Mask-writing Strategies for Increased CD Accuracy and Throughput

1
Mask-writing Strategies for
Increased CD Accuracy and
Throughput
Calibrating Achievable Design Annual Review
September 2003
Swamy V. Muddu, Andrew B. Kahng (Joint work with
Sergey Babin and Ion Mandoiu)
Abstract Resist heating and proximity effects
in e-beam mask writing affect critical dimension
(CD) accuracy and throughput. Tight CD control is
important for minimizing on-chip variability in
future technology nodes. High mask-writing
throughput is needed for reducing soaring mask
costs. Resist heating is a significant
contributor to CD distortion on mask. Current
e-beam writing strategies optimize beam current
density, number of passes etc., but at the cost
of decreasing throughput. We propose a new e-beam
writing strategy that reduces CD distortion while
maintaining throughput. Simulation results
indicate non-sequential writing of subfields lead
to effective dissipation of heat and improve CD
distortion. References S. Babin, A.B. Kahng,
I.I. Mandoiu, S. Muddu, Resist heating
dependence on subfield scheduling in 50kV
electron beam maskmaking, Proc. of Photomask
Japan, April 2004, to appear Sergey Babin,
Measurement of resist heating in photomask
fabrication, J. Vac. Sci. Technol. B 15(6),
Nov/Dec 1997, pp. 2209-2213

• Subfield Scheduling
• Key observation scheduling of subfields
  decreases maximum resist temperature
• Non-sequential writing ? throughput overhead due
  to beam settling time
• To maintain throughput, equalize mask write times
  by increasing beam current density
• Rise in temperature due to increased current
  density is offset by non-sequential writing
  schedule

• Simulation Setup
• Resist heating simulations performed using
  TEMPTATION resist heating simulator
• Simulated subfield scheduling strategies (1)
  Sequential and (2) Greedy
• A two-phase simulation setup was used to simulate
  16 x 16 subfields
• Phase I Every subfield is flashed using 4 coarse
  flashes with total dose equal to that of detailed
  fracture flashes
• Phase II The simulation is repeated with the
  critical subfield (i.e., the subfield with
  maximum temperature before writing in phase I)
  flashed using detailed fracture flashes (512 2µm
  x 2µm fractures)

• Greedy Subfield Scheduling
• Greedy algorithm starts from a random ordering of
  subfields and iteratively modifies the ordering
  by swapping pairs of subfields
• Evaluating the cost function takes O(n2) time,
  and thus the greedy algorithm requires O(n4) time
  per improving swap, where n is the number of
  subfields in a main deflection field
• Our implementation evaluates only pairs (i,j) in
  which i is a subfield with max temperature this
  reduces runtime to O(n3) per improving swap

Greedy scheduling
1. Start with random subfield order ? 2. Repeat forever For all pairs (i,j) of subfields, compute cost of ? with i and j swapped If there exists at least one cost-improving swap, then modify ? by applying a swap with highest cost gain Else exit repeat

• Motivation
• Mask writing in DSM regimes is limited by resist
  heating effects, such as CD distortion
• Current techniques for reducing resist heating
  (reducing e-beam density, multi-pass writing,
  etc.) reduce mask writing throughput
• To reduce resist heating, avoid successive
  writing of subfields
• To maintain throughput we increase beam current
  density such that reduction in dwell time
  compensates for increase in travel time

• Scheduling Results
• Critical subfield temperature profiles before
  occurrence of flash for 1616 subfield pattern

Mask Writing Schedule Problem Given Beam
voltage, resist parameters, threshold temperature
Tmax Find Beam current density and subfield
writing schedule such that the maximum resist
temperature never exceeds Tmax

• Cost Computation
• The cost of a subfield order ? is ? Tmax (1-
  ?)TavgTmax ? max temperature before
  writingTavg? avg temperature before writing
• Tmax corresponds to CD distortion due to resist
  heating, while Tavg corresponds to increase in
  mask write time
• To find an ordering, we can associate different
  weightings to Tmax, Tavg. In our experiments we
  use ? 0.5
• The temperature rise of a subfield s due to the
  writing of subfield f depends on the distance
  between s and f, the energy deposited while
  writing f, and the thermal properties of resist
• The temperature of each subfield decays
  exponentially between flashes
• With this model, evaluating the cost function for
  a given subfield order requires O(n2) time

• Variable-shaped E-beam Writing
• Taxonomy of mask features
• Fractures smallest features written on the mask
  dimensions in the range 0.5µm-2µm
• Minor field collection of fractures
• Subfield collection of minor fields typical
  subfield size 64µm X 64µm
• Major field or cell collection of subfields
• E-beam writing technology context
• High power densities (up to 1GW/c.c.) needed to
  meet SIA Roadmap requirements
• Power densities induce local heating causing
  significant critical dimension (CD) distortion
• Scheduling of fractures incurs large positioning
  overheads
• Scheduling subfields incurs very low overheads,
  yet is still effective in reducing excessive
  heating

Detailed temperature profile Sequential
Max105.10?C

• Conclusions
• Self-avoiding subfield ordering reduces the
  maximum temperature of resist by spacing
  successive writings
• To normalize the throughput due to scheduling, we
  decrease the dwell time of each subfield by
  increasing the current density
• Increase in current density does not increase
  resist heating significantly because of subfield
  ordering

• Future Work
• Use accurate temperature modeling approach in
  cost computation in greedy scheduling
• Quantify the improvements in CD and throughput
  due to decrease in resist temperature