Ranges and standard deviations of implanted ions

This paper presents a theoretical analysis and simple expressions for the calculation of ranges and standard deviations of implanted ions in amorphous targets. Nuclear energy loss models are discussed to introduce an approximation formula for the nuclear stopping cross section appropriate for Thomas-Fermi, Lenz-Jensen and intermediate type potentials. The Firsov electronic stopping model has been used to show its successful application. Algebraical expressions for the total range of ions in monoatomic and biatomic targets as a function of ion energy result from the considerations presented. A quasi-elastic multiscattering model is suggested, which permits an easy estimate of projected ion ranges. The standard range deviation is obtained by determining the total average-square energy loss fluctuations. Finally a comparison of calculated and experimental results is made to show that calculations based on the Firsov electronic stopping model and the nuclear stopping cross section proposed here provide a better agreement with the experimental results than the wellknown Johnson-Gibbons LSS-calculations.     

New model interaction potential for the description of charged particle motion in matter

A new model interaction potential, in the form of a screened Coulomb potential, is proposed. Analytical expressions are derived for the stopping power of ions in elastic collisions. A program is written for Monte Carlo calculations of the ion ranges in an amorphous substance, taking inelastic losses into account in the continuous-slowing approximation and taking elastic collisions into account in the approximation of the new model interaction potential. The ranges of Cu and Rb ions in C and B targets are calculated. The results of the calculations are in good agreement with experiment.     

The channeled stopping powers of Boron ions and range calculations in Si

An analytical fitting expression is obtained for the channeled stopping power of B ions in crystalline silicon. Ions incident in the Si 〈100〉 direction at energies from 50 keV/amu to 900 keV/amu are considered. The mean projected ranges of ions have been determined within the framework of the transport theory formalism where the fitting relation obtained for the stopping power was used. For this purpose, a first order ordinary differential equation including second order stopping coefficients is solved numerically by usingFehlberg fourth-fifth order Runge-Kutta method. By using the results for the channeled ion ranges, a transformation relation is proposed for the conversion of channeled/random ion ranges for the ion target system under consideration. The obtained results are compared with widely used standard programs such as Crystal-TRIM, SRIM and PRAL and our program applied to crystalline targets is in good agreement with Crystal-TRIM.     

Ranges and profiles of distribution of low-energy ions channeling in metal and semiconductor single crystals

In the present work peculiarities of trajectories and energy losses, ranges and profiles of distribution of low-energy different-mass ions channeling in thin single crystals of metals and semiconductors have been thoroughly studied by computer simulation in binary collision approximation. The character of oscillations of channeled-ion trajectories depending on their energies, aiming points from the axis of a channel, kind of interaction potential, crystal lattice type and temperature has been determined. It has been found that, in the case of light ions even at low energy, the main contribution to energy loss is made by inelastic energy losses, whereas for heavy ions, already at E < 10 keV, elastic energy losses exceed inelastic ones. Profiles of the distribution of channeled ions have been calculated depending on crystal lattice type, kind of ions and their energy.     

Low-energy antimony implantation in silicon

Abstract

Antimony is known to be a donor in silicon, Low-energy implantations of Sb in Si produce very shallow profiles which have many device applications. Gibbons et al. ¹ calulated the projected ranges of Sb ion-implanted in Si, using the LSS (Lindhard, Scharff, and Schiott) method. Oetzmann et al. ² measured projected ranges and range straggling for several heavy ions in Si, Al, and Ge, using high-resolution backscattering; in the energy region of interest to us, e = 10^?2 to 10^?1, their results were about 30% higher than those reported by Gibbons et al. In the study reported here, we implanted 5 × 10¹⁴ Sb/cm² in Si at 5–60 keV, measured the resulting depth distribution by secondary ion mass spectrometry, and checked the measurements by backscattering. Our results showed the experimental projected ranges to be about halfway between those reported in the earlier studies. The discrepancies between theoretical calculations and experimental results are due not to the electronic stopping cross section, which is negligible in the range of interest here, but to the nuclear stopping power. Using a modified nuclear scattering potential given by Wilson et al.,³ we calculated the projected range distribution according to the method described by Winterbon.⁴ Our results are in very good agreement with the experimental measurements.     

Stopping cross sections of 50- to 230-keV nitrogen ions in silicon measured by ion backscattering spectroscopy

The energy dependence of the total stopping cross section of 50- to 230-keV nitrogen ions in silicon (σ _S (E)) is measured in order to develop the diagnostics of heavy impurities in films of a nanometer thickness by heavy ion backscattering (HIBS) spectroscopy. At ion energies lower than 150 keV, this σ _S (E) dependence occupies an intermediate position between the dependences given in the SRIM and MSTAR data-bases; at higher energies, our dependence is closer to the former dependence. The estimation of the effect of inelastic processes on the stopping cross section demonstrates that the effect of these processes for nitrogen ions can be neglected when heavy impurities in such films are studied by HIBS.     

Ranges of low-energy heavy ions in beryllium, boron, carbon, and silicon

Based on a theory of the passage of low-energy, heavy ions through matter, simple analytical expressions are obtained for calculating the average projected ranges of the ions and the rms deviations of the projected ranges. The theoretical and experimental ranges of heavy ions with atomic numbers 29⩽Z ₁⩽83 in targets of Be, B, C, and Si are compared. The theory is found to be in good agreement with experiment. Zh. Tekh. Fiz. 68, 33–36 (September 1998)     

化合物和合金中离子投影射程分布矩的计算(Ⅱ)——轻离子(Z1≤10)的射程分布矩

本文根据离子在固体材料中电子阻止截面的实验资料,给出了低能Li⁺,Be⁺,B⁺,C⁺,N⁺,O⁺,F⁺,Ne⁺等离子在固体中电子阻止截面S_e的经验公式。这些经验公式既能够很好地反映电子阻止本领的Z₁和Z₂振荡、又能正确地给出S_e随离子能量E的变化关系。用这种以实验为基础的S_e经验公式和符合于WHB势的核散射函数,计数了从H⁺到Ne⁺十种轻离子在非晶Al₂O₃,SiO₂,20/25/Nb不锈钢,LiNbO₃和UO₂等材料中的投影射程分布的一次至三次矩。将计算值与近几年的实验测量及其他人的计算结果进行了比较,在低能端,我们计算的平均投影射程R_p与实验符合得更好。 关键词：     

Annealing of radiation damage in graphite

Abstract

The electronic stopping of heavy ions with 7 ≤ Z, ≤ 54 in low-index directions of thin gold single crystals is measured in the energy range 200 keV ≤ E ≤ 1100 keV. Large oscillations in electronic stopping power are observed for constant ion velocity. The stopping powers of different low-index directions are compared.     

Inelastic collisions of medium energy atomic elements in solids

The stopping of medium atomic elements in solids has been calculated in the framework of classical approximation, taking into account elastic and inelastic collisions. The calculations are based on the 1) revised equations for the law of energy and impulse conservation, which were earlier used to describe inelastic collisions of atomic particles, 2) theory of quasi-small angle scattering, 3) power potential of LNS, and 4) limitation of the maximum distance of atoms approach determined by the interatomic distance in solids. Analytical equations have been obtained to calculate 1) a differential cross-section of elastic scattering in the presence of inelastic collisions, 2) energy transferred, 3) cross-sections of elastic and inelastic stopping, and penetration depth. Implantation into solids was found to be of threshold character.     

Density effects of heavy-ion stopping power in high temperature matter

Abstract

The stopping power and range for Xe ions in high temperature matter (partially ionized plasmas) have been calculated using the dielectric response function method. Calculations have been made for a target matter Al (Z = 13) over a wide range of temperatures and densities considering a finite temperature model. The stopping powers obtained have smaller values in comparison with those of a zero temperature model. The stopping power strongly depends on the density and temperature of the target material, and the projectile ion energy.     

Study on the dynamic energy spectra of mev heavy ions penetrating biological sample

In order to study the probability for heavy ions to have a long projectile range in botanic sample, transmission energy spectra of 1.5 MeV F⁺, 3 MeV F²⁺ and 1.5 MeV H⁺ penetrating 100 µm seed cotyledon samples were measured as a function of ion dose. Results show that very fewer ions can penetrate through the samples, though their theoretical ranges are much shorter than sample thickness. Besides, the measured energy spectra of 1.5 MeV and 3.0 MeV F ions change dynamically while increasing the ion dose, they extend to the high energy direction and the count rates of the transmission ions increases quickly. These phenomena can be understood with the special composition and structure of the biological material.     

Theory of the stopping of fast heavy highly charged structured ions in their collisions with complex atoms

We have developed a nonperturbative theory of the energy losses by fast heavy structured ions in their collisions with neutral complex atoms by taking into account all of the possible, including multiple, excitations and ionizations of both projectile and target. We have been able to achieve a significant simplification of the problem by considering multielectron targets and by restricting our analysis to highly charged structured ions with charges much larger than unity, when the characteristic size of the electron coat of the projectile ion is much smaller than that of the neutral target atom. The errors in the approximations used and in the calculations of inelastic cross sections are estimated. We have derived formulas for the effective stopping similar to the well-known Bethe-Bloch formulas. To illustrate the contribution from multielectron excitations of the ion coat to the effective stopping, we make a comparison with the calculations based on the perturbation theory. The energy losses of U ^q+ (10 ≤ q ≤ 70) ions in their collisions with argon atoms and the energy losses of Pb and Bi ions on several targets have been calculated. A comparison with experiment is made.     

Inelastic effect in low energy ion-surface collisions: He+Au,Ag

Energy distributions of He⁺ ions scattered by Au and Ag surfaces are measured by an ISS system with high energy resolution, at a scattering angle of 90° and at incident ion energies ranging from 277 to 977 eV. It is found that the observed peak energies deviate toward the low energy side by several electron-volts with respect to the calculated elastic single collision energies. Both the deviation Q' and the inelastic loss energy Q are plotted as a function of incident ion energy for the Au surface.     

Elastic atomic displacements and color center creation in LiF crystals irradiated with 3-, 9- and 12-MeV Au ions

Creation of color centers in LiF under irradiation with 3–12-MeV Au ions was studied. Comparison of experimental data of color center creation with computer simulation of the energy deposition and elastic atomic displacements reveals the role of elastic collisions in defect creation by these ions, which have comparable magnitudes of electronic and elastic stopping. The experimentally measured efficiency of color center creation and that predicted by the simulation of elastic displacements have a similar dependence on the projectile energy. Thus, the color center creation is mainly associated with the elastic collisions, despite the relatively large values of the electronic stopping power for these ions.     

非晶合金的离子辐照效应

非晶合金作为一种快速凝固形成的新型合金材料,引起了材料研究者的极大兴趣.微观结构上长程无序、短程有序的特征使其具有独特的物理、化学和力学性能,在许多领域展现出良好的应用前景,尤其是有望成为核反应堆、航空航天等强辐照环境下的备选结构材料.本文深入探讨非晶合金的辐照效应,主要讨论离子辐照对非晶合金微观结构、宏观力学性能以及其他物理化学性能的影响,可为进一步理解非晶合金的微观结构和宏观力学性能之间的关系提供有效的实验和理论基础,也可为非晶合金在强辐照环境下的服役性能预测提供实验依据,对推进非晶合金这一先进材料的工程化应用具有重要的理论与实际意义.     

Range and range straggling of oxygen implanted into silicon at energies between 2 and 20 MeV

Oxygen profiles in silicon implanted with energies between 2 and 20 MeV by means of a Tandem accelerator have been investigated with a microprobe after bevelling the sample surface. It is shown that the measured profiles correspond to the implantation profiles when the microprobe is operated with a well focussed 2 keV electron beam. The projected ion ranges and the profiles thus obtained are compared with theoretical profiles which have been calculated by a Monte Carlo simulation of the stopping procedure. Takingk=1.30k _LSS for the electronic stopping coefficient in the LSS region up to 2.55 MeV and a constant value of 162 eV/Å for the electronic stopping at higher energies the calculation yields satisfactory range estimates, whereas the range straggling is systematically too small up to 13% in comparison with the experimental results.     

Thermal conductivity degradation induced by heavy ion irradiation at room temperature in ceramic materials

The thermal conductivity degradation induced by irradiation with energetic heavy ions at room temperature is studied and quantified. Three semi-metallic systems: titanium and zirconium carbides, titanium nitride, as well as a covalent compound: 6H silicon carbide were irradiated by 25.8 MeV krypton ions at 10¹⁶ and 6 . 10¹⁶ ions.cm^-2 doses to produce defects. During ion irradiation, inelastic collisions and elastic collisions occur at a different depth in a material. Two collision domains can be defined. Modulated thermoreflectance microscopy measurements were performed at differing frequencies to characterize the thermal conductivity degradation in these two domains for each of the investigated materials. Our results reveal a significant thermal conductivity degradation in the two collision domains for all materials. Elastic collisions are shown to degrade more strongly the thermal properties than inelastic ones. Scattering of thermal energy carriers is larger in elastic collision domain because displacement cascades produce a very high concentration of point defects: vacancies, interstitials and implanted Kr ions. The degradation coming from electronic interactions that seems to be more important in SiC can be explained by the presence of large populations of generated extended defects, facing to generated individual point defects in TiC, TiN or ZrC.     

Relative contribution of various factors to the formation of the energy spectrum of fast, medium-energy, charged particles and ions transmitted through a thin target with fluctuations of the target thickness

The characteristics of the energy spectra of kiloelectron-volt protons transmitted through a free-standing foil are investigated theoretically and experimentally as functions of the angle of incidence of the beam on the target. Analytical expressions for the average characteristics of the transmitted-particle energy spectrum are determined for the case of small-angle scattering. The combined influence of various factors affecting the formation of the energy spectra is taken into account: systematic stopping of particles in the medium, fluctuations of the particle energy losses in inelastic collisions, bending of the particle trajectories due to multiple elastic scattering, and fluctuations of the target thickness. It is shown that the contributions of these factors to the width of the transmitted-particle energy spectrum depend differently on the angle of incidence of the beam on the target surface. On the basis of this differentiation it is inferred from the experimental dependence of the width of the energy spectra of kiloelectron-volt protons transmitted through a free-standing foil on the angle of incidence of the beam that fluctuations of the particle energy losses in inelastic collisions are the predominant factor in the formation of the proton energy spectra. Zh. Tekh. Fiz. 67, 81–93 (May 1997)