Beyond Thermal Budget: Simple Kinetic Optimization in RTP

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Beyond Thermal Budget Simple Kinetic
Optimization in RTP

• Lecture 13a Text Overview

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Two Approaches to Kinetic Modeling

• Sophisticated
• Detailed kinetics
• Treatment integrated with uniformity, strain
• Computationally intensive
• Not-so-sophisticated
• Simplified kinetics
• Heuristic integration of process constraints
• Computationally simple

Here we employ second approach
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Thermal Budget Basic Idea

• Definition varies in common usage
• Product of T and t
• Area under a T-t curve
• Area under a D-t curve

• Principle minimum budget optimizes against
  unwanted rate processes
• Diffusion
• Interface degradation
• Many others

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Merits of the Concept

• Positives
• Appealing metaphor like fiscal budget
• Successfully predicts kinetic advantages of RTP
  over conventional furnaces
• Negatives
• Definition varies, ambiguous treatment
• Focuses excessively on initial, final states
• Tends to ignore transformations during ramp
• Ignores rate selectivity

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Controlled Test of the Concept

• Simultaneous Si CVD (desired) and dopant
  diffusion (undesired)
• Undoped Si on B-doped Si
• Undoped Si on Cu-doped Si
• Fix CVD thickness, measure dopant profile by SIMS
• See whether budget minimization works for
• Eundes gt Edes
• Eundes lt Edes

See R. Ditchfield and E. G. Seebauer, JES 40
(1997) 1842
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T-t Curves B on Si

• Undoped Si grown epitaxially on B-doped Si(100)
• Tgt730C, 57.5 nm
• Hi T ? lowest budget
• Ediff 3.6 eV Edep 0.52 eV

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Boron Profiles

• Lowest budget (Hi T) gives worst spreading
• Thermal budget prediction fails

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T-t Curves Cu in Si

• Undoped Si grown epitaxially on Cu-doped Si(100)
• Tlt700C, 57.5 nm
• Hi T ? lowest budget
• Ediff 1.0 eV Edep 1.5 eV

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Copper Profiles

• Lowest budget (Hi T) gives best spreading
• Thermal budget prediction OK

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Summary of Experiments

• T-t budget minimization fails completely when
  Eundes gt Edes
• D-t minimization works
• x2 6Dt is always smallest for minimum budget
• but
• Ignores rate selectivity doesnt give unique
  prediction for T-t profile

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Ambiguity of Budget Minimization
Minimize t
Minimize T

• These scenarios give different kinetic results
• Need consideration of rate selectivity

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Setting the Stage Desiderata

• Typical desired rate processes
• CVD
• Silicidation
• Oxidation/nitridation
• Post-implant annealing/activation
• Typical undesired rate processes
• TED
• Interface degradation
• Silicide agglomeration

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Problem Formulation

• Restrict attention appropriately
• Ignore strain, uniformity, control
• Focus on one desired, one undesired rate
• Assume suitable rate data exist
• Focus on integrated (not instantaneous) rates

? r(t,T) dt vs. r(t,T)
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Phenomenological View of Activation Energy

• Ignore notions of activation barrier
• Applies to single, elementary steps only
• Qualitative view
• Describes strength of T dependence
• Higher Ea ? stronger T variation of rate
• Quantitative description

Ea d(lnK)/d(1/kBT)
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Effects of Activation Energy

• Eact higher

• t varies strongly with T
• High slope

• Eact lower

• t varies weakly with T
• Low slope

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A Subtle Distinction

• We use t-T curves to represent actual time and
  temperature

• We use T-t curves to represent total process
  times for design purposes

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Rate Selectivity

• Principle
• Processing Rules
• If Eundes gt Edes ? favor low T
• If Eundes lt Edes ? favor high T
• Corollaries
• Get to and from soak T (or max T in spike) as
  fast as possible
• No kinetic advantage to mixture of ramp and soak

At high T, rate with stronger T dependence wins
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Eundes lt Edes

• Use fast ramp and cool
• High T best, limited only by process constraints
  on Tmax

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Eundes gt Edes

• Use fast ramp and cool
• Low T best, limited only by process constraints
  on tmax

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Accounting for Constraints Examples

• T constraints
• Tmax ? wafer damage, differential thermal exp.
• Tmin ? thermodynamics (dopant activation)
• t constraints
• tmax ? throughput
• tmin ? equipment limitations (maximum heating
  rate)

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Formulation of Constraints

• Half-window upper or lower limit
• Most undesired phenomena upper limit
• Degree of interface degradation
• Extent of TED
• Some desired phenomena lower limit
• Defect annealing
• Silicidation
• Full window upper and lower limit
• Some desired phenomena
• Film deposition
• Oxidation

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Window Collapse
max
min

• Hopefully shaded area is nondegenerate!

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Mapping of Constraints Half Window

• Eundes gt Edes

• Eundes lt Edes

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Mapping of Constraints Full Window

• Eundes gt Edes

• Eundes lt Edes

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Superposing other Process Constraints

• Eundes gt Edes

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Final Optimization

• From a kinetic perspective, its usually best to
  operate
• Better along an edge of allowed window
• Best at a corner

• Example Eundes gt Edes
• Lowest T gives best selectivity
• Lowest t gives best throughput

• Alternatives
• Highest T gives best rate at cost of selectivity

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Spike Anneals

• Characteristics
• No soak period
• Sometimes very fast ramp (gt 400/C)
• Motivation
• Takes selectivity rules for high T to their
  logical extreme
• Improved kinetic behavior, esp. in post-implant
  annealing

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An Idealized Spike

• Assume
• Linear ramp up at rate ? (?C/s)
• Cooling by radiation only
• Constant emissivity
• Surroundings at negligible temperature
• Assumptions satisfactory only for
  semiquantitative results

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Mathematical Analysis

• Simplified kinetic expressions
• Desired
• differential r A exp(Ed /kT)
• integral R ? r dt
• Undesired
• integral x 2 6Dt
• 6Do exp(Eu /kT)t

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Integrated Rates during Ramp Up

• Ramp up
• Desired
• Undesired
• These integrals need an approximation to evaluate
  analytically

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Laplace Asymptotic Evaluation

• Integrals like have the form

for y gtgt 1

• Let

so that

• Thus

and
so
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Behavior of Laplace Approximation

• With E/kTM ? 30, approximation is good to 7

• More accurate (1) approximation comes from the
  Incomplete Gamma Function

• See E. G. Seebauer, Surface Science, 316 (1994)
  391-405.

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Laplace Approximations to Rates during Ramp Up

• Ramp up
• Desired
• Undesired

• Note 1/? trades off with E the way t does in
  non-ramp expressions

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Effects of Activation Energy

• Eact higher

• t varies strongly with T
• High slope

• Eact lower

• t varies weakly with T
• Low slope

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Laplace Approximations to Rates during Cool-Down

• Cool down
• Desired
• Undesired

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Total Integrated Rates

• Desired
• Undesired
• Control variables ? and TM only
• If ? gtgt CTM4, increasing ? brings little extra
  return

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Mapping of Constraints Half Window

• Eundes gt Edes

• Eundes lt Edes

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Mapping of Constraints Full Window

• Eundes gt Edes

• Eundes lt Edes

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Mapping of Constraints Full Window

• Optimal point shown to give most throughput

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Summary

• Concept of thermal budget problematic
• Rate selectivity more reliable
• Simple graphical procedure helps conceptualize
  2-rate problems, including constraints
• Framework can be generalized to 3 or more rates
• Laplace approximation useful for variable-T
  applications

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For Further Reference

• R. Ditchfield and E. G. Seebauer, General
  Kinetic Rules for Rapid Thermal Processing,
  Rapid Thermal and Integrated Processing V (MRS
  Vol. 429, 1996), 133-138. (General rules, child
  metaphor)
• E. G. Seebauer and R. Ditchfield, Fixing Hidden
  Problems with Thermal Budget, Solid State
  Technol. 40 (1997) 111-120. (Review, exptl
  data, mapping concepts)
• R. Ditchfield and E. G. Seebauer, Rapid Thermal
  Processing Fixing Problems with the Concept of
  Thermal Budget, J. Electrochem. Soc., 144 (1997)
  1842-1849. (Detailed exptl data)
• R. Ditchfield and E. G. Seebauer, Beyond Thermal
  Budget Using D?t in Kinetic Optimization of
  RTP, Rapid Thermal and Integrated Processing VII
  (MRS Vol. 525, 1998), 57-62. (More mapping
  concepts)
• E. G. Seebauer, Spike Anneals in RTP Kinetic
  Analysis, Advances in Rapid Thermal Processing
  (ECS Vol. 99-10, 1999) 67-71. (Extension of
  concepts to spikes)