Ion Implantation and Synthesis of Materials - Studium

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58 5 Ion StoppingThe complete energy-loss formula (often referred to as the Bethe formula) containscorrections that include relativistic terms as high-velocities and correctionsfor the nonparticipation of the strongly bound inner shell electrons. For ions withZ ≥ 2 in the energy regime of a few mega-electron-volts, relativistic effects arenegligible, and nearly all the target electrons participate in the stopping process(I e = NZ 2 ). Consequently, (5.15) can be used to estimate values of dE/dx| e .For example, the electronic energy-loss of 2 MeV 4 He ions in Si has a value(calculated from (5.15)) of 273 eV nm −1 using values of n e = NZ 2 = 700 nm −3 andI = 10Z 2 = 140 eV. Experiments give a value of dE/dx| e = 246 eV nm −1 . Thus, thefirst-order treatment gives values to within 10% of the experimental values.A fully stripped, high-energy ion can also transfer energy to the nuclei of thesolid as well as to target electrons. From Fig. 5.3, we see that the nuclear stoppingcross-section is approximately equal to 10 −3 S e (ε) for ions with energies ε > 30. Toconfirm this, one could calculate S n (E) using (5.13).5.5.2 Low-Energy Electronic Energy-LossIn the projectile velocity range v < v 0 , the Bethe theory of stopping expressed by(5.15) breaks down, and a different approach to electronic stopping theory isneeded. Three major models of electronic stopping in this velocity regime havebeen developed over the years, all of which give the result that the stopping crosssectionis proportional to the projectile velocity.Fermi and Teller analyzed the stopping of energetic particles in a Fermi gas atvelocities v = v F , where v F is the Fermi velocity. Since Fermi velocities in solidstypically fall in the range of 0.7 to 1.3v 0 , the Fermi–Teller analysis corresponds toprojectile ions that are not fully stripped. From Fig. 5.3 we would anticipate thatelectronic stopping in this velocity regime would be proportional to the projectilevelocity. While the Fermi–Teller model of stopping shows that the electronic energy-lossis proportional to the projectile velocity, its quantitative abilities arequestionable.2/3For energetic projectiles moving with velocities v< v0Z1, the majority ofthe target electrons are moving much faster than the ions. For ions moving in thisvelocity regime, the electrons cannot pick up energy by direct collisions with the2/3ion as was possible when the ion velocities were greater than vZ0 1. In a model2/3proposed by Firsov (1959), electronic stopping in the velocity regime v
5.5 Electronic Stopping 59Table 5.1. SRIM stopping data for As ion in SiIon energy (KeV) [dE/dx] e (eV nm −1 ) [dE/dx] n (eV nm −1 )10.00 63.86 942.911.00 66.98 965.312.00 69.96 985.313.00 72.81 1,003.014.00 75.56 1,020.015.00 78.22 1,035.016.00 80.78 1,049.017.00 83.27 1,061.018.00 85.68 1,073.020.00 90.32 1,093.022.50 95.79 1,115.025.00 101.00 1,133.027.50 105.90 1,149.030.00 110.60 1,162.032.50 11.510 1,173.035.00 119.50 1,182.037.50 123.70 1,191.040.00 127.70 1,197.045.00 135.50 1,208.050.00 142.80 1,216.055.00 149.80 1,221.060.00 156.40 1,224.065.00 162.80 1,226.070.00 169.00 1,226.080.00 180.60 1,224.090.00 191.60 1,219.0100.00 202.00 1,212.0development of the Firsov and Lindhard–Scharff models is found in the choice ofinteratomic potential.For calculational purposes, the Lindhard–Scharff stopping cross-section can beexpressed as7/61 2Z Z E1/2Se( E) = 3.83 =3/2 ⎜ ⎟ KLE,M2/3 2/3( Z1 + Z2)⎛⎝1⎞⎠1/2(5.17)whereK7/6Z1 Z2L= 3.831/2 2/3 2/33/2M1 Z1 Z2( + )(5.18)
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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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Page 18 and 19: 8 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
Page 28 and 29: 182 Particle Interactionswhere the
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 and 42: 3.5 Motion under a Central Force 31
Page 43 and 44: 3.5 Motion under a Central Force 33
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: 5.5 Electronic Stopping 575.5.1 Hig
Page 71: Problems 61Problems5.1 Calculate th
Page 74 and 75: 64 6 Ion Range and Range Distributi
Page 88 and 89: 78 7 Displacements and Radiation Da
Page 104 and 105: 94 8 Channeling1.00.8Non-aligned Im
Page 106 and 107: 96 8 ChannelingMeV ION BEAMSUBSTITU
Page 108 and 109: 98 8 ChannelingThe channeling effec
Page 110 and 111: 100 8 Channeling4.0Silicon2.0P (mic
Page 112 and 113: 102 8 ChannelingdσσD( ψc) = ∫
Page 114 and 115: 104 8 ChannelingDechanneled fractio
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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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