Paper review:
Fractional Order Plasma Position Control of the
STOR-1M Tokamak
Outlook of FOC in Plasma Etching:
Challenges and Opportunities
Zhuo Li
PhD student, Dept. of ECE, USU.
zhuo.li@aggiemail.usu.edu
References
• [1]. Shayok Mukhopadhyay, YangQuan Chen, Ajay Singh and Farrell Edwards, “Fractional Order
Plasma Position Control of the STOR-1M Tokamak”, 48th IEEE CDC, Dec, 2009, pp.422-427.
• [2]. Mukhopadhyay, Shayok, "Fractional Order Modeling and Control: Development of Analog
Strategies for Plasma Position Control of the Stor-1M Tokamak" (2009). All Graduate Theses and
Dissertations. Paper 460. [online available], http://digitalcommons.usu.edu/etd/460
• [3]. M. Emaami-Khonsari, “Modelling and Control of Plasma Position in the STOR-M Tokamak,”
Ph.D., University of Saskatchewan, Saskatoon, April 1990.
• [4]. Shane Lynn, “Virtual Metrology for Plasma Etch Processes”, PhD thesis, Electronic Engineering
Department, National Univ. of Ireland.
• [5] John V. Ringwood, Shane Lynn, Giorgio Bacelli, Beibei Ma, Emanuele Ragnoli, and Sean
McLoone, “Estimation and Control in Semiconductor Etch: Practice and Possibilities”, IEEE TRANS
ON SEMICONDUCTOR MANUFACTURING, VOL. 23, NO. 1, FEBRUARY 2010
• [6]. Lynn Fuller, “Plasma Etching”, [lecture slides], Microelectronic Engineering, Rochester Institute
of Technology.
• [7]. Henri Janseny, Han Gardeniers, Meint de Boer, Miko Elwenspoek and Jan Fluitman, “A survey
on the reactive ion etching of silicon in micro-technology”, J. Micromech. Microeng. 6 (1996), 14–
28.
• [8]. Lab modules, webpage, [online], http://matec.org/ps/library3/secure/modules/047/,
[Mar.16.2012]
Slide
2
The Physical System
• Tokamak: is a device using a magnetic field to confine a
plasma in the shape of a “doughnut”. [Wikipedia.org]
Fig3-1. The schematic of Tokamak as a transformer.[1]
Fig3-2. The STOR-1M Tokamak in USU. [1]
Slide
3
Bank Current Waveforms
•
•
•
•
•
BT - Toroidal field bank
IOh - Ohmic heating bank
IVe - Vertical equilibrium bank
IHc - Horizontal compensation bank
IVc - Vertical compensation bank
Slide
4
Fig4. The bank current waveforms of STOR-1M. [1]
Measurement Mechanism
• Plasma position estimation mechanism [3]
• Four magnetic “pickup” coils measure the
magnetic field produced by the toroidal
plasma current.
• By comparing
the strengths of this measured magnetic
field one can estimate the position
of the current.
• Proposed technique in the paper
Fig5-1. The Plasma position estimation system.[3]
• Ratio of the voltages
•
𝐵𝑜 = 𝛼𝑜 𝑉𝑜 =
𝐵𝑖 = 𝛼𝑖 𝑉𝑖 =
𝜇𝑜 𝐼𝑝
2𝜋𝑟𝑜
𝜇𝑖 𝐼𝑝
(𝛼𝑜 ≈ 𝛼𝑖 )
2𝜋𝑟𝑖
• 𝑟𝑖 + 𝑟𝑜 = 100
• E.g.
𝑉𝑜
𝑉𝑖
=
𝐵𝑜
𝐵𝑖
=
𝑟𝑜
𝑟𝑖
= 5.6667
Slide
5
(Must hit the wall)
Fig5-2. Proposed position estimation approach. [3]
Plasma Position Modeling
• The transfer function
• 𝑌 𝑠 =
2.84𝑠 3 +1.14𝑒7𝑠 2 +1.12𝑒14𝑠+4.5𝑒20
𝑈(𝑠)
𝑠 4 +1.51𝑒4𝑠 3 +3.9𝑒13𝑠 2 +4.3𝑒17𝑠+2.15𝑒21
• First order plus delay model approximation
• 𝐺 𝑠 =
𝐾
𝑒 −𝐿𝑠
𝑇𝑠+1
=
0.2096
𝑒 −0.0007𝑠
0.0864𝑠+1
Slide
6
Fractional Order Controller
• Controller parameters
Table: CONTROLLER PARAMETERS FOR THE STOR-1M TOKAMAK
Controller
Kp
Ki
Kd
order
FO-PI
170.2649
32.0719
0
0.7425
ZN-PID
706.584
714.285
0.00035
1
• Results and comparison (on emulator)
Slide
7
Fig8-1. Position control results. [3]
Fig8-2. Position control results. [3]
Conclusion
• FO-PI controller is better than the ZN-PID controller in
terms of response time, control effort and steady state
error.
Slide
8
Outlook-challenges
• Plasma etching process in semiconductor
manufacturing
• Etching variables hard to measure
• Real-time control hard to achieve
• Measurement technology in the literature [5]
•
•
•
•
•
Virtual metrology [4]
Optical emission spectroscopy (OES)
Mass spectrometry
Plasma impedance monitoring
Etc.
Fig9. OES. [4]
Slide
9
Plasma Etching - Intro
• Etching outcome and profile
• Isotropic (non-directional removal of material from a substrate)
• Anisotropic (directional)
Ideal etch
Poor etch
Fig10-1. No process is ideal, some
anisotropic plasma etches are close. [6]
Fig10-2. One-run multi-step RIE process. Top left: after
anisotropic etching the top Si of an SOI wafer. Top right: after
etching the insulator and sidewall passivation. Middle left:
during isotropic etching of the base Si. Middle right: after
isotropic etching the base Si. Bottom: typical finished MEMS
products. [7]
Slide
10
The Plasma Etching Chamber
Fig11-1: Typical parallel-plate RIE system. [*]
Fig11-3: Typical RF sputtering system. [*]
Fig11-2. RIE Process Chamber. [8]
Fig11-4. Physical etch process chamber. [8]
* MEMSnet®, https://www.memsnet.org/mems/beginner/etch.html
Slide
11
Controls in the Literature
Fig12. Etch tool control possibilities with information flow. [4]
Slide
12
Controls in the Literature
•
•
•
•
Run-to-Run (R2R) Control [a],[b],[c].
Predictive functional control [4].
Neural network control
Etc.
[a], M. Hankinson, T. Vincent, K.B. Irani, and P.P. Khargonekar. Integrated real-time and run-to-run
control of etch depth in reactive ion etching. IEEE T. Semiconduct. M., 10(1):121-130, Feb. 1997.
[b]. X.A. Wang and R.L. Mahajan. Articial neural network model-based run-to-run process controller.
IEEE Trans. Components, Packaging, and Manufacturing Technology, Part C., 19(1):19-26, Jan. 1996.
[c]. J.P. Card, M. Naimo, and W. Ziminsky. Run-to-run process control of a plasma etch process with
neural network modelling. Qual. Reliab. Eng. Int., 14(4):247-260, 1998.
Slide
13
Outlook-Opportunities
• Data
Fig10. Endpoint mono-chromtor output over four
preventative maintenance (PM) cycles. [4]
Slide
14
Outlook-Opportunities
• Other efficient “learning machines”
• RVM
• Other fitting methods
• TLS fitting for “data boxes” (not point)
• Interval computation tools (IntLab)
• Dynamic VM – R2R VM
• Fractional Order ANN based VM
• Neuronal dynamics is inherently “fractional order”
• Fractional order iterative learning control
• Cognitive process control
Slide from Dr.Chen’s Lam Research Talk
Slide
15
Outlook-Opportunities
• Dynamic Virtual Metrology in Semiconductor
Manufacturing
Slide
16
http://bcam.berkeley.edu/research/new_researchframes.html
Slide from Dr.Chen’s Lam Research Talk
Thank you!
Q&A
Slide
17