Compensation of Time-of-Flight Drift Using an Internal Reference Ion during Long-Duration LIMAS Depth Profiling

Abstract

In this study, the temporal behavior and compensation of time-of-flight (TOF) drift during long-duration depth profiling using Laser Ionization Mass Nanoscope (LIMAS) were investigated. Noble gas depth profiling by LIMAS requires detection of weak isotope signals with nanometer-scale depth resolution. However, such measurements often take several hours to a couple of days, during which TOF peak-position drift and statistical uncertainty may affect analytical precision. In this study, a ⁴He-implanted olivine substrate was analyzed as a test sample. The TOF spectra were processed by depth-layer stacking, peak extraction, and peak-position analysis. The ²⁴Mg²⁺ peak was used as a matrix-derived internal reference to monitor and compensate for TOF drift. The peak-position shifts of measured ions showed clear linear correlations with the ²⁴Mg²⁺ peak shift, indicating that the observed TOF drift is largely systematic. A ²⁴Mg²⁺-based compensation reduced the peak-position fluctuations of the other ion species to less than 1 ns and improved the mass resolving power. These results demonstrate that the ²⁴Mg²⁺ peak can be used as an internal reference for TOF drift compensation during long-duration measurements, providing a robust approach for micro- to nanoscale noble gas depth profiling using LIMAS.

1. INTRODUCTION

Secondary ion mass spectrometry is a powerful technique for determining the spatial distributions of trace elements and isotopes in solid materials. Laser Ionization Mass Nanoscope (LIMAS), a time-of-flight (TOF) secondary neutral mass spectrometer equipped with laser post-ionization, has extended this capability to noble gas isotope imaging at micro- to nanoscale spatial resolution.^1–7) This apparatus is able to analyze noble gas isotopes in the outermost surfaces of extraterrestrial materials, because their distributions record solar wind irradiation histories.^2,3,5)

Depth profiling of noble gases derived from solar wind ion implantation requires both high sensitivity and nanometer-scale depth resolution.^8,9) In such measurements, a large number of TOF spectra must be accumulated to obtain sufficient counting statistics for implanted noble gas isotopes.⁵⁾ Consequently, LIMAS depth profiling is often a long-duration measurement. The total measurement time is typically several hours even for relatively short-duration measurements and can extend to approximately a couple of days for long-duration measurements. During the measurements, temporal drift of TOF peak positions can broaden accumulated peak widths and decrease mass resolving power when a fixed integration window is used. The objective of this study is therefore to reduce the additional peak broadening caused by TOF drift during long-duration spectral accumulation. The proposed method is intended to recover the resolving power degraded by data accumulation.

TOF drift in the multi-turn mode may be related to voltage fluctuations in the toroidal sector electrostatic fields (EFs) of MULTUM II.¹⁰⁾ The use of a reference ion to compensate for instrumental drift is well established in mass spectrometry, particularly in lock-mass approaches for maintaining mass accuracy. This study adapts this concept to long-duration LIMAS depth profiling by using a continuously detected matrix-derived ion as an internal reference for TOF drift compensation. The aim is to reduce measurement-induced peak broadening during long-duration spectral accumulation. The TOF drift behavior during long-duration LIMAS depth profiling was evaluated using a ⁴He-implanted olivine standard, with the ²⁴Mg²⁺ peak serving as an internal reference. The peak shifts of ⁴He⁺, ¹⁶O⁺, ²⁸Si⁺, and ⁵⁶Fe²⁺ were compared with the ²⁴Mg²⁺ peak shift to determine whether the drift was systematic among ion species. Based on these correlations, a ²⁴Mg²⁺-based compensation method was developed and evaluated using the compensated peak widths and peak positions of the measured ions.

2. EXPERIMENTAL METHODS

2.1 Sample and analytical conditions

A ⁴He-implanted olivine standard, hereafter He-Ol, was used in this study. Implantation energy and fluence into the polished olivine were 20 keV and 2 × 10¹⁵ atoms cm⁻², respectively. This sample is a working standard for LIMAS depth profiling of rock samples.⁹⁾ LIMAS is equipped with the MULTUM II multi-turn TOF mass spectrometer.^10,11) Depth profiling was conducted over an analytical area of 15 × 22 μm². The analytical area was divided into 25 × 25 pixels. Mass-separated ions were detected and amplified using a 2-stage microchannel plate (MCP; F1217, Hamamatsu Photonics) and were output as pulsed electron signals. The electron signals were AC-coupled through a 0.5-pF capacitor and then amplified and pulse-shaped using a high-speed preamplifier (THS4302EVM, Texas Instruments, Dallas, TX, USA). Details of the detector configuration, operating conditions, and signal-acquisition system have been reported previously.^11,12) The measurement sequence was synchronized to the femtosecond-laser trigger, and trigger synchronization among the PXI modules was performed through the RTSI bus on the PXI Express backplane. Data acquisition was carried out using a PXIe-5162 digitizer (National Instruments, Austin, TX, USA), with a sampling rate of 5 GS s⁻¹ and a vertical resolution of 10 bits. At each pixel, 200 TOF waveforms were sequentially acquired and averaged to obtain a TOF spectrum. One depth cycle corresponded to 1 complete raster scan of the 25 × 25 pixel analytical area, representing 1 sputtering-depth layer. A total of 300 depth cycles were acquired sequentially layer by layer, corresponding to a total analytical duration of 10.4 h. The implanted ⁴He⁺ and the major matrix-derived ions ²⁴Mg²⁺, ¹⁶O⁺, ²⁸Si⁺, and ⁵⁶Fe²⁺ were measured. In the multi-turn mode, the total flight time was controlled. Consequently, ions with different m/z values completed different numbers of turns within the specified flight time. The numbers of turns for ⁴He⁺, ²⁴Mg²⁺, ¹⁶O⁺, ²⁸Si⁺, and ⁵⁶Fe²⁺ were 110, 64, 55, 42, and 42, respectively.

During sputtering, crater-edge effects cause mixing of signals from the crater bottom and crater edge. To reduce the crater-edge effects, the central 15 × 15 pixels of the total 25 × 25 pixels analytical area were used for data analysis. This restriction improves the stability of both depth-profile and peak-position analyses.

2.2 TOF spectral data processing and peak-position analysis

At each pixel, 200 TOF waveforms were sequentially acquired and averaged to obtain a TOF spectrum. The spectra acquired within the same depth cycle were then accumulated over the selected central 15 × 15 pixels to construct a depth-cycle spectrum representing 1 depth layer. Thus, each depth-cycle spectrum represented a total of 45000 TOF waveforms. Acquisition of 1 depth cycle required 125 s. The reference TOF position for each ion species was first determined from the spectrum accumulated over all 300 depth cycles.

The peak position of each ion species was determined for each depth-cycle spectrum. Ion intensities were calculated within a fixed ±10-ns window around the predefined TOF position.¹²⁾ For each ion species i, the peak shift was defined as

$$\Delta t_{i,j}=t_{i,j}-t_{i,\mathrm{r}\mathrm{e}\mathrm{f}},$$ (1)

where t_{i, j} is the peak position of ion i in depth cycle j, and t_{i, ref} is the reference TOF position of ion i. In practice, t_{i, ref} was defined as the intensity-weighted centroid of the peak in the spectrum accumulated over 300 depth cycles without TOF drift compensation. The centroid t_{i, j} was determined from the signal within a ±20-ns window centered on t_{i, ref} as follows:

$$t_{i,j}=\frac{\sum _k{t}_k{I}_k}{\sum _k{I}_k},$$ (2)

where t_k and I_k are the TOF and ion intensity of the kth data point, respectively. All sampled points within the window were included in the calculation, and no adaptive peak-boundary determination was applied. Baseline subtraction was not performed because the baseline level of the averaged TOF waveform was negligible under the present analytical conditions. Neighboring ion peaks were sufficiently resolved to avoid interference with the centroid determination. This centroid-based approach provides a more stable estimate of the peak position than simply using the maximum-intensity position.

For TOF drift compensation, the TOF shift of the internal reference ion was calculated as

$$\text{Δ}{t}_{\mathrm{M}\mathrm{g},j}=t_{\mathrm{M}\mathrm{g},j}-t_{\mathrm{M}\mathrm{g},\mathrm{r}\mathrm{e}\mathrm{f}},$$ (3)

where t_{Mg, ref} represents the reference TOF position of ²⁴Mg²⁺. The value Δt_{Mg, j} was used as the numerical compensation value for all ion signals acquired within the same depth cycle.

To construct the compensated peak profiles, the ±20-ns waveform segment centered on the reference TOF position of each target ion was extracted from each depth-cycle spectrum. To reduce computational cost, each extracted waveform segment was shifted along the TOF axis by −Δt_{Mg, j}. Because the digitizer sampling interval was 0.2 ns, the measured ²⁴Mg²⁺ peak shift, Δt_{Mg, j}, was converted to a number of sampling bins by dividing by 0.2 ns and rounding to the nearest integer. Each extracted waveform segment was then shifted by the corresponding number of samples before accumulation. No interpolation or resampling was applied. The compensated waveform segments from all 300 depth cycles were then accumulated to reconstruct the compensated peak profile for each ion species.

3. RESULTS AND DISCUSSION

3.1 Magnesium peak drift during long-duration analysis

Figure 1 shows the TOF spectrum accumulated over 300 depth cycles without the TOF drift compensation. The spectrum contains a peak corresponding to implanted ⁴He⁺, as well as olivine-matrix-derived peaks of ²⁴Mg²⁺, ¹⁶O⁺, ²⁸Si⁺, and ⁵⁶Fe²⁺. These peaks were used to evaluate peak-position stability during the 10.4 h measurement. Figure 2 shows the ²⁴Mg²⁺ peak shift, Δt_{Mg, j}, as a function of depth cycle j. The average ²⁴Mg²⁺ count rate was approximately 5 ions per mass scan. The observed variation indicates that the ion peak positions were not stable during the 10.4-h measurement. The standard deviation of Δt_{Mg, j} was 2.8 ns, and the peak-to-peak fluctuation, defined as the difference between the maximum and minimum Δt_{Mg, j} values, was 12.8 ns.

Fig. 1. Accumulated TOF spectrum from the He-Ol sample. Peaks corresponding to ⁴He⁺, ¹⁶O⁺, ⁵⁶Fe²⁺, ²⁸Si⁺, and ²⁴Mg²⁺ are indicated. TOF, time-of-flight.

Fig. 2. Temporal variation of the ²⁴Mg²⁺ TOF peak position during 10.4 h depth profiling. The ²⁴Mg²⁺ signal was monitored throughout the measurement to evaluate TOF drift. TOF, time-of-flight.

Because ion intensities were calculated within a fixed ±10-ns window, the observed drift can cause systematic underestimation of peak intensities and degradation of mass resolving power. To avoid these effects, it is necessary to evaluate peak positions for each depth layer and to account for TOF drift during data processing.

3.2 Cause of TOF drift during long-duration analysis

To identify the dominant source of the ²⁴Mg²⁺ peak drift shown in Fig. 2, the contributions of voltage fluctuations in the ion optical system of MULTUM II were evaluated using the relationship proposed by Tonotani et al.,¹⁰⁾ who described the TOF peak width, Δt, using the following equation:

$$\mathrm{\Delta }t=\sqrt{{(\mathrm{\Delta }{t}_0)}^2+{(\mathrm{\Delta }{t}_{\mathrm{L}1})}^2+{\left\{\left(\frac{\mathrm{\Delta }U}{2U}\right)t_u\right\}}^2+{\left\{\left(\frac{\mathrm{\Delta }E}{E}\right)\left(t-t_u\right)\right\}}^2}$$ (4)

where Δt₀ denotes the initial full width at half maximum (FWHM) of the ion peak, excluding temporal fluctuation components. Δt_L1 represents the timing jitter associated with the application of the ion injection pulse voltage to L1 in the ion injection optics. U and ΔU represent the acceleration voltage and its fluctuation, respectively, whereas E and ΔE represent the voltages applied to the 4 EFs of MULTUM II and their fluctuation, respectively. t_u is the TOF from the ion source to the starting point of the MULTUM II ion trajectory,¹³⁾ and t is the total TOF, including t_u.

Δt_L1 was experimentally determined to be approximately 1.5 ns. Although this term contributes to the overall peak width, it does not account for the long-term temporal variation. The parameters Δt₀ and t_u are fixed under the present instrumental conditions and therefore do not vary with time. Accordingly, ΔE/E is expected to be the dominant contributor to the time-dependent increase in Δt. According to the datasheet of MPD10N¹⁴⁾ (Spellman High Voltage Electronics Corporation, Hauppauge, NY, USA), the power supply used for the acceleration voltage, ΔU/U varies by approximately 25 ppm over 8 h. The flight distance from the ion source to the starting point of MULTUM II is 0.56 m. With an acceleration voltage (U = 4500 V), t_u for ²⁴Mg²⁺ is calculated to be 2.08 μs. In Eq. (4), the contribution of the acceleration–voltage fluctuation is given by (ΔU/2U)t_u. Using t_u = 2.08 μs, this contribution is only 0.026 ns. Therefore, the contribution of ΔU/U to Δt is negligible.

The observed FWHM of the ²⁴Mg²⁺ peak at a flight time of 314.53 μs was 11.4 ns, whereas the peak width in linear mode was 8.0 ns. Because the contribution of ΔU/U is negligible, the additional peak broadening observed in the multi-turn mode can be attributed mainly to fluctuations of the EF voltage. Using t = 314.53 μs and t_u = 2.08 μs for ²⁴Mg²⁺, the effective relative fluctuation of the EF voltage (ΔE/E) is estimated to be 26 ppm. The electrostatic-field term in Eq. (4) is based on the experimentally evaluated MULTUM II characteristics reported by Tonotani et al.¹⁰⁾ They demonstrated that modulation of the EF voltage produces a TOF modulation given by Δt = (ΔE/E) (t – t_u), and that the measured field modulation was quantitatively consistent with the observed limitation in mass resolving power. The estimated value of 26 ppm exceeds the previously reported stability of 5 ppm.¹⁰⁾ This discrepancy may be due to the difference in analytical duration. The previous evaluation was based on short-term measurements, ranging from several seconds to at most approximately 1 minute, whereas this study was conducted continuously for 10.4 h. Therefore, the larger ΔE/E estimated in this study likely reflects time-dependent instability of the EF voltage over the long-duration measurement, which results in TOF peak broadening in the multi-turn mode.

3.3 Correlation between ²⁴Mg²⁺ peak shifts and other ion peak shifts

To evaluate whether the TOF drift observed during the 10.4 h measurement was caused by common instrumental instability or by ion-specific effects, the peak shift of each ion was compared with that of ²⁴Mg²⁺. Here, Δt_{Mg, j} and Δt_{i, j} denote the TOF peak shifts of ²⁴Mg²⁺ and ion i, respectively, at the same depth cycle j, where i represents ⁴He⁺, ¹⁶O⁺, ²⁸Si⁺, and ⁵⁶Fe²⁺. As shown in Fig. 3, Δt_{i, j} shows a clear linear correlation with Δt_{Mg, j}. Most data points are distributed along the one-to-one correlation line. A linear regression constrained to pass through the origin yielded an R² value of 0.980, indicating that the TOF peak shifts of ⁴He⁺, ¹⁶O⁺, ²⁸Si⁺, and ⁵⁶Fe²⁺ are synchronized with that of ²⁴Mg²⁺. This nearly one-to-one relationship indicates that the observed peak shifts are mainly caused by common TOF-axis drift rather than independent ion-specific fluctuations. According to the relationship experimentally reported for MULTUM II by Tonotani et al.,¹⁰⁾ the TOF displacement caused by EF voltage modulation is proportional to (ΔE/E) (t − t_u). Because different numbers of turns were used in the present measurement to obtain similar total TOFs for the analyzed ion species, their t_i − t_u,i values were also similar. The ratios of t_i − t_u,i values to the corresponding value of ²⁴Mg²⁺ were approximately 0.99 for the other ion species.

Fig. 3. Correlation between ²⁴Mg²⁺ peak shifts and the peak shifts of other ion species. The dotted line represents the one-to-one correlation line. A linear regression constrained to pass through the origin yielded an R² value of 0.980, indicating a strong proportional relationship between the ²⁴Mg²⁺ peak shifts and the shifts of the other ion peaks. These results indicate that ²⁴Mg²⁺ can be used as an internal reference for TOF drift compensation. TOF, time-of-flight.

The scatter around the linear trend is likely attributable to differences in peak intensity and centroid-determination uncertainty among ion species. In particular, the ⁴He⁺ peak has a lower ion intensity, and therefore its peak-position determination is expected to have larger uncertainty. Nevertheless, the overall linear relationship demonstrates that ²⁴Mg²⁺ can be used as an internal reference for compensating for the TOF drift during long-duration measurements.

3.4 TOF drift compensation using ²⁴Mg²⁺ as an internal reference

Based on this proportional relationship, the ²⁴Mg²⁺-based compensation was defined as follows:

$${t_{i,j}}^{\text{comp}}=t_{i,j}-\text{Δ}{t}_{\mathrm{M}\mathrm{g},j}.$$ (5)

This procedure compensates for the peak position of each ion according to the TOF drift of ²⁴Mg²⁺. To evaluate the efficiency of this compensation, the standard deviations of the compensated peak positions (t^comp_{i, j}) were calculated for the 4 ion species other than ²⁴Mg²⁺. The standard deviations decreased from 2.9 to 0.6 ns for ⁴He⁺, from 2.8 to 0.11 ns for ¹⁶O⁺, from 2.5 to 0.37 ns for ²⁸Si⁺, and from 2.7 to 0.2 ns for ⁵⁶Fe²⁺. These reductions demonstrate that the ²⁴Mg²⁺-based compensation effectively suppresses TOF drift for all analyzed ion species.

Figure 4 compares the accumulated peak profiles obtained with and without compensation. After compensation, the FWHM values of all 5 ion profiles became narrower. These results indicate that ²⁴Mg²⁺ can be used as a practical internal reference for TOF drift compensation during long-duration measurements.

Fig. 4. Enlarged TOF peak profiles reconstructed from the ±20-ns waveform segments extracted for each ion from all 300 depth cycles. (A) ²⁴Mg²⁺, (B) ⁴He⁺, (C) ¹⁶O⁺, (D) ²⁸Si⁺, and (E) ⁵⁶Fe²⁺. Gray curves indicate spectra accumulated without TOF drift compensation, whereas black curves indicate spectra accumulated after compensation. The compensated profiles are narrower for all 5 ions. These FWHM values decrease from 11.4 to 8.4 ns for ²⁴Mg²⁺, from 9.2 to 7.8 ns for ⁴He⁺, from 9.0 to 7.4 ns for ¹⁶O⁺, from 11.4 to 9.4 ns for ²⁸Si⁺, and from 10.0 to 7.8 ns for ⁵⁶Fe²⁺. FWHM, full width at half maximum; TOF, time-of-flight.

The observed TOF peak width contains both intrinsic and time-dependent contributions. For ²⁴Mg²⁺, the standard deviation of the TOF shift was 2.8 ns (Fig. 2), whereas the FWHM decreased from 11.4 ns to 8.4 ns after compensation (Fig. 4A). Assuming approximately Gaussian broadening, the compensated FWHM corresponds to a standard deviation of approximately 3.6 ns. To assess whether the observed peak narrowing is quantitatively consistent with the measured TOF drift, the expected uncompensated peak width was estimated by combining the compensated peak width with the standard deviation of the TOF shift. Quadratic addition of these 2 contributions predicts an uncompensated FWHM of approximately 10.7 ns, which is reasonably consistent with the observed value of 11.4 ns. This agreement indicates that the observed peak narrowing is consistent with suppression of the long-term TOF variation among depth cycles. The present compensation reduces only the additional broadening caused by temporal displacement of the TOF axis among depth cycles. Intrinsic ion-packet width, detector response, trigger timing, and short-term fluctuations within each depth cycle are not removed by this procedure.

3.5 Implications and further improvements for depth profiling

For the He-Ol sample, spectral accumulation combined with ²⁴Mg²⁺-based compensation improved the peak shape and mass resolving power of ⁴He⁺ (Fig. 4B), enabling more reliable evaluation of its depth-dependent intensity variation. This compensation is therefore useful for accurately integrating weak signals during long-duration measurements.

Several improvements are required to further increase analytical precision. First, real-time compensation of the TOF drift would be highly effective. If an intense peak such as ²⁴Mg²⁺ can be used as an internal reference during measurement, the influence of peak drift during long-duration analysis could be reduced. Second, in future analyses, reducing the number of TOF waveforms at each pixel would shorten the acquisition time per depth cycle and enable the TOF drift to be monitored with finer time resolution. Third, peak extraction methods from TOF spectra should be further improved. In addition to fixed-width peak integration, machine-learning-based peak detection may also be useful for extracting weak peaks in low signal-to-noise regions.

4. CONCLUSIONS

This study evaluated TOF spectral drift during long-duration LIMAS depth profiling of a He-Ol sample and developed a ²⁴Mg²⁺-based internal compensation method. The ²⁴Mg²⁺ peak position varied during the 10.4-h analysis, with a standard deviation of 2.8 ns. This drift is large enough to shift ion peaks relative to a fixed integration window of ±10 ns. The observed broadening corresponds to an effective EF voltage fluctuation of approximately 26 ppm, suggesting long-term instability of the EF system.

The peak shifts of ⁴He⁺, ¹⁶O⁺, ²⁸Si⁺, and ⁵⁶Fe²⁺ showed clear linear correlations with the ²⁴Mg²⁺ peak shift, demonstrating that the TOF drift is largely systematic rather than ion-specific. The ²⁴Mg²⁺ peak can therefore be used as an internal reference to compensate for TOF peak positions at each depth cycle. After applying the ²⁴Mg²⁺-based compensation, the standard deviations of the compensated peak positions for the 4 analyzed ions were reduced from 2.5–2.9 ns to 0.11–0.6 ns. The compensation narrowed the accumulated peak profiles for all 5 measured ions and stabilized peak integration. The proposed compensation therefore improves the reliability of long-duration depth profiling. Future implementation of real-time ²⁴Mg²⁺-based compensation should further improve drift compensation.

Mass Spectrom (Tokyo) 2026; 15(1): A0201

This article is part of the Virtual Issue “Mass Spectrometry for the Future of Isotope Science.”