Stress Analysis of Tungsten Deposition in a 3D Trench Mold With Regard to Initial Nuclei Shape

Tungsten has been commonly used for fine interconnects due to its good gap-filling characteristics in 3D molds, such as trench patterns. However, tungsten shows high deposition stress. This causes mold distortion because tungsten has low ad-atom mobility, and diffusion-driven relaxation does not occur. To reduce tungsten’s deposition stress, the shape of the nuclei can be controlled, which is an effective way to suppress the mechanical deformation caused by the formation of a grain boundary between free surfaces during the coalescence stage. In this study, elliptical tungsten nuclei with various aspect ratios, which suppress coalescence in the early stage of deposition, were proposed to reduce the deposition stress. Stress was calculated using the finite element method (FEM) in the range of 0.5 to 8 radius ratios of the tungsten nuclei. The bending of the trench mold was calculated due to tungsten stress and additional coalescence between films during the filling process. As a result, the wider the elliptical nucleus was, the lower the film stress, and mold bending between line patterns was also reduced. The defects in the depth and width of the periodic trench influenced the mold bending in the early growth stage and the stage of coalescence between films, respectively.

shows good gap-filling characteristics due to its high step 23 coverage obtained through chemical vapor deposition; thus, 24 it has been used to fill the inside of a deep mold and make 25 vertical structures with high aspect ratios, such as via and plug 26 structures [4], [5], [6], [7]. Tungsten is commonly used as an 27 interconnection metal for highly integrated patterns due to its 28 The associate editor coordinating the review of this manuscript and approving it for publication was Wen-Sheng Zhao . advantage of being able to fill the inside of a deep trench mold 29 with a narrow width and pitch. 30 However, when tungsten is used to fill a 3D trench mold 31 with a high aspect ratio and narrow pitch, distortion, such as 32 the bending of the mold, occurs by deposition stress in the 33 metal thin films [8], [9], [10]. Fig. 1 the bending of the vertical mold, which separates the line 47 patterns in Fig. 1 under the low-temperature deposition of tungsten [21], [23].

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Therefore, stress control in the early stage, such as the metal 78 nucleation stage, is more important to reduce the deposition 79 stress than in the case of high ad-atom mobility metals.

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Our study proposes a method for calculating deposition 81 stress considering the continuous stress evolution (intergran-82 ular coalescence) and additional stress evolution of a 3D 83 structure (interfilm coalescence). The initial shape of the 84 tungsten nuclei was controlled to suppress zipping deforma-85 tion and reduce the stress of the tungsten film in the inter-86 granular coalescence stage. The zipping phenomenon was 87 simulated and analyzed using finite element (FE) simulation, 88 and the stress depending on the nuclei shape was calculated 89 during the growth of the tungsten film. Based on the film 90 stress, the mold bending of the vertical mold was calculated 91 by a 2D cross-sectional model of a deep trench. In addi-92 tion, the mold bending resulting from interfilm coalescence 93 between the films on the walls in the middle of the trench was 94 analyzed.

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Finite element (FE) simulation was conducted using a 97 static implicit solver, ABAQUS/Standard (Dassault System, 98 France), which has advantages for structural analysis with 99 solid-solid contacts under nonlinear deformation. All simula-100 tions were performed in 2D models with plane strain elements 101 (CPE4 in ABAQUS), which is a 2D-type element that is used 102 in cross-sections in thick structures and is assumed to have 103 zero strain in the thickness direction [24]. The material prop-104 erties of tungsten were assumed to exhibit linear isotropic 105 elasticity with a Young's modulus of 300 GPa and Poisson's 106 ratio of 0.28 [25]. The height of the tungsten nucleus is 107 t i = 30 Å, and the radius of the width, r, is 15∼240 Å, 108 as shown in Fig. 2(a). The mechanical properties of the Si 109 trench mold were also considered to exhibit linear isotropic 110 elasticity with a Young's modulus and Poisson's ratio of 111 127 GPa and 0.278, respectively [26]. Two cases of mold 112 pattern defects with depth and width differences from the 113 ideal pattern are presented to calculate mold bending from 114 the asymmetric bending moment in Fig. 2(b). There are two 115 major stress generation stage analysis models: intergranular 116 coalescence and interfilm coalescence, and the nuclei and 117 film on mold models shown in Fig. 2(a) and (b) were used, 118 respectively. The stress calculation proceeded in the order of 119 the flow chart of Fig. 3(c). Stress calculation was conducted 120 by an elastic model under static conditions, the boundary 121 condition between the nucleus and the mold at the bottom 122 of the mold was pinned, and an x-axis symmetric boundary 123 condition was given to both sides of the model for periodic 124 planes. Then, the zipping analysis was performed by applying 125 the boundary condition of the force that the metal surfaces 126 feature traction toward each other. The strain energy and 127 zipping distance (z 0 ) were calculated by applying a surface 128 traction from 0 to 20 GPa on the surface of the nucleus, 129 depending on the width-to-height ratios of the nuclei island 130 (r/t i ). The energy change from zipping was calculated by 131 equation (1), which considers decreasing free surface energy 132 and increasing grain boundary energy due to the zipping 133 FIGURE 2. (a) Schematic of the model used to calculate film stress in intergranular coalescence caused by contact between metal nuclei, depending on the ratio of width-to-height (r/t i ) of nuclei. Surface traction on the nuclei surface was applied to calculate the average stress and strain energy due to intergranular coalescence. (b) Schematic of the trench mold used to calculate mold bending due to interfilm coalescence during the trench filling process. Mold bending was calculated under two cases of pattern defect: depth difference and width difference. (c) The flow chart of the simulation procedure of intergranular coalescence (blue box) and interfilm coalescence (red box), respectively. (d) Schematic image of the simulation model of intergranular coalescence between tungsten islands during film growth and (e) the simulation model for interfilm coalescence occurring in the center of the trench mold to form a line pattern. Both models were deformed by surface traction to calculate film stress and mold bending.

process [17]
: where γ gb is the grain boundary energy and γ s is the surface  schematic procedure for the calculation of stress during film 150 growth is shown in Fig. 2 where P is the internal pressure, f is the surface tension, A 156 is the surface area of the nucleus, and V is the volume of the 157 nucleus.

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The zipping between the tops of the films was also ana-159 lyzed, and the average stress in the horizontal and vertical 160 directions inside the film was calculated, as shown Fig. 2(d). 161 Surface traction was applied to the surface of the film, and 162 strain energies due to deformation and z 0 , which formed as a 163 grain boundary, were calculated. The average stress was also 164 calculated at the state when the balance between the strain 165 energy and the energy reduced by grain boundary formation 166 was lowest. To quantify the bending of the trench mold due to 167 geometrical defects, mold bending was defined in this study 168 by measuring the displacement of the tip of the vertical mold 169 between the trenches during the growth of the tungsten film 170 on each wall until the pattern was closed.

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Intergranular zipping simulations for molybdenum and 172 ruthenium, which have the same growth mechanism as tung-173 sten, were performed. The stress depending on the nuclei 174 shape was calculated by applying the mechanical proper-175 ties of molybdenum and ruthenium. The Young's moduli of 176 molybdenum and ruthenium were 324 GPa and 414 GPa, 177 respectively, and Poisson's ratios were 0.29 and 0.25, respec-178 tively [30]. The surface energies of molybdenum and ruthe-179 nium were 2.05 J/m 2 and 3.08 J/m 2 , and the grain boundary 180 energy was 0.61 J/m 2 and 1.12 J/m 2 , respectively [27], [31], 181 [32]. (normalized) zipping distance and the (normalized) average 185 nuclei stress, which show the nuclei shape effect on inter-186 granular coalescence at initial contact. The zipping distance 187 and average stress decrease as the ratio r/t i increases, which 188 corresponds to the increased principal axis of the elliptical 189 shape of the nuclei along the horizontal direction. A wide 190 elliptical nucleus can be formed in the horizontal direction 191 instead of a spherical one by controlling the nucleation of 192 the metal nucleus [33], [34]. This leads to reduced stress in 193 the nuclei and substrate distortion by the suppressed zipping. 194 When the r/t i ratio increases above 5, zipping becomes neg-195 ligible, and stress is not generated. This is because the strain 196 energy due to deformation increases significantly, while the 197 reduced energy due to grain boundary formation decreases 198 as the nucleus becomes wider elliptically. Note that the first 199 and second contributions correspond to a counter force of 200 the zipping phenomenon and a driving force of the zipping 201 phenomenon, respectively. Therefore, zipping is suppressed 202 as the nuclei converge to an ellipse with a wider shape, and 203 the shape factor with a r/t i above 5 can be regarded as the 204 critical ratio.  mold geometry, respectively. The two figures show that the 235 distortion of the vertical mold represents either a gradual 236 (Fig. 5(a)) or constant ( Fig. 5(b)) increase before the tungsten 237 film begins zipping at the center of the trench mold (or film 238 thickness of approximately 12.5 nm). In both cases 1 and 2, 239 the mold bending resulting from the interfilm coalescence is 240 larger than that resulting from the intergranular coalescence. 241 This can be explained by the fact that a larger free surface can 242 be reduced by mold bending through interfilm coalescence. 243 In the stage of intergranular coalescence, a different trend 244 of mold bending was observed for the two defect patterns. 245 When the mold has a depth difference (case 1), the mold 246 is continuously bent as the film stress increases, while the 247 bending of the mold with a width difference is nearly inde-248 pendent of the film growth. The main factor in mold bending 249 by intergranular coalescence is the difference in the bending 250 moment produced by the thin film stress on both walls of 251 the mold. When there is a difference in depth in the trench 252 mold, the areas of tungsten film covering the mold walls are 253 different, which results in the difference in depth. Therefore, 254 this unbalanced film growth (equivalently asymmetric stress 255 distribution on each wall) causes additional bending. On the 256 other hand, when two thin films contact the center of the 257 trench by zipping, abrupt changes in the model bending occur 258 for the case of mold width difference (Fig. 5(b)). When the 259 mold is already bent, it is easier to form an additional inter-260 face, which appears to induce more mold bending. Fig. 5(c) 261 shows the mold bending assuming both defects (depth and 262 width) exist. In this case, the mold bending by the depth 263 difference becomes more dominant during film growth on the 264 wall, but the bending by the width difference increases after 265 the films contact the center of the mold.

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In addition, the cross-sectional area of the metal intercon-267 nects was calculated to determine the electrical resistance. 268 The pattern defect with a depth difference of 10 nm and a 269 width difference of 1.5 nm decreases the cross-sectional area 270 of the metal line compared to a symmetric trench without a 271 pattern defect. If there is no stress on the film and no bending 272 FIGURE 5. Simulation results for mold bending by the pattern defects of two cases, i.e., the results of the mold bending of an Si mold due to film stress and interfilm coalescence. An asymmetric structure was used to calculate mold bending due to patterning error or other defects: (a) depth difference, (b) width difference and (c) both differences.   When the grain boundary formed due to zipping, the energy 294 reduction of molybdenum was smaller than that of tungsten 295 because of its low surface energy. On the other hand, the 296 driving force of zipping is stronger in the ruthenium case, 297 and the zipping distance and stress increased. Furthermore, 298 higher stress is also generated because of the higher Young's 299 modulus of ruthenium, and the critical ratio of r/t i where 300 zipping does not occur increased from 5 to 6, confirming that 301 wider nuclei are needed to minimize stress in ruthenium.

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Our stress calculation model has a limitation attributed to 303 the assumptions made in the finite element analysis. First, 304 in the finite element simulation, the materials are all con-305 sidered continuum bodies, and the interactions of the surface 306 atoms during the zipping process are simplified as tied bound-307 ary conditions. Additionally, the anisotropy of the tungsten 308 film is not considered, although crystalline solids such as 309 tungsten have strong anisotropy at the grain scale. Therefore, 310 more accurate analysis can be achieved if these simplify-311 ing assumptions are removed by introducing atomic level 312 computations, such as density functional theory or molecular 313 dynamics, for the calculation of zipping stress by interatomic 314 interactions. Furthermore, for the stress calculation in the 315 case of a hole-type structure such as deep via and plug, all 316 three-dimensional zipping between the thin films growing on 317 all sidewalls should be calculated, and a 3D model is needed. 318

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Tungsten exhibits higher stress than conventional intercon-320 nection metals when it is used as a gap filler by chemical 321 vapor deposition. High deposition stress by zipping results in 322 severe distortion of the thin vertical mold, which is designed 323 to fabricate interconnects with fine pitch. Our study based 324 on the shape optimization of tungsten nuclei through finite 325 element simulation proposes elliptical nucleation with high 326 width, which is intended to relax the zipping stress during 327 growth on the trench mold. In the simulation, two sources 328 of vertical mold distortion were investigated: the film stress 329 induced by zipping between the two neighboring nuclei and 330 the secondary zipping stress resulting from the coalescence 331   In 1997, he completed his postdoctoral research 511 with the Max-Planck-Institut für Metallforschung, 512 Stuttgart, Germany. In 1999, he was with 513 Advanced Micro Devices Inc., Sunnyvale, CA, 514 USA. Since 1999, he has been with the Department of Materials Science and 515 Engineering, Seoul National University, as a Professor. His research interests 516 include the reliability and development of next-generation electronic mate-517 rials and devices. 518 519 VOLUME 10, 2022