Estimation and Control in Semiconductor Manufacturing

1
Estimation and Control in Semiconductor
Manufacturing

• Pramod P. Khargonekar
• Department of Electrical Engineering and Computer
  Science
• University of Michigan
• Ann Arbor, MI
• Now with University of Florida

2
PRESENTATION OUTLINE

• Introduction and Background
• Control Issues
• Estimation of Etch Depth for Blanket Wafers
• Estimation for Patterned Wafers
• Concluding Remarks

3
Bit of Personal History

• Started my career in the late 70s in algebraic
  system/control theory
• From mid 80s to early 90s, I worked in robust
  and H-infinity control theory
• In early 90s, I became keen to work on something
  more immediate and compelling
• Started to work with a group of faculty and
  students in semiconductor manufacturing

4
SEMICONDUCTOR MANUFACTURING

• Key unit processes
• Photolithography Physical and Chemical Vapor
  Deposition
• Thermal Processing Plasma Etching
• Chemical-Mechanical Polishing
• Process technology - critical driver for Moores
  law
• Currently at .18 mm linewidth, .13 mm and .07 mm
  generations next
• Wafers are becoming bigger - 300 mm wafers
• Expensive manufacturing equipment
• A high end machine can cost 5 M
• A large fraction of technology advancements come
  from equipment and process advances
• A modern megafab can cost as much as 2.5 B
• 70 of the cost is the equipment
• Large industry
• gt US300 B

5
Semiconductor Manufacturing
(Scientific American)
6
Moores Law
G. Moore
Pentium 4 has 42 million transistors
http//www.physics.udel.edu/wwwusers/watson/scen10
3/intel.html
7
Control in Semiconductor Manufacturing

• Manufacturing System Design and Optimization
• Process scheduling and sequencing
• Re-entrant manufacturing lines
• Factory optimization
• Wafer handling and transport
• Precision robotics for 300 mm wafers
• Automation of material transport systems
• Machine Vision for Wafer Inspection
• Defect detection and analysis
• Single loop controllers for gas flows,
  temperature, pressure, etc.

8
UNIT PROCESS CONTROL - CURRENT STATE

• PID Controllers on machine inputs
• Gas flows into machines - Mass flow controllers
• Pressure Controllers
• Matching networks for RF Power delivery
• Statistical Process Control
• Detection of out of control status based on
  prespecified upper and lower limits
• Root cause analysis
• Run-to-run control is still not widely accepted
  and practiced
• Little real-time in situ multivariable control
• Some reports suggest that more than 50 of
  machine downtime can be attributed to controls

9
WHY IS PROCESS CONTROL DIFFICULT?

• It is difficult to build in-situ wafer sensors
• Wafer is inaccessible - lack of ports
• Deducing key wafer parameters from optical
  measurements is a challenging and difficult
  problem
• Some of the process variables can be sensed
• Environment around the wafer
• Processes are very complex
• Lack of good first principles models
• Empirical models have limited utility
• Equipment is not designed for real-time control
• Lack of actuators
• Computing hardware and software is closed
  architecture

10
Michigan Program in Control of Semiconductor
Manufacturing

• Started in 1993
• Support from
• SRC (Semiconductor Research Corporation)
• NSF
• AFOSR/DARPA
• Industry
• AFOSR/DARPA MURI Center on Intelligent Control of
  Semiconductor Manufacturing
• Research Goal Significant improvements in the
  robustness and performance of processes used in
  the manufacture of integrated circuits and flat
  panel displays

11
Research Team

• Faculty
• J. S. Freudenberg
• J. W. Grizzle
• P. Kabamba
• J. Kanicki
• P. P. Khargonekar
• M. Kushner (Illinois)
• V. Nair
• D. Srolovitz
• F. L. Terry, Jr.
• G. Was

• Research Staff
• D. Grimard
• P. Klimecky
• J. Moyne
• S. Rauf (Illinois)
• T. van der Straaten
• W. Sun
• Lab Staff

Graduate Students L. Dong, X. Dong, C.
Galarza, C. Garvin, E. Hamby, K. Khan, H. Kim, J.
Kim, W. Kong, J. Lee, T. Li, Z. Ma, O. Patterson,
B. Stutzman, T. Vincent, L. Xu, Q. Zhao B. Lay,
J. Lu, and D. Zhang (Illinois)
12
SCHEMATIC OF A PLASMA ETCHER
13
CONTROL OBJECTIVES
Polysilicon
SiO2

Silicon
Silicon

• Etch depth
• Selectivity - Etch only polysilicon but not the
  photoresist or SiO2
• Anisotropy - vertical walls
• Spatial uniformity

14
CONTROL STRATEGY

• Process variables and product variables
• Process variables parameters that characterize
  the plasma environment that the wafer sees
• Product variables wafer state parameters which
  define etch process goals
• Process Sensors based Control
• Select key process parameters which can be
  measured
• Concentration of fluorine, bias voltage, ion
  energy flux
• Devise controllers to use the process information
  with the aim of controlling the wafer etch
• Experiments are necessary to check the efficacy
  of the control strategy
• Product Sensors based Control
• Estimation of product parameters based on
  indirect measurements
• Combined use of Process and Product Sensors

15
CONTROL STRATEGY
16
PROCESS VARIABLE BASED CONTROL OF RIE

• We have designed and implemented several
  real-time controllers
• Controlled Variables Fluorine concentration,
  Bias Voltage or Ion Energy Flux, Pressure
• RF Power, Throttle angle, O2 as actuators
• Linear and nonlinear controller designs have been
  performed using both system identification as
  well as phenomenological models
• Experimental tests to evaluate the performance
  and robustness of the closed loop system

17
A LOADING EFFECT STUDY

• Loading effect etch rate decreases as the amount
  of exposed area of silicon increases
• Greater consumption of reactant as area increases
• Becomes more pronounced towards the end of the
  etch run as some areas are etched before some
  others due to spatial nonuniformity
• Known to be a significant problem in etching of
  silicon using fluorine chemistry
• Inverse of etch rate is linearly proportional to
  the exposed area - Mogab, Flamm
• We did a systematic study to evaluate the
  improvement against loading effect offered by
  real-time closed loop control
• Patterson and Khargonekar

18
LOADING EFFECT UNDER CONVENTIONAL CONTROL

• The plots show thickness of remaining silicon as
  a function of time for various loads
• As the load increases, the etch rate decreases
• These results are for a multiwafer reactor but
  similar phenomenon occurs in single wafer
  reactors as the exposed area varies

19
REDUCTION IN LOADING EFFECT

• Under real-time closed loop control, the slope of
  the line is much smaller than under conventional
  control.
• 80 reduction in loading effect

20
Wafer State Estimation

• GOAL Use non-invasive optical sensors to
  estimate wafer state
• If this can be done in situ and real-time, it has
  the potential to lead to major gains in the
  performance of semiconductor manufacturing
  systems
• Also useful as a diagnostic
• Can be useful in process design optimization
• For etching, key wafer states
• Etch depth, Wall angle, line width, spatial
  uniformity
• Two projects
• Etch depth estimation for blanket wafers
• Wafer state estimation for gratings

21
Dynamic Model

• Problem Estimate remaining thickness of a-Si in
  the presence of various uncertainties
• Nonlinear estimation problem
• Nonlinearity at the output

22
Adaptive Estimation Strategy

• Finite set of possible models - Magill (1965)

fit
d2750
x (k)
d2800
y(k)
x (k)
...
d3000
Voting mechanism winner take all
parallel filters
23
A NONLINEAR ESTIMATION PROBLEM

• Consider the system
• z - slow sensor drift, u - known input, w, v
  noise
• Problem estimate x (and z) given y
• A nonlinear filtering problem which captures a
  key part of the etch depth estimation problem
• A family of estimators for this problem that
  include EKF, IKF, etc. as special cases
• Also, a general stability result Vincent
  Khargonekar (IEEE TAC99)

24
Endpoint for a TFT Backchannel Recess Etch
a-SiH(i)

• Desired result Etch through a-SiH(n) and
  endpoint at a-SiH(n)/a-SiH(i) interface
• Can not use OES to solve this endpoint problem.
• a-SiH(i) thickness impacts device performance

Ta Gate
25
Reflectometry

• Multi-point laser reflectometer installed on the
  Plasma-Therm Plasma Etcher

26
Light Reflection from Material Stacks

• Total reflectance Er/Ei h(d, n)
• d film thicknesses, n optical constants

27
Problems with Reflection-Based Film Thickness
Monitoring

• Accurate knowledge of optical constants for
  various materials
• Gains and offsets in optical system
• Sample Alignment
• Window Coatings
• Transmission Changes (gain)
• Window Reflection (offset)
• Amplifiers and Other Electronics
• Manufacturing variations in underlying film
  thicknesses

28
ENDPOINT EXPERIMENT-II
a-Si
H(i
)
SiN
x
1000Å
a-Si
Glass Substra
te
3000Å
Ta
SiNx
Experimental Stack

• Goal Etch 500 Å of 1000 Å thick a-Si film
• 10 Etch Experiments
• 5 timed etches (standard practice.) Etch time 100
  seconds
• 5 etches endpointed using estimated etch depth
  from EKF-R

29
EXPERIMENTAL METHOD

• EKF setup
• Noise covariances tuned using simulated and
  actual data. Held fixed throughout experiment.
• Initial guess for a-Si thickness 1000 Å
• Independent Verification
• Pre-etch thickness measured using a Spectral
  Photometer
• Accuracy /- 20 Å
• Information not supplied to EKF
• Pre-etch a-Si thickness 3???128?Å?
• Post-etch thickness measured ex-situ using a
  Spectroscopic Ellipsometer
• Accuracy /- 5 Å

30
Adaptive Estimation Strategy

• Finite set of possible models - Magill (1965)

fit
d2750
x (k)
d2800
y(k)
x (k)
...
d3000
Voting mechanism winner take all
parallel filters
31
EXPERIMENTAL RESULTS
95 reduction in standard deviation
Vincent et al.
32
RESULTS - SiNx THICKNESS
33
Patterned Wafers

• Recent efforts to extend these ideas to patterned
  wafers
• Several possible optical techniques Spectral
  ellipsometry, reflectance difference
  spectrometry, 2 channel spectral reflectometry
  (2CSR)
• Grating structure
• .17 mm linewidth
• .78 mm height
• .7 mm period

34
Two Channel Spectroscopic Reflectometer

• Similar to Ellipsometer but Fixed Prisms (No
  Moving Parts)
• Measures Rs2, Rp2 ? tan(y)
• 6 ms Integration Time/20 Hz Sampling Rates
• Low Construction Cost (7K)
• Very Good Reproducibility and Near SE Level
  Accuracy Demonstrated
• Reported at APS 98

F. L. Terry, Jr and his students
35
Reflectance Measurements
time
time
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
Wavelength (?m)
Wavelength (?m)
36
Rigorous Coupled-Wave Analysis (RCWA)

• The Groove is Sliced into a Number of Thin
  Layers
• Numerical Eigen-Matrix Solution for Maxwells
  Equations
• Amplitudes Phases of Different Diffraction
  Orders Are
• Obtained by Matching the EM Boundary
  Conditions
• Non-linear Regression to Obtain the Depth, CD,
  and Wall Angle
• F. L. Terry, Jr and his students

37
RCWA Fit vs. 2CSR Measurement
RS2
RP2
0.174 µm
0.780 µm
84.2
0.333 µm
38
Estimation Problem

• Sensor data measured reflectances (92 dim
  vector)
• Problem Estimate height, wall angle, and top
  width from the measured data in real time
• First principles based computational model
  relating the feature geometry to measured
  reflectances (RCWA model)
• Takes one minute for each forward model
  computation
• 15 minute for NLSQ state estimation per sample
• Not suitable for real-time estimation
• A nonlinear real-time estimation problem
• Ji-Woong Lee, Hsu-Ting Huang, Brooke Stutzman,
  Craig Garvin, Pramod Khargonekar, Fred Terry

39
Inverse RCWA by RBF Network

• Training Data
• D ? ?d1, ?, dN?? wafer states forming a regular
  grid. h(D) ? ?h(d1), ?, h(dN)?
• G ?g1, ?, gN? ? artificial Gaussian noise
• (D, h(D) ? G) ? (training output, training
  input)
• Offline Training Orthogonal Least Squares.
• Online RBF Approximation of h?1

RBF Network
2 CSR Output
State Estimate
40
Real-Time Pattern Profile Monitoring by RBF
Network
41
Recursive Nonlinear State Estimation

• RCWA Model Simulation
• D ? ?d1, ?, dN? h(D) ? ?h(d1), ?,
  h(dN)? (D, h(D)) ? simulated state-output
  pairs.
• Online State Estimation Algorithm An
  optimization based algorithm

2CSR Output
Estimate
State Estimator with (D, h(D))
zk1
xk?1k?1
xkk
Unit Delay
42
Stochastic Model

• Wafer State Evolution xk?1 ? fk(xk) ? wk
• 2CSR Output zk ? h(xk) ? ek (h is
  1-1)

• How do we estimate xk given zk?
• Inversion of RCWA using radial basis function
  (RBF) network
• Recursive nonlinear state estimation.

43
State Estimation Algorithm

• Initialization x0?1 ? initial prediction of x0
  
• W ? a box in R3 centered at the origin k ? 0.

• Recursive Estimation Routine

• Constrained convex optimization
• Box Xk moves around prediction xkk?1.
• Given points Dk in Xk, express the unique point
  in the convex hull of h(Dk) nearest to zk as a
  convex combination of h(di)s. Let the estimate
  xkk be the same combination of dis.
• Computation time ? 0.25 sec. on 600MHz PIII,
  Matlab.

44
Now an Animation Clip
45
Real-Time Pattern Profile End Point Control
Endpoint Detection of Targeted Bottom CD at 0.25
µm
46
Real-Time End Point Detection

• Target? bottom width of 250nm
• Initial State (k ? 3 sec)?
• NF NLSQ
• Thickness? 761 756 (nm)
• Top width? 167 170 (nm)
• Wall angle? 84.1 84.0 (deg)
• Bottom width? 325 329 (nm)
• Result (k ? 183 sec)?
• NF NLSQ
• Thickness? 568 569 (nm)
• Top width? 113 115 (nm)
• Wall angle? 83.2 83.2 (deg)
• Bottom width? 249 251 (nm)

47
Short-Term Future Efforts

• MURI Program ended in September 2001
• NIST ATP Program
• ATP Advanced Technology Program
• Aimed at enabling technology transfer
• Involves KLA-Tencor and Lam Research as major
  partners
• Path to commercial adoption of our research

48
CONCLUDING REMARKS

• Advanced control and estimation problems for
  semiconductor manufacturing processes present
  many challenges
• Lithography, CMP, RIE, Thermal Processing,
• Nonlinear estimation can be very useful in
  getting more out of existing sensors
• How does one use complex first principles models
  in estimation and control?
• Emergence of nanoelectronics and nanophotonics

49
Thoughts on Future Directions in Control

• Autonomous and intelligent systems
• How can we make goal oriented autonomous systems
  that are robust to environmental uncertainty
• Cooperative systems of such agents
• Original idea behind Wieners cybernetics
• New transportation systems with different energy
  sources such as fuel cells
• Biological (cell-micro), bio-mimetic, and
  biomedical systems
• Pervasive proliferation of information technology
  will make large scale systems control both
  important and feasible