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1 Beyond Thermal Budget: Simple Kinetic Optimization in RTP Lecture 13a Text Overview

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2 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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3 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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4 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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5 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 E undes > E des E undes < E des See R. Ditchfield and E. G. Seebauer, JES 40 (1997) 1842

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6 T-t Curves: B on Si Undoped Si grown epitaxially on B-doped Si(100) T>730°C, 57.5 nm Hi T lowest budget E diff = 3.6 eV E dep = 0.52 eV

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7 Boron Profiles Lowest budget (Hi T) gives worst spreading Thermal budget prediction fails

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8 T-t Curves: Cu in Si Undoped Si grown epitaxially on Cu- doped Si(100) T<700°C, 57.5 nm Hi T lowest budget E diff = 1.0 eV E dep = 1.5 eV

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9 Copper Profiles Lowest budget (Hi T) gives best spreading Thermal budget prediction OK

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10 Summary of Experiments T-t budget minimization fails completely when E undes > E des D-t minimization works x 2 = 6Dt is always smallest for minimum budget but Ignores rate selectivity: doesn’t give unique prediction for T-t profile

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11 Ambiguity of Budget Minimization These scenarios give different kinetic results Need consideration of rate selectivity Minimize tMinimize T

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12 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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13 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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14 Phenomenological View of Activation Energy Ignore notions of “activation barrier” Applies to single, elementary steps only Qualitative view Describes strength of T dependence Higher E a stronger T variation of rate Quantitative description E a = – d(lnK)/d(1/k B T)

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15 Effects of Activation Energy t varies strongly with T High slope t varies weakly with T Low slope E act higher E act lower

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16 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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17 Rate Selectivity Principle: Processing Rules: If E undes > E des favor low T If E undes < E des 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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18 E undes < E des Use fast ramp and cool High T best, limited only by process constraints on T max

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19 E undes > E des Use fast ramp and cool Low T best, limited only by process constraints on t max

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20 Accounting for Constraints: Examples T constraints T max wafer damage, differential thermal exp. T min thermodynamics (dopant activation) t constraints t max throughput t min equipment limitations (maximum heating rate)

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21 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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22 Window Collapse Hopefully shaded area is nondegenerate! maxmin

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23 Mapping of Constraints: Half Window E undes > E des E undes < E des

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24 Mapping of Constraints: Full Window E undes > E des E undes < E des

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25 Superposing other Process Constraints E undes > E des

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26 Final Optimization From a kinetic perspective, it’s usually best to operate… Better: along an edge of allowed window Best: at a corner Example: E undes > E des Lowest T gives best selectivity Lowest t gives best throughput Alternatives: Highest T gives best rate at cost of selectivity

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27 Spike Anneals Characteristics No “soak” period Sometimes very fast ramp (> 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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28 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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29 Mathematical Analysis Simplified kinetic expressions Desired differential:r = A exp(–E d /kT) integral:R = r dt Undesired integral:x 2 = 6Dt = 6D o exp(–E u /kT)t

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30 Integrated Rates during Ramp Up Ramp up: Desired Undesired These integrals need an approximation to evaluate analytically

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31 Laplace Asymptotic Evaluation Integrals likehave the form : for y >> 1 Letso that Thusand so

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32 Behavior of Laplace Approximation More accurate (1%) approximation comes from the Incomplete Gamma Function With E/kT M 30, approximation is good to ~7% See E. G. Seebauer, Surface Science, 316 (1994)

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33 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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34 Effects of Activation Energy E act higher E act lower t varies strongly with T High slope t varies weakly with T Low slope

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35 Laplace Approximations to Rates during Cool-Down Cool down: Desired Undesired

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36 Total Integrated Rates Desired Undesired Control variables: and T M only If >> CT M 4, increasing brings little extra return

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37 Mapping of Constraints: Half Window E undes > E des E undes < E des

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38 Mapping of Constraints: Full Window E undes > E des E undes < E des

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39 Mapping of Constraints: Full Window Optimal point shown to give most throughput

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40 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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41 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), (General rules, child metaphor) E. G. Seebauer and R. Ditchfield, “Fixing Hidden Problems with Thermal Budget,” Solid State Technol. 40 (1997) (Review, expt’l 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) (Detailed expt’l 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), (More mapping concepts) E. G. Seebauer, “Spike Anneals in RTP: Kinetic Analysis,” Advances in Rapid Thermal Processing (ECS Vol , 1999) (Extension of concepts to spikes)

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