Molecular dynamics simulation of copper reflow in the damascene process

Transcription

1 Molecular dynamics simulation of copper reflow in the damascene process Ming-Horng Su a) Department of Mechanical Engineering, Wu Feng Institute of Technology, Chiayi, Taiwan, Republic of China Chi-Chuan Hwang b) Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan 701, Republic of China Jee-Gong Chang c) National Center for High-Performance Computing, Hsinchu, Taiwan 30077, Republic of China Shin-Pon Ju Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 701, Republic of China Received 24 October 2001; accepted 24 June 2002 This article presents a molecular dynamics simulation of the copper reflow process for the recently developed damascene process, in which copper replaces aluminum as the interconnect material. A deposition simulation is performed, and one of the results from this simulation, namely a morphology with a void defect within the filling trench, is used as the initial morphology for the annealing process. The influence of variations in the annealing process parameters on void filling within the trench and on the copper microstructure is investigated. The article establishes a three-dimensional trench model and also provides deposition and reflow models. The annealing procedure is modeled by employing the Langevin technique to simulate heating and cooling of the thermal layer located beneath the Ti barrier layer which covers the trench. The many-body, tight-binding potential model is adopted to simulate the interatomic force between atoms. The results of this study indicate that the duration for which a constant annealing temperature is maintained plays an important role in determining the success of the reflow process. A short duration fails to produce motion of the atoms located in the trench above the void, and this motionless region of atoms prevents atoms from flowing into the trench to fill the void. The motion trace of trench atoms during the reflow process shows that circular motion is evident in the atoms that are located in the region surrounding the void, while atoms in the region above the void migrate for a long distance in the direction of the void. Finally, it is determined that a longer heating duration is beneficial in improving the microstructure of the interconnects American Vacuum Society. DOI: / I. INTRODUCTION The damascene process is a metallization technique that uses copper in place of aluminum as the interconnect material. The technique involves the filling of multiple-layer interconnects, such as vias, contact, and trenches, which are etched into the dielectric interlayer. As the device density increases, so it becomes necessary to increase the interconnects aspect ratio of depth to width in order to meet highspeed requirements. 1 Furthermore, the manufacturing difficulties encountered in filling these high aspect ratio trenches also increase. It is found that void defects are readily formed within the trench during the deposition process, and so a copper reflow process is subsequently utilized to alleviate these defects once the deposition process is complete. Copper reflow is achieved by using an annealing procedure, in which the copper atoms within the trench are heated and then a Electronic mail: mhsu@sun5l.wfc.edu.tw b Author to whom correspondence should be addressed; electronic mail: chchwang@mail.ncku.edu.tw c Electronic mail: n00cjg00@nchc.gov.tw subsequently cooled. This process promotes motion of the copper atoms which, in turn, leads to a filling of the void defect. The copper reflow process not only serves as a means of producing void free interconnects, but is also an effective way of improving the microstructure of the interconnects. A detailed insight into the filling mechanism involved in the reflow process, and the relationship of the interconnect microstructure to the annealing parameters is required if the damascene process is to be fully understood. Due to the very small scale of the features involved, it is difficult to observe, and therefore to understand fully, the reflow morphology at a transient state from physical experimentation. However, several experiments have been conducted to observe grain growth and residual stress during the reflow process, 2 and to observe the final morphology for different annealing temperatures by using the electron cyclotron resonance plasma sputtering method. 3 Furthermore, numerical methods have been developed to assist in understanding the reflow mechanisms. These methods include continuumbased methods, 4 6 particle-based methods; molecular dynamic MD simulation, 7 and a combined MD and Monte 1853 J. Vac. Sci. Technol. B 20 5, SepÕOct Õ2002Õ20 5 Õ1853Õ13Õ$ American Vacuum Society 1853

2 1854 Su et al.: Molecular dynamics simulation of copper reflow 1854 Carlo MC method. 8 Friedrich and his co-workers 4 6 have developed a continuum-based simulator to study the copper reflow phenomenon which occurs during annealing. In this simulator, a macro model, which uses metal diffusion mechanisms such as volume diffusion, grain boundary diffusion, and surface diffusion, is adopted. These various researches have provided a profound insight into the reflow process, and claim that the initial film profile is one of the most important factors in determining the success of the subsequent reflow process. Most of these research projects have focused on the reflow of the two deposited clusters which overhang the trench opening. To date, the reflow of the deposited film within the trench where void defects are present has not been explored. The MD method describes the nuclear motion of constituent particles which satisfy the laws of classic mechanics at the atomic scale. 9 The superiority of the MD approach becomes apparent as the characteristic size of the system decreases. An analysis of formerly published literature shows that most research studies employed continuum-based methods, and that MD simulation of the reflow process is very scarce. However, as the feature size becomes increasingly smaller, there is undoubtedly a need for atomic simulation of the reflow process if a better insight into the reflow mechanism is to be provided. Saito et al. 7 used MD simulation to analyze the reflow process of a sputtered aluminum Al film. The pairwise, Morse and Lennard-Jones potentials were employed to simulate the atomic force between the aluminum film and the silicon substrate. They found that droplet formation depends strongly on the initial film-thickness distribution, the film temperature, and the bond energy between the film and the substrate. In their analysis, distribution of the sputtered aluminum was assumed to be completed before the start of the reflow process. However, this assumption is at variance with actual practice. Baumann and Gilmer 8 employed combined MC and MD methods to simulate the Al sputtering and reflow process. However, in their work, the hard-sphere model was used to represent a cluster of the deposited material. This model cannot accurately reflect the forces of attraction and repulsion which occur when two atoms are in close proximity to each other. Furthermore, their article did not clearly investigate the reflow mechanisms. Fairly recently, the many-body, tight-binding potential model has been derived, which considers the long-range force acting among atoms. 10,11 In contrast to the pairwise potential model, the many-body potential method considers that the interaction between two atoms depends on the local environment around the atoms as well as just the two atoms themselves. The advantages provided by this method are that the Cauchy discrepancy of the elastic constant is well satisfied, and that the surface relaxation, adatom diffusion can be appropriately modeled. 12,13 It has been proven that this method is the equal of other many-body potential approaches, such as the embedded atom method EAM. In fact, some material properties obtained using this method are superior to those obtained with nonpairwise potential methods. 10 Moreover, its calculation methodology is straightforward. Although this article reports upon the simulation of the deposition process, and provides a brief discussion of the filling mechanism of the deposited atoms, the main objective of this study is to investigate the reflow mechanisms which occur during the annealing procedure. Taking one of the results of the deposition simulation as the initial morphology for the reflow process, this study uses the duration for which a constant annealing temperature is maintained as a variable parameter, and investigates the influence of this parameter on the reflow morphology, the Cu atom coverage percentage, the diffusion ability of the Cu atoms, and finally, on the microstructure of the interconnect material. A three-dimensional model of the trench is established, which comprises the barrier Ti layer and a thermal control layer. The deposition process is a simulation of collimated magnetron sputter deposition, in which the incident atoms are controlled such that they fall within a cutoff angle. 14 The Langevin algorithm is employed to simulate the annealing procedure. Finally, the many-body, tight-binding potentials approach is used to model the interatomic force between atoms. II. SIMULATION MODEL The schematic diagram of the trench used as an interconnect in the damascene process, and the corresponding simplified trench model, are shown in Figs. 1 a and 1 b, respectively. A three-dimensional model is adopted to simulate the deposition and reflow processes. As shown in Fig. 1 b, the trench surface is covered by a Ti barrier film, which is assumed to be flat along the trench boundary. In this study, it is assumed that this film is in place before the deposition process begins. In this way, the influence of low-k dielectric material in the trench material may be neglected in the simulation, i.e., the Ti film thickness is larger than the truncation distance of the interaction between the low-k material and the Cu atoms. The layers below the Ti film are used to control the thermal state of the Ti film. These layers are indicated in Fig. 1 b, and will henceforth be referred to as the thermal layer. The thermal layer is controlled according to the Langevin equation, given as follows: m i v i F i m i i v i R i t, 1 where m i is the atom mass, v i is the atom velocity, i is the damping constant, F is the potential energy, and R(t) is the random force that satisfies the following equation: R i t R j t 2m i i kt 0 ij, 2 where T 0 is the reference temperature of the substrate and is the Kronecker delt symbol. A detailed description of this equation is not presented in this article. However, interested readers are directed to the comprehensive computation of this thermal control algorithm presented in Refs The thermal layer is used to control the thermal energy flow into and out of the trench. The simulation of the com- J. Vac. Sci. Technol. B, Vol. 20, No. 5, SepÕOct 2002

3 1855 Su et al.: Molecular dynamics simulation of copper reflow 1855 TABLE I. Parameters used in a tight-binding potential. Parameters A ev ev P q r 0 Å Cu Cu Ti Ti FIG. 1. a Schematic diagram of trench used in damascene process and b simplified trench model used in MD simulation. plete damascene process comprises two stages, namely the deposition process and the reflow process, which occurs once the deposition process is complete. In the deposition process, the thermal layer is controlled so as to maintain a constant substrate temperature, while in the reflow process, it is used to model the copper annealing procedure. Modeling of the annealing procedures includes the gradual heating of the substrate temperature to the required annealing temperature, maintaining a constant annealing temperature for a predetermined duration, and, finally, a gradual cooling down to the original substrate temperature. Both the Ti film and the thermal layer are arranged according to their hexagonal close-packed hcp structure. The trench constructed by the Ti film together with the thermal layer consists of 1194 atoms. The lowest layer is fixed to prevent the trench atoms from shifting. Periodic boundary conditions are applied in the x, y directions. In the deposition process, the velocity of individually deposited atoms is given by the following expression: V atom 2 E atom M, 3 where E atom represents the incident energy, and M is the atomic mass. In the simulation, the angular distribution of the incident atoms is controlled such that it lies within a cutoff angle. 14 In practice, angular distribution is controllable in several deposition processes, such as collimated magnetron sputter deposition and ionized magnetron sputter deposition. The simulation uses a random distribution function to generate the incident angle and incident position of the deposited atoms. The distance between two subsequently deposited atoms is controlled such that it is larger than their truncated distance. This is to represent the fact that in practice the atoms rarely interact with each other before reaching the substrate due to the distribution of atoms in a vacuum. The many-body potential of the tight-binding second moment approximation TB-SMA model is employed to simulate the interatomic force among atoms. The prediction of some properties by the TB-SMA method is more accurate than when using the EAM method. Furthermore, the computing algorithm used within the TB-SMA method is simpler than the one used by the EAM method. The TB-SMA model commences by summing the band energy, which is characterized by the second moment of the d-band density of state, and a pairwise potential energy of the Born Mayer type, 11 i.e., E i 2 j exp 2q r 1/2 ij r 0 1 j A exp p r ij 1, 4 r 0 where is an effective hopping integral, r ij is the distance between atom i and j, and r 0 is the first-neighbor distance. The parameters A, p, q, and, which are used in the tightbinding potential model, are determined by the experimental data of cohesive energy, lattice parameter, bulk modulus, and two shear elastic constants i.e., C 44 and C (1/2) (C 11 C 12 )], respectively. The tight-binding potential parameters relating to the Cu Cu and Ti Ti interactions simulated in this study are listed in Table I, and are taken from Ref. 10. Parameters describing the interatomic potential of Cu Ti have not previously been published. A method of establishing these parameters, without recourse to rigorous mathematics or theory, is to average the corresponding parameters for the pure interatomic potential relating to Cu Cu and Ti Ti. 23,24 Finally, the interaction force on atom i can be expressed as F i j i E i E j r ij r ij r ij. 5 r ij The simulation uses the Gear s predictor corrector algorithm 25 to calculate the trajectories of atoms in the simulation. JVST B-Microelectronics and Nanometer Structures

4 1856 Su et al.: Molecular dynamics simulation of copper reflow 1856 FIG. 2. Illustration of temperature history and time sequence for deposition and reflow process. III. RESULTS AND DISCUSSION This section comprises two subsections. The first subsection concerns the simulation of the deposition process, and discusses the deposited film morphologies at final steady state for different incident energies. A brief discussion is included on the mechanism of void defect formation at these different incident energies. The second subsection focuses on the alleviation of these void defects by using the copper reflow process, and takes one of the results of the deposition simulation as the initial film morphology prior to annealing. An illustration of the temperature history and time sequence for the complete deposition and reflow process is shown in Fig. 2. It can be seen that the reflow process begins immediately after deposition has been completed. In the deposition process, the substrate is maintained at a constant temperature of 300 K. However, in the reflow process, the substrate temperature undergoes a three-stage change. These changes include a temperature rise at the beginning of the reflow process, referred to as the heating stage hereafter. This is followed by a period in which the temperature of the substrate is maintained at a constant value for a short time duration. This constant heating stage is followed by a cooling stage in which the temperature of the substrate cools back down to its original temperature of 300 K. A. Deposited film morphology The parameters adopted in the deposition simulation include a deposition rate of 5 atoms/ps and a substrate temperature of 300 K. Figures 3 a 3 c show the final deposited morphology for incident energies of 1, 5, and 10 ev, respectively. It will be seen in Figs. 3 a and 3 b that the trench is not completely filled by the deposited atoms. This is particularly true in the case of a relatively low incident energy of 1 ev, as seen in Fig. 3 a where the formation of a void defect within the trench is very evident. As the incident energy increases, the void size decreases, as seen in Fig. 3 b for an incident energy of 5 ev. The void finally disappears, and the trench is completely filled, when the incident energy is increased to 10 ev, as shown in Fig. 3 c. An increased incident energy is beneficial to trench filling since it improves the migration ability of the deposited atoms, and in particular it allows the deposited atoms to migrate along the two trench walls. However, a comparison of Figs. 3 a and 3 c shows that the appearance of Ti atoms represented by black dots within the trench in the figures increases at higher incident energies. This observation may be attributed to the fact that the kinetic energy imparted to the substrate is greater when the incident energy is increased, and this causes some Ti atoms to escape from their equilibrium positions. For low incident energies, the deposited atoms tend to accumulate at the two corners of the trench opening, leading to the formation of an overhanging structure. This structure prevents subsequently deposited atoms from entering the lower part of the trench. The results of this phenomenon are clearly shown in Fig. 3 a. It will be observed that the formation of an overhanging structure has resulted in the bottom corners of the trench being scarcely covered. Although a void is still formed in the trench at an intermediate level of incident energy, 5 ev, its size is far smaller than that formed at the lowest level of incident energy, 1 ev. The void formation mechanism at this intermediate level of incident energy is similar to that for the lowest level of incident energy. However, it will be noted that the kissing point of the two streams of deposited atoms along the two trench walls is lower than in the previous case. The most successful trench filling pattern is one where the deposited atoms progressively fill the trench from bottom to top, and where there is no kissing of the two streams of deposited atoms along the two trench walls before the trench is completely filled. B. Copper reflow process 1. Effect of heating duration The reflow process is modeled by heating the trench temperature to the prescribed annealing temperature, maintaining this temperate for a short period, and then cooling the trench temperature back down to the initial temperature of 300 K. Maintenance of the annealing temperature for a short duration is necessary to ensure sufficient time for the heating energy to diffuse into the atoms within the trench. The degree of heat energy diffused into the trench greatly influences the final filling properties. This article considers the influence of maintaining a constant annealing temperature for different durations on the following issues: atom motion patterns, coverage percentage, diffusion ability mean square displacement MSD, and finally, the microstructure of the interconnect material after annealing. The morphology chosen to be the initial morphology immediately prior to the annealing process is shown in Fig. 3 b, in which a void has been formed within the trench. The parameters adopted in the simulation include a heating rate of 3 K/ps, an annealing temperature of 800 K, and a cooling rate of 1 K/ps. These parameters are used throughout the entire simulation, unless noted otherwise. In order that the reader may better understand which particular stage of the reflow process the morphologies discussed in the subsequent subsections and presented in Figs. 4 6 belong to, Table II provides details of the time duration for each individual stage of the deposition and reflow process for three different constant annealing temperature durations. J. Vac. Sci. Technol. B, Vol. 20, No. 5, SepÕOct 2002

5 1857 Su et al.: Molecular dynamics simulation of copper reflow 1857 FIG. 3. Deposited morphology at final state for incident energy of: a 1eV, b 5 ev, and c 10 ev. JVST B-Microelectronics and Nanometer Structures

6 1858 Su et al.: Molecular dynamics simulation of copper reflow 1858 FIG. 4. Snapshot of reflow morphology for an annealing temperature of 800 K and a constant heating duration of 25 ps at: a 750 ps, b 950 ps, c 1050 ps, and d 1300 ps. It can be seen from the table that the reflow process comprises three distinct stages, namely: heating, constant heating, and cooling. These stages are clearly illustrated in Fig. 2. It is also noted that the beginning of the deposition process is taken as the zero time reference. Therefore, the times given for the various snapshots of morphology all refer to the total time elapsed from the beginning of the deposition process. a. Constant heating at 800 K for 25 ps. Figures 4 a 4 d show four snapshots of the morphology during the reflow process. In this example, the annealing temperature is maintained at an annealing temperature of 800 K for 25 ps. Figure 4 a provides a snapshot of the morphology of the filling atoms at 750 ps which, by reference to the second row Table II, falls within the heating stage of the reflow process. At this time the substrate temperature reaches 780 K. It will be noted that atom motion is commencing in the vicinity of the void, and that the atom arrangement in this area has changed, especially in the region to the right ride of the void close to the trench wall. However, at this instant in time, the rest of the atoms in the trench are in an almost motionless J. Vac. Sci. Technol. B, Vol. 20, No. 5, SepÕOct 2002

7 1859 Su et al.: Molecular dynamics simulation of copper reflow 1859 FIG. 5. Snapshot of reflow morphology for an annealing temperature of 800 K and a constant heating duration of 50 ps at: a 790 ps, b 840 ps, c 900 ps, d 1000 ps, and e 1300 ps. state. This indicates that sufficient time is necessary to allow thermal energy to be transferred into the trench. Figure 4 b shows the morphology at 950 ps, i.e., during the cooling stage of the reflow process. In this stage of the process the speed of the atom motion is gradually reducing. It can be seen that the original void space has now been completely occupied by the atoms, which have become excited by the thermal energy, and which are in a state of motion. The freer motion of the atoms is indicated by the fact that the relative distance between atoms in the lower portion of the trench and above the trench opening is larger than when in the equilibrium state. Figure 4 c shows the trench morphology at 1050 ps, i.e., still in the cooling stage, when the trench temperature has cooled to 500 K. Several voids, their perimeter indicated by blue circles, may be seen in this figure. Figure 4 d shows the morphology at almost the final steady state. Two larger voids are evident in the trench, as indicated by the blue dots. It is to be noted that the color of the individual atoms represents its coordination number, as indicated by the legend located to the right of the figure. The coordination number represents the number of atoms immediately adjacent to a reference atom. For a perfect fcc crystal structure, the coordination number is 12. Therefore, a coordination number less than 12 implies that the structure is imper- JVST B-Microelectronics and Nanometer Structures

8 1860 Su et al.: Molecular dynamics simulation of copper reflow 1860 fect. The deviation of each atom from the perfect fcc crystal coordination number of 12 is usually referred to as its miscoordination. The issue of miscoordination of the trench atoms will be discussed later. b. Constant heating at 800 K for 50 ps. Figures 5 a 5 e show five snapshots of the morphology during the reflow process with a constant annealing temperature maintained for 50 ps. Figure 5 a, showing a snapshot at 790 ps, i.e., in the constant heating stage, indicates a freer motion of the atoms around the void, while the remaining atoms in the trench are in an almost motionless state. At 840 ps, i.e., at the beginning of the cooling stage, the moving atoms have occupied the former void. In Fig. 5 b, it may be seen that in addition to atom motion occurring around the void, the atoms located above the trench opening are also excited by the thermal energy and are undergoing a more violent motion than those in the void region. A close observation of the morphology of this snapshot reveals that the atoms in the region below the trench opening have not been excited sufficiently to cause motion. However, as further time elapses, it will be noted that atoms in the center of this motionless region begin to move, as shown in Fig. 5 c, which provides a snapshot at 900 ps, i.e., during the cooling stage at cooling stage. The momentum of the atoms located in this area, and in the area above the trench opening begins to cause diffusion of the atoms between these two regions. Meanwhile, the atoms above the trench opening are in a severe state of motion, which causes the formation of a bulgy area in this region. It will be noted that the spatial distribution of the atoms in Fig. 5 c is coarser than the distribution observed in Fig. 5 a. This is due to the volume expansion caused by the thermal energy, which causes the distance between atoms to be larger than when the system is in a state of thermal equilibrium. After the volume expansion reaches its maximum value, the volume begins to contract, as shown in Figs. 5 d and 5 e. Figure 5 e indicates the morphology at the final steady state when the trench temperature has cooled down to 300 K. A close observation of Fig. 5 e shows mismatches occurring in the inner part of the trench and above the trench opening where two adjacent crystals meet with different orientations, i.e., a grain boundary. However, it will be observed that most of the atoms located near the trench wall retain the same arrangement as the originally deposited atoms shown in Fig. 5 a. It can be seen from the above results that atom motion commences in the vicinity of the void and then takes place above the trench opening. The atoms surrounding these two regions are less constrained than those in the bulk. In other words, the diffusion mechanism occurs at the surface rather than in the bulk. The result obtained here is consistent with that obtained from the macroscopic viewpoint, 5 which claimed that surface diffusion is dominant for trench filling during a reflow process. c. Constant heating at 800 K for 100 ps. Figures 6 a 6 d show four snapshots of the morphology during the reflow process with a constant annealing temperature maintained for 100 ps. Similar to the results presented in Fig. 5, it can be seen that motion of the atoms commences in the region around the voids, and then begins to take place in the region above the trench opening, as shown in Fig. 6 a. The longer heating duration results in more atoms becoming excited to the point of motion, as seen in Fig. 6 b. Heating duration is a critical factor in the reflow process, since if it is longer, the atoms located at both the trench opening and the inner trench receive sufficient thermal energy to cause motion. This is beneficial since it allows the atoms which are located at the trench opening to flow into the inner trench to fill the void. Recalling the result of Fig. 4 c, it was found that a heating duration of 25 ps was insufficient to cause motion of all of the atoms within the trench. Close observation of Figs. 4 a 4 d reveals a region of atoms located a little below the trench opening where the atoms are motionless. This region acts as a barrier, which hinders the atoms in the region above the opening from migrating down into the trench to fill the void. Therefore, as may be seen in Figs. 4 c and 4 d the voids remain within the trench in the final steady state condition. 2. Motion pattern Figures 7 a and 7 b present a motion trace of trench atoms at different locations during the reflow process for a typical heating duration of 25 ps. These locations are labeled using Roman numerals in the figure. Figure 7 a presents a global view of motion within the complete trench, while Fig. 7 b gives a magnified view of atom activity in the void region. An atom s trajectory is obtained by connecting the x, y, and z coordinates of that atom over a determined time period. In order to distinguish the atom s trajectory sequentially in time, the trajectory is labeled by Arabic numerals. In Fig. 7 a only the start and end points of the trajectory are indicated, i.e., by 1 and 2, respectively. However, in the magnified view provided in Fig. 7 b, intermediate points in the atom s trajectory are also marked. Note that the sequential trajectories of atoms in locations iv, v, vi, and vii are not indicated since the motion in these locations takes place within a very small area. In addition, in order to show the geometrical relationship of the atoms being traced, the perimeter of the void at the beginning of the reflow process is indicated by the open circles in both figures. In Fig. 7 a, it can be observed that the atoms located above the trench opening, indicated by i and ii in the figure, have migrated a long distance toward the trench opening. The initial upward motion, followed by a downward motion, indicates that the atoms undergo a thermal expansion and contraction process. The atoms located within the upper part of the trench, indicated by iii, undergo a similar motion pattern. It is interesting to note that the atoms located near the trench wall, indicated by iv and v, remain virtually unmoved from their equilibrium position despite the fact that they are very close to the heating source. This may be explained by the fact that their motion is constrained by the atoms within the trench which are not in the vicinity of the void, and which are therefore not in a state of free motion. J. Vac. Sci. Technol. B, Vol. 20, No. 5, SepÕOct 2002

9 1861 Su et al.: Molecular dynamics simulation of copper reflow 1861 FIG. 6. Snapshot of reflow morphology for an annealing temperature of 800 K and a constant heating duration of 100 ps at: a 850 ps, b 1000 ps, c 1200 ps, and d 1400 ps. Figure 7 b indicates the motion trace of atoms located exactly at the void position, indicated by ix and x, and also atoms located slightly above and below the void, indicated by viii and xi, respectively. It can be observed that although the degree of constraint imposed on atoms in the void position is the smallest of all atoms within the trench, the migration of these atoms is actually the smallest, and in fact migration takes place only within the void. Comparison of the migration distance of atoms located at ix and x Fig. 6 b with those located at iii Fig. 7 a reveals the difference in migration distance of atoms in these two locations. In addition, it should be noted that the motion pattern of atoms located at the void is slightly different from those atoms which are located far from the void. The motion trace of atoms located at the void tends to be circular, as indicated in ix and x. The exact pattern of the motion within the void depends on the void shape, since atom motion is constrained by the void boundaries. As may be seen in iii, atom motion at locations above the void tends toward the direction of the void, indicating that atoms migrate downward to fill the void. Motion of atoms initially located below the void, indicated by xi, may be described as follows: the atoms JVST B-Microelectronics and Nanometer Structures

10 1862 Su et al.: Molecular dynamics simulation of copper reflow 1862 TABLE II. Details of time duration for each individual stage of the deposition and reflow process for three different annealing cases. Reflow process Annealing cases Deposition process constant temperature of 300 K Heating 3 K/ps Constant heating 800 K Cooling 1 K/ps End of reflow process constant temperature of 300 K Constant heating for 25 ps Fig. 4 Constant heating for 50 ps Fig. 5 Constant heating for 100 ps Fig ps ps ps ps 1312 ps ps ps ps ps 1337 ps ps ps ps ps 1387 ps first move upward in the direction of the void and then migrate in a downward direction. After having completed several circular motions the atoms finally return to a position that is very close to their original position. Referring to Fig. 7 a, it can be seen that atoms located beneath and distant from the void, vi and vii, experience migration that is less than those atoms located at the void position and those atoms which are located above the void iii. The motion degree of the trench atoms can be summarized as follows: typically greatest motion of the atoms occurs in a position located directly above the trapped void, followed by the motion of atoms which are located exactly at the void position. Of the remaining atoms, it is noted that the motion of atoms located beneath the void is greater than those located in the vicinity of the trench walls, whose positions scarcely move from the original equilibrium position. 3. Coverage percentage comparison Figure 8 shows the coverage percentage for the annealing process where the annealing temperature of 800 K is maintained for a heating time of 25, 50, and 100 ps. Figure 8 also shows the heating and cooling history of the substrate in the case where a constant temperature of 800 K is maintained for 25 ps. Ideal coverage is defined as the situation when the deposited atoms completely fill the trench, and the number of atoms required to do so is equal to the total number of atoms that would be required if the trench were to be filled with Ti atoms arranged according to their hcp structure. Figure 8 presents the coverage percentage for two major processes, namely the deposition process and the reflow process. During deposition, the coverage percentage continually increases as the deposited atoms gradually fill the trench. A saturation value is finally reached when deposited atoms are no longer able to enter the trench. At the beginning of the reflow process, the coverage percentage remains virtually unchanged while the temperature of the substrate is heated to the annealing temperature of 800 K, and while this temperature is maintained for the determined duration. It will be noted that there is a decrease in the coverage percentage during the cooling stage in the cases where a constant annealing temperature has been maintained for 50 and 100 ps. The decrease of the coverage percentage indicates a fall in the number of atoms within the trench. This is due to the fact that the atoms within the trench undergo an expansion process as a result of the heat energy transferred during the annealing stage. This phenomenon is clearly visible in Figs. 5 c and 6 b. It will also be observed from Fig. 8 that the decrease in coverage percentage is greater for the longer heating duration than for the shorter duration since a longer heating duration causes a greater thermal excitation of the atoms, and therefore a greater expansion of the atoms. Conversely the shorter heating duration of 25 ps results in a less significant decrease in the coverage percentage. 4. Mean square displacement comparison Figure 9 shows the MSD for the annealing process where the annealing temperature of 800 K is maintained for a heating time of 25, 50, and 100 ps. Figure 9 also shows the heating and cooling history of the substrate in the case where a constant temperature of 800 K is maintained for 25 ps. The value of the MSD is used to quantify the diffusion ability of the trench atoms during the annealing process, and its slope is taken to quantify the diffusion coefficient of the trench atoms. The MSD is calculated by the equation n MSD d i t d i 0 2 /n, i 1 where d i is the displacement vector of the atom i and n is the total number of Cu atoms in the trench. A comparison of the MSD for different heating durations shows that both the slope and the magnitude of the MSD increase as the heating duration increases. This indicates that the diffusion ability of the atoms improves as the heating duration increases. It will be observed in Fig. 8 that the trench atoms remain in a motionless state, and that the MSD value therefore remains unchanged with a value of zero, as the substrate is gradually heated up. This may be partly explained by the fact that the transfer of thermal energy into the inner trench atoms necessarily requires a little time. However, there is a second factor to be considered, namely the magnitude of the annealing temperature which will energize the Cu trench atoms into a flow state. In order to verify this issue, Fig. 9 plots the MSD for an annealing temperature of 700 K and a heating duration of 250 ps for comparison purposes. The results indicate that the annealing temperature does indeed have a significant influence on the diffusion behavior, and it will be J. Vac. Sci. Technol. B, Vol. 20, No. 5, SepÕOct 2002

11 1863 Su et al.: Molecular dynamics simulation of copper reflow 1863 FIG. 8. Coverage percentage comparison for constant heating durations of 25, 50, and 100 ps. cause activation of the Cu atoms. Former literature has reported the adoption of an annealing temperature of 723 K 450 C. 5 The simulation results presented in this article indicate that the diffusion ability of atoms is poor when the annealing temperature is lower than 723 K 450 C, compared to annealing temperatures in excess of this value. This result demonstrates the validity of the present simulation. 5. Annealing microstructure The main goal of the reflow process is to alleviate, if not to remove, the void defects formed during the deposition process. The success of the reflow process depends upon controlling the annealing parameters, such as heating duration and annealing temperature. As has been mentioned pre- FIG. 7. Motion trace of trench atoms during reflow process: a global view and b magnified view of void vicinity. seen that the MSD for an annealing temperature of 700 K is far less than in the case of an annealing temperature of 800 K, despite the fact that the heating duration is 250 ps for the lower annealing temperature. Considering once again the situation where the MSD remains at zero during the gradual heating of the substrate, it is likely that this is due to the fact that the temperature is below the threshold value which will FIG. 9. Mean square displacement vs time for different constant heating durations and annealing temperatures. JVST B-Microelectronics and Nanometer Structures

12 1864 Su et al.: Molecular dynamics simulation of copper reflow 1864 viously, the void is successfully filled when the heating duration is longer than 25 ps. However, complete filling of the trench by the Cu atoms is not the only criterion by which the success, or otherwise, of the reflow process should be measured. As is well known, the annealing process has a great influence on the final microstructure of the interconnects in the trench. In determining the success of the annealing process, the structure of the interconnects should also be considered. This issue is now discussed in a little more detail. Figure 10 shows the miscoordination number of the trench atoms after annealing for the three different heating durations. The miscoordination number represents the deviation number of each atom from the perfect crystal coordination of 12 for fcc atomic structures, and therefore can be used to characterize the quality of the annealing microstructure. The coordination distribution of the trench atoms is also provided in Figs. 4 d, 5 e, and 6 d, which show the morphology of the trench atoms after completion of the annealing process for different heating durations. Figure 10 indicates that the annealing microstructure is improved by prolonging the heating duration, i.e., the number of atoms within the trench with a larger miscoordination number is reduced. A detailed observation of the figure reveals that the number of atoms with a miscoordination number in excess of 2 is less for an annealing time of 100 ps than for the other two annealing durations. Conversely, the number of atoms with a miscoordination number of 1 and 2 is greater at this heating duration. An implication of this result is that the microstructure becomes denser when the heating duration is more prolonged. IV. CONCLUSION This article has presented an investigation of copper reflow in the damascene process using molecular dynamics simulation. A simulation of the deposition process, with an investigation into the growing mechanisms of the deposited atoms within the trench, has also been included. Particular emphasis has been placed upon the influence of the duration for which the annealing temperature is maintained at a constant value upon the final reflow morphology, the coverage percentage of the trench, the diffusion ability of the atoms, and the interconnect microstructure at final steady state conditions. Although the current study has employed the sputter deposition process the results relating to the alleviation of morphology defects by the reflow process are equally valid for defects that occur when other thin film technologies are employed. The simulation results presented in this study confirm the importance of the heating duration in achieving a successful reflow process in which the trench becomes completely filled by the deposited atoms. The results indicate that it is vital that the heating duration be maintained for a sufficient period of time if voids trapped within the trench during deposition are to become filled during the reflow process. If the heating time is too short, atoms located at the upper regions of the trench do not become excited, and so they hinder atoms from above the trench opening from moving down into the trench. FIG. 10. Miscoordination number comparison for different constant heating durations. Furthermore, the present study has also shown that an appropriate annealing temperature should be chosen in order to increase the efficiency of the reflow process. Analysis of the coverage percentage value has indicated that the Cu trench atoms first expand and then contract during the reflow process. During the process of expansion it has been noted that the coverage percentage decreases. Conversely, the coverage increases as thermal contraction occurs. The motion trace of trench atoms during the reflow process has shown that circular motion is evident in atoms that are located in the region surrounding the void, while atoms in the region above the void migrate a long distance toward the void. Finally, it has been shown that a longer heating duration is beneficial in improving the microstructure of the interconnects. ACKNOWLEDGMENT The authors gratefully acknowledge the support provided to this research by the National Science Council, Republic of China, under Grant No. NSC E C. S. Pai, Mater. Chem. Phys. 44, S. Y. Lee, S. H. Choi, J. Y. Kang, and C. O. Park, J. Appl. Phys. 88, S. Shibuki, H. Kanao, and T. Akahori, J. Vac. Sci. Technol. B 15, L. J. Friedrich, D. S. Gardner, S. K. Dew, M. J. Brett, and T. Sym, J. Vac. Sci. Technol. B 15, L. J. Friedrich, S. K. Dew, M. J. Brett, and T. Sym, J. Vac. Sci. Technol. B 17, L. J. Friedrich, S. K. Dew, M. J. Brett, and T. Sym, IEEE Trans. Semicond. Manuf. 12, Y. Saito, S. Hirasawa, T. 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