To verify the operation strategy of dynamic-tuning, some models/mechanisms which are presented in previous chapters will be employed to simulate in this chapter.
Before the numerical simulations, what the operation input has to be clarified first.
In last chapter, the operation profile (removal rate curve) is set and shown as Fig. 3.11.
However, to realize this operation scheme coordinating the mechanical loads and chemical loads in harmony will be the critical point of “dynamic tuning” operation, i.e.
decomposing the operation profile appropriately will be the critical point in forming the strategy of “dynamic tuning” operation. This strategy will be described in detail in this chapter and some verification of ability of the strategy will be followed.
4.1 Operation Input Concretization
To clarify the control/operation input u, the mechanism which is presented in section 2.2.3 is repeated here. From the system dynamic equation (2.15) and the material removal model (2.8), the control input is shown by differentiating (2.8), and (2.15) can be formulated as
( )
x t,d , can be transferred to the design/actuators of equipment. Note
that constraints of applied downward pressure and linear relative velocity are not considered in (4.1). Because of the lack of model of chemical factors in CMP process, the detailed equation is difficult to be expressed here. However, from the research by Y.-C. Kao et al. [38], some experiments were carried out over wide range of oxidizer concentration. They indicated that the copper removal rate of copper CMP will follow a specific trend as the concentration increases. Coincidentally, the trend, shown in Fig. 4.1, is similar to the operation profile which is shown above (Fig.
3.11). Therefore, the oxidizer concentration can be included into the operation mechanism easily because of this similarity. With the constraints of downward pressure and relative velocity, the chemical factor, RC can be introduced into the operation mechanism. The control input and input matrix B can be reformed as
T
between oxidizer concentration and RC (with specific slurry) was proposed by Q. Luo et al. [34], as shown in Fig. 4.2. It should be mentioned that reduction of removal rate at higher H2O2 concentration in both figures, Fig. 4.1 and 4.2, are due to the formation of passivation layer (copper oxide film).
Because of the important interdependence of chemical and mechanical effects, it has to be mentioned that a phenomenon in changing the process parameters. The phenomenon has been proposed in the works of J. M. Steigerwald et al. [43] and Y.-C.
Kao et al. [38], that is, two polishing regimes, a dissolution rate limited regime (chemical reaction controlled regime) and an abrasion rate limited regime (mechanical abrasion controlled regime), exist in CMP process. Besides, the effects of slurry chemistry on dishing have been proposed by V. Nguyen et al. [14]. They revealed that less dishing would be obtained from higher oxidizer concentration in the slurry.
These investigations could be great foundations for setting the manner of the chemical
factor.
To integrate these research achievements [14, 32, 33, 38, 43], the control inputs integration of control inputs described must be coordinated in harmony with each other. In other words, the objective mentioned in section 1.3 can be implemented with these considerations of chemical effects. The dynamic tuning operation of CMP process is then coordinated, as shown in Fig. 4.3. Fig. 4.1 above is used to illustrate the concept of dynamic tuning operation.
It must be mentioned again that most superior feature of dynamic tuning operation is the higher degree-of-freedom/flexibility of the process parameters. If all of the parameters can be assigned arbitrarily during the process, the possibility of figuring out the optimal operation condition/profile is much larger.
The acceleration stage in Fig. 4.3 means the increasing of removal rate (before about 0.2 minutes of second plot of Fig. 3.11). It is followed by deceleration stage after the peak value of removal rate is achieved. Because all of the operation parameters (means P, V and RC here) are all changeable, increasing and decreasing of removal rate can be realized by tuning them. Besides, the operation can be designed with more appropriate sequence to obtain better performance. The proposed sequence is to set the system at mechanical abrasion controlled regime in the beginning. At this regime, the passivation layer is formed and the rate of forming is higher than the mechanical abrasion rate. Therefore, it can be expected that lower region of wafer surface is protected by the passivation layer. Continuously, the load is increased (larger values of parameters) to raise the removal rate until the peak value of removal rate. Note that relative velocity will be the major factor in increasing removal rate because of the lower influence on dishing. In the representation of Fig.
4.3, the values of operation parameters, P, V and Rc, can be assigned with 3.5 p.s.i., 93rpm, 300nm/min, respectively. (this set of parameter represents the constraint which
is assigned in this thesis) As soon as the peak value is achieved, these parameters can be decreased for suppressing dishing, especially the applied downward pressure P.
Moreover, higher oxidizer concentration (causes lower RC value) will cause less dishing from the results shown by V. Nguyen et al. [14] because a more effective passivation layer is formed with higher oxidizer concentration and protects the recess areas.
Because the operation inputs are decomposed directly from the removal rate curve and the bound is the only one constraint for each input, the operation profile can be set in many ways. In other words, there can be infinite solutions because of three variables (P, V and Rc) and only one equation (removal rate curve, Fig. 3.11).
Therefore, a new problem will be raised, what is the best tuning/operation profile? It will not be discussed in this work. Here, one possible operation profile will be chosen to verify the effect of dynamic tuning operation of CMP process. To formulate the dynamic-tuning operation profile at first time, the composition of parameters will be obtained by hand based on the trend of Fig. 4.3 and the mechanism of (2.8). Three process parameters, P, V and the oxidizer (H2O2) concentration, will be tuned in specific profile dynamically during single wafer polishing. The bounds of P, V and the oxidizer concentration are set by 1.7 p.s.i. to 3.5 p.s.i., 40 rpm to 95 rpm and 2% to 5%, respectively. Note that relative velocity is transferred to platen/carrier rotational speed. The detailed procedure of setting operation profiles is shown in appendix Ⅱ.
4.2 Verification
The dishing model (2.9) is used to verify the ability of dynamic tuning method and the result is shown in Fig. 4.4. It is clear that dishing is suppressed from 1106Å
to 950Å in Fig. 4.4(a) while the dynamic tuning is applied to process operation/control. The improvement is more than 14% with maintaining the copper removal (throughput) of constant input. Fig. 4.4(b) displays the sketch of variations of parameters during the over-polish stage.
To complete simulate the dynamic tuning and integrate the whole process, step-height reduction model shown in (2.11) is included here. Before the simulation, the model has to be checked for validity of all of processing time. The results reveal that step height will keep decreasing with time increasing and will be close to zero step height when the polishing endpoint is arrived (not shown here). However, from the work by K. Wijekoon et al. [23], as shown in Fig. 4.5, dishing will exist before the end of process and linearly increases with overpolish/time. This experiment data might imply that initial value of dishing will not be zero (i.e. non-zero step height will be transited to dishing) and the step-height reduction model (2.11) may break down for describing/predicting the step height in the back-end stage of bulk copper CMP process. Therefore, the simulation presented below will show the front-end only.
In Fig. 4.6(a), the step-height reduction results of dynamic-tuning and constant input are shown. The better ability of step height reduction (more efficient planarization) of dynamic tuning can provide a weighty evidence for the efficiency of the strategy shown in Fig. 4.3. The variations of parameters during this interval of process are shown in Fig. 4.6(b).
It has to be mentioned again that one of the main goals in this thesis is to maintain acceptable throughput and get better performance. From the operation input concretization, it can be pointed out clearly that the employment of chemical load is the key point in this way of operation profiles setting. In other words, not only increasing the degree-of-freedom/flexibility of CMP process but also deriving better performance (and throughput) with the injection of chemical parameter in
operation action could be the key factor.
4.3 Discussion
In CMP process, the chemical and mechanical effects have to be operated in harmony for maintaining acceptable performances and throughput. The procedure is an optimization problem. To optimize the recipe (a set of specific process parameters) becomes a major work of improving the process. For most research on CMP process, the general characteristics of the process are described roughly.
However, some limitations (due to constant input) will be led into the process in typical operation. Based on the existing knowledge and the typical operation, some new operation methods are figured out, like two or three stage polishing. The multi-stage method is widely used in real production but it is not good enough in the growing requirement of planarization. In dynamic tuning method the degree-of-freedom/flexibility of process parameters will be increased (while breaking away from the typical operation). That will increase the possibility of formulating the set of process parameters. The opportunity of further improving the performance of CMP process will be feasible. In this thesis, the most striking way to increase the degree-of-freedom/flexibility is the variation of oxidizer concentration (chemical load) based on present knowledge of dishing in CMP process. It is expected that the operation profile can be further modified as the understanding of CMP process increase.
The distinguishing feature of operation by dynamic tuning is the process parameters varying during single wafer polishing. It involves within-wafer control of fabrication process. Although it is not an easy subject in process control of semiconductor production, the tendency of progress of fabrication technique seems to
be inevitable. From the simulations shown in last section, the operation of dynamic tuning method reveals outstanding improvement in dishing. The feature of deriving better performance and maintaining throughput simultaneously is the other important advantages of this strategy. Moreover, setting the operation profile via sliding mode theory, not only the violent switching is avoided but the lower loads of parameters are employed. It will make this method much more applicable in real world.
It has to be mentioned again that problem about validity of the step height reduction model and to explain why only the segment simulation result is shown above. The exact definitions of “step-height” and “dishing” are the surface height difference between high and low area of copper and the height difference between oxide and copper line, respectively. During single wafer polishing, the step height of copper may be transited into dishing when endpoint of CMP process is arrived (the oxide is exposed). The dishing exists before zero over-polish in Fig. 4.5 may represent the non-zero step height. However, the step height reduction model predicts that step height in reasonable polishing time will be close to zero. (It may be due to the assumptions in establishing model.) It will conflict with the experiments results shown in Fig. 4.5. Furthermore, the dishing and erosion problems caused by CMP process will not be so serious if the surface is so flat before over-polish stage.
Because the problems will be reduced significantly while an appropriate slurry (selectivity Ta to Cu is large) is used in the over-polish stage.
Except the numerical simulations, significant evidences for proving the capability of the operation profile have been revealed. (Note that the profile is the removal rate curve in Fig. 3.11.) Because the recipe of low removal rate will be employed in the final stage of this operation, it will have better performance, low copper dishing. [23, 24, 38] The “deliberate” (low load on the process) operation at final stage will reduce the damages caused by over-polish effectively, and the
over-polish time will be easier to control. [14, 32, 33] Additionally, the operation profile of SMC design is closer to the shape on concept of soft-landing because the process almost stops near the endpoint of polishing. In case of the measurement uncertainties, a correct realization of soft-landing should be more effective using SMC approach.
To control the removal rate or the other parameters precisely is a difficult objective because of the existence of uncertainties and disturbances of the prediction model or the working environment. One important point about dynamic tuning method needs to be emphasized here: even though the removal rate can not be performed perfectly with the designed trajectory, the performance can be improved by using the strategy of dynamic tuning (as described in Fig.4.3). (This point is shown in the difference between Fig. 4.4(a) and Fig. 3.11.) In other words, dynamic-tuning operation approach flexibility and degree of freedom for improvement is more important than what is the exact operating profile. It is the future work to determine what the best operation profile is, how to implement the complete control scheme via sliding-mode theory. The dynamic response of the operation of actual CMP tools needs to be looked to ensure proper following of soft landing model in real world.