alternatively finite. The analytical solutions for the semi-infinite case are simple and have been worked out by Whipple 16 and Suzuoka 17 and discussed by LeClaire 1a. According to their treatment, the product of the grain boundary width and its diffusivity in a serial sectioning technique can be evaluated from the expression [81n~21-s/a[nD, i1/2F ~ln~, 2 q5/3 where K is the diffusant segregation factor (equal to unity in the case of selfdiffusion), C2 is the concentration of the diffusant out of the grain boundary to the adjoining lattice, ~l = Y(Dlt)-1/2 The third term in eqn. (3) is quite insensitive to ~l(Kfl)-1/2 variations. Furthermore, for Kfl > 10, it reduces to 0.78 for an infinite source and to {0.72(Kfl)°'°°a} for the instantaneous source condition. Consequently, eqn. (3) can be simplified as /~ In C2 ~- Slal4DlV/2

KDb~O.66118-ff~3-- ]

t-~l

(4)

for Kfl >>.10. Equation (4) has been widely used in sectioning experiments utilizing tracer profiling and also in AES. For diffusion in thin films with a finite thickness, the analytical solutions become complex and have been discussed by CampbelP 9 and by Gilmer and Farrel 2°. It is no longer possible to use a single expression since numerical integration is involved in obtaining a solution.

3.3. C-type kinetics: permeation techniques As discussed in Section 2, the atomic transport in the C-type kinetic regime is confined to the grain boundaries which limits the quantity of the diffusant available for analysis in the sectioning techniques. Consequently the sputter-sectioning techniques employing radiotracers, AES or similar methods lose their sensitivity. In this situation, techniques based on the permeation of the diffusant through the film thickness with surface accumulation on the exit surface would be more expedient. The material accumulation can be observed by one of several surface spectroscopy techniques; AES is most commonly used z 1.22. The strength of these techniques is in the small sampling depth and the capability of detecting small fractions of a monolayer of the element on the top of another and makes them attractive for diffusion studies based on surface accumulation. Even though the grain boundaries have small widths of the order of 5 A, they can transport sufficient material to cover, at least partially, the exit surface despite the fact that lattice diffusion is frozen out.

406

D. GUPTA, P. S. HO

In these measurements the surface condition of the entrance and exit planes is an important factor to consider. As the grain boundary medium can be visualized as connected in series with the entrance and the exit surface, the amount of material transport through the boundaries not only is defined by its diffusion kinetics but also depends on the efficiency of material supply to the entrance plane and of material uptake on the exit surface. In most experiments, the exit surface is particularly susceptible to various contaminations and environmental effects23. Data obtained by surface accumulation techniques show considerable scatter because of these factors. In a few instances it is also possible to use radiotracers for grain boundary permeation studies utilizing high nuclear absorption in the host sample. For the success of the experiment, it is necessary for the radiotracer emission to be absorbed completely in the thickness of the specimen which is usually a foil approximately 50 Ixm thick. Consequently, only the radiotracers with emissions of the order of 20 keV X-rays or 13 emitters with absorption coefficients/1 not less than 500 cm-1 are considered. Wuttig and Birnbaum 24 and Baker et al. 2 s have used 6aNi in nickel and Ni-Co foils for diffusion studies along polygonized boundaries. More recently, Gupta and Campbell 26 have used 119Sn in lead foils for studying permeation along grain boundaries. A satisfactory match between the host and the radiotracer with respect to the absorption coefficient is usually possible only in a few systems. In addition, analytical treatment of the data becomes complex since nuclear counts below the specimen surface also need to be accounted for, unlike the situation in the AES surface accumulation technique. 4.

DIFFUSION DATA IN THIN FILMS

In recent years a large amount of diffusion data in thin films has become available from the various techniques discussed in Section 3. These data are invariably on the nature of diffusion along grain boundaries or in some cases along dislocations. They can be put into two categories. The first contains data obtained using serial sectioning techniques and the second consists of data obtained from permeation and surface accumulation techniques. We discuss the two categories separately. In all cases a reduced temperature abscissa T~/T is used. When comparing the diffusivities in various systems obtained by differing techniques, two factors must be considered. (1) All diffusivities measured by radiotracer profiling or surface spreading include a correlation factor which is estimated at about 0.54 for self-diffusion at the grain boundaries 27 but for impurity tracers its value is not known. (2) For impurity diffusion the measured quantity is the product KDbt~ (see eqn. (3)) where the segregation factor K is usually greater than unity. The magnitude of K appears to depend on the temperature, the nature of the solute and the solute-solid solubility limit in the host. The solid solubility limit in the host has been shown to be related to the grain boundary-solute binding energy 2a. The combination of these factors, and particularly the inability to separate K from KDb6 in the absence of independent information on K, may lead to considerable scatter in the diffusion data from various investigations. In addition, the grain boundary data are very sensitive to the grain boundary structure. For example,

DIFFUSION PROCESSES IN THIN FILMS

407

textured films are likely to show much smaller diffusivities. Recent AES surface accumulation diffusion studies of silver into gold films by Hwang et al. 23 have shown the effect of surface conditions on diffusion in thin films at low temperatures. Notably, carbon surface contamination from the ambient was found to suppress the rate of silver out-diffusion through gold films whereas an oxidizing atmosphere produced an enhancement. A similar effect can arise in the profiling experiments although in an opposite sense where an instantaneous source at the free surface may be contaminated.

4.1. Microsectioning diffusion measurements As mentioned earlier, the microsectioning diffusion measurements in thin films are carried out most fruitfully in the B-type kinetic regime where the lattice diffusion distance is small but finite, typically in the range 100-1000 A. In Fig. 4, a typical tracer profile in a polycrystalline gold specimen is shown 29. Since bulk specimens in general contain large-angle grain boundaries and small-angle subgrains in addition to the lattice, the penetration profile is seen to have three distinct segments relating to diffusion along these paths. As the profile is traversed from right to left, the diffusivities along these paths are progressively smaller owing to the larger activation energies involved. In thin films, however, one or more processes may be absent depending on their structure. In Fig. 5, tracer penetration profiles are reproduced from our earlier publications 9' 30 in two different kinds of gold films: curve a is for a polycrystalline film grown on a fused quartz substrate showing high angle grain boundariesa°; curve b is for a film epitaxially grown on (001) MgO, containing dissociated dislocations9. The diffusion kinetics in the polycrystalline film are considerably faster as the tracer penetrates deep into the film in a few minutes at a low temperature of 117 °C. In the epitaxial films, however, diffusion is very sluggish since even at 275 °C it takes 4 d to achieve a measurable tracer penetration. Another important difference between the two films is the lattice diffusion, which is negligible in the polycrystalline thin films. In the epitaxial films, however, a sizable diffusion in the lattice was observed in the well-developed segment of the profile near the film surface under the conditions stated above. The epitaxial films were analyzed for lattice diffusion. In Fig. 6 an AES microsectioning profile exhibits the same general features as above for diffusion of copper into a polycrystalline aluminum films at 175 °C. Whipple's solution (eqns. (3) and (4)) was used in all cases for extraction of the grain boundary diffusivities. In this case, however, the product KDb6 is obtained rather than 6Db as in the self-diffusion measurements. In Table I we give the recent grain boundary diffusion data measured by the microsectioning technique and employing either a radiotracer or a surface-active analytical technique. Some critical grain boundary diffusion data in bulk materials are also included. These data are plotted in Fig. 7 against the reciprocal homologous temperature TJT. The two broken lines refer to the expected diffusion behavior of large-angle and small-angle grain boundaries discussed in Section 2 for which the activation energies differ significantly, w e notice that grain boundary diffusion data in bulk materials and thin films with known large-angle grain boundaries do indeed lie close to the line expressed by 0.3t5 exp( - 17Tm/RT ), when a reasonable value for 6 of 5 A is assumed, indicating that the grain boundary diffusion activation energy

408

D. GUPTA, P. S. HO PENETRATION DISTANCE Y(lO-4cm) 2.0 3.0 4.0 5.0

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Qb ~' ½QI-I n a d d i t i o n the diffusion d a t a in specimens which were deliberately m a d e to h a v e special b o u n d a r i e s , e.g. the nickel b i c r y s t a l (curve h) with a (112> tilt b o u n d a r y , the s u b b o u n d a r y diffusion d a t a for the A u - l . 2 % T a alloy (curve i), the e p i t a x i a l films with (a/6)(112>-type t h r e a d i n g d i s s o c i a t e d dislocations (where a is the lattice p a r a m e t e r ) (curve j) a n d the A E S d a t a o n silver diffusion t h r o u g h (111) A u e p i t a x i a l films o n m i c a (curve m), all s h o w slower diffusion kinetics closer to the line expressed b y 2c5 e x p ( - 25Tm/RT ). W e therefore suspect t h a t the scatter in the thin

409

DIFFUSION PROCESSES IN THIN FILMS

TABLE I GRAIN BOUNDARYDIFFUSIONDATA OBTAINEDBY SECTIONINGTECHNIQUES

Sample

Diffusant; matrix

6D~,(cm3 s-~)

Q (eV)

Remarks

Reference.

a b c d e f g h i

63Ni; Ni 2°3pb; Pb 11°Ag; Ag 19SAu; Au 19SAu; Au-l.2%Ta AI; Cu 195Au; Au 63Ni; Ni ~95Au; Au-l.2%Ta

7 x 10 -1° 6.1 X 10 -9 1.3 x 10 -9 3.1 x 10- lo 5 x 10- 7 5.1 x 10 -7 9.0 x 10- lo 2.2 x 10 - s 1 x 10 .9

1.08 0.46 0.80 0.88 1.26 0.94 1.0 1.77 1.2

31 32 27 29 33 34 30 31 33

j k 1 m n o

195Au; Au Cu; A1 Cu; A1 Ag; Au z95Au; Ni--0.5%Co Co; Au-0.186%Co

1.9 x 10- lO 4.5 x 10-s 1.8 x 10 -1° 9.3 x 10 - s (D~) 1.4 x 10- lO 0.013 (D~,)

1.16 1.0 0.87 1.2 1.6 1.20

45°(100) . Polycrystalline b Polycrystalline ~ Polycrystalline a Polycrystallinea Polycrystalline films ~ Polycrystalline filmsd 10°(112) Low angle grain boundary ~ (100) epitaxial a Polycrystalline films~ Polycrystalline films~ (111) epitaxiaP Polycrystalline filmsd Polycrystalline electro films~

9 35 34, 36 37 38 39

"Autoradiography. b Microtome. Lathe. d Tracer ion sputtering. "AES ion sputtering.

T(K) AS FRACTION OF TIn(K) 0.9 0.8 Q7 0.6 0.5 0.4 0.3 PN~%L [ I I ~ r I --~-(Ni-BULK) Ni (o) ~ (Fb-BULK) Pb*(b) I0-15 X "~~"~(Ag- BULK}Ag*(c)

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sectioning techniques against the reciprocal normalized temperature Tm/T (see Table I for the source of these data).

410

D. GUPTA, P. S. HO

film grain boundary diffusion data is at least partly due to variable film textures which are common in thin films grown on varying substrates. The other sources of scatter are the aforementioned factors, namely the state of purity, the surface condition of the host and the diffusant, the state of stresses in the films, the nature of the ambient etc.

4.2. Permeation and surface accumulation diffusion data Diffusion data in thin films obtained from permeation and surface accumulation techniques are listed in Table II and displayed in Fig. 8 using the normalized temperature scale. These data also include the surface spreading of tin on lead films in the cross-stripe configuration employing the electron microprobe technique4°, permeation of the 119Sn isotope in lead foils observed using its nuclear absorption and diffusion of silver through copper films observed by Rutherford backscattering41. Owing to a wider applicability of the surface techniques, more material combinations are possible here. Most of the surface measurements listed in Table II were made for C-type kinetics and at temperatures below 0.4Tm(see Fig. 3). The scatter in the various data is similar to those found in microsectioning techniques shown in Fig. 7 and is within the limits of the broken lines discussed earlier, but the activation energies in general appear to be somewhat lower. The factors responsible for scatter among the various investigations are the same as discussed previously. In addition, it appears that the permeation and surface accumulation data are more susceptible to the structure of the grain boundary since the transport of the diffusant is mainly through the grain boundary, so it will appear first at the highest angle boundaries on the exit surface. Consequently, lower activation energies for diffusion are likely to occur. TABLE II GRAIN BOUNDARY DIFFUSION DATA OBTAINED BY PERMEATION AND SURFACE ACCUMULATION TECHNIQUES

Sample

Diffusant; matrix

D~,

Q

(cm 2 s - 1)

(eV)

b c d e f g h i

l l g z n ; Pb Sn; Pb Cr; Au Ag; Cu Pt; Cr Cu; Au-0.29/oCo Ag; Au Ag;Au Ag; Au

1.1 x 10 -a 6.9 x 10 - s (fiDe) 10- 3 3.1 x 10 -6 10- 2 2 × 10- 7 (6D~,) 10- s 10 -6 250 °C, 4.07 x 10-17

j

Cu; A1

a

Remarks

Reference

0.46 0.62 1.09 0.75 1.69 0.56 0.63 1.1 __

Foils a Polycrystalline filmsb Textured filmc Polycrystalline filmsa Polycrystalline filmsc Polycrystalline films° Polycrystalline filmsc (100) epitaxial films ¢ Polycrystalline filmsb

26 40 22 41 42 43 21 44 45

__

Polycrystalline filmsb

10

Polycrystalline filmsb

10

(K6Db) 250 °C, 2.7 x 10-14

(K6DO 300 °C, 1.3 x 10-13

(K,SDO a Nuclear absorption and permeation. b Cross-stripe and microprobe. c AES surface accumulation. d Surface accumulation and Rutherford backscattering.

411

DIFFUSION PROCESSES IN THIN FILMS

T(K) AS FRACTION OF Tm (K) 0.90.80.70.6 Q5 Q4 0.3 I\

J

I

I0-14

,

I

r

J

,

n(o)\

Io- o

",

,~"

N~/Sn

-~

Cb)xx x f 0 3 a "\. x

exp

~/Ag

(-17Tm/T)

3

(g)

N...-....

-

\ \ L (Au-O.2CollCu (f) ]

IO-Z4

-

A_u/Ag (h) 10.26

~.o

i

I

~.5

=

I

2.o

=

2.5

3.o

I

I

3.5

0

I

4.o

t

4.5

Tm/T(K) Fig. 8. Plots of the grain boundary diffusion data in thin films obtained by permeationtechniquesagainst the reciprocal normalized temperature Tm/T (see Table II for the source of these data). The activation energies are smaller compared with those in Fig. 7 whereas the scatter remains about the same.

This effect can be seen in the contact autoradiograms of entrance and exit surfaces for 119Sn permeation in lead foils shown for two specimens at 90 and 34 °C in Fig. 9 and compared with the microstructure. It is seen that exit surface tracer accumulation is grain boundary dominated and there is a corresponding tracer depletion on the entrance surface. Furthermore, a comparison between the micrographs and the autoradiograms reveals the absence of certain grain boundaries, notably the twin boundaries, which is obviously due to variable diffusional kinetics in grain boundaries of differing orientations. In addition, variable analytical treatments used in the surface accumulation investigations appear to lead to the large scatter in Fig. 8 since a standard analytical solution similar to the Whipple and Suzuoka solutions for the microsectioning technique has not been available. Indeed, in some cases diffusivities have been estimated simply by equating the film thickness to the diffusion distance (Dbt) 1/2. It is only in the last 2 years or so that a satisfactory solution to the surface accumulation experiments seems to have emerged following the work of Hwang et al. 2 5. DIFFUSION IN ALLOY AND MULTIPHASE THIN FILMS

In Section 4 we considered the idealized situation where the composition of the host film and its phase remained unchanged during diffusion. This is accomplished by making the diffusion source film negligibly thin compared with the host film and also by choosing a solid solubility system. In practice, however, these idealized conditions are seldom met. Consequently in this section we consider such situations in polycrystalline films and divide them into three cases: (a) diffusion of the host (major component) constituent in the already alloyed film; (b) when massive interdiffusion occurs in the thin film couples without any distinction between the

412

D. GUPTA, P. S. HO

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 9. Contact autoradiograms of llgSn radiotracer diffusion of lead foils 50 pm thick: (a) the source surface at 34 °C; (b) the source surface at 90 °C; (c) the exit surface at 34 °C; (d) the exit surface at 90 °C; (e) the microstructure at 34 °C; (f) the microstructure at 90 °C. The field of view is 1.25 cm in all cases. The similarity in the grain structure should be noted, particularly in the 90 °C foil; it should also be noted that some grain boundaries are missing in the autoradiograms.

413

DIFFUSION PROCESSES IN THIN FILMS

host and the solute but the resulting film still consists of a homogeneous single phase; (c) when interdiffusion leads to formation of layered compound structures. (a) The diffusion of the host constituent in an already alloyed thin film has been studied in the context of the electromigration problem where current-dependent mass transport of the solvent is the primary concern and small percentages of solutes are added with the intention of suppressing it. Such beneficial examples are the addition of approximately 4 at.% Cu to aluminum thin film conductors 2' a and approximately 1 at.% Ta to gold films46 where marked improvement of the electromigration lifetimes were noted. Subsequent studies showed that the dominant mechanism of mass transport in thin film electromigration was the grain boundary diffusion process and certain solute additions reduced it at low temperatures 2'a'2s. The effect has been studied in detail in the Au-l.2at.%Ta system2S, 33. In Fig. 10 the grain boundary diffusivities for the 195Au host tracer in the Au-l.2at.%Ta alloy (see Table I, sample e) are compared with those in pure gold (see Table I, samples d and g) using polycrystalline bulk and thin film specimens, which enabled measurements over a wide range of temperature. It is seen that the introduction of approximately 1 at.% Ta increases the activation energy for grain boundary diffusion by approximately 0.3 eV. In fact, the grain boundary diffusivities themselves show a cross-over at approximately -300°C and lower values in the alloy are realized only below the cross-over temperature. This observation satisfactorily explained the improvement in the electromigration lifetimes after tantalum addition to gold films noted by Revitz and Totta 46. The existence of the grain boundary diffusivity cross-over has been explained on the basis of the grain boundary segregation of the solute 28. 10.15

IO-m

I~

400 I

=

TEMPERAT~ °C 300 200 I

~,N~,-llama., li.'X + ~

;

I

I00

I

GB IN Au-l.2 To (5 x 10_Tcm3/sec' 1.26eV)

10-17 \~9xlO

10-18

E

"10 cm31wc,0.95eV)

i0-19

I0-20 Io-tl 10-22 Io-~

1.5

I 1.5

I 1.7

I I 1.9 2.1 1000/T (K)

I 2.3

I 2.5

2.7

Fig. 10. Temperature dependence of~iDb in the gold and Au-l.2at.%Ta polycrystalline specimens. The temperature data for gold were obtained using bulk specimens and the low temperature data using thin films.

414

D. GUPTA, P. S. HO

(b) When massive interditfusion occurs in a thin film couple A/B, the two species move with unequal diffusivities, as shown in Fig. 1. The overall diffusion in this case is described by an interdiffusivity /)b which is related to the individual diffusivities DbA and DbB by the expression /)b = NADbB+ NBDb A where N A and N B are the molar fractions of the species A and B respectively. The mass imbalance due to the unequal flux (JB > JA) generates vacancies in film B and, if the grain boundaries are not able to provide an effective sink for them because of the limited film thickness and the presence of impurities, they may agglomerate to form what are known as Kirkendall voids45, shown schematically in Fig. 1. These voids impair the mechanical stability of the thin film package and also reduce its electrical conductivity. The undesirable intermixing of thin films is generally prevented by providing diffusion barriers between the two films. For example, chromium is used between aluminum and gold thin film packages in some devices. In other situations, advantage is taken of the massive interdiffusion for homogenization of successively evaporated films. The homogenization of Pb-In films used in Josephson superconducting integrated circuits is accomplished in this manner 47. (c) Depending on the nature of the phase diagram, a thin film couple may form a layered intermetallic compound structure as shown in Fig. 1 where the films B and C have reacted to form a hypothetical compound BxC. The problem has been reviewed recently by Baglin and Poate 4s. In this paper we only discuss some salient features of the problem. In the compound-forming situation it is often not possible to associate a distinct activation energy for the process because chemical reaction and diffusion occur simultaneously, thereby complicating the process. The reaction kinetics may consequently be either linear or parabolic depending on which process is rate limiting. In polycrystaUine thin films the compound formation is generally assisted by grain boundary diffusion for transport of matter to the reaction interface. The role of the grain boundary diffusion in Pb2Pd compound formation in Pb/Ag/AgPd thin film packages has been studied by T U '~9 who showed unequivocally that the palladium atoms are transported to the silver grain i~oundaries for the reaction to proceed. Furthermore, a movement of the Ag-AgPd interface was noted because of the migration of palladium atoms from underneath. The undesirable feature of the compound formation is that it introduces mechanical stresses and reduces electrical conductivity, particularly when an envelope is formed around the grains. However, certain intermetallic layered structures are considered more favorably as diffusion barriers in comparison with the elemental structures (such as nickel and chromium) since they are more stable and permit no diffusion. For example, the HfAI 3 layered structure examined by Lever et al. s° is considered to be a more ideal barrier. 6.

ELECTROMIGRATION AND OTHER THIN FILM APPLICATIONS

In the previous sections we emphasized the basic nature of diffusion processes pertinent to thin film structures and the experimental methods for their study. In this section the applied aspect of thin film diffusion is considered. The vast variety of practical problems prevents us from detailed discussions with.in the scope of this paper. Therefore we choose to limit our discussions to two topics; the first is the problem of local divergence of the diffusion flux and the second is a specific example

DIFFUSION PROCESSES IN THIN FILMS

415

of the use of intermetallic layers to improve electromigration resistance in micronsize conductor lines. This example is used to illustrate the solution to a practical problem by changing the film layered structure in order to control the diffusion process. The diffusion flux can be expressed as a product of the density of the mobile defects, the defect diffusivity and the driving force, For most applications the presence of a diffusion flux does not nececessarily cause problems, but the occurrence of local flux divergence which leads to localized depletion or accumulation of mobile defects may cause problems. Flux divergence can arise from a local inhomogeneity in any of the factors contributing to the flux; for thin films the divergence is mainly related to the microstructure. Some common examples are (a) grain boundary junctions or the so-called triple points, (b) a transient region separating two areas of different grain sizes, (c) the interface of two layers with different materials and (d) a surface exposed to a chemical environment which can react preferentially with one of the constituents in the film. There are many other examples which can also be cited. Clearly for most film reactions it is important to correlate the flux divergence to the overall structural inhomogeneity. Problems have frequently been solved by structural modifications, e.g. the use of uniform grain size to reduce local mass depletion and the use of reaction barriers to reduce intermixing between two dissimilar layered materials. Electromigration describes the mass transport in metals induced by a direct electrical current. The driving force is proportional to the current density and is usually expressed in terms of a parameter called the effective charge. In polycrystalline films the flux is dominated by grain boundary transport and, because of the high (greater than 105 A cm -2) current density involved in the thin film conductors used in integrated circuits, electromigration damage is of concern to device reliability. The damage is usually initiated by mass depletion at flux divergence sites such as grain boundary junctions or from the outer surface of the film, which eventually develops into line open circuits. With the current trend for device miniaturization, the reduction in conductor width increases the current density and reliability concern for electromigration damage as well. For conductors about 1 I~m wide, a current density of about 106 A crn -2 is estimated during typical operation. Under such a current density the commonly used A1-4~Cu line was observed to have a significant reduction in lifetime, below the device requirements. It was found that the copper, which was originally added to reduce aluminum electromigration, was itself depleted under the high current density by electromigration from the cathode to the anode. The loss of the copper solute consequently reduces the overall electromigration resistance of the line. In addition, since the grain size is about 1 pm (comparable with the film thickness which is usually about 1 ~m), there are only one or two grains spanning across the line. This means that mass depletion at one grain boundary junction could stretch across the line and cause open failure of the whole line. In contrast, lines several microns wide would require a statistical linkage of depletion openings across several grains for an open failure. This grain size effect leads to a large statistical standard deviation a in lifetime for a I I~mline, which is undesirable because of the difficultyin predicting early failure under device-operating conditions. The problem of large a can be solved by reducing the grain size. Unfortunately, this has the consequence of

416

D. GUPTA, P. S. HO

providing a larger grain boundary area for electromigration which causes faster copper depletion and a shorter lifetime. It is clear that other methods, instead of copper addition, have to be found for improving electromigration resistance. One effective method incorporates a sandwiched layer of a transition metal-Al intermetallic compound 51. The compound layer can be formed by first evaporating a layered film with an A1-Cu/transition metal/A1--Cu structure; then on annealing, the transition metal reacts with the aluminum to form the compound layer. A vertical-sectioning micrograph showing such a structure using the A13Ti compound is shown in Fig. 1l(a). Lifetime tests on lines formed with various transition metal compounds indicated that the lifetime is increased by more than an order of magnitude and the standard deviation also improves significantly. Detailed studies on the compound formation kinetics 52 and the film microstructure showed that several characteristics of the intermetallic layer are essential for the improvement. Firstly, the compounds should have a high aluminum concentration (usually higher than a 3:1 ratio) which not only limits the resistivity increase but also provides a suitable medium for current passage in case severe aluminum depletion occurs in the top or the bottom layer. Secondly, the compound should be much more stable than AI-Cu against electromigration, so even when voids develop in the top or the bottom layer their linkage through the film is blocked by the presence of the

(a)

(b)

(c) Fig. 11. Angle sections through an A1-Cn/TiAIffAI-Cu test stripe after over 6000 h of testing at 250 °C and a current density of 1 x 106 A cm-2: (a) TiAI 3 layer (arrow) near contacts; (b) hole formation concentrated in the lower A1-Cu layer; (c) hole formation blockage at TiAl 3 layer as shown by the lack of voids in the upper Al-Cu layer.

DIFFUSION PROCESSES IN THIN FILMS

417

compound layer. This reduces failure by eliminating complete opening through the line. An example can be seen in Fig. 1 l(b) where the presence of depletion regions in the top and bottom layer did not produce an electrical open circuit in this particular sample. Diffusion in the compound was not quantitatively measured but it is estimated that the magnitude of the diffusion flux in the compound is several orders of magnitude less than that in A1-Cu at 400 °C. Thirdly, the top AI-Cu layer has a relatively uniform grain texture which reduces the number of divergent sites for mass depletion, so it is less susceptible to electromigration damage (see Figs. 1 l(b) and l l(c)). This, together with the uniform small grain size in the intermetallic layer, makes a reduction in the statistical deviation of the lifetime possible. Another effective solution for improving the electromigration resistance in aluminum conductors involves the concept of elimination of the flux divergence sites alluded to above. Recently, Vaidya e t al. 53 have fabricated AI-0.5%Cu conductors of 2 lam width with a "bamboo" grain structure where the grain boundaries generally run perpendicular to their length and the direction of the current flow. The reduction of the flux divergence sites, namely the triple points in the grain boundaries, so coupled with a small electromigration driving force at the boundary increased the electromigration lifetime by an order of magnitude in the conductors of width less than 2 ttm. REFERENCES

1 R . W . BalluffiandJ. M. Blakely, ThinSolidFilms, 25(1975) 363. 2 R. d'Heurle and R. Rosenberg, Phys. Thin Films, 7 (1973) 257. 3 P.S. Ho, F. M. d'Heurle and A. Gangulee, in R. E. Hummel and H. B. Huntington (eds.), Electroand Thermo-Transport in Metals and Alloys, American Institute of Mining, Metallurgical and Petroleum Engineers, New York, 1977, p. 108. 4 N.A. Gjostein, Diffusion, American Society for Metals, Metals Park, Ohio, 1973, p. 241. 5 R.W. Balluffi, Phys. Status Solidi, 42 (1970) 11. 6 H. Gleiter and B. Chalmers, Prog. Mater. Sci., 16 (1972) 77. 7 D. Gupta, D. R. Campbell and P. S. Ho, in J. M. Poate, K. N. Tu and J. W. Mayer (eds.), Thin Films." lnterdiffusion and Reactions, Wiley, New York, 1978, p. 161. 8 L.G. Harrison, Trans. Faraday Soc., 57 (1961 ) 1191. 9 D. Gupta, Phys. Rev., 7 (1973) 586. 10 P.S. HoandJ. K. Howard, J. Appl. Phys.,45(1974)3229. 11 K . L . Tai, P.H. SunandM. Ohring, ThinSolidFilms, 25(1975)343. 12 P.H. Sun and M, Ohring, J. AppL Phys., 47 (1976) 478. 13 D. Gupta, Thin Solid Films, 25 (1975) 231. 14 P.F. Kane and G. B. Larrabee (eds.), Auger Electron Spectroscopy, Plenum, New York, 1977. 15 G. Brebec, R, Seguin, C. Sella, J. Bevenot and J. C. Martin, Acta Metall., 28 (1980) 327. 16 R. T. P. Whipple, Fhilos. Mag., 45 (1954) 1225. 17 T. Suzuoka, Trans. Jpn. Inst. Met., 2 (1961) 25. 18 A.D. LeClaire, Br. J. AppL Phys., 14 (1963) 351. 19 D.R. Campbell, Bull. Am. Phys. Soc., 19 (1974) 347. 20 G.H. Gilmer and H. H. Farrell, J. Appl. Phys., 47 (1976) 3792, 4373. 21 J . M . C . Hwang, J. D. Pan and R. W. Balluffi, J. Appl. Phys., 50 (1979) 1349. 22 P.H. Holloway, D. E. Amos and G. L. Nelson, J. Appl. Phys., 47 (1976) 3769. 23 J . M . C . Hwang, P. S. Ho and R. W. Balluffi, Appl. Phys. Lett., 33 (1978) 458. 24 M, Wuttig and H. K. Birnbaum, Phys, Rev., 147 (1966) 495. 25 C. 'Baker, M. Wuttig and K. K..Birnbaum, Trans. ,lpn. Inst. Met. (Suppl.), 9(19~18) 268. 26 D. Gupta and D. R, Campbell, Philos. Mag., in the press. 27 J.T. Robinson and N. L. Pcterson, Surf Sci., 31 (1972) 586.

418

28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

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D. Gupta, Metall. Trans. A, 8 (1977) 1431. D. Gupta, J. Appl. Phys., 44 (1973) 586. D. Gupta and K. W. Asai, Thin Solid Films, 22 (1974) 121. W.R. Upthegrove and M. J. Sionnott, Trans. Am. Soc. Met., 50 (1958) 1031. D. Gupta and K. K. Kim, J. Appl. Phys., 51 (1980) 2066. D. Gupta and R. Rosenberg, Thin Solid Films, 25 (1975) 171. M.P. Shearer, C. L. Bauer and A. G. Jordon, Thin Solid Films, 61 (1979) 273. M.P. Chamberlain and S. L. Lehoczky, Thin Solid Films, 45 (1977) 189. H.S. Wildmann, J. K. Howard and P. S. Ho, J. Vac. Sci. Technol., 12 (1975) 75. F. SoriaandJ. L. Sacedon, ThinSolidFilms, 60(1979) l13. D. Gupta and K. W. Asai, Electrochemical Society Meet., Extended Abstracts, 1975, Vol. 75-1, Electrochemical Society, Princeton, New Jersey, 1975, p. 255. H.G. Tompkins, J. Electrochem. Soc., 122 (1975) 983. P.S. Ho, to be published. J.M. Shoen, J.M. Poate, C.J. DohertyandC. M. Melliar-Smith, J. Appl. Phys.,50(1979)6910. S. Danyluk, G. E. McGuire, K. M. Koliwad and M. G. Yang, Thin Solid Films, 25 (1975) 483. H.G. Tompkins and M. R. Pinnel, J. Appl. Phys., 47 (1976) 3804. K. Meinel, M. Klaua and H. Bethge, Thin Solid Films, 34 (1976) 157. P.S. Ho, J. E. Lewis and J. K. Howard, Thin Solid Films, 25 (1975) 317. M. Revitz and P. A. Totta, Electrochemical Society Meet., Extended Abstracts, 1972, Vol. 72, Electrochemical Society, Princeton, New Jersey, 1972, p. 631. S.K. Lahiri, Thin Solid Films, 28 (1975) 279. J. E. Baglin and J. M. Poate, in J. M. Poate, K. N. Tu and J. W. Mayer (eds.), Thin Films: lnterdiffusion and Reactions, Wiley, New York, 1978. K. N. Tu, J. ApplC.Phys., 48 (1977) 3400. R.F. Lever, J. K. Howard, W. K. Chu and P. J. Smith, J. Vac. Sci. Technol., 14 (1977) 158. J.K. Howard, J.F. WhiteandP. S. Ho, J. Appl. Phys.,49(1978)4083. J.K. Howard, R. F. Lever, P. Smith and P. S. Ho, J. Vac. Sci. Technol., 13 (1976) 68. S. Vaidya, T. T. Sheng and A. K. Sinha, Appl. Phys. Lett., 36 (1980) 464.