Ion Implantation and Synthesis of Materials - Studium

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126 9 Doping, Diffusion and Defects in Ion-Implanted SiProblems9.1 What is the value of the diffusion length λ = (4Dt) 1/2 for Boron in Siannealed at 1,000°C for 10 s? Compare with the B profile shown inFig. 9.12.9.2 What is the value in eV for the activation energy, E A , when the diffusionvalues change by a factor of 10 for a value of 1,000/T of 0.65 and 0.70.9.3 Consider a drive in diffusion step for implanted As into Si. The As dose is1 × 10 14 As cm −2 and the drive temperature is 1,000°C(a) How much time is required to reduce the surface concentration to ½ ofits initial value?(b) What will the value of the diffusion length be?9.4 What is the atomic jump frequency for Si self-diffusion at 1,000°Cassuming that the atomic jump distance is 0.235 nm?9.5 Calculate the activation energy for Si self-diffusion assumingD 0 = 1.5 × 10 3 cm −2 s −1 .9.6 During ion implantation in Si, the vacancy concentration can be very high.Using SRIM, calculate the vacancy concentration at the damage peak for40 keV B implanted to a dose of 1 × 10 14 B cm −2 . The sample will beheated to 1,000°C for 10 s to activate the B. What enhancement isexpected in the diffusivity due to radiation-enhanced diffusion?
10 Crystallization and Regrowth of Amorphous Si10.1 IntroductionDuring ion implantation, each ion produces a region of disorder around the iontrack. As the implantation dose increases, the disorder increases until all the atomshave been displaced and an amorphous layer is produced over a depth R p . Thebuildup and saturation of disorder are shown in Fig. 10.1 for 40 keV phosphorusions incident on Si. In this example, about 4 × 10 14 phosphorus ions cm −2 arerequired to form an amorphous layer. Except for low doses or implantation withlight ions, we can anticipate that an amorphous layer is formed during theimplantation process. This assumes that no recovery of lattice order occurs aroundthe ion track.Amorphous regions also can be formed by light ion implantation at suitabletarget temperatures and doses. For light ion implantation the defect density in thesingle collision cascade is quite low, and amorphization occurs when the materialaccumulates enough damage that it reaches a critical threshold in the defectdensity (Rimini 1995). In general, for light ion amorphization, cascade overlap isrequired and the layer becomes amorphous when the free energy of the cascadeinduceddefect-rich region equals the free energy of the amorphous phase.In terms of energy deposition, it has been found that amorphous formationrequires an energy deposition of 6 × 10 23 keV cm −3 at low temperature and lowenergy. The deposited energy for a given implant is given by φν/R p , where φ is thedose and ν is the damage energy (see Chap. 7, Sects. 4 and 5). In the case of a Bimplant at low energy with dE/dx| n ~ 0.6 eV nm −1 , a fluence of 1.6 × 10 15 cm −2 isrequired for amorphization. These estimates are valid at sufficiently lowtemperatures where defect mobility is low and therefore defect recombination islimited. For any ion, the threshold dose for amorphization increases withincreasing target temperature up to a critical value, above which amorphizationdoes not occur. The critical temperature depends on the ion mass and energy, i.e.,on the energy density deposited into nuclear collisions. Experimental results areshown in Fig. 10.2.127
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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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Page 86 and 87: 76 6 Ion Range and Range Distributi
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Page 104 and 105: 94 8 Channeling1.00.8Non-aligned Im
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Page 108 and 109: 98 8 ChannelingThe channeling effec
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Page 118 and 119: 108 9 Doping, Diffusion and Defects
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176 12 Surface Erosion During Impla
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178 12 Surface Erosion During Impla
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180 13 Ion-Induced Atomic Intermixi
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194 14 Application of Ion Implantat
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15 Ion Implantation in CMOS Technol
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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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