عملیات برنامه ریزی مکانیکی شیمیایی از طریق برنامه ریزی پویا

In this paper, the impact on non-planarization index by the down force and rotational speed during a SiO2 or Cu CMP process was investigated. Since the magnitudes of down force and rotational speed have limits, we choose the dynamic programming approach because of its ability to achieve constrained optimization by the down force and rotational speed. The duration and the amount of input were computed based on the chemical mechanical polishing model by Luo and Dornfeld [J. Luo, D.A. Dornfeld, IEEE Trans. Semiconduct. Manufact. 14(2) (2001) 112–132.] when the other parameters were fixed. Experiments done for blanket wafers based on dynamic programming operation and conventional constant removal rate operation was compared with each other. The non-planarization index could be improved consistently by dynamic programming operation versus constant removal rate operation. The improvement ranges from 2% to 39% improvement over the base recipe of constant removal rate in all experiments as shown in Table 3 and Table 6. The thickness removal error is consistently smaller by constant removal rate operation versus dynamic programming operation in all experiments as shown in Table 3 and Table 6. To get the best performance of both planarization and thickness removal, it is recommended that planarization step and overpolish step in SiO2 and Cu CMP should use different mode of operation, i.e., dynamic programming operation during planarization step for minimizing non-planarization index and constant removal rate operation during overpolish step for minimizing thickness removal error. The incremental time calculation for eliminating thickness removal error during overpolish step can be done using the thickness error and removal rate derived from Luos’ removal rate model based on constant wafer pressure and platen speed at the end of planarization step. Our contribution is a new approach for CMP. Standard CMP uses constant removal rate operation in both planarization step and overpolish step. Our new approach uses dynamic programming operation during planarization step and constant removal rate operation during overpolish step.

Chemical mechanical planarization (CMP) is a widely accepted technique to provide a globally planarized surface for microelectronic wafer fabrication nowadays. CMP was developed during the early 1980s when multilevel interconnect technology was pushed to the limits of circuit density and performance. This technique produces excellent planarization across the wafer surface and improves both photolithography and deposition process [1]. In recent years, the device levels and densities increased continuously, at the same time the problem of resistance–capacitance (RC) time delays which can appreciably slow down circuit speeds must be solved quickly. As a result, copper has emerged as the optimal interconnect material because of its low resistivity and high electromigration resistance compared with aluminum [2] and [3]. Patterned Cu lines are produced by a damascene process when using Cu as an interconnect material. In the damascene process, the dielectric is patterned, followed by the barrier and metal deposition. The barrier is required to prevent the rapid diffusion of the Cu into the dielectric. The final step in this process is CMP that removes the excess metal and provides global planarization. Fig. 1 schematically shows a single layer Cu interconnect structure before and after CMP. Two key problems in Cu pattern wafer CMP, namely copper dishing and oxide erosion, generate surface non-planarity which gives rise to problems in integrating multiple layers of metal. Copper and oxide thinning results in increased RC delay which leads to inferior device performance. Therefore, we focus on the experiments for SiO2 and Cu CMP. Full-size image (26 K) Fig. 1. Schematics of a single layer Cu interconnect: (a) before polishing, (b) ideal case after polishing and (c) real case after polishing. Figure options Several research efforts have been reported on modeling the CMP process and the most well known equation is the Preston’s equation [4]. Preston’s equation reflects the influence of process parameters including wafer pressure and relative velocity. In the last several years, the revised Preston’s equations concentrated on different elements of CMP. For example, Zhang and Busnaina [5] proposed an equation taking into account the normal stress and shear stress acting on the contact area between abrasive particles and wafer surfaces. Tseng and Wang [6] showed that the removal rate is proportional to the terms P5/6 and V1/2. Zhao and Shi [7] and [8] consider the effects of the pad hardness and the contact between wafer and pad. Luo and Dornfeld [9] assumed an indentation-sliding model for the penetration of the pad and included an empirical accommodation of chemical reaction at the wafer surface. Compared with experiment results, the Luo and Dornfeld model more accurately predicts the removal rate. (Therefore, the Luo and Dornfeld model will be employed to predict thickness removal rate in this paper). Most of the research work on CMP is focused on removal mechanism and slurry chemistry. Chiu et al. [10] applied the concept of soft landing of a spacecraft to CMP operation. Therefore, the CMP operation can be formulated as a minimum time optimal control problem. They treat the oxide surface as the landing surface, the polishing pad as a fly vehicle, and the removal rate as the vertical velocity. The equations describing the thickness removal process can be expressed as: View the MathML sourceH˙R˙R=0-100HRR+01a-amax⩽a⩽amax Turn MathJax on where H is the thickness of material to be removed, RR the removal rate, and a the rate of change of the removal rate. The constraints in removal rate and rate of change of removal rate are applied because the parameters of CMP machine have physical limit, e.g., platen speed, wafer pressure, and slurry flow rate. They also set the final condition to H(tf) = 2000 Å and RR(tf) = 2000 Å/min in order to reduce the dishing and erosion according to the experimental data proposed by K. Wijekoon and S. Tsai etc. [17]. Fig. 2a and Fig. 2b shows that copper dishing and oxide erosion are proportional to platen speed and wafer pressure. Once the landing point is reached (H(tf) = 2000 Å), the polisher continues the removal with the smaller removal (RR(tf) = 2000 Å/min) until the end point is detected. Fig. 3 shows the result of optimal operation. Through their inspiration, we plan to use dynamic programming as our method of optimal operation in this research. Full-size image (17 K) Fig. 2a. Dependence of copper dishing and oxide erosion on platen speed. Wafer pressure was kept constant [17]. Figure options Full-size image (18 K) Fig. 2b. Dependence of copper dishing and oxide erosion on wafer pressure. Platen speed was held constant [17]. Figure options Full-size image (20 K) Fig. 3. Trajectory for RRmax = 9000 Å/min, Hsmall = 2000 Å, and RRsmall = 2000 Å/min [10]. Figure options Lin and Chi [11] employed the sliding-mode control to set the operation profile of CMP process through “Dynamic Tuning” method to enable the CMP process behave closer to the soft landing. However, the experimental verification may be hard to carry out because of the continuous time control and the lack of available operation mechanism. Hence, the dynamic programming control will be employed to deal with the discrete time control. Dynamic programming was developed by Bellman and his colleagues in the 1950s [12]. The method of dynamic programming will be explained in Appendix A of this paper. It has the advantage of dealing with constrained inputs. That means the problem of available operation mechanism can be solved for constrained inputs and multiple finite stages CMP. Experiments based on dynamic programming were carried out in this research for both SiO2and Cu blanket wafers. In this paper, the removal rate representation will be presented in Section 2. In Section 3, the simulation results via dynamic programming will provide the basis of dynamic programming of wafer pressure and platen speed as part of recipe for CMP tool. The experimental results for CMP operation via dynamic programming were obtained and discussed in Section 4. Section 5 is for conclusion.

In this study, we focused on the mechanical parameters of CMP process. The wafer pressure and platen speed were taken as the control parameters. We applied the control method of dynamic programming to carry out experiment for CMP process with blanket SiO2 and Cu wafers. The influence of dynamic programming operation and constant removal rate operation on the non-planarization index for CMP process were compared carefully. We arrived at the following conclusions: (1) The non-planarization index could be improved consistently by dynamic programming operation versus constant removal rate operation. The dynamic programming operation has 2% to 39% improvement over the base recipe of constant removal rate in all experiments as shown in Table 3 and Table 6. (2) The thickness removal error is consistently smaller by constant removal rate operation versus dynamic programming operation in all experiments as shown in Table 3 and Table 6. (3) To get the best performance of both planarization and thickness removal, it is recommended that planarization step and overpolish step in SiO2 and Cu CMP should use different mode of operation, i.e., dynamic programming operation during planarization step for minimizing non-planarization index and constant removal rate operation during overpolish step for minimizing thickness removal error. The incremental time calculation for eliminating thickness removal error during overpolish step can be done using the thickness error and removal rate derived from Luo’s removal rate model based on constant wafer pressure and platen speed at the end of planarization step. (4) The platen speed is a more consistent factor to influence the non-planarization index (about 25% improvement over base recipe of constant removal rate) during planarization step using dynamic programming operation as shown in Table 3 and Table 6. The removal thickness error (about 1%) is also minimum in overpolish step using constant removal rate operation by constant platen speed and wafer pressure as shown in the third row of Table 3 and Table 6. (5) In SiO2 CMP, dynamic programming of platen speed during planarization step is followed by constant removal rate operation during overpolish step using platen speed of 20 rpm and wafer pressure of 4.0 psi. (6) In Cu CMP, dynamic programming of platen speed during planarization step is followed by constant removal rate operation during overpolish step using platen speed of 30 rpm and wafer pressure of 3.5 psi. (7) Best known method (BKM) for CMP planarization is recommended to use dynamic programming operation of platen speed for coarse control of non-planarization index during planarization step and use constant removal rate operation via constant platen speed and wafer pressure at the end of planarization step for fine control of thickness removal error during overpolish step.