Ion Implantation and Synthesis of Materials - Studium

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170 12 Surface Erosion During Implantation: SputteringN AJ BJ AJ iDepthSurfaceR pFig. 12.8. A model for the buildup of implanted concentration as a function of implantationdose. Assuming a very efficient atomic mixing, this model approximates the implantedprofile with a constant shape, but with an increasing amplitude. The rate of increase of theimplanted concentration is due to the difference between the flux of incident ions of speciesA, J i , and that of the sputtered particles of species A, J AJJBAx= Yir + xr= YJir + x(12.18)(12.19)Substituting (12.7) and (12.8) into (12.6), yieldsd ⎛ x ⎞xR = −d⎜1 +⎟N J YJt ⎝ x⎠r + xp 0 i i{}.(12.20)Where N 0 ≡ N A + N B . After some rearrangement, (12.20) becomesr + x1d x = (d φ2A ),(1 + x) [ r + (1 − Y) x]NR0P(12.21)where dφ A ≡ J i dt is the incremental ion dose. Equation (12.21) is a differentialequation for x(φ A ), which can be solved by taking the partial fractions for the lefthandside and integrating. The result is⎡ Ax ⎛ 1 + x ⎞⎤YφAY+ Bln⎜⎟=⎢⎣1 + x ⎝1 − x/ x( ∞)⎠⎥⎦N0RP(12.22)
12.6 Concentrations of Implanted Species 171where A ≡ (r − 1)/[r −(1 − Y )], B = Yr/[(1 − Y )− r] 2 , and x(∞) = r/(Y − 1). Notethat Yφ A /N 0 R P can be interpreted as the amount of material sputtered in units ofthickness, normalized by the ion range. An example of the calculated x(φ A ) isgiven in Fig. 12.9.The steady-state compositions are the same as those predicted by (12.10), i.e.N A /N B = r(Y − 1) −1 . Note that for r = 2, it takes about twice as much sputtering toreach the steady-state composition.12.6 Concentrations of Implanted SpeciesThis section will examine the influence of sputtering yield, Y, and the sputteringparameter r, on the buildup of the concentration of implanted species. Specificexamples will include implanting Pt and Si into Si, Pt and PtSi.12.6.1 Si Implanted with 45 keV Pt IonsAs (12.6) illustrates, the parameter r, for the case of Pt implanted into Si, isdefined by the expression J = r(N ). A value of r = 2 is assumed basedSi/J PtSi /N Pt0.15Y = 200.10N AN B r = 20.05r = 12Y– 11Y– 10.000 1 2 3 4 5 6Sputtered ThicknessR pFig. 12.9. Buildup of the implanted concentration calculated from the simple model ofFig. 12.8. Examples with Y = 20 and r = 1 or 2 are shown. With a preferential sputtering ofthe target material (r = 2), a correspondingly higher implanted concentration can beachieved. The curves are calculated from (12.11) (Liau and Mayer 1980)
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M. Nastasi J.W. MayerIon Implantati
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To our loved ones
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xContents4 Cross-Section ..........
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Contentsxiii14.3.2 Punch-Through St
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2 1 General Features and Fundamenta
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10 1 General Features and Fundament
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12 2 Particle InteractionsThe restr
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142 Particle Interactions(a)V(r)r 0
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162 Particle InteractionsHowever, a
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182 Particle Interactionswhere the
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202 Particle Interactionsa0.8853a0L
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3 Dynamics of Binary Elastic Collis
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3.3 Kinematics of Elastic Collision
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3.4 Center-of-Mass Coordinates 27Fi
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3.4 Center-of-Mass Coordinates 29an
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3.5 Motion under a Central Force 31
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3.5 Motion under a Central Force 33
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Problems 35The reduced energy for 1
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4 Cross-Section4.1 IntroductionIn C
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4.2 Scattering Cross-Section 39unit
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4.2 Scattering Cross-Section 41Rdθ
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4.3 Energy-Transfer Cross-Section 4
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4.4 Approximation to the Energy-Tra
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Problems 47ReferencesNastasi, M., M
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5 Ion Stopping5.1 IntroductionWhen
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5.3 Nuclear Stopping 51MeV mg −1
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5.3 Nuclear Stopping 531−m1−2mC
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5.4 ZBL Nuclear Stopping Cross-Sect
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5.5 Electronic Stopping 575.5.1 Hig
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5.5 Electronic Stopping 59Table 5.1
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Problems 61Problems5.1 Calculate th
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64 6 Ion Range and Range Distributi
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78 7 Displacements and Radiation Da
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94 8 Channeling1.00.8Non-aligned Im
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96 8 ChannelingMeV ION BEAMSUBSTITU
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98 8 ChannelingThe channeling effec
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100 8 Channeling4.0Silicon2.0P (mic
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102 8 ChannelingdσσD( ψc) = ∫
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104 8 ChannelingDechanneled fractio
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106 8 ChannelingProblems8.1 Calcula
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108 9 Doping, Diffusion and Defects
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Page 130 and 131: 120 9 Doping, Diffusion and Defects
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15.2 Implanters Used in CMOS Proces
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15.3 Low Energy Productivity: Beam
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15.5 Angle Control 233Fig. 15.13. O
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15.5 Angle Control 235Fig. 15.15. I
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References 237No. of implants504540
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Appendix ATable of the Elementselem
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Appendix A 241elementatomicnumber(Z
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Appendix A 243element atomicnumber(
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Appendix BPhysical constants, conve
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IndexAlpha particle 8amorphization
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Index 259differential cross-section
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Index 261layer transfer 143Lennard-
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Index 263thermodynamiceffect ion be
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