Jul 15, 2005 - The present paper addresses the driving force of the grain growth of the Cu thin films based on the strain energy criterion model. (Received ...
Materials Transactions, Vol. 46, No. 7 (2005) pp. 1737 to 1740 #2005 The Japan Institute of Metals
RAPID PUBLICATION
Grain Growth Mechanism of Cu Thin Films Masanori Murakami1 , Miki Moriyama2 , Susumu Tsukimoto1 and Kazuhiro Ito1 1 2
Department of Materials Science and Engineering, Kyoto University, Kyoto 606-8501, Japan Optoelectronics Division, Toyoda Gosei Co., Ltd., Heiwa-cho, Nakashima, Aichi 490-1312, Japan
Since Cu was found to be attractive as interconnect materials for ultra-large scale integrated (ULSI) Si devices, the electrical properties of Cu films have been extensively studied to prepare low resistance films. It was found in our previous papers that reduction of the electrical resistance of the Cu films was achieved by increasing grain sizes of the Cu films and large-grained Cu films were essential for the low resistance Cu interconnects. The primary factor to increase the grain sizes was also found to be intrinsic and/or extrinsic strain (or stress) introduced into the films. The present paper addresses the driving force of the grain growth of the Cu thin films based on the strain energy criterion model. (Received March 9, 2005; Accepted June 2, 2005; Published July 15, 2005) Keywords: grain growth, copper thin film, strain energy
1.
Introduction
Since performance of ULSI Si devices was found to be controlled by RC delay (where R is the electrical resistance at the interconnects and C is the capacitance of the insulators), efforts have been continued to reduce the wiring resistance and the insulator capacitance. Replacement of aluminum alloy interconnect materials by copper (which has about 40% lower resistivity compared with the aluminum alloy) reduced not only the device switching times but also the fabrication cost. However, the resistivity of the Cu wires was demonstrated experimentally to increase rapidly1) when the wiring width approached to the mean free path (39 nm) of the conducting electrons as predicted by theories.2–4) Our experiments suggested that the conducting electrons primarily scattered at the grain boundaries in Cu thin films,1) causing an increase in the electrical resistivity of sub-micron scale Cu wires with small grains. Thus, large-grained Cu interconnects are essential to realize high performance ULSI Si devices. To develop a fabrication technique of large-grained Cu interconnects, understanding of a grain growth mechanism of Cu thin films is essential. Although several parameters (such as surface energy, grain boundary energy, impurities, etc) to control the grain growth of the Cu thin films were proposed,5–8) we demonstrated experimentally in our previous papers9,10) that the strain (or stress) introduced into the thin films was the primary factor to enhance the grain growth specially at low temperatures in addition to surface/grain boundary energy. The purpose of the present paper was to understand a grain growth mechanism of Cu thin films based on the strain energy criterion model.11) For this purpose, the previous experiments9,10) were briefly reviewed which demonstrated importance of strain (or stress) in thin Cu films to enhance grain growth. Then, a mechanism why the strain (or stress) in the films enhanced growth of Cu grains was explained based on the strain energy criterion model.11) 2.
Review of Previous Experiments and Theory
2.1 Review of experiments In order to study the effect of intrinsic and extrinsic strains
Sample A
Sample B
Sample C
Cu(100nm) Si3N4(60nm)
Cu(100nm)
Cu(100nm)
NaCl
NaCl
(100)Si
Fig. 1 Cross-sections of samples used for a grain growth study of Cu films deposited on different substrates.
on the grain growth of the Cu thin films, 100 nm-thick Cu films were prepared on different substrates by a magnetron sputter-deposition technique with base pressure of 2:7 106 Pa.9) The cross-sections of the samples were schematically shown in Fig. 1 The choice of the Si3 N4 /Si substrate (sample A) was that an amorphous thin Si3 N4 layer was easily coated on the (100)Si substrate. In addition, 100 mm square Si window could be opened by etching the Si substrate without breaking the Si3 N4 layer, which was needed to observe the microstructure of the Cu film without removing the films from the substrate by transmission electron microscopy. Since the thermal expansion coefficients of Si are smaller than those of Cu, the compressive strain was introduced into the Cu film upon heating sample A. The choice of the rock salt substrate (sample B) was that the thermal expansion coefficients of the rock salt are larger than those of Cu and thus the tensile strain was introduced into the Cu film upon heating sample B. Another reason to use the rock salt substrate was that a free-standing Cu film (sample C) could be prepared simply by dissolving the rock salt of sample B in water. Microstructural observations of samples A, B, and C were carried out by transmission electron microscopy before and after annealing the samples in vacuum or in 5% H2 /N2 mixed gas ambient. Sample C was supported by copper meshes to eliminate introduction of thermal strain in the films during annealing at elevated temperatures. The important conclusions obtained in the previous experiment9) are summarized below. (1) Grain growth of the Cu films was strongly enhanced by existence of the substrates during storage of the samples at room temperature. Although grain growth of sample C was not observed, significant grain growth was
M. Murakami, M. Moriyama, S. Tsukimoto and K. Ito
2.2 Review of theory The strain energy criterion model11) (which was originally developed to determine the maximum thermal strain that could be supported elastically in Pb thin films12) deposited on the Si substrates) was applied here to understand the grain growth mechanism of the Cu thin films observed in our previous experiments.9,10) This model is briefly reviewed here. The total strain energy E of a film (which is strained intrinsically or extrinsically and the strain is partially relaxed by dislocation glide) is divided into two parts, 0 E ¼ Eelast þ Edisloc
Eelast ¼
1 2 2 Y" g h 2
ð2Þ
0 is where Y is the Young’s modulus of the film. The Edisloc given by, 0 Edisloc
¼ Edisloc N
ð3Þ
where Edisloc is the energy associated with a dislocation loop present in the film, and N is the number of dislocations given by, N ¼ ð"0 "Þ="
ð4Þ
where " is the amount of strain each dislocation can relax, and is given by " ¼ f b0 =g (where b0 is the projection of the edge component of the Burgers vector on the film surface and f is the average displacement in units of the Burgers vector). The total energy E0 (per unit volume) of the film is given by, E0 ¼
1 2 ð"0 "ÞEdisloc Y" þ 2 b0 fg h
ð5Þ
The energy Edisloc represents the energy of the dislocation
rm te er gy en
cia
te
d
ε* Strain
0
ε0
Fig. 2 Schematic illustration of total energy (E0 ), elastic energy (Eelast ), 0 and energy associated with dislocations (Edisloc ) (normalized by unit volume) as a function of strain ".
loop and is expressed by, Edisloc ’ ED g þ ED h ED
ð6Þ
ED
where and are energies per unit length of the dislocation loop. The total energy E0 given by eq. (5) is schematically shown in Fig. 2 as a function of " together with the elastic energy term (the first term of eq. (5)) and the energy associated with dislocations (the second term). The critical strain " at which E0 is minimum is given by, " ¼ Edisloc =b0 Y fgh
ð1Þ
where Eelast is the energy associated with a uniform elastic 0 strain and Edisloc is the energy of the dislocation strain field. These energies are calculated in a grain with rectangular volume (g g h) with grain size g and thickness h. Assuming N dislocations glide across a grain and relaxed the intrinsic (or thermal) strain level from "0 to an average level ", the Eelast term is given by,
E0
E wi ner th gy dis te loc rm at as ion so
El as tic
observed in both samples A and B. (2) Grain growth of samples A and B was enhanced upon annealing at elevated temperatures, which was believed to be due to introduction of thermal strains into the Cu films. Although both the compressive (sample A) and tensile (sample B) strains are introduced into the Cu films, the grain growth behaviors were not influenced by the sign of the strains. (3) Grain growth of sample A was initiated at locations close the substrate surface where the large strain was observed in the Cu film.10) (4) (111) oriented Cu grains were found to grow at the expense of the small grains with other orientations, and introduction of dislocations in large grains was observed after grain growth was completed. (5) Carbral et al.12) observed simultaneously relaxation of strain in the film and grain growth during room temperature storage.
Energy
1738
ð7Þ
Figure 2 indicates that when the strain "0 is applied to the film with grain size g and thickness h, the strain is (plastically) relaxed at the amount of ("0 " ) and the film is elastically supported by the amount of " . An excellent agreement between strains calculated by eq. (7) and the residual elastic strains measured in Pb thin films which were deposited onto the Si substrates and cooled to 4.2 K was observed,13) indicating the validity of this model to calculate the elastic strain supported by the film under tensile or compressive strain. 3.
Grain Growth Mechanism Based on Strain Energy Criterion Model
When a polycrystalline film with various grain size gi (as shown schematically in Fig. 3) is strained intrinsically or extrinsically to the value of "0 and the residual elastic strain in the grain is ", the strain energy (per unit volume) stored in the grain is given by, ! 1 2 ð"0 "Þ ED ED 0 Ei ¼ Y" þ þ ð8Þ 2 b0 f h gi The energies E10 and E20 are schematically shown in Fig. 4 for the films with grain sizes g1 and g2 , respectively, where g1 > g2 . The E1 and E2 represent the minimum elastic energies stored in the grains with sizes g1 and g2 , respectively, and are given by,
Grain Growth Mechanism of Cu Thin Films
gi
gj
gi
1739 110
g j E j0
(x1011Pa)
E i0 E k0
gk
111 5.2
gk
h
010 2.3 011 4.7
Substrate 112
Fig. 3 Schematic illustration of a film with thickness h deposited on the substrate: gi and Ei0 indicate grain size and energy stored in a grain i, respectively.
001
111 2.4 3.0 4.0
112
111 5.0
Fig. 5 Stereographic projection of equicontour curves of strain energy Ehkl normalized by 1/2 ("2 ) for a Cu thin film at 298 K (1011 Pa). The Ehkl values were calculated for Cu films where the elastic constants of C11 ¼ 168:4 GPa, C12 ¼ 121:4 GPa, and C44 ¼ 75:4 GPa.
E20(g=g2)
E0(111)
E10(g=g1) E1*
0
Energy
Energy
E2*
g1>g2
ε1*
(111)
ε0
ε2* Strain
(100)
Fig. 4 Schematic illustration of total energies E10 and E20 for grains with grain size g1 and g2 , respectively, as a function strain ", where g1 > g2 .
Ei ¼
ðED
ED
"
gi þ hÞ "0 b0 fgi h
ðED
ED
gi þ hÞ 2Yb0 fgi h
# ð9Þ
where i ¼ 1 or 2. The grain with small size g2 stores the strain energy (per unit volume) larger than that of the grain with large size g1 . Therefore, the best way to reduce the strain energy stored in the grain with small size is to grow the grain size which enhances the strain relaxation by dislocation glide. Therefore, grain growth was observed in samples A and B which introduce strain into the films from the substrate and not in free-standing sample C.9) Also, based on the present grain growth model, a higher density of dislocations are expected to be introduced into the grains after grain growth. These dislocations were observed experimentally in the previous TEM experiment.9) Although eq. (8) gives the strain energy in a film with isotropic elastic constants, metallic films such as Cu have, in general, anisotropic elastic constants. The elastic energies (Ehkl ) of the Cu film which has various (hkl) grain orientations were calculated by, Ehkl ¼
1 0 0 S 0 2 ij ijlm lm
E0(100)
0 Strain
ε0
Fig. 6 Schematic illustration of total energies E0 (111) and E0 (100) for grains with (111) and (100) crystal orientations, respectively, as a function of strain ".
oriented grains, the values were plotted on the upper halfsphere of (111) stereographic projection as shown in Fig. 5, where [111] direction is normal to the figure and [1 10] direction is the vertical axis. The maximum and minimum values in Ehkl are observed in (111) and (100) oriented grains, respectively, and the Ehkl value of the (111) oriented grains is more than a factor of two larger than that of (100) oriented grains. This result indicates that at a given strain a (111) oriented grain stores an elastic strain energy larger than that of a (100) oriented grain with the same grain size (Fig. 6). Therefore, to reduce the strain energy efficiently, relaxation of the elastic strain in the (111) oriented grain by increasing the grain growth is more favorable. Therefore, growth of (111) oriented grains was observed in the Cu films upon annealing at elevated temperatures. 4.
Summary
ð10Þ
0 where ij0 is the stress and Sijlm is the compliances of a (hkl) oriented grain. The Ehkl values were calculated for Cu films where the elastic constants of C11 ¼ 168:4 GPa, C12 ¼ 121:4 GPa, and C44 ¼ 75:4 GPa measured at room temperature were used.14) In order to read off easily the Ehkl values of any
A new grain growth model for Cu thin films was proposed based on the strain energy criterion model at temperatures where dislocation glide was the dominant strain relaxation mechanism. Based on this model, the grains of the Cu films under tensile or compressive strain were explained to grow primarily to reduce the elastic strain energy by dislocation
1740
M. Murakami, M. Moriyama, S. Tsukimoto and K. Ito
glide, because the dislocations are easily introduced into large grains upon introduction of strain into the films. This model agreed very well with our previous experiment in which rapid grain growth was observed in the strained films bonded to the rigid substrates during room temperature storage, but no grain growth was observed in the strain-free (free-standing) films. Also, this model explained well the experimental results in which the growth mechanism was not influenced by sign of the strain introduced into the films and the (111) oriented grains grew preferably with introduction of a high density of dislocations after grain growth. REFERENCES 1) M. Moriyama, M. Shimada, H. Masuda and M. Murakami: Trans. Mater. Res. Soc. Jpn. 29 (2004) 51. 2) K. Fuchs: Proc. Camb. Phil. Soc. 34 (1938) 100. 3) E. H. Sondheimer: Adv. Phys. 1 (1952) 1.
4) A. F. Mayadas and M. Shatzkes: Phys. Rev. B 1 (1970) 1382. 5) C. Lingk and M. E. Gross: J. Appl. Phys. 84 (1998) 5547. 6) J. M. E. Harper, C. Cabral, Jr., P. C. Andricacos, L. Gignac, I. C. Noyan, K. P. Rodbell and C. K. Hu: J. Appl. Phys. 86 (1999) 2516. 7) S. H. Brongersma, E. Richard, I. Vervoot, H. Bender, W. Vandervorst, S. Lagrange, G. Beyer and K. Maex: J. Appl. Phys. 86 (1999) 3642. 8) P. Chaudhari: J. Vac. Sci. Technol. 9 (1972) 520. 9) M. Moriyama, K. Matsunaga and M. Murakami: J. Electron. Mater. 32 (2003) 261. 10) M. Moriyama, K. Matsunaga, T. Morita, S. Tsukimoto and M. Murakami: Mater. Trans. 45 (2004) 3033. 11) M. Murakami, T.-S. Kuan and I. A. Blech: Treatize on Mater. Sci. Technol. 24 (1982) 163. 12) C. Cabral, Jr., P. C. Andricacos, L. Gignac, I. C. Noyan, K. P. Rodbell, T. M. Shaw, R. Rosenberg, J. M. E. Harper, P. W. DeHaven, P. S. Locke, S. Malhotra, C. Uzoh and S. J. Klepeis: MRS Conf. Proc. ULSI XIV (1999) p. 81. 13) M. Murakami: CRC Critical Review in Sol. Stat. Mater. Sci. 11 (1984) 317. 14) R. E. S. Hearmon: Revs. Modern Phys. 18 (1946) 409.
