Ion Implantation and Synthesis of Materials - Studium

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323 Dynamics of Binary Elastic Collisions3.5.2 Angular Orbital Momentum and the Impact ParametersConsider an interaction potential-energy, V(r), which tends to zero as r approachesinfinity. This situation corresponds to the condition that a moving particle haspositive kinetic energy at infinity. If V(r) is everywhere positive, but decreasingmonotonically with r, the potential is repulsive and the radial motion of thisparticle in the field V(r) will have no bounds or limits in its maximum value of r.However, there is a minimum in r, the distance of closest approach, r min , whichdepends on the particle’s total energy and the nature of the interaction potential.In Fig. 3.4a, the energy curves for attractive potential-energy are presentedalong with an arbitrarily defined centrifugal energy curve. In Fig. 3.4b, theeffective potential-energy curve, given bylV′ ( r) = V( r)+2Mr22(3.23)is shown. Figure 3.5 gives a schematic representation of how the effectivepotential-energy affects the trajectories of a particle moving with energy,E = Mv 2 /2. The distance of closest approach is determined by the value of r thatsatisfies the condition E = V′(r).At large distances away from the center of force, the magnitudes of V(r) andl 2 /2Mr 2 will be negligible (Fig. 3.5). Under such conditions a particle with energyE travels in a straight line with a speed v 0 = (2E/M) 1/2 . The particle’s direction ofmotion is offset from a parallel line through the center of force (target atom) by adistance b that is directly related to the centrifugal energy and the angular orbitalmomentum. From the law of conservation of angular momentum,l= Mrminvθ(3.24)approachesl = Mv b0(3.25)for r approaching infinity. Since angular momentum is conserved in central forcescattering, l is defined by either form given by (3.24) or (3.25). The distance b iscalled the impact parameter and is very useful in characterizing a particle thatapproaches a center of force.From Fig. 3.4, the distance of closest approach, r min , is shown to be determinedfrom the condition E = V′(r), which translates tolE = V( r ) + .2min 22Mrmin(3.26)
3.5 Motion under a Central Force 33EnergyEnergyV(r) +V'(r) +/2Mr 20 r0 rb(a)Fig. 3.4. (a) Centrifugal potential-energy curve (dashed) and a potential-energy curve thatmight arise from electrical interactions of like charges. (b) Effective potential-energycurves corresponding to the case shown in (a), indicating the distance of closest approach,b, for a given positive total energy (French, 1971)(b)br minMv 0Fig. 3.5. Plan view of trajectory of a particle moving with the impact parameter b and witha repulsive center of force (French, 1971)
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Page 7 and 8: xContents4 Cross-Section ..........
Page 10 and 11: Contentsxiii14.3.2 Punch-Through St
Page 12 and 13: 2 1 General Features and Fundamenta
Page 20 and 21: 10 1 General Features and Fundament
Page 22 and 23: 12 2 Particle InteractionsThe restr
Page 24 and 25: 142 Particle Interactions(a)V(r)r 0
Page 26 and 27: 162 Particle InteractionsHowever, a
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Page 30 and 31: 202 Particle Interactionsa0.8853a0L
Page 33 and 34: 3 Dynamics of Binary Elastic Collis
Page 35 and 36: 3.3 Kinematics of Elastic Collision
Page 37 and 38: 3.4 Center-of-Mass Coordinates 27Fi
Page 39 and 40: 3.4 Center-of-Mass Coordinates 29an
Page 41: 3.5 Motion under a Central Force 31
Page 45 and 46: Problems 35The reduced energy for 1
Page 47 and 48: 4 Cross-Section4.1 IntroductionIn C
Page 49 and 50: 4.2 Scattering Cross-Section 39unit
Page 51 and 52: 4.2 Scattering Cross-Section 41Rdθ
Page 53 and 54: 4.3 Energy-Transfer Cross-Section 4
Page 55 and 56: 4.4 Approximation to the Energy-Tra
Page 57 and 58: Problems 47ReferencesNastasi, M., M
Page 59 and 60: 5 Ion Stopping5.1 IntroductionWhen
Page 61 and 62: 5.3 Nuclear Stopping 51MeV mg −1
Page 63 and 64: 5.3 Nuclear Stopping 531−m1−2mC
Page 65 and 66: 5.4 ZBL Nuclear Stopping Cross-Sect
Page 67 and 68: 5.5 Electronic Stopping 575.5.1 Hig
Page 69 and 70: 5.5 Electronic Stopping 59Table 5.1
Page 71: Problems 61Problems5.1 Calculate th
Page 74 and 75: 64 6 Ion Range and Range Distributi
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82 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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128 10 Crystallization and Regrowth
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144 11 Si Slicing and Layer Transfe
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160 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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