Range Straggling Research Articles

Relationship between CT number and electron density, scatter angle and nuclear reaction for hadron-therapy treatment planning

The precise conversion of CT numbers to their electron densities is essential in treatment planning for hadron therapy. Although some conversion methods have already been proposed, it is hard to check the conversion accuracy during practical therapy. We have estimated the CT numbers of real tissues by a calculational method established by Mustafa and Jackson. The relationship between the CT numbers and the electron densities was investigated for various body tissues as well as some tissue-equivalent materials used for a conversion to check the accuracy of the current conversion methods. The result indicates a slight disagreement at the high-CT-number region. A precise estimation of the multiple scattering, nuclear reaction and range straggling of incident particles has been considered as being important to realize higher-level conformal therapy in the future. The relationship between these parameters and the CT numbers was also investigated for tissues and water. The result shows that it is sufficiently practical to replace these parameters for real tissues with those for water by adjusting the density.

Depth distribution of rare earth ions implanted into KTiOPO 4 determined by the Rutherford backscattering technique

Potassium titanyl phosphates (KTiOPO 4 or KTP) samples were implanted with rare earth ions such as Tm +, Er +, and Yb +. The ion energy implanted was varied from 100 keV up to 400 keV. The fluence was 1–2 × 10 15 ions/cm 2. The depth distributions of the implanted rare earth ions were determined using the Rutherford backscattering technique. The experimental data were compared with TRIM (transport of ions in matter) code. It is found that for Tm + and Er + the experimental mean projected ranges are in relatively good agreement with values calculated by the TRIM code after taking into account inelastic effects in the energy transfer. But that in the case of Yb + the ranges are overestimated by theory, anyway the deviation of experimental values from calculated one is less than 9% for all cases. The deconvoluted experimental range stragglings are in all cases higher than the calculated values.

Analysis of depth profiles of implanted lead ions in silicon

Lead ions at energies of 40, 80, 100, 150, and 360keV were implanted into silicon wafers at room temperature. Depth profiles of lead ions implanted in silicon were measured using both secondary-ion mass spectrometry and a Pearson distribution. The set of five fourth-order coupled differential equations developed from the Biersack theory was employed to make theoretical predictions of projected range, range straggling, and skewness. The Gibbons parabolic fitting formula along with calculated skewness was employed to obtain calculated kurtosis. It was found that the calculated range parameters correlated closely with measured values. The average differences between calculated and measured values of projected range, range straggling, skewness, and kurtosis were 10%, 19%, 4%, and 4%, respectively.

Critical issues in ion implantation of silicon below 5 keV: Defects and diffusion

Continued use of ion implantation for doping of silicon integrated circuits will soon require implantation energies below 5 keV in order to form electrical junctions < 50 nm deep. At such low energies, dopant diffusion and formation of extended defects may be modified by both the proximity of the surface and by the large volume concentrations of point defects and dopant atoms that will arise from reduced range straggling. This brief review summarizes our recent experiments measuring defect formation and evolution, as well as transient enhanced diffusion (TED), in silicon implanted with Si + and B + ions < 10 nm deep. The results have demonstrated that {311}-type extended defects are generated from Si implants even within 3 nm of the surface. However, when these defects eventually dissolve, the surface acts as a perfect sink to efficiently annihilate the released interstitials. As a result, the amount of TED measured at epitaxially-grown B markers decreases approximately linearly with decreasing ion energy (at least, for Si + implantation). For low energy B + implants typical doses required for source-drain doping lead to the formation of a fine-grain polycrystalline silicon boride phase during activation annealing.

The high-fluence effect on the lateral spread of ions within a masked target

By including the high-fluence (Φ) effect, we reproduced a three-dimensional ion distribution in a crystal under a rectangular mask. The means of access was the microscopic lateral range straggling, Δ R L( z), that represents the mean deviation of the scattered distance of laterally spread ions within a thin slab cut out parallel to the crystal surface at the depth z. The quantity Δ R L( z) was expressed by the incident energy, the ion fluence and the incident tilt angle. We introduced the high-fluence effect into Δ R L( z) by means of the macroscopic lateral range straggling, Δ R L, using the help of a Monte-Carlo simulation code called TRIDYN. Here we looked at B ions implanted into Si(100) with 10 13 ≤ Φ(ions cm −2) ≤2×10 16 in an incident energy range of 1 keV ≤ E 0 ≤ 200 keV. Our results show that the present procedure works well in a low-energy regime of less than 10 keV.

A proton dose calculation algorithm for conformal therapy simulations based on Molière's theory of lateral deflections.

An algorithm is developed for computing proton dose distributions in the therapeutic energy range (100-250 MeV). The goal is to provide accurate pencil beam dose distributions for two-dimensional or three-dimensional simulations of possible intensity-modulated proton therapy delivery schemes. The algorithm is based on Molière's theory of lateral deflections, which accurately describes the distribution of lateral deflections suffered by incident charged particles. The theory is applied to nonuniform targets through the usual pencil beam approximation which assumes that all protons from a given pencil beam pass through the same material at each depth. Fluence-to-dose conversion is made via Monte Carlo calculated broad-field central-axis depth-dose curves, which accounts for attenuation due to nuclear collisions and range straggling. Calculation speed is enhanced by using a best-fit Gaussian approximation of the radial distribution function at depth. Representative pencil beam and spread-out Bragg-peak computations are presented at 250 MeV and 160 MeV in water. Computed lateral full-widths-at-half-maximum's in water, at the Bragg peak, agree with the expected theoretical lateral values to within 1% at 160 MeV and to within 3% at 250 MeV. This algorithm differs from convolution methods in that the effect of the depth of any inhomogeneities in density or atomic composition are accounted for in a rigorous fashion. The algorithm differs from Fermi-Eyges based methods by accounting in a rigorous way for the effect of nonsmall-angle scattering and screening due to atomic electrons. The computational burden is only slightly greater than that expected using the less-rigorous Fermi-Eyges theory.

Damage, defects and diffusion from ultra-low energy (0–5 keV) ion implantation of silicon

Continued use of ion implantation for doping of silicon integrated circuits will soon require implantation energies below 5 keV to form electrical junctions less than 50 nm deep. At such low energies, dopant diffusion and formation of extended defects is modified by both the proximity of the surface and by the large volume concentrations of point defects and dopant atoms that arise from reduced range straggling. This brief review summarizes our recent experiments which measured defect formation and evolution, as well as enhanced diffusion, in silicon implanted with Si + and B + ions at energies as low as 0.5 keV. The results have demonstrated that {311}-type extended defects are generated from Si + implants even within 3 nm of the surface. However, when these defects eventually dissolve, the surface acts as a perfect sink to efficiently annihilate the released interstitials. As a result, the amount of TED from Si + implantation measured by epitaxially-grown B markers decreases approximately linearly with decreasing ion energy. For sub-keV B + implants typical doses currently used for source-drain doping lead to a boron diffusion enhancement of 3–4× despite the proximity of the surface. Enhanced diffusion is also observed from molecular beam-deposited silicon layers containing a high boron concentration. This newly emerged diffusion enhancement mechanism, boron-enhanced-diffusion (BED), is associated with the formation of a fine-grain polycrystalline silicon boride phase in the implanted layer during activation annealing. These investigations of ultra-low energy (ULE) implantation have thus reinforced and validated our understanding of the role of implantation damage in enhancing dopant diffusion in silicon, while simultaneously revealing some important new materials issues which will impact semiconductor processing in coming device generations.

On anomalous concentration depth profiles of atoms implanted into polymers

Different polymers were implanted with 50–200 keV heavy ions to fluences of ≥ 1 × 10 15cm −2 and the concentration depth profiles of the implanted atoms were measured by standard Rutherford backscattering technique (RBS). The experimental projected ranges were found to be 10–30% lower than those estimated by the TRIM91 code. The measured range stragglings, on the other hand, are by a factor of 1.4–2.4 higher than the calculated ones. The discrepancies are explained by the loss of matter during the implantation process.

Lateral Spread of Tungsten Ions Implanted in Silicon

Silicon wafers were irradiated at tilted geometry to measure the lateral spread of tungsten ions in silicon for implantation energies between 40 and 360 keV. The depth profiles of implanted tungsten ions were measured by means of secondary ion mass spectrometry. The measured transverse range stragglings were obtained by using Furukawa and Matsumura's formula. An analysis of the measured transverse range stragglings as compared to the values calculated from the Biersack theory and SRIM reveals that the calculated transverse range stragglings from the Biersack theory correlated closer to the measured ones.

Three-dimensional implantation profiles: The ratio of lateral to longitudinal straggling

The presently available database on lateral and longitudinal range stragglings of energetic particles implanted into amorphous solids has been compared with theoretical predictions, and the agreement is found to be, in general, good. The lateral-to-longitudinal ratio is below 1 for ϵ<0.1, above 1 for ϵ>1, and around 1 for 0.1⩽ ϵ⩽1, where ϵ is the generalized energy. In a few cases deviations have been found from this general trend which are attributed to thermal or radiation enhanced diffusion (RED).

Deconvolution of the Gaussian-convoluted profiles of mercury ions implanted into nickel

Based on a nonlinear least squares optimisation, a deconvolution method is proposed to remove the system resolution from the ion implantation profiles measured. The method is applied to the range distributions of 200 keV Hg ions implanted into nickel at various tilt angles. The results show that the range straggling is markedly reduced after the deconvolution, the skewness and kurtosis are slightly larger than those of the experimental measured profiles, and they all can be represented by a Pearson IV distribution that is different from the Pearson I distribution predicted by TRIM. The longitudinal and lateral range straggling for normal incidence could be deduced from the angular dependence of the deconvoluted range straggling.

Range parameters of bismuth ions in polystyrene

In this study, the Rutherford-backscattering spectrometry was used with a 2 MeV He+ ion beam to measure the projected ranges and range stragglings of bismuth ions implanted into polystyrene in the energy range of 40–360 keV. Range-projection equations following the modified Biersack model and including the first four moments of the nuclear and the electronic energy losses were also employed to perform the theoretical calculations. The feasibility of including the finite maximum-impact parameter and the inelasticity effect in simulating nuclear stopping processes was considered, as well as the surface effect in simulating a finite target medium. Experimental results demonstrate that measurements closely correspond to theoretical values, with average differences of 9% for projected ranges and 21% for range stragglings.

An investigation of range distribution parameters of implanted 19F ions in Au, Ag and Cu noble metals

Depth profiles of fluorine implanted in gold, silver and copper metal have been accurately measured using the 19F(p,αγ) 16O resonance nuclear reaction at E R = 872.1 keV. A proper deconvolution calculation method was used to extract the depth profile of fluorine from the experimental excitation yield curves. The range parameters, R p, ΔR p, and SK obtained in this work were compared with the theoretical calculations. The comparison shows that for all materials studied here the experimental R p values are in good agreement with the results obtained by the TRIM96 code, while the experimental range stragglings, ΔR p, are systematically larger than the TRIM simulation results.

Range and thermal behaviour studies of Tm+, Er+ and Yb+ implanted into LiNbO3 and quartz crystal

Tm+, Er+ and Yb+ have been implanted into LiNbO3 and quartz crystal (SiO2) in the energy range 100–400 keV. The profile of implanted ions was measured by Rutherford backscattering of MeV He ions. The mean projected range and range straggling obtained were compared with TRIM code. The result shows that (1) The mean projected range and range straggling are in well agreement with TRIM prediction except for 100 keV for LiNbO3 (2) The mean projected range is in good agreement with TRIM prediction within 8%, but the experimental range straggling is higher than the calculated value by TRIM code for quartz crystal. After 800°C annealing for 30 min, it is found that there is no obvious diffusion for the case of 300 keV Er+, but for the case of 300 keV Yb+ the diffusion occurs and the diffusion coefficient D estimated is 2.77×10−15 cm2 s−1.

Distribution of impurities implanted in InSb and InAs before and after annealing

Experimental estimation of distributions of implanted ions was done for Be +, Mg + and S +. Energies of ions were up to 250 keV and doses up to 10 15 cm −2. Experimental distributions were measured by the use of ion microprobe MIQ-256 (CAMECA/Riber). Simulation of impurity and defect distributions for 10000 ions of each species was carried out by using TRIM-94 code. It was found that mean ranges R p of experimental and calculated distributions were very similar. Range stragglings ΔR p of experimental distributions exceeded the calculated ones for all species. The difference between the range stragglings of experimental and calculated distributions was up to 35%. It was found that after 550°C post-implatation annealing of sulphur implanted layers there was no broadening of ion implanted distributions. It is believed that sulphur in the implantation process, interacting with defects, took places in As sublattice sites and even annealing did not change sulphur state in InAs and motion was not observed.

Projected range and range straggling of ion-implanted lead in polystyrene materials

lead ions/cm2 at energies from 40 to 360 keV at room temperature. Projected ranges and range stragglings were measured using SIMS. Experimental results are compared with calculated values obtained using the modified Biersack theory and TRIM-95 Monte-Carlo calculations. The comparison shows that large discrepancies between TRIM-95 calculations and measured values are significantly reduced by applying the modified Biersack theory along with taking the first four moments of nuclear and electronic energy losses into consideration. The differences between calculated values obtained using the modified Biersack theory and measured values are, on average, 9% and 20% projected ranges and range stragglings, respectively.

Argon-surface interactions in ibad-deposited molybdenum films

ABSTRACTArgon incorporation and defect creation were studied experimentally. Direct desorption measurements have been used to establish the argon implantation profile. A projected range and range straggle of 0.8 and 3.5 Å were found. Argon is incorporated at substitutional positions. The creation rate of defects by argon was studied by helium desorption spectrometry. A net creation rate of (0.7 ± 0.4) × 10−3 vacancy/argon atom was found. Ion assisted deposition at elevated substrate temperatures shows that all incorporated argon acts as helium trap. Argon fluence variations show an effective cross-section for self sputtering of 31 Å2, a trapping probability of 6.5%, and a maximum achievable argon concentration of 4 × 10−3

Range parameter study of Au and Bi implanted into carbon nitride films

Range profiles of 15 to 200 keV Au and Bi in carbon-nitride films have been measured for the first time. It turns out that the measured ranges deviate by as much as 30% for Bi and 25% for Au from theoretical predictions. The measured range stragglings are even larger by a factor of two than theoretically expected. These differences can be explained by contributions of cross terms between electronic and nuclear energy transfer which are not yet taken into account in the presently available computer codes.

Improved algorithm for calculation of range and range straggling in ion implantation

Range-projection equations based on the modified Biersack model are advanced to fourth-order coupled differential equations. The first four moments of the nuclear and the electronic energy losses are consolidated in the equations leading to a simple and accurate method for evaluating statistical range projections for any ion-target combination. Furthermore, an algorithm of reducing differential orders and implementing iteration schemes is proposed to solve the equations to simply the computation and obtain more accurate results. An investigation of projected ranges and range stragglings of various ions implanted into target materials ranging from one to seven constituents is performed to test the applicability and reliability of the proposed method. The results show an good overall agreement between the calculated and the experimental projected ranges and range straggling, with errors mostly under 10%. A considerable improvement in the accuracy of the range straggling prediction is obtained when the proposed iteration schemes are applied to solve the range-projection equations.

Range profile parameter of Hg + implanted in SBN crystal

Range profiles of Hg + implanted at energies from 50 to 200 keV in Nd 0.05 Ce 0.02Na 0.47(Sr 0.61Ba 0.39) 0.66Nb 2O 6 and Pr 0.03(Sr 0.61Ba 0.39) 0.955Nb 2O 6 crystals are studied by Rutherford backscattering of MeV He ions. The measured projected range and range straggling are compared with calculated values based on Biersack's angular diffusion model. The result shows that the agreement between experimental and calculated values is good for the mean projected ranges. After considering second energy loss terms, a better agreement for the range straggling is obtained.