TiN(001) and TiN(111) island coarsening kinetics: in-situ scanning tunneling microscopy studies

Thin Solid Films 392 Ž2001. 164᎐168

TiNŽ 001. and TiNŽ 111. island coarsening kinetics: in-situ scanning tunneling microscopy studies S. Kodambaka, V. Petrova, A. Vailionis, P. Desjardins, D.G. Cahill, I. Petrov, J.E. GreeneU Materials Science Department and the Frederick Seitz Materials Research Laboratory, Uni¨ ersity of Illinois, 104 South Goodwin A¨ enue, Urbana, IL 61801, USA

Abstract In-situ high-temperature scanning tunneling microscopy was used to follow the coarsening ŽOstwald ripening. and decay kinetics of two-dimensional TiN islands on atomically-flat TiNŽ001. and TiNŽ111. terraces at 750᎐950⬚C. The rate-limiting mechanism for island decay was found to be adatom surface-diffusion on Ž001. and attachmentrdetachment at step edges on Ž111. surfaces. We have modeled island decay kinetics based upon the Gibbs᎐Thomson and steady-state diffusion equations to ˚ with an activation energy of 3.4" 0.3 eV for adatom formation obtain a 001-step edge energy per unit length of 0.23" 0.05 eVrA and diffusion on TiNŽ001.. The activation energy for adatom formation and attachmentrdetachment on TiNŽ111. is 3.5" 0.3 eV. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Titanium nitride; Scanning tunneling microscopy ŽSTM.; Surface diffusion; Surface energy

1. Introduction TiN is widely used as a diffusion barrier in microelectronics, as a hard wear resistant coating on cutting tools, and as a corrosion and abrasion resistant layer on optical components. Even though its diffusion barrier and elastic properties are known to be extremely anisotropic, and hence depend upon grain orientation, little is known regarding the mechanisms and reaction paths leading to the development of preferred orientation in polycrystalline TiN layers deposited by reactive evaporation and sputter deposition. Greene et al. w1x have shown that TiN films grown by ultra-high vacuum ŽUHV. reactive-magnetron sputter deposition on amorphous SiO 2 at low temperature ŽT F 450⬚C. with little or no ion irradiation exhibit 111 preferred orien-

U

Corresponding author. Tel.: q1-217-3331370; fax: q1-2172442278. E-mail address: [email protected] ŽJ.E. Greene..

tation via competitive grain growth even though Ž001. is the low energy surface w2x. Deposition at elevated temperatures or in the presence of low energy Ž, 20 eV. . q high-flux ŽNq 2 rTi) 5 N2 ion irradiation leads to 001preferred orientation from the initial monolayers w1x. Understanding and modeling the evolution of film texture and competitive grain growth mechanisms requires knowledge of adatom transport energies as a function of surface orientation. Here, we present the first results of an in-situ high-temperature scanning tunneling microscopy ŽSTM. study of the temperaturedependent coarsening and decay kinetics of adatom islands on atomically flat non-polar TiNŽ001. and polar TiNŽ111. surfaces. 2. Experimental procedure

˚ thick, Epitaxial TiNŽ001. and TiNŽ111. layers, 3000-A Ž . Ž . were grown on MgO 001 and Al 2 O 3 0001 , respectively, by UHV magnetically-unbalanced magnetron sputter deposition w3x using the procedure described in

0040-6090r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 1 . 0 1 0 2 2 - 7

S. Kodambaka et al. r Thin Solid Films 392 (2001) 164᎐168

165

w1x. The samples were transferred to a multi-chamber UHV Ž5 = 10y1 1 Torr base pressure. system with facilities for e-beam evaporation, ion etching, Auger electron spectroscopy ŽAES., low energy electron diffraction ŽLEED., and STM. The layers were degassed in UHV at 800⬚C for ) 20 min. TiN buffer layers, ˚ thick, were deposited at 750⬚C in the STM 50᎐100-A chamber by reactive evaporation from Ti rods Ž99.999% pure. in N2 Ž99.999%. at 1 = 10y7 Torr and annealed in N2 for 4 h at temperatures Ta ranging from 750 to 950⬚C. The annealed buffer layers exhibited sharp 1 = 1 LEED patterns with an interplanar spacing equal to that of TiN. AES analyses show that the films contain a small amount of oxygen, probably in the form of TiO which is isostructural and mutually soluble with TiN. Partial TiN monolayers with coverages ␪ s 0.1᎐0.4 ML were deposited on the epitaxial TiN layers by reactive-evaporation at Ts s 750⬚C. This resulted in a distribution of two-dimensional Ž2D. square TiN is˚ on TiNŽ001. and triangularlands of size 15᎐40 A ˚ on TiNŽ111.. STM shaped islands with sizes 35᎐70 A images were acquired at a rate of 20᎐180 s per frame during annealing in N2 . Typical tunneling conditions were 0.5 nA at 1.5᎐2.0 V. The digital images were processed using image analysis software w4x. 3. Results and discussion Fig. 1 shows representative STM images obtained at times ta s 0, 74, and 171 min from a TiNŽ001. sample with ␪ s 0.2 ML during a 3-h anneal 1 at Ta s 890⬚C. Most of the smaller islands observed at ta s 0 Že.g. islands 1᎐4 shown in Fig. 1a. have disappeared by ta s 171 min. Note that a denuded zone is formed around island 5 ŽFig. 1c. which coarsens at the expense of the smaller neighbors. The radial extent of this region corresponds to the quasi-equilibrium adatom diffusion length at this temperature. Fig. 2 shows typical STM images, acquired at ta s 0, 161, and 426 min, from a TiNŽ111. sample with ␪ s 0.25 ML during a 7-h anneal at Ta s 805⬚C. Smaller islands disappear as time progresses. Note the incorporation of island 10 into the step edge in Fig. 2b and the subsequent smoothening of the step edge in Fig. 2c. Island decay occurs by adatom detachment and migration across terraces to down steps Že.g. islands 1 in Fig. 1a and 9 in Fig. 2a. andror to up steps Že.g. island 7 in Fig. 2a.. The fact that all islands, on both TiNŽ001. and TiNŽ111., retain their equilibrium shapes during annealing indicates relatively fast edge-atom diffusion at these temperatures. Small islands decay in the presence of larger islands due to coarsening ŽOstwald ripening.. The process is

1

ta s 0 corresponds to the time immediately following thermal equilibration of the STM tip at Ta .

˚2 . from a TiNŽ001. sample with Fig. 1. STM images Ž1000 = 830 A ␪ s 0.20 ML during annealing at Ta s 890⬚C for times Ža. ta s 0, Žb. 74 and Žc. 171 min.

described by the Gibbs᎐Thomson equation in which the equilibrium free adatom concentration Cr , associated with an island of radius r, is related to its curvature and is given by the relation Cr s C⬁expŽ ␥⍀rrkT ., where C⬁ is the equilibrium free adatom concentration associated with a straight step Ž r s ⬁., ␥ is the island line tension and ⍀ is the adatom area in the condensed phase. Small islands have higher curvature and hence a higher two-dimensional spreading pressure than larger islands. Thus, coarsening is simply a curvature-driven mass transport from small islands to larger islands. The process involves adatom detachment, migration across the terrace and adatom attachment. Classical mean-field theory of three-dimensional cluster coarsening was developed by Lifshitz et al. w5x and extended to two-dimensional clusters on surfaces by McLean et al. w6x. In both cases, coarsening is described by a power law relationship, A A tan where A is the island area. The exponent n is 2r3 when adatom

166

S. Kodambaka et al. r Thin Solid Films 392 (2001) 164᎐168

stant rate irrespective of island size and local geometry. This is the signature of detachment-limited behavior. Since TiNŽ001. island coarsening is strongly dependent upon local environment, mean-field theory cannot be used. Thus, we extract surface transport activation energies from time- and temperature-dependent STM measurements by modeling the diffusion-limited decay kinetics for single and multiple islands on terraces and in single-atom-deep vacancy pits. A simulation code was developed based upon adaptive finite-element methods to solve the two-dimensional diffusion equation ⭸C Ž x, y .r⭸t s ⵜŽyDsⵜC . at steady-state using an iterative procedure. C is the local adatom concentration and Ds is the surface diffusivity. Island edges are discretized and represented by a finite number of points. The boundary conditions at island edges correspond to the adatom concentrations given by the Gibbs᎐Thomson relation. At each time step, we solve the steady-state diffusion equation in the region surrounding each island and calculate net diffusive fluxes into or out of

˚2 . from a TiNŽ111. sample with Fig. 2. STM images Ž880 = 680 A ␪ s 0.25 ML during annealing at Ta s 805⬚C for times Ža. ta s 0, Žb. 161 and Žc. 426 min.

terrace diffusion is the rate-limiting step for coarsening and 1 when adatom detachmentrattachment is the rate-limiting mechanism w6x. However, the scaling exponents do not account for the effects of local environment and island size and, therefore, fail to describe the coarsening behavior of small islands in the presence of island fields in a diffusion-limited regime. Fig. 3a shows typical plots of A vs. ta for islands 1᎐4 ŽFig. 1a. on TiNŽ001.. Island 2 decays at a slower rate than 1 Žboth islands on upper terraces . even though 2 is initially smaller than 1. This is due to the fact that 1 is the only island on its terrace while 2 is surrounded by smaller islands 3 and 4 which lose atoms to 2 until they disappear. Thus, the decay of island 2 is delayed, resulting in a crossover of the decay curves for islands 1 and 2. This is the signature of diffusion-limited behavior. In contrast, A vs. ta plots for two-dimensional TiN islands on TiNŽ111. ŽFig. 3b. exhibit a linear decay at a con-

Fig. 3. Island area A vs. ta during annealing of Ža. islands 1, 2, 3, and 4 Žsee Fig. 1a. on TiNŽ001. at Ta s 890⬚C and Žb. islands 6, 7, and 8 ŽFig. 2a. on TiNŽ111. at Ta s 805⬚C.

S. Kodambaka et al. r Thin Solid Films 392 (2001) 164᎐168

each island edge. The corresponding island size is increased or reduced by moving its boundaries normal to the direction of the flux. ␥ and the product C⬁ Ds , the only unknown parameters in the calculation, were determined by fitting experimental results for samples at seven different annealing temperatures. ␥ defines the shape of the decay curves and the product C⬁ DsŽTa . determines the time over which an island decays. Detachment-limited island decay rates on TiNŽ111. are described by the relationship d Ardt A 2 ␲ rK d Ž Cr y C R ., where K d ŽTa . is the rate of attachmentrdetachment and C R the equilibrium adatom concentration at a distance R from the island w6x. Cr and C R , given by the Gibbs᎐Thomson equation, are expanded to the first two linear terms and we take R 4 r such that C R , C⬁ . We obtain decay rates d Ardt A C⬁ K d which were determined by least-square analyses of the experimental data, including that shown in Fig. 3b, as a function of Ta . Figs. 4a and c are typically measured and calculated A vs. ta results on TiNŽ001. and TiNŽ111. surfaces, respectively. All TiNŽ001. island decay curves were equally well fit with a line tension ␥ s 0.23" 0.05 ˚ Values obtained for the product C⬁ Ds are ploteVrA.

167

ted vs. Ta for islands on TiNŽ001. terraces and in vacancy pits in Fig. 4b. From least squares analyses, the activation energy Eas,t for decay of islands on TiNŽ001. terraces is 3.6" 0.3 eV with a pre-factor of 10 12.5 " 1.5 sy1 while for islands in pits Eas,p is 3.4" 0.3 eV with a pre-factor of 10 12 " 1.5 sy1 . From d Ardt vs. Ta data in Fig. 4d, we obtain the activation energy for adatom formation and attachmentrdetachment on TiNŽ111., Ead s 3.5" 0.3 eV. Fig. 5 is a schematic diagram of the surface activation barriers near a step edge. In the diffusion-limited regime, Eas , Ef q Es , while in the adatom attachmentrdetachment-limited regime, Ead s E f q Es q Ed . Ed is the barrier for adatom attachmentrdetachment, Ef is the adatom formation energy and Es is the adatom surface diffusion barrier. There are few results in the literature for ␥, Eas and ˚ for Ead . ␥ has recently been reported to be 0.07 eVrA two-dimensional islands on AgŽ111. w7x and 0.12 w8x and ˚ w9x on CuŽ111.. ␥ is higher for TiN than for 0.06 eVrA metals due to the mixture of strong covalent and ionic bonds in the nitride. Similarly, Eas for TiNŽ001. is larger than corresponding values on metals, 0.71 eV on AgŽ111. w10x and 0.78 eV on CuŽ111. w11x. Ead for CuŽ001. is 0.78 eV w12x, while values of 1.4᎐1.7 eV have

Fig. 4. Typical experimentally measured and calculated island areas A vs. ta for Ža. the TiNŽ001. island labeled 1 in Fig. 1a, and Žb. a TiNŽ111. island at Ta s 905⬚C. Žc. C⬁ Ds obtained from fitting the decay rates of single TiN islands on atomically-smooth TiNŽ001. terraces ŽI. and in vacancy pits Ž ⌬ . vs. Ta . Žd. d Ardt vs. Ta for TiNŽ111. islands.

168

S. Kodambaka et al. r Thin Solid Films 392 (2001) 164᎐168

formation and attachmentrdetachment on TiNŽ111. is 3.5" 0.3 eV. These results provide important insights for understanding and modeling microstructural evolution and preferred orientation in TiN polycrystalline films. Acknowledgements The authors gratefully acknowledge the financial support of the NSFrDARPA VIP Program and the US Department of Energy under contract DEFG0296ER45439. Fig. 5. Schematic diagram of surface activation barriers near an island step edge. Es is the surface diffusion barrier, Ed is the attachmentrdetachment barrier, Ef is the adatom formation energy and E b is the Ehrlich barrier.

been reported for SiŽ001. w13x. Given the fact that the melting point, a measure of the bonding and cohesive energy in a solid, of TiN is more than a factor of 2 higher than for Cu and Si, our values of Eas s 3.4 eV for TiNŽ001. and Ead s 3.5 eV for TiNŽ111. are reasonable. The Ehrlich barrier E b for adatom transport over step edges corresponds to the difference in Eas values for islands on a terrace and in a vacancy pit. Our results in Fig. 4c show that E b for TiNŽ001. is less than the experimental uncertainty in Eas,t and Eas,p . 4. Conclusions TiN island coarsening and decay kinetics on TiNŽ001. and TiNŽ111. were determined using in-situ high-temperature STM. The rate-limiting step for island decay is adatom diffusion on TiN Ž 001 . and adatom attachmentrdetachment on TiNŽ111.. The island line ˚ and the actitension on TiNŽ001. is 0.23" 0.05 eVrA vation energy for adatom formation and surface diffusion is 3.4" 0.3 eV. The activation energy for adatom

References w1x Ža. J.E. Greene, J.-E. Sundgren, L. Hultman, I. Petrov, D.B. Bergstrom, Appl. Phys. Lett. 67 Ž1995. 2928.; Žb. L. Hultman, J.-E. Sundgren, J.E. Greene, D.B. Bergstrom, I. Petrov, J. Appl. Phys. 78 Ž1995. 5395. w2x L. Hultman, J.-E. Sundgren, J.E. Greene, J. Appl. Phys. 66 Ž1989. 536. w3x I. Petrov, F. Adibi, J.E. Greene, W.D. Sproul, W.-D. Munz, ¨ J. Vac. Sci. Technol. A 10 Ž1992. 3283. w4x Image SXM, developed by Prof. Steve Barrett, Liverpool, UK ŽŽhttp:rrreg.ssci.liv.ac.uk... w5x Ža. I.M. Lifshitz, V.V. Slyozov, J. Phys. Chem. Solids 19 Ž1961. 35.; Žb. C. Wagner, Z. Elektrochem. 65 Ž1961. 581. w6x J.G. McLean, B. Krishnamachari, D.R. Peale, E. Chason, J.P. Sethna, B.H. Cooper, Phys. Rev. B 55 Ž1997. 1811. w7x K. Morgenstern, G. Rosenfeld, G. Comsa, Phys. Rev. Lett. 76 Ž1996. 2113. w8x G. Schulze Icking-Konert, M. Geisen, H. Ibach, Surf. Sci. 398 Ž1998. 37. w9x D.C. Schlosser, L.K. Verheij, G. Rosenfeld, G. Comsa, Phys. ¨ Rev. Lett. 82 Ž1999. 3843. w10x K. Morgenstern, G. Rosenfeld, E. Lægsgaard, F. Besenbacher, G. Comsa, Phys. Rev. Lett. 80 Ž1998. 556. w11x M. Geisen, H. Ibach, Surf. Sci. 431 Ž1999. 109. w12x C. Klunker, J.B. Hannon, M. Giesen, H. Ibach, G. Boisvert, L.J. Lewis, Phys. Rev B 58 Ž1998. R7556. w13x N.C. Bartelt, W. Theis, R.M. Tromp, Phys. Rev B 54 Ž1996. 11741.