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

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 timeMask Writing Schedule ProblemGiven: Beam voltage, resist parameters, threshold temperature Tmax

Find: Beam current density and subfield writing schedule such that the maximum resist temperature never exceeds Tmax

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

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

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 scheduling1. 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

Cost Computation• The cost of a subfield order is Tmax + (1- )Tavg;

Tmax 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

2Sf

rise f)d(s, TT

(s)T-

c =

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)

Phase-1: coarse subfield ordering simulation

Phase-2: detailed critical subfield simulation

Chess board pattern within critical subfield

Scheduling Results

• Critical subfield temperature profiles before occurrence of flash for 16×16 subfield pattern

Max48.85CMean27.59C

(a) Sequential schedule

Max32.68CMean16.07C

(b) Greedy schedule

Detailed temperature profile

Sequential: Max=105.10C

Detailed temperature profile

Greedy: Max=93.70C

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