Short stripe effect and electromigration stress

Microelectronic Engineering 64 (2002) 383–389 www.elsevier.com / locate / mee

Short stripe effect and electromigration stress E.E. Glickman* Department of Electronics, Faculty of Engineering, Tel Aviv University, 69978 Tel Aviv, Israel

Abstract From the perspective of the recent contributions to the field, we discuss essential physics behind the short-stripe effect in drift velocity electromigration (EM), transition to the creep controlled electromigration in short, near-threshold interconnects, the role of dynamic EM stresses and possible mechanism of their relaxation by non-constrained diffusional creep into hillocks.  2002 Elsevier Science B.V. All rights reserved. Keywords: Drift velocity electromigration; Stress; Hillocks; Diffusional creep mechanisms

1. Short stripe effect and stress in drift velocity EM: role of creep Electromigration (EM) threshold and short-stripe effect (SSE) in EM kinetics are important issues because advanced narrow interconnects are either short or comprise even shorter poly-granular segments. Since the pioneering works by Blech et al., it has been recognized that a continuous decrease of electromigration (EM) drift velocity V, as the stripe length L becomes shorter with time t, approaching an apparent threshold length L *th , reflects counteraction between two diffusion fluxes: the EM flux IEM , and the stress gradient driven back flux, Is [1–3]. The drift of the cathode edge with the velocity V 5 (IEM 2 Is )V 5 IN V causes material accumulation and compression build-up. It was found that the biaxial compression stress s increases as we go closer to the anode edge of the conductor stripe, that s reaches there 10 2 –10 3 MPa, and relaxes by plastic flow into hillocks [1–3]. Hillocks, which often have ‘tooth paste extrusion’ appearance, form in the adjacent to anode zone LX in which s exceeds some threshold stress for plastic deformation, sTH . The mechanism of EM hillock formation is still rather unclear. The classical Blech description of SSE ignores the kinetic aspect of EM stress relaxation, assumes perfect plasticity of thin film material with compressive yield stress sY , and takes sTH ± f (current density j, L) 5 sY . More recently, Glickman et al. [4,5,8,9] proposed that plastic flow into hillocks occurs by a time-dependent process (diffusional creep) in * Fax: 1972-3-642-3508. E-mail address: [email protected] (E.E. Glickman). 0167-9317 / 02 / $ – see front matter PII: S0167-9317( 02 )00812-2

 2002 Elsevier Science B.V. All rights reserved.

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which the strain rate (d´ / dt) 5 (s 2 sTHC ) /h depends on the creep viscosity h, and the creep threshold stress sTHC . They noted that in the drift velocity test this process of stress relaxation by creep operates in series with electrotransport, and therefore may be the rate controlling step in stationary drift velocity EM, in particular for short stripes. These works described continuous transition from the classical, ‘migration controlled’ EM regime in long stripes, to the ‘creep-affected’, and finally ‘creep controlled’ EM regime (CCEM), the latter operating in short, near-threshold interconnects [4,8,9].

2. Creep controlled EM regime In this limit of ‘creep controlled’ EM (which corresponds to the a and b criteria conditions formulated in Ref. [8] and was found to operate in bare polygranular Al films at L , (15–30) mm [5,8]) the overall rate of EM displacement V is controlled by a strictly local mechanical process, creep into hillocks, and V does not depend explicitly on the diffusivity D along the stripe. Instead, V ~1 /h and the creep viscosity evolves to be the major material property that determines EM kinetics [5,8]: V((0.5 r Z* /h )j(L 2 Lth )2 .

(1)

Here r is the resistivity, Z* is effective charge. Lth 5 VsTHC /jr Z* is the true threshold length which the measured, apparent length L*(t) approaches asymptotically, as t → ` [4,5,8]. This ‘creep kinetics’ model of EM was applied to the analysis of the EM drift velocity and threshold data in short, unpassivated, polygranular Al and Cu stripes in Refs. [4,5,8]. It was found that the agreement with the data is considerably better than that for the Blech ‘sharp yield stress’ model which leads to the widely used expression [3]: V/Vd 5 1 2 (Lth /L)

(2)

where Vd 5 (Dr Z* /kT )j 5 Md j is V for L → `, Md is the EM mobility, and Lth 5 sY V /r Z*. It is remarkable that while Eq. (2) attributes SSE directly to the presence of a threshold for plastic flow (compressive yield stress, sY ) and predicts that V 5 const ± f(L) at sY 50, Eq. (1) predicts SSE, namely V ~L 2 , even in the absence of any threshold for plastic flow, that is at sTHC → 0. Retaining the major Blech idea on the EM back-stress s, it is instructive to understand why s exists even when the ‘static’ threshold for initiation of plastic flow, sTHC → 0.

3. Static and dynamic components of EM stress [4,8] Following the Refs. [4,8,9] which have emphasized the role of ‘dynamic stress’, it is worth noting here the following. (i) Coupling the net flux IN of material towards the anode with the flux of plastic flow into hillocks—and meeting thus mass conservation for a stationary EM—requires specific rate of

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Table 1 The creep viscosity h and EM threshold values for bare Al and Cu thin film interconnects. Derived in Refs. [4,5,12] from the EM kinetics [4,13–16] and threshold [12] data for short, polygranular stripes Notation in Figs. 1, 2

Metal, film thickness h 0 (mm)

Grain size d (mm)

Underlayer

j (MA / cm 2 )

T (K)

h 3 10 24 (GPa s)

* Lth /L th (mm)

Ref.

a b c d e f

Al, 0.4 Al, 0.5 Al, 0.2 Cu, 0.35 Al Al, 0.1

0.7 0.1–0.25 0.1 0.5 0.08 0.08

TiN TiN V W/ Ta TiN TiN

1 1.5 2.1 2.1 0.1–4 1.5

473 500 451 623 548615 548

50 0.37 7 1 0.55 a 0.5

3 / 12 0.5 / 5.5 2/8 1.5 / 2.5

[13] [14] [15] [16] [12] [4]

a

From the dependence of the EM threshold on the current density L *th ( j).

plastic flow (creep) into hillocks; increase in IN , e.g. due to increase in j, requires larger dynamic stress which can cause larger creep rate d´ / dt. (ii) Specific ‘dynamic’ stress sd 5 (d´ / dt)hT is required to maintain the specific creep rate into an individual hillock-extrusion, with hT being here the ‘microscopic’ h. (iii) What matters in mass conservation is the total flux of materials into all the hillocks; considering hillocks as cylindrical mounds with a base radius a, regularly spaced with the centers 2b 4 a apart on a film surface in the hillocked zone LX , it was shown that the surface coverage u ¯ (a /b)2 determines the relation between the effective viscosity h, which was derived from the EM experiments, and hT [5,8]: 2

(h /hT ) 5 1 /u 5 (b /a) .

(3)

Large j and large h both favor development of such a high dynamic stress sd at the anode end of the stripe that the total stress acting here samax 5 (sd 1 sTHC ) 4 sTHC may cause failures through delamination from substrate, or crack formation in a passivation layer [10,11]. Very small h makes plastic flow into hillocks so easy that small sd ~h does not contribute considerably to the total stress samax ¯ sTHC ; in this limit, EM behavior was found [4,9] to approach that described by the classical Eq. (2). The creep viscosity h values derived in Refs. [4,5,12–16] for Al and Cu interconnects are shown in Table 1. In what follows we attempt to make a systematization of these data by normalizing the h values over the relevant microstructure parameters and temperature, and by fitting them to several diffusional creep mechanisms which may participate in the EM hillock growth.

4. On the possible mechanism of EM hillock formation Bulk diffusion controlled Nabarro–Herring (N–H ) creep may control hillock growth providing that EM brings excess material to grain boundaries (GBs), which moves then with smaller bulk diffusivity

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Dv down the stress-gradient into the grain interiors. Combining hNH 5 kTd 2 / 15V Dv for the viscosity in the N–H process [17,18] with the well known expression for the volume diffusion coefficient Dv (cm 2 / s) in f.c.c. metals Dv 5 c exp (218T m /T ), with T m being the melting temperature and c between 1 and 10 21 , one gets: ln (15V hNH /d 2 kT ) 5 18(T m /T ) 1 C

(4)

where the intercept C should fall in the range (0–2.3). Fig. 1 illustrates this dependence plotted with the h, d and T values taken from Table 1. One can see that the N–H process is definitely in conflict with a single h observation on Cu and that, even though Eq. (4) yields the right order of magnitude for h in Al, correlation of the normalized h with temperature is rather poor. In addition, the N–H mechanism should lead to a uniform film thickening in the near anode zone LX , rather than to discrete hillocks, which are typically observed. Unconstrained GB diffusion controlled (Coble) creep is operating in a parallel way with N–H creep and at (T m /T ) # 2.2 (Fig. 1) and rather small grain size d | (0.1–1) mm (Table 1) the Coble process dominates. The creep viscosity hC for this mechanism, which assumes the diffusion distance l SS ¯ d, is hC ¯ (1 / 50) (d 3 kT /Dgbdgb V ), where (Dgbdgb ) is the GB diffusivity [18]. The hC s calculated this way turn out to be much smaller than the experimental ones: by 4–5 orders of magnitude for Al and by about 1.5 orders for Cu. This shows that the classical Coble creep seems to be too fast to control growth of EM hillocks—even in unpassivated lines—and stimulates the analysis of constrained Coble process [6,7], or / and the unconstrained interface diffusion controlled creep, in which l SS is considerably larger than the grain size d [5]. The model of interface diffusion controlled creep with l SS 4 d accounts for the localized distribution of hillocks over the film surface and can be traced back to studies by Chaudhari and Lindborg on thermal hillocks. It was more recently reviewed by Tu et al. [19]. It considers the hillock nuclei as local ‘stress free’ regions, which grow due to stress gradient driven diffusion from their compressive surroundings to the bottom of the hillocks. Recent TEM observations in unpassivated polygranular Al films have shown that also electromigration hillocks grow by the addition of material at their bottoms [20].

Fig. 1. Normalized creep viscosity data derived from the EM experiments on unpassivated polycrystalline Al and Cu short stripes (Table 1) vs. the normalized temperature. The Nabarro–Herring mechanism predicts the points to fall within the band.

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Assuming somewhat idealized hillock formation pattern [19] with u ¯ (a /b)2 , considered in Section 3, the effective interface diffusion coefficient involved in the hillock growth Doff ¯ Dgb , and applying Eq. (3), it was found [5]:

hd /h 0 5 (1 /Md ) ? b 2 ? ln (b /a) ? ( r Z* / 2V )

(5)

with h 0 being the initial film thickness. Eq. (5) shows that h has only a weak dependence on a hillock diameter a and a rather strong dependence on the interhillock distance 2b. Eq. (5) predicts close to linear relationship between the normalized viscosity (hd /h 0 ) and the inverse EM mobility (1 /Md ), providing the hillock separation distance 2b is about constant. Fig. 2a

Fig. 2. Normalized creep viscosity data (Table 1) vs. the electromigration mobility Md 5Vd /j (the Md s were found from the drift velocity experiments on long stripes). (a) Assumed is constant interhillock distance 2b; CLT model of hillock growth with 2b 5 const predicts the regression line with unit slope (for 2b 5 20 mm it is line 2) and the scatter band with vertical deviation62.3 from it (see ‘1’ and ‘3’). (b) Assumed is direct proportionality between b and the EM threshold length * ; with this, CLT model predicts unit slope line which is shown for g 5 0.3. Correlation in (b) includes data for both b 5 g L th Al and Cu films and is stronger than in (a).

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shows however rather poor correlation, suggesting dependence of 2b on the microstructure and / or EM stressing conditions. The statistical observations of Kraft et al. [21] suggest that b should be proportional to L *th with a proportionality factor g of the order of one. This correlation can be expected in view of an analogy which exists between formation of small voids and hillocks at the microstructural sites of diffusion flux divergence [21], on the one hand, and large voids and hillocks formed at the ends of drift velocity stripe—the sites of perfect flux divergence, on the other hand. With b ¯ g L *th , the normalized viscosity in the left side of Eq. (6) is in a linear relation to (1 /Md ) 2

2

* ) 5 (1 /Md ) ? ( r Z* / 2V ) ? g ? ln (b /a). (hd /h 0 L th

(6)

Fig. 2b shows that such a close correlation does exist; it includes the Al and Cu points (Table 1) and is much better in comparison with Fig. 2a. This is conceptually an important finding, which enables correlation of EM displacement kinetics with the hillock pattern and growth by diffusional creep.

5. Conclusion The significance of Fig. 2b lies in the fact that it quantitatively correlates for the first time hillock formation to EM kinetics through the diffusional creep viscosity introduced in the proposed description of the creep-controlled EM regime. However, understanding of the problem is still incomplete. Systematical experimental data on SSE in passivated and alloyed near-threshold conductors are lacking. They are necessary to test the model of creep-controlled EM and its modifications which may be required for these interconnect structures used in actual practice.

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[18] J. Cadek, in: Creep in Metallic Materials, Academia, Prague, 1988, p. 376. [19] K.-N. Tu, J.W. Mayer, L. Feldman, in: Electronic Thin Film Science, Macmillan, New York, 1992, p. 428. [20] A. Straub, Factors Influencing the Critical Product in Electromigration, Max-Planck Institut fur Metallforschung, Stuttgart, 2000, Ph.D. thesis. [21] O. Kraft, J.E. Sanchez, M. Bauer, E. Arzt, J. Mater. Res. 12 (1997) 2027.