RuntoRun Control of Linewidth and Overlay in Semiconductor Manufacturing

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Run-to-Run Control of Linewidth and Overlay in
Semiconductor Manufacturing

• Christopher Allen Bode
• Dr. Thomas F. Edgar, Advisor
• University of Texas at Austin
• February 18, 2001

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Lithography Overlay

• Control objective minimization of eight lot mean
  overlay error parameters
• includes x and y translation, x and y scale,
  wafer and reticle rotation, magnification, and
  orthogonality

Orthogonality
Y translation
X translation
Magnification
X scale
Reticle rotation
Y scale
Wafer rotation
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Linewidth

• Linewidth is determined by the combined effects
  of the lithography and etch processes.
• The control objective is to meet a device
  linewidth specification.
• The polysilicon gate linewidth one of the most
  critical device specifications in the manufacture
  of logic devices.

Lithography
Etch
Resist Linewidth
Device Linewidth
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Resist etch process

• An additional step is added to the etch process
  which etches the resist pattern.
• The incoming pattern is masked with linewidths
  greater than required.
• The resist etch step trims the lines to the
  proper resist linewidth.
• The rest of the etch transfers the resulting mask
  pattern into the polysilicon, creating the poly
  gate structures.

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LMPC Run-to-run Control

• LMPC offers significant advantages over standard
  EWMA-based controllers prevalent in semiconductor
  industry
• Explicitly handles MIMO systems with constraints
• Includes constraints on yk, uk, and ?uk
• Control action is decoupled from state estimation
• Typically employs Kalman linear observer
• Can be used in a predictive capacity over an
  infinite horizon
• Less so for batch processes with little
  auto-correlation
• Augmentation of the state-space model can
  compensate for input and output disturbances

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LMPC Formulation of overlay controller

• Overlay control employs the output step
  disturbance model
• The model intercept is accounted by the
  disturbance term, pk
• This can be expressed in the standard state-space
  formulation by combining the plant and
  disturbance states
• In the case of overlay control, A 0, B C I

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LMPC formulation of linewidth controller

• The linewidth model adds two disturbance states,
  the etch bias and the measured resist linewidth.
• The disturbance state, pk, is the etch chamber
  bias, and cdk is the measured resist linewidth.
• A33 is a gain on the resist linewidth
  measurement, as it is an intermediate calculation
  and also subject to more noise than the final
  device linewidth measurement. The residual
  linewidth is absorbed into the etch chamber bias
  estimate.

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Linear observer form

• Both controllers have linear filters with the
  same general form
• Open loop estimation on plant states
• The linewidth controller has a direct measurement
  of resist linewidth
• The state observer is open loop, as the number of
  estimated stated from a single metrology even
  must be less than or equal to the number of
  measurements
• This also prevents the use of combined
  input/output disturbance model
• All variation in the process is captured as
  changes in the disturbance states

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Control thread methodology

• Control threads collect wafer lots into groups
  with like states.
• The context within which a lot is processed, both
  during upstream processing and current operation,
  determines the wafer and process state.
• The identification of the actual contribution to
  the state from each context variable is not
  necessary rather, the cumulative effect is
  identified through feedback metrology.
• Through the use of control threads, the amount of
  variability in the aggregate control state is
  much smaller than the overall state variation.
• Each thread context is controlled separately.
  Variability is reduced, but so is the the amount
  of feedback data available to each thread.
• Proper definition of the control threads is key.
  Over-definition of the thread criteria can lead
  to large numbers of threads and data poverty.

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Reduction of state variation with threads

• Demonstration of the reduction in state
  variability due to the application of control
  threads to linewidth control.

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LMPC control of overlay - example
Uncontrolled
Controlled
Actual trend in magnification performance on a
Fab 25 exposure tool - Shows three step
disturbances due to maintenance events -
Uncharacteristic lot performance is prevalent
throughout - LMPC shows good control to target,
adequate recovery from step disturbances
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Summary

• For both the linewidth and overlay controllers
• Compiled a set of known sources of control state
  variation.
• Identified key sources to define control threads.
• Developed a run-to-run Linear Model Predictive
  Control method.
• Implemented complete control solution into
  high-volume semiconductor manufacturing
  environments at AMD.
• Results
• Increased the linewidth process capability (Cpk)
  by 44 over existing control methods.
• Decreased average standard deviation of overlay
  error by 40, with 10 of this decrease coming
  from the transition from an EWMA to a LMPC
  control formulation.