An Iterative Learning Control In Rapid Thermal ... - CiteSeerX

An Iterative Learning Control In Rapid Thermal Processing  Yangquan Chen y, Jian-Xin Xu z, Tong Heng Lee x, Shigehiko Yamamoto { Control and Simulation Laboratory, Department of Electrical Engineering National University of Singapore 10 Kent Ridge Crescent, Singapore 119260 February 27, 1997

Abstract

mm) with future technology generations.

This paper presents an application of Iterative Learning Control (ILC) methodology to the temperature pro le control of a Rapid Thermal Processing (RTP) system for single wafer processing (SWP), a trend in semiconductor manufacturing. The motivation and the basic ideas are brie y introduced. The eectiveness of the proposed method is demonstrated by the simulation studies of a simpli ed model of rapid thermal processing of chemical vapor deposition (RTPCVD).

Conventional semiconductor factories use batch furnace for various thermal fabrication steps and batch liquid systems for wafer cleaning steps for high-throughput wafer processing. Single-wafer processing is an alternative to batch equipment for a signi cant number of fabrication unit processes. Despite the lower fabrication throughput, single-wafer processing will be preferred over batch equipment for many applications as the wafer size increases beyond 150-200 mm. Factors in favor of single-wafer processing include  compatibility with multi-chamber cluster equipment for vacuum-integrated processing,  improved fabrication cycle time, and  enhanced fabrication process repeatability due to improved process control. A major argument against single-wafer processing has been its lower processing throughput compared with batch equipment. However, many applications can trade-o somewhat lower fabrication throughput in turns for enhanced capabilities for integrated processing and improved manufacturing process control. Rapid Thermal Processing has been used as a versatile single-wafer processing technique for various thermal processing applications.

Keywords: Rapid Thermal Processing; Wafer Fabrication; Batch-Process Control; Iterative Learning Control;

1 Introduction

The continuing demand for higher chip packing densities and enhanced system-level performance are the main technology and device scaling drivers in the microelectronic industry. Advanced microprocessor chips now require device integration levels of well over 1 million transistors based on advanced sub-micrometer(e.g., 0.35 m-0.8m) CMOS and BiCMOS technologies. The chip integration density is expected to exceed 100 million transistors by the end of this decade. Moreover, future generations of memory chips will pack 1 billion memory bits at the turn of this century. This level of integration density places stringent demands on device fabrication technologies, microconductor processing equipment, and manufacturing process control in order to meet the overall IC manufacturing yield, cycle time, and throughput requirements. Semiconductor technology scaling also aects wafer size. Currently, the state-of-art chip factories are set up for 200 mm diameter wafer processing. The wafer size is expected to grow to 300 mm and beyond (i.e., 350 mm and 400

One of the technologies of signi cance in single-wafer microconductor processing is rapid thermal processing (RTP). Rapid thermal processing systems are singlewafer, cold-wall chambers that utilize one or more radiant heat sources to rapidly heat up the semiconductor substrate at high temperatures for short times. Moslehi et al.[1, 2] have successfully demonstated the use of RTP for all thermal fabrication steps required in two 0.35 m CMOS technologies. These rapid thermal procesing steps include:  dry and wet oxidations,  low pressure chemical vapor deposition (LPCVD) of poly-silicon, amorphous-silicon, silicon nitride, silicon dioxide and anneal, and  source/drain and well formation,

 For submission to the IASTED Int. Conf. on Modeling, Simulation and Optimization, Singapore, 1997. This work was supported in part by NUS under RP-3950628. y URL: http://www.ee.nus.sg/.yangquan/project.html; E~ mail: [email protected] z Corresponding author. E-mail: [email protected]; Tel.:(+65)7722566(o); Fax: (+65)7721103(o) x E-mail: [email protected] { Visiting Professor. On leave from Kogakuin University, Japan. E-mail: [email protected]

1

 silicide formation and anneal, and  sintering processes.

remains an open question as to the level of hierarchical integration required for satisfactory control in a production RTP environment. Eorts at the supervisory and run-to-run levels include [4, 5].

Future generations of semiconductor chips will increasingly use RTP instead of batch furnacs, since its potential in terms of in-situ process engineering, clustering, and sensor-based process control reaches far beyond batch furnace technology. For instance, RTP has advantages over a batch furnace for producing highquality thin lms because of its much faster transient temperature ramps and shorter processing timesused. High-quality thin silicon dioxide gate dielectrics have been produced by rapid thermal oxidation (RTO). RTP has been used in research to produce chamically modi ed thin oxides. In particular, excellent results have been obtained by rapid thermal nitridation (RTN) in an NH3 ambient. The short RTP processing times result in minimum dopant redistribution, which can be used to fabricate shallow junctions. The higher temperature, however, means that the thermal budget for a process needs to be considered carefully.

We concentrate ourself on the real-time control and RtR control.

2 Iterative Learning Control Scheme The proposed scheme Iterative Learning Control is meant to combine the aforementioned real-time control and RtR control in a new framework. This ILC framework is based on the facts that the single-wafer RTP is a repetitive process. Thus, how to utilize this operation repetition to improve the control performance and increase the robustness is the main concern of ILC method. The term `Iterative Learning Control' (ILC) was coined by Arimoto and his associates [6] for a better control for the repetitive systems. We can intuitively nd that learning is a bridge between the knowledge and the experience. That is to say, the lack of knowledge is bridged by the experience. Knowledge and Experience in technical language can be obtained by `modeling' and by 'repetitions after applying some learning control law'. One way to describe the learning is as a process where the objective of achieving a desired result is obtained by experience when only partial knowledge about the plant is available.

Various problems associated with wafer temperature measurement and dynamic temperature/process uniformity control have hindered the widespread use of RTP in semiconductor device manufacturing. It is critical to maintain a uniform temperature pro le across the wafer during steady-state and transient operation to avoid the generation of slip dislocations and to ensure process uniformity. As the semiconductor industry reduces critical dimensions on VLSI circuits, tighter control of process and wafer parameters will be required. One technology for achieving improved process control is single wafer processing (SWP), as discussed in the above. Furthermore, process control can be divided into a three tier hierarchical model consisting of  supervisory control,  run-to-run (RtR) control, and  real-time control. Supervisory control, at the highest level, in uences changes on a lot to lot basis. Run-to-run control updates occur after each wafer is processed. Supervisory and RtR control have the advantage that oine sensors are available for desired measurements; these measurements are often unavailable in-situ. Real-time control can often be subdivided into wafer state and process state control. Wafer state refers to physical quantities associated with the processed silicon wafer (e.g. spatial temperature distribution, lm thickness, etc.). Process state, on the other hand, refers to physical quantities which are not wafer parameters (e.g. reactor wall temperatures, partial pressures of gases, etc.).

Roughly speaking, the purpose of introducing the ILC is to utilize the system repetitions as the experience to improve the system control performance even under incomplete knowledge of the system to be controlled. It should be pointed out that the ILC is not an open-loop control operation, although the ILC only modi es the input command for the next repetition. ILC is closed-loop in repetitions since updates are performed for the next repetition using the feedback measurements of the previous repetition, as opposed to the closed structure of conventional controllers in time which updates the control signal of the next time step using the feedback at current or past time steps. The dierence is that the thinking in ILC is in the repetition domain, which makes it appears as open-loop control in the time domain. Taking Arimoto's simple D-type ILC scheme[6] as an example, it can be clearly illustrated by Figure 1. From [7], it is clear that better ILC performance can be achieved by introducing a feedback loop. Then the system considered is actually controlled by an ILC controller in the iteration number direction and a feedback controller in the time direction simultaneously. This is illustrated in Figure 2.

Badgwell et al.provide a comprehensive survey of modelling and control issues in the semiconductor industry [3]. From application examples, it is apparent that the entire hierarchy may or may not be required for a particular semiconductor application. The real-time control is only performed on the spin speed and bake temperature, which are both process state variables. It

Iterative learning controller can also be regarded as an intelligent feedforward controller which is with a `plug-in' form. In the real world, the ILC should be taken as an additive to the existing conventional 2

.. .

memory pool

y

memory w

memory

ui (t) plant ei (t)



the iterative learning control property.

yd (t)

yi (t)? e+ qr

As the most practical systems have a nite escape time, the stability problem of ILC is mainly concentrated in the repetition direction, which sometimes is studied in terms of the ILC convergence. Some ILC convergece analysis can be found in recent literatures, e.g., [8, 9, 10, 11], and the references therein.

updating: - ui (t) = ui (t) + ?e_i(t) +1

ui+1 (t)- plant yi+1 (t?) e+ r ei+1 (t)



3 Simulation Studies

?yd(t)

.. .

To illustrate the idea of ILC is applicable to RTP system, a RTPCVD model is used. The nal objective is to control the deposition thickness on the wafer at the end of thermal processing.

Figure 1: Block-Diagram of Iterative Learning Control .. . k-th repetitive operation

uff k (et) uk (t)

-

-

+ 6 +

ufb k (t)

3.1 RTPCVD Model and Parameters

In this section, we emulate the situation with a very simple model for RTPCVD of poly-Si, which includes the temperature dependence of deposition rate and the quartz window eect [12, 5] as follows:

yk (t) g yd (t)

plant

? +

8 < :

?+

e+

ILC

ek (t)



-e + 6 +

-

ufb k+1 (t)

?g++ uff k+2 (t)

?

The control objective is to nd a lamp control pro le

yk+1(t) gyd(t)

plant

P (t) such that the controlled wafer temperature Tw (t) follows the given wafer temperature pro le Twd (t) as tight as possible in a given time interval [0; T ]. The Twd (t) is pre-designed to satisfy the RTP requirements and especially to guarantee the nal deposition thickness (RTPCVD) S (T ).

?+

Feedback C.

ILC



d w d d q d d d

A more complex model is used in [13], where the method also incorporates state estimation based on nal deposition thickness measurements.

(k + 1)-th repetitive operation

uff k+1 (tu)k+1 (t)

T Tt St t

= [Aw Ew (Tq4 ? Tw4 ) + fEw QP ]=Mw (1) = [QP + hAq (Tamb ? Tq )]=Mw = k0 exp(? RT w ) where, the meanings of variables and the relevant parameters are given in Table 3.1.

Feedback C.

ek+1 (t)

.. .

?

Figure 2: Block-Diagram of Feedback-Assisted Iterative Learning Control

The initial values of (1) are Tw (0) = Tq (0) = 300  K , S (0) = 0m. T = 220s. The desired wafer temperature pro le is

Twd (t) =

( 300 + 700t=15 ( K) ; t 2 [0; 15]s; 1000 ( K) ; t 2 (15; 210]s; 1000 ? 50(t ? 210) ( K) ; t 2 (210; 220]s:

(2) Such designed wafer temperature pro le will result in a nal DT (deposition thickness) of 0.5 m. In the following simulations, we assume the wafer temperature Tw (t) can be measured.

controller. The main target of the ILC is to utilize the system operation repetition to improve the control performance, when the system executes a given task repeatedly. When analyzing the property of the ILC, considerations should be taken both in the time axis and in the repetition number direction, which is in essence in the category of the 2-D system theory. However, as the repetitive task is to be executed in a xed nite time interval, more attentions should actually be paid in the repetition axis in the analysis of

3.2 Simple Iterative Learning Control

The key point in ILC is the control updating law as discussed in Section 2. A simple form of ILC

Pi+1 (t) = Pi (t) + ?1 (Twd (t) ? Tw(i) (t)) 3

(3)

symbol value

Aq Aw Ew f h P Q R S Tw Tq Tamb Mw Mq k0



400 0.8 0.5

2 [0; 1] 1076 1.9872

1 100 591000 39200 1:356  10?12

meaning quartz window area wafer area wafer emmisivity lamp power absorbed by wafer heat transfer coecient for forced convection lamp power control factor lamp power constant gas constant polysilicon deposition thickness wafer temperature quartz window temperature ambient temperature wafer thermal mass quartz window thermal mass pre-exponential constant of polysilicon deposition activation energy of polysilicon deposition Boltzmann constant 4 1:84 cal/s/  K hAq =

unit cm2 cm2 unitless unitless cal/cm2/s/  K unitless cal/s cal/(gmol
 K )  m K K K cal/  K cal/  K m/s cal/gmol cal/(s
cm 2
 K 2 )

is applied, where i is the iteration (run) number, ?1 is the learning gain. In Figs. 3(a)-3(c), three cases with dierent initial lamp power coecients P0 (t). ?1 is chosen as 0.002, which is based on the ILC convergence results in [10].

which is in an integral (I) controller form in the idirection. If we use the PI controller in the i-direction

It is quite clear that the ILC method, although it is very simple, is eective for RTP temperature pro le tracking control. The dierences of ILC method to the proposed RtR control [5, 13] are  no backward integration of adjoint system is required,  no line-searching is required,  no deposition thickness measurement or estimation is needed,  global convergence can be guaranteed as shown in [8, 10, 10, e.g.],  robustness to dierent initial lamp settings.

the ILC updating law takes the form that ui+1 (t) = ui (t) + ?e_ i (t) + ?1 e_i?1 (t) where ? = kP + kI and ?1 = ?kP . By using the dierence e_i (t)?e_i?1 (t) as the approximation of the derivative along the i-direction, the PID controller in i-direction

ui+1 (t) = kP e_i (t) + kI

ui+1 (t) = kP e_ i (t) + kI

It is quite intuitive that if more of the previous control eorts and the resulted tracking errors are used, better ILC performance can be expected.

ui+1 (t) = ui (t) + ?e_ i (t) for the control of the dynamics along the ILC iteration number i-direction, it is obviously a pure integral controller. Suppose the initial control u0 (t) = 0, then j =0

e_j (t);

e_ j (t) + kD (e_ i (t) ? e_ i?1 (t))

Similarly, a simple second order ILC is used for the illustration. Pi+1 (t) = Pi (t)+?1 (Twd (t)?Tw(i) (t))+?2 (Twd (t)?Tw(i?1)(t)): (4) Use ?1 = 0:002; ?2 = 0:1?1. Fig.4 compares the learning processes of the rst and second order ILC updating law. Clearly, the second order ILC gives better result.

It is interesting to investigate the ILC laws in the interation number i-direction. If we look at the conventional ILC updating law [6]

i X

j =0

j =0

will result in the following form of the ILC updating law ui+1 (t) = ui (t) + ?e_ i (t) + ?1 e_ i?1 (t) + ?2 e_ i?2 (t): where ? = kP + kI + kD , ?1 = ?kP ? 2kD and ?2 = kD . This is a high-order iterative learning controller. The above arguments indicate that the high-order ILC is capable of giving better ILC performance than the traditional rst-order case where only an integral controller is actually used.

3.3 High-order Iterative Learning Control

ui+1 (t) = ?

i X

i X

3.4 ILC plus Feedback Controller

From [7], it is clear that better ILC performance can be achieved by introducing a feedback loop, as shown in Fig. 2. Then the system considered is actually controlled

e_ j (t) 4

Final wafer thickness 3

600 500 400 300 200 100 0

2

4 6 8 ILC iteration number

2

1 2

0.5 0

10

desired wafer thickness first order ILC second order ILC

2.5

1.5

2

4 6 8 ILC iteration number

S(T) (micron)

Wafer S(T) (um)

RMS (Twd−Tw) (K)

2.5

10

1.5

Tw(t) and Twd(t) (K)

Power P(t)*100%

1 0.8 0.6 0.4 0.2 0 0

50

100 150 time (s)

1000

600

0.5

400 200

0 1

0 0

200

(a)

1

800

50

100 150 time t(sec.)

:

Wafer S(T) (um)

RMS (Twd−Tw) (K)

50

0

2

4 6 8 ILC iteration number

0.4 0.3

0.1 2

4 6 8 ILC iteration number

+1

10

Tw(t) and Twd(t) (K)

Power P(t)*100%

1 0.8 0.6 0.4 0.2 0 0

50

100 150 time (s)

(b)

800 600 400 200 0 0

100 150 time t(sec.)

200

:

150

2.5

Wafer S(T) (um)

RMS (Twd−Tw) (K)

50

( )=05

P0 t

100

50

2 1.5 1 0.5

0

2

4 6 8 ILC iteration number

0

10

2

4 6 8 ILC iteration number

Tw(t) and Twd(t) (K)

Power P(t)*100%

0.6 0.4 0.2 0 0

50

100 150 time (s)

(c)

800 600 400 200 50

100 150 time t(sec.)

200

11

1

( )

(5)

References

( )=10

P0 t

10

A new method, Iterative Learning Control, is proposed for the nite-time temperature pro le control of RTP systems in wafer fabrication in semiconductor industry. Simulation studies have veri ed the eectiveness of the proposed novel scheme. Constraints in actual eld conditions such as the nal DT measurement, pyrometer sensor conversion and so on are under investigation.

1000

0 0

200

9

4 Concluding Remarks

10

1 0.8

8

where P f (t) and P b (t) are iterative learning control input (feedforward) and feedback control respectively. For the RTP system, the cases of the ILC with and without feedback controller are compared in Fig. 5(a) where the gains are set as ?1 = Kp = 0:002. Doubling the gains gives the results comparison in Fig. 5(b). It can be observed from Figs. 5(a) - 5(b) that better ILC performance can be achieved by introducing a feedback controller into the ILC method, as illustrated in Fig. 2. Especially from Fig. 5(b), an unwanted oscillatory convergence in the ILC without the assistance of feedback controller can be elliminated by introducing a feedback controller. To have a clear comparison, the two cases of feedback-assisted ILC with dierent gains are summerised in Fig. 6.

1000

200

5 6 7 ILC Iteration Number

8 P (t) = P f (t) + P b(t) < f i f d : PiP b ((tt)) == PPis +(t)K+p(?T d(T(tw)(?t) T?wT(tw)) (t)) w

0.2

0

10

4

by an ILC controller in the iteration number direction and a feedback controller in the time direction simultaneously. The detailed controller is as follows:

0.5

100

3

Figure 4: Eect of high-order iterative learning control of RTP process.

( )=00

P0 t

2

200

:

[1] M. M. Moslehi, \Process uniformity and slip dislocation patterns in linearly ramped-temperature transient rapid thermal processing of silicon," IEEE Trans. Semicond. Manufact., vol. 2, no. 4, pp. 130{140, 1989.

Figure 3: Simple ILC of RTP process with dierent initial lamp power settings.

5

RMS (Twd−Tw) (K)

600

[2] M. M. Moslehi, R. A. Chapman, L. Velo, J. Kuehne, A. Paranjpe, C. Schaper, S. Huang, H. Najm, T. Breedijk, D. Yin, and C. Davis, \Rapid thermal processing for sub-half-micron CMOS IC manufacturing," in VLSI Technol. Symp., 1993. [3] T. Badgwell, T. Breedijk, S. Bushman, S. Butler, S. Chatterjee, T. Edgar, A. Toprac, and I. Trachtenberg, \Modeling and control of microelectronics materials processing," Computers in Chemical Engineering, vol. 19, pp. 1{40, 1995. [4] P. Mozumder, S. Saxena, and D. J. Collins, \A monitor wafer based controller for semiconductor processes," IEEE Trans. on Semiconductor Manufacturing, vol. 19, pp. 400{411, 1994. [5] E. Za riou, R. Adomaitis, and G. Gattu, \An approach to run-to-run control for rapid thermal processing," in Proc. of American Control Conf., (Seattle, WA, USA), pp. 1286{1288, 1995. [6] S. Arimoto, S. Kawamura, and F. Miyazaki, \Bettering operation of robots by learning," J. of Robotic Systems, vol. 1, no. 2, pp. 123{140, 1984. [7] S. Arimoto, \Robustness of learning control for robot manipulators," in Proc. of the 1990 IEEE Int. Conf. on Robotics and Automation, pp. 1528{1533, 1990. [8] Y. Chen, M. Sun, B. Huang, and H. Dou, \Robust higher order repetitive learning control algorithm for tracking control of delayed repetitive systems," in Proc. of the 31st IEEE Conf. on Decision and Control, (Tucson, Arizona, USA), pp. 2504{2510, Dec. 1992. [9] Y. Chen, Z. Gong, and C. Wen, \A high order iterative learning control algorithm for uncertain nonlinear systems," in Revised for Automatica, June 1995. [10] Y. Chen, J.-X. Xu, and T. H. Lee, \Feedbackassisted high-order iterative learning control of uncertain nonlinear discrete-time systems," in Presented at the ICARCV'96: Int. Conf. on Control, Automation, Robotics and Vision, (Singapore), pp. 1785{9, Dec. 1996. [11] Y. Chen, J.-X. Xu, and T. H. Lee, \Current iteration tracking error assisted iterative learning control of uncertain nonlinear discrete-time systems," in Proc. of the 35th IEEE Conference on Decision and Control, (Kobe, Japan), pp. 3040{ 5, Dec. 1996. [12] R. S. Gyurcsik, T. J. Riley, and F. Y. Sorrell, \A model for rapid thermal processing: achieving uniformity through lamp control," IEEE Trans. on Semiconductor Manufacturing, no. 4, pp. 9{ 13, 1991. [13] E. Za riou, H. W. Chiou, and R. Adomaitis, \Nonlinear model based run-to-run control for rapid thermal processing with unmeasured variable estimation," in Electrochemical Society Proceedings (Vol. 95-4), pp. 18{31, 1995.

Gamma=0.002; Kp=0.002 Gamma=0.002; Kp=0

500 400 300 200 100 0

2

4

6

8

10 12 ILC iteration number

14

16

18

20

18

20

18

20

18

20

Wafer S(T) (um)

2.5 Gamma=0.002; Kp=0.002 Gamma=0.002; Kp=0

2 1.5 1 0.5 0

2

4

6

8

10 12 ILC iteration number

(a) ?1 = 0 002; RMS (Twd−Tw) (K)

:

Kp

600

14

16

= 0 0 002 ;

:

:

Gamma=0.004; Kp=0.004 Gamma=0.004; Kp=0

500 400 300 200 100 0

2

4

6

8

10 12 ILC iteration number

14

16

Wafer S(T) (um)

2.5 Gamma=0.004; Kp=0.004 Gamma=0.004; Kp=0

2 1.5 1 0.5 0

2

4

6

8

10 12 ILC iteration number

(b) ?1 = 0 004; :

Kp

14

16

= 0 0 004 ;

:

:

RMS (Twd−Tw) (K)

Figure 5: Comparison of iterative learning control with a feedback controller 150

Gamma=0.002; Kp=0.002 Gamma=0.004; Kp=0.004

100 50 0

2

4

6

8

10 12 ILC iteration number

14

16

18

20

18

20

Wafer S(T) (um)

0.5 0.4 0.3 0.2 Gamma=0.002; Kp=0.002 Gamma=0.004; Kp=0.004

0.1 0

2

4

6

8

10 12 ILC iteration number

14

16

Figure 6: Comparison of feedback-assisted iterative learning control.

6