Evaluation of the accuracy of stopping and range of ions in matter simulations through secondary ion mass spectrometry and Rutherford backscattering spectrometry for low energy heavy ion implantation

Determination of ion species and energy for ion implantation is the first step in performing an ion implantation experiment.^1–7 Ion implantation is used in semiconductor device fabrication since it allows dopant profiles to be tailored in the substrate.^8–12 Furthermore, knowing the end of the range and associated ion damage is paramount for high yield fabrication of devices.¹³ For the fabrication of shallow junctions and nanometer scale devices, the dopant distribution profile and the location of the dopant play a role on a few nanometers level.^14,15 More recently, ion implantation has been used in membrane formation, for example, enabling nitrogen-vacancy rich membranes for quantum sensing.^16–18 Other applications requiring accurate knowledge of ion range at low energy are physical confinement problems, such as those involved in the fabrication of donor-based qubits through localized ion implantation.^19–24 Additionally, near-surface implantation is required for efficient coupling of implantation-created single photon sources to optical waveguides.^25–32 

The accuracy of stopping and range of ions in matter (SRIM) predictions has been experimentally tested with overall good agreement between SRIM predictions and experimental results for light ions (H, He) to less than a 5% error over all investigated targets.³³ A key parameter in the SRIM calculation is the nuclear stopping power at low energy (20 keV and below). Since end-of-range stopping is always dominated by low energy stopping events, the low energy stopping power is simultaneously relevant for low energy implantation and high energy stopping calculations.^34–36 Particularly for heavy ions, where the discrepancy between SRIM predictions and experimental results is larger, a precise measurement of the low energy nuclear stopping power is needed. For Au, differences larger than 20% are regularly reported between SRIM prediction and measured implantation depth.^37–41 One reason for this discrepancy is data availability. For light ions such as H, He, and Li, there are thousands of datapoints built into the stopping and range calculation with experimental data available for most target elements. In contrast, only a few experimental results exist to support heavy ion stopping power calculations. Recent experiments have shown disagreement of the stopping power built into SRIM simulations for a variety of low energy ion species; however, Ar was the heaviest ion studied.^42,43 The lack of data for heavy ions in SRIM prompted us to evaluate the performance of SRIM with heavy ions; in this case, we evaluate the stopping power of Sb. Since SRIM does not consider channeling effects, we tilted our samples to minimize channeling effects since ion channeling can drastically change the ion range.^44–46 

We obtained the implant depth distribution with secondary ion mass spectrometry (SIMS) and Rutherford backscattering spectrometry (RBS) after implanting Sb into Si samples. To achieve a strong signal in SIMS and RBS, high fluence was required, and we show effects of ion beam induced surface modifications, such as surface sputtering, reimplantation of Sb, and saturation of the Si lattice with Sb, for samples implanted with sufficiently high fluences. However, for each energy investigated, there is a range of fluences where sufficient signal is detected in RBS and SIMS, allowing us to compare the simulated implantation profiles from SRIM to the experimental data. All SRIM results are within a few nanometers of the SIMS and RBS measurements for implantation of low energy Sb ions. However, due to the small range of ions, even a few nanometer errors lead to a relative error between predicted and experimental values up to 25%.

We implanted Sb into a clean Si wafer with a native oxide. To minimize effects from channeling, the Si wafer is mounted at a $7°$ angle during implantation relative to the incident beam. The depth was then evaluated using SIMS and RBS and compared to the SRIM calculations.

The native oxide thickness was measured by SIMS since in contrast to RBS, it can easily detect low mass ion species on a heavier substrate. The oxygen concentration of the sample was fit with a Gaussian yielding a concentration depth of $2.9±1.2$ nm, in agreement with reported oxide thicknesses in the literature.^47,48 Implantation was performed by Innovion (now II-VI), with Sb implantation energies in the range of 10–150 keV.⁴⁹ The fluence for each energy is varied, and at high fluences, the implanted samples were degraded by surface sputtering, redeposition of Sb, and saturation of the Si lattice with Sb. The saturation threshold value was extracted from the data shown in Fig. 1. To determine the saturation threshold, a linear interpolation between the datapoints is used and the crossover fluence with the 80% range from SRIM is given as the saturation threshold in Table I. Since SRIM does not take into account effects from surface modifications due to high implant fluences, only data below the saturation threshold are used for comparison between simulation and experiment.

We reproduced the $7°$ incident angle and ran SRIM with the default displacement energies for Si and O, summarized in Table II. Additional parameters of the SRIM simulation are the number of simulated ions, the type of damage calculation, as well as the assumed density of the target material. We performed simulations for 99 999 ions using the full damage cascade calculation model and assume a density of $2.32$ and $2.329g/cm3$ for $SiO2$ and Si, respectively.

To evaluate the Sb concentration as a function of depth, two complementary techniques were used. SIMS excels at determining the near-surface composition of materials and hence is well-suited for analyzing the content of implanted Sb in the sample.⁵⁰ The depth resolution of SIMS is $≥$0.5 nm, dependent on the sputtering rate of the substrate,⁵¹ which was calibrated by measuring the sputtering rate of a sacrificial location on the Si wafer and then assuming the same sputtering rate at the implant region. However, the measurement of the oxide thickness and our measurements of the Sb range point to an uncertainty between 1 and 1.5 nm in the SIMS experiment through averaging over the whole set of samples measured. Figure 2 shows the Sb profile measured by SIMS for different Sb energies and fluences below saturation. As the ion energy was reduced, the Sb implant profile shifted to shallower depth with a narrowing implant peak. The concentration measurements have been normalized since we were interested in the peak location and width of the ion straggle. The corresponding SRIM simulation results are shown as the same color curve, with an overall similar shape but a different peak center.

Normalized results from the SIMS measurement on a sample implanted with fluences ranging from $5×1013to5×1016ions/cm2$ at 50 keV Sb are shown in Fig. 3. For fluences from $5×1013to5×1015ions/cm2$⁠, the measured Sb concentration profiles overlap while for the highest fluence implant at $5×1016ions/cm2$⁠, the Sb concentration is skewed and shifted to a lower depth. We attribute this shift to surface sputtering and the change in the shape of the implantation profile to redeposition and surface sputtering. The result of the SRIM calculation is also shown as the magenta points and curve in Fig. 3. The depth of ions was evaluated from Gaussian fits to the SIMS data, shown as the corresponding color curve. While the Gaussian is a good approximation for the lower fluences, it fails to properly capture the peak shape for $5×1016ions/cm2$⁠. For lower ion fluences, the depth was measured to be $27.5±1.3$ nm while the depth according to SRIM simulation is 32.8 nm, a difference of 5.3 nm. The 1.3 nm uncertainty in depth from our SIMS measurement is close to the resolution we expect for the SIMS measurement and is in agreement with the 1.2 nm error in oxide thickness. While the SRIM calculation overestimates the range of Sb ions, the overall shape of the measured implant profile was reproduced along with the 9.7 nm straggle seen in the SIMS measurement.

To account for sputtering, redeposition of Sb, and saturation of the Si lattice, TRIDYN simulations were performed.⁵² TRIDYN relies on SRIM simulations for straggle and range predictions, but different from SRIM simulations, the target lattice composition is dynamically modified to account for surface sputtering and enrichment of the lattice with implanted ions. The comparison between TRIDYN, SRIM simulations and SIMS measurement is shown in Fig. 4. The black line is the predicted range using SRIM while the yellow shaded area denotes the straggle in range. The red symbols show the range measured using SIMS for various fluences and the error bar is the measured straggle. While the range measured using SIMS is constant up to $5×1015ions/cm2$⁠, just below the measured saturation threshold of $6×1015ions/cm2$ as mentioned in Table I, the range decreases at fluences higher than $1016ions/cm2$⁠. The TRIDYN results are shown as blue symbols with the calculated straggle as the error bars. From the linear fit to the TRIDYN simulations, the saturation threshold according to TRIDYN is $5.6×1015ions/cm2$⁠, in close agreement with the measured $6.0×1015ions/cm2$ in Table I. A decreasing trend of implantation depth for fluences larger than $3×1015ions/cm2$ is visible for range simulations using TRIDYN. Additionally, TRIDYN gives a better estimate of the range relative to SIMS even for low fluences. The linear fit is a fit to the TRIDYN simulation results for doses larger than $3×1015ions/cm2$⁠. From the fitting, we extract the depth dependence of $−12$ nm/order of magnitude ion fluence.

In addition to SIMS, we also performed RBS experiments. While SIMS has excellent depth resolution, it is a destructive technique. Contrary to low energy, high mass ions used for sputtering in SIMS, high energy light ions are used in RBS. In this measurement, a light, high-energy projectile elastically scatters off a nucleus in the sample and into a detector. The backscattered cross section of the particle depends on the mass of the backscattering atom as well as the detection angle. The detector needs to cover a small solid angle in order to maintain high mass resolution; hence, the cross section of this experiment is low and relatively high fluences of projectiles are required to collect sufficient ion energy distribution. Depending on the weight of the scattering nucleus, the projectile loses energy, analyzed using an analog to digital converter (ADC). Additionally, the projectile loses energy to electronic stopping while traversing the sample, giving access to the depth profile.

RBS is performed using a single-ended van de Graaff accelerator with up to 3 MV acceleration potential.⁵³ A 2 MeV $α$ beam is used for the RBS experiment as a compromise between mass resolution, ion range, and scattering cross section. The RBS detector used is an Ortec model number BE-12-25-100. The detector is biased at 60 V and mounted at $165°$ backscattering angle. The solid angle enclosed by the detector is calculated to be 11.8 msr. To obtain absolute depth information from RBS, a calibration is required. Here, the calibration is performed on three standards, graphite, $Si3N4$⁠, and Au on C. The calibration yields a conversion from channel numbers on the ADC to ion energy. In our case, we obtain 2.23 keV/ch.

Results from the RBS experiment are shown as the datapoints in Fig. 5, while the line corresponds to the spectrum produced by SIMNRA.⁵⁴ The SIMNRA spectrum is produced using the experimental conditions outlined above and the target Sb composition is iteratively adjusted using SIMTarget until the spectrum produced by SIMNRA reproduces the Sb peak at high energy, shown in the Inset. The near-Gaussian shaped peak around 1.7–1.75 MeV energy corresponds to backscattering from implanted Sb ions. The dashed line is the expected energy of an $α$ particle recoiling from a surface Sb atom. To measure the depth using RBS, the energy loss relative to the surface is used where lower energy corresponds to a deeper recoiling atom. The high energy edge of the Si substrate is at 1.1 MeV, the energy of an $α$ particle backscattering from a surface Si atom. The edge contains a peak due to channeling at the near surface for all but the 10 keV Sb implantation energy. This peak is typical for channeling and tells us that the Si surface is becoming more amorphous for decreasing implantation energy. While SIMNRA also uses SRIM to perform energy loss calculations, the underlying data for the high energy $α$ stopping power is more reliable than the data used to calculate the Sb stopping power. SRIM contains stopping power data from 21 references with 388 data points for $α$ particles into Si targets. In contrast, only two references with a total of 5 data points exist for the Sb stopping power and those are not for Si but for a normalized target.

To measure the ion ranges across our experimental results, the SIMS data is fit with a Gaussian function

The center of the Gaussian $μ$ is the range and the standard deviation $σ$ corresponds to the distribution, or straggle. For RBS, the detection of $α$ particles using an Si detector relies on measuring the electronic energy loss in an Si substrate, which is a stochastic process. Using our Au on C calibration standard, we measure the FWHM using the 80/20% rise method and obtain an FWHM of approximately 17 keV, close to the expected 15 keV resolution of Si detectors. In principle, to measure the ion straggle, it needs to be deconvolved with the detector response. However, since the Sb straggle even for the narrowest implant profile of 10 keV is over 30 keV wide, the contribution from the detector response is negligible. Figure 6 shows that SRIM overestimates the range for all energies. The relative error is increasing for smaller ion energy while the absolute error increases with energy. The black dashed line is the predicted range with SRIM, the red (blue) circles denote the range measured by SIMS (RBS), and the error bars are the measurement error. The inset of Fig. 6 shows the absolute range where the error bar denotes the straggle in range. The increased range in SRIM can be attributed to an erroneous stopping power built into SRIM for low energy heavy ions. The electronic stopping power has been shown to be overestimated by SRIM.^42,55 We have shown that the total stopping power is too small, giving rise to a too large predicted ion range.

A quantitative analysis and improvement of the partitioning will require additional measurements, although a systematic overestimation of the range is clearly visible throughout the energies investigated here. The largest error in our measurement lies in the determination of the thin oxide layer which has a >40% error on its thickness. However, we observe an upward trend in the error in the range between SRIM and SIMS/RBS measurement with increasing Sb energy, and we cannot ascribe the deviation between SRIM simulation and experimental results to a systematic error in the measurement of the oxide thickness.

To summarize, SRIM simulations accurately capture the straggle of low energy Sb ions implanted into Si. For implant fluences below the saturation threshold, the peak shape is also well reproduced. The range is overestimated by a few nm, which translates to up to a 25% error in the predicted vs the measured range for the lowest energy implantation performed here. Our results for 50 keV Sb ions using TRIDYN simulations point to an improved range prediction using TRIDYN code; however, it comes at an additional computational cost. Due to the absolute error in range increasing for larger implantation energies, the stopping power built into SRIM can likely be improved to more accurately capture the range of low energy ions.

This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under Contract No. DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government SAND2021-13560 J.

The data that support the findings of this study are available from the corresponding author upon reasonable request.