Evaluating cluster counting of Cs complexes through the study of nitrogen implanted zirconium

Abstract

The cluster counting method (including all Cs complexes missed out in the usage of single Cs complex per element) has previously been reported to provide a significantly better composition estimate than using a single Cs complex per element, for a D9 steel sample. The current study evaluates this method with a nitrogen-implanted zirconium specimen with high oxygen impurity concentrations. Therefore, this system is prone to experiencing strong matrix effects. Quantified elemental depth profiles of the specimen were obtained using XPS to compare with SIMS results. The study confirms that cluster counting of Cs complexes yields significantly better composition estimates than the single Cs complex approach. While fluorine and chlorine are trace-level impurities, their concentrations dominate the composition estimates in both cluster counted and single Cs-complex approaches because the $Cs_2$ complexes of halogens exhibit orders of magnitude higher sensitivities than those of the other elements. Applying relative sensitivity factors of a few tens for these species renders the concentrations of these impurities insignificant. With this correction, the composition estimates by both Cs complex methods improved towards that provided by XPS. At this stage also, the match of the cluster-counted composition with the XPS estimate remains markedly better than that by the single Cs-complex estimate. Additionally, the sensitivity factor values for all cluster-counted Cs complexes were incorporated and adjusted to ensure that the elemental compositions obtained by SIMS matched exactly with those determined by XPS. These relative sensitivity factors are also provided for academic purposes, aiding future studies on secondary ion and cluster formation. Notably, a comparable match could not be achieved between the single CsX species and the XPS profiles, even when varying the sensitivity factor values for the individual CsX species. Furthermore, the cluster counting method provides a means to estimate the sputter rate at each depth of the depth profile.

Introduction

Secondary Ion Mass Spectrometry (SIMS) is a powerful tool to detect elements with dynamic range of concentrations, ranging from 100% to ppm or even ppb or lower under suitable conditions. However, quantification of secondary ion intensities is highly challenging mainly because of the problem known as matrix effect^1,2 and dynamic sputter rate variation (continuously varying sputter rate) to a lesser extent. Matrix effect is the variation in secondary ion intensity with respect to the matrix from which an ion is ejected. If the studied system is simple enough, matrix matched standards are used for quantification of SIMS data. For a general system where the composition is complex and varies spatially, making standards is nearly impossible. Hence, methods to quantify without using standards is desirable. Detecting Cs complexes ($Cs_mX^+$) where X represents the elements in the specimen sputtered by Cs ion beam was introduced as an easy attempt to get relatively better quantified SIMS data^3,4,5. In this method, neutral X combining with ionic Cs is expected to produce better quantified data since the fraction of neutral X generally dominates the sputtered plume. However, in reality, other types of combinations like ionic X combining with neutral/ionized Cs atoms are also possible. Moreover, direct emission of Cs complexes as ions is also possible. Such possibilities can bring in matrix effect in Cs complex intensities also. Despite these complexities, the intensity of a Cs complex of an element is reported to be remarkably more quantitative than the intensity of an atomic secondary ion of that element. Including the intensities of those Cs complexes, which were missed out in this single Cs complex approach, was reported to further increase the quantification, through the analysis of a pure D9 steel sample⁶. In that system, the concentrations of electro-active elements were low. Hence, the matrix effect was relatively less severe in that analysis. However, matrix effect was evidenced through the relatively higher participation of negative ions like $Cr^-$ and $Ni^-$ in the formation of complexes like $Cs_2Cr^+$ and $Cs_2Ni^+$ respectively. This led to a higher estimate of Cr concentration and compensation of the lower Ni concentration with CsNi alone. It is useful to evaluate the cluster counting method in a system with higher concentrations of electro-active elements.

In this work, the cluster counting method was employed in the analysis of a nitrogen implanted zirconium specimen that has high concentrations of oxygen as impurity. Oxygen and nitrogen are known to form $Cs_2X^+$ complexes with high intensities through the participation of $O^-$ and $N^-$ ions. Hence, this is a representative sample with a stronger matrix effect in order to study the efficiency of cluster counting. The cluster counted elemental depth profiles are compared with the quantified elemental depth profiles obtained using XPS. We also introduce a sensitivity factor for each cluster species counted and estimate its value such that the cluster counted elemental depth profiles match the XPS depth profiles. A brief description of the cluster counting method, including the sensitivity factors and a method to estimate the sputter rate at every depth of the depth profile is provided in “Methods”.

Methods

Mass spectral analysis

Although the mathematics of mass spectral analysis is standard, it is provided here for a quick reference. A measured mass spectrum is the composite of the fingerprint mass spectra of the species going through the mass analyser. If $N_s$ is the number of species constituting the mass spectrum, the intensity $I_{m_i}$ measured at mass $m_i$ is given by

$$\begin{aligned} \sum \limits _{j=1}^{N_s} a_{ji} I_{s_j} +\delta I_{m_i} = I_{m_i} \end{aligned}$$

(1)

$a_{ji}$ is the isotopic abundance of the $j^{th}$ species at mass $m_i$, with the sum $\sum \limits _i a_{ji}$ is normalized to unity. $I_{s_j}$ is the intensity of the $j^{th}$ species. $\delta I_{m_i}$ is the error in the measurement of $I_{m_i}$. If there are $N_p$ number of peaks in the composite spectrum, there are $N_p$ number of such equations. This set of equations can be represented by the matrix equation given below.

$$\begin{aligned} \textbf{A} \mathbf {I_s} + \varvec{\delta }_{m} = \mathbf {I_m} \end{aligned}$$

(2)

$\textbf{A}$ is an $N_p \times N_s$ matrix with components $a_{ji}$. $\mathbf {I_m}$ is the vector containing the measured spectrum. $\varvec{\delta }_{m}$ is the vector containing the error terms. $\mathbf {I_s}$ is the vector containing the intensities of the species that contribute to $\mathbf {I_m}$. $\mathbf {I_m}$ and $\textbf{A}$ are known quantities. $\mathbf {I_s}$ is the solution to the equation. Since measurement error is an unknown quantity, Eq. (2) has to be solved without including the error term $\varvec{\delta } \textbf{m}$, leading to a solution $\widetilde{\textbf{I}_s}$ in place of the expected solution $\mathbf {I_s}$.

$$\begin{aligned} \textbf{A} \widetilde{\textbf{I}_s} = \mathbf {I_m} \end{aligned}$$

(3)

In general, $\textbf{A}$ is a rectangular matrix since the number of peaks $N_p$ need not be equal to the number of species $N_s$. Hence, the least square deviation form of Eq. (3) is solved as given below.

$$\begin{aligned} \textbf{A}^\intercal \textbf{A} \widetilde{\textbf{I}_s} = \textbf{A}^\intercal \mathbf {I_m} \end{aligned}$$

(4)

$\textbf{A}^\intercal$ is transpose of $\textbf{A}$. The solution $\widetilde{\textbf{I}_s}$ could differ significantly from $\mathbf {I_s}$ and even become physically meaningless with negative components if the error contribution ($\delta _m$) in Eq. (2) is significant or if the choice of species is incorrect. If one or more components in $\widetilde{\textbf{I}_s}$ is negative even with correct choice of species, the solving process must be appropriately regularized^7,8. Gautier et al.^7,8 use smoothness and positivity as the conditions of regularization in the process of inversion to obtain meaningful depth profiles after deconvolving the ion beam broadening function from the measured sputter depth profiles. While solving for $\mathbf {{I}_s}$, the condition of positivity alone is imposed. The condition of smoothness is not required since the intensity does not need to vary smoothly from one species to another.

Identifying the clusters

After getting a mass spectrum from the specimen, the peaks in the spectrum are considered one after another preferably in the order of their intensities, in order to identify the species contributing to them. Since we are interested in the Cs complexes of clusters, the analysis can be limited to the peaks having mass higher than 133u of Cs. Once a peak is selected for identification, the species most likely to contribute to this and its surrounding peaks is identified, and its fingerprint mass spectrum is constructed. The matrix $\textbf{A}$ in Eq. (4) is constructed from the fingerprint mass spectrum of the assumed species and the equation is solved to find its intensity. In general, there can be other species, which have their fingerprint mass spectra overlapping with the one of this species and not included in $\textbf{A}$, causing the residue vector $\mathbf {I_m} - \textbf{A} \widetilde{\textbf{I}_s}$ to have a few components of considerably high value. These other species can be included in the equation sequentially. Inclusion of a species can widen the composite spectrum leading to the inclusion of furthermore overlapping species.

The intensities of a few species may turn out to be negative and/or the residue vector may have high intensities if the choice of species is incorrect and/or error in measurement is too high. In such cases, the process of ‘regularization’⁷ is applied to impose the condition of positivity for the solution. If the solution contains one or more negative components even after regularization, the choice of species must be revised until the solution is nonnegative and satisfies Eq. (4) with ignorable intensities of residue. A typical example of such overlapping species can be found in Fig. 3 of work published by Balamurugan et al.⁶.

This process must be followed for all the groups of peaks having mass above 133u. Even the clusters that do not have a Cs atom but have peaks of considerable intensity above 133u should be included in the analysis since otherwise Eq. (4) will not be satisfied. However, they are not included in the computation of composition since we are interested only in the Cs complexes for quantification. Analysis of the peaks below mass 133u can also be useful since it provides clues about atoms that can be found in clusters having mass above 133u.

Estimating the composition

The secondary ion intensity $I_{e_i}$ corresponding to an element $e_i$ is computed as the linear combination of the intensities $I_{s_j}$ of all the Cs complexes.

$$\begin{aligned} I_{e_i} = \sum \limits _{j=1}^{N_s} n_{ij} I_{s_j} \end{aligned}$$

(5)

$N_s$ is the total number of Cs complex species. $n_{ij}$ is the number of atoms of element $e_i$ in the species $s_j$. The concentration $c_i$ of an element $e_i$ is computed by normalizing the total intensity of the $N_e$ number of elements counted to the known total concentration C of these elements.

$$\begin{aligned} c_i = \frac{I_{e_i}}{\sum \limits _{j=1}^{N_e} I_{e_j}}C \end{aligned}$$

(6)

Here, the factors like matrix effects and variations in affinity between atoms, clusters, or ions forming different species, (which can depend among others on polarizability^9,10), are ignored, as done in the single Cs complex approach. The aim here is to improve the Cs complex method by including previously ignored Cs complexes.

Ion intensity correction

Although quantification through $CsX^+$ expects X to be neutral combining with a $Cs^+$ ion, the other combination, an $X^+$ ion combining with a neutral Cs ($Cs+X^+$) is also possible. Another common problem is that Cs complexes of type $CsX_2$ are predominantly formed if X is highly electronegative, by combinations such as $X^-\! + Cs^+\! + Cs^+\!$,  $XCs + Cs^+$ or  $X + Cs_2^+$. If an X is electropositive and a Y is electronegative, Cs complexes of type XYCs are formed with considerable intensity, through combinations such as $X^+\! + Y^-\! + Cs^+$,   $XY + Cs^+$,   $X^+ + YCs$.... Even the neutral clusters such as XCs, YCS or XY in these combinations could be formed by the combination of neutrals or ions. Direct emission of Cs complexes like $XCs^+$, $CsX_2^+$, ...is also possible. Thus, the intensities of Cs complexes are also prone to matrix effect although to a lesser extent than non Cs complexes are. In addition to matrix effects, the differences in the affinities between the different atoms/clusters forming the Cs complexes can also influence the intensities of the different Cs complexes. In effect, the SIMS sensitivity for different Cs complexes differ. Hence, it is desirable to correct the intensities of Cs complexes for differences in sensitivities, if their relative sensitivity factors are known or can be approximated by some means. While cluster counting improves quantification of composition, sensitivity factor correction will further improve it.

The intensity of every species $I_{s_j}$ in Eq. (5) is divided by its sensitivity factor $\varepsilon _{s_j}$ to get the sensitivity corrected intensity $I_{e_i}'$ for an element $e_i$.

$$\begin{aligned} I_{e_i}' = \sum \limits _{j=1}^{N_s} \frac{n_{ij}I_{s_j}}{\varepsilon _{s_j}} \end{aligned}$$

(7)

The elemental composition is computed by replacing $I_{e}$ in Eq. (6) with $I_{e_i}'$ as below.

$$\begin{aligned} \begin{aligned} c_i&= \frac{I_{e_i}'}{\sum \limits _{j=1}^{N_e} I_{e_j}'}C \\ \end{aligned} \end{aligned}$$

(8)

The set of $\varepsilon _{s_j}$ values can be scaled up or down by any constant to get the same composition estimate using Eq. (8) since this constant in the numerator and denominator of this equation cancel out each other. We choose in this work that $\varepsilon _{s_j}$ has a minimum value of 1.

Depth calibration

The sum of sensitivity corrected intensities $\sum _{i=1}^{N_e}I_{e_i}'$ of all the species, where $I_{e_i}'$ is given by Eq. (7) is expected to be proportional to the sum of atoms sputtered, as given below.

$$\begin{aligned} \sum _{i=1}^{N_e} I_{e_i}'\propto & \rho A \sigma \end{aligned}$$

(9)

$$\begin{aligned}= & \kappa \rho A \sigma \end{aligned}$$

(10)

$\rho$ is the total atomic density of the $N_e$ number of elements at the surface of the specimen. A is the area of sputtering and $\sigma$ is sputter rate. $\kappa$ is a factor that depends on parameters like the instrument’s detection efficiency and the factors such as ionization probability, combination probability...absorbed in $\varepsilon _{s_j}$ as discussed in “Ion intensity correction”. SIMS records secondary ion intensities as a function of sputtering time to provide depth profiles. The ratio of total intensities from Eq. (10) computed at two different sputtering times $t_i$ and $t_j$, assuming $\kappa$ to be constant along depth as a first approximation, is

$$\begin{aligned} \frac{\sum \limits _{k=1}^{N_e} I_{e_k}'(t_i)}{\sum \limits _{k=1}^{N_e} I_{e_k}'(t_j)} = \frac{\rho(x_i)\sigma (x_i)}{\rho(x_j) \sigma (x_j)} \end{aligned}$$

(11)

$x_i$ and $x_j$ are the depths sputtered until times $t_i$ and $t_j$ respectively. If the value of the ratio $\frac{\rho (x_i)}{\rho (x_j)}$ is known, it can be plugged in Eq. (11) or it can be assumed to be unity in the absence of this information. In this work, it is assumed to be unity and Eq. (11) becomes,

$$\begin{aligned} \frac{\sum \limits _{k=1}^{N_e} I_{e_k}'(t_i)}{\sum \limits _{k=1}^{N_e} I_{e_k}'(t_j)} = \frac{\sigma (x_i)}{\sigma (x_j)} \end{aligned}$$

(12)

Thus, any variation along depth in the sum of intensities is proportional to the variation in sputter rate along the depth. Before converting the sputtered time into depth, this variation in sputter rate along depth must be evened out with reference to a depth slab, typically the first one. If the first slab is taken as the reference, the sum of intensities $\sum _{k=1}^{N_e} I_{e_k}'(t_i)$ at every sputtering time $t_i$ is normalized to the sum of intensities at start of sputtering $\sum _{k=1}^{N_e} I_{e_k}'(t_1)$ by normalizing the intensity of every element as given below.

$$\begin{aligned} I_{e_j}''(t_i) =I_{e_j}'(t_i) \frac{\sum \limits _{k=1}^{N_e}I_{e_k}'(t_1)}{\sum \limits _{k=1}^{N_e}I_{e_k}'(t_i)} \end{aligned}$$

(13)

$I_{e_j}''(t_i)$ is the sputter rate normalized intensity of the $j^{th}$ element at sputtering time $t_i$. The width of every time slab is divided by the same normalizing factor and stacked at the end of the previous slab to get the sputtering time that would have happened if the sputtering rate were constant.

$$\begin{aligned} t_i^\prime = t_{i-1}' + {(t_i-t_{i-1})}\big /{\frac{\sum _{k=1}^{N_e}I_{e_k}'(x_1)}{\sum _{k=1}^{N_e}I_{e_k}'(x_i)}} \end{aligned}$$

(14)

Thus, the area under every profile is conserved by this process of sputter rate normalization. The sputtering time $t_i^\prime$ can be converted to depth by multiplying $t_i^\prime$ by the sputter rate (${D}\big /{t_{end}'}$), which is the ratio of the measured crater depth D to the normalized total time $t_{end}'$ as shown below.

$$\begin{aligned} x_i = \frac{D}{t_{end}'} t_i^\prime \end{aligned}$$

(15)

The concentration $c_i$ of an element $e_i$ is computed by substituting $I_e^\prime$ in 8 with $I_{e}''$ from 13 as given below.

$$\begin{aligned} c_i = \frac{I_{e_i}''}{\sum \limits _{j=1}^{N_e} I_{e_j}''}C \end{aligned}$$

(16)

Iterative intensity correction and depth calibration

The sensitivity factor values ($\varepsilon$) must be chosen such that the cluster counted composition matches with the expected composition, when known. However, after the $\varepsilon$ values of one or more species are changed, the depth, according to “Depth calibration”, must be recalibrated. The recalibration can call for further refinement of the $\varepsilon$ values. Thus, tuning of $\varepsilon$ values and depth recalibration must be repeated iteratively until reaching the desired match with the known composition.

Experimental

Zirconium thin film was grown to a thickness of $\approx$ 500 nm on a silicon substrate by magnetron sputtering of a zirconium target. This film was implanted with 10 keV $^{14}N^+$ ions to a fluence of approximately $5 \times 10^{17}$ ${\text {ions/cm}}^2$ using a linear particle accelerator. The aim of this implantation was to study surface nitridation by shallow ion implantation. However, in this work, this specimen is used to study the effect of the cluster counting technique in quantification of SIMS data. The SIMS analyses were done on this specimen using a Cameca ims-7f Secondary Ion Mass Spectrometer. The mass spectrum from this specimen was acquired using 9 nA of 5 keV $Cs^+$ primary ions, rastered over a square area of width 250 $\upmu$m. The most abundant Cs complexes constituting this mass spectrum were identified as discussed in “Methods”, whose isotopic representatives are listed in Table 1. They are listed in the order of their mass numbers.

Table 1 List of most abundant Cs complex species.

The depth profiles of the species listed in Table 1 were acquired using $Cs^+$ primary ion beam of 2.4nA current and 5keV energy, rastered over a square area of 250 $\upmu$m width. The secondary ions were collected from a circular area of 62 $\upmu$m diameter at the center of the rastered area. The depth profiles of these species after correcting their intensities for isotopic abundances are plotted in Fig. 1. The vertical axes of the Figs. 1c,d are split up into two to reveal the features in the implantation region while containing the surface spikes. The depth is represented by sputtering time. The depth of the sputter crater was measured to be 115.7 nm by a Dektak 6M surface profilometer. The sputter time will be calibrated for depth as discussed in “Depth calibration”. The intensity of every species was measured for one second after waiting for sufficient time for the magnet to settle at the field value for the species. One such cycle of measurement took 31.68 seconds. The depth profiles were acquired for 9504 seconds through 300 such cycles of measurement. The mass interference from CsZr in $^{133}Cs\,^{90}Zr\,^1H$ through $^{133}Cs\,^{91}Zr$ is subtracted. Similar subtractions are also done for interference from CsZrO in $^{133}Cs\,^{90}Zr\,^{16}O\,^1H$, $Cs_2Zr$ in $^{133}Cs_2\,^{90}Zr\,^1H$ and $Cs_2\,Zr\,H$ in $^{133}Cs_2\,^{96}Zr\,^1H_2$ through $^{133}Cs_2\,^{96}Zr\,^2H$ although negligible.

Figure 1

Depth profiles of the most abundant Cs complex species after correcting for their isotopic abundances, split up into four groups according to their intensities.

The XPS spectra of this specimen were acquired using a PHI 5000 VersaProbe 3 XPS equipment employing Al K-$\alpha$ X-ray. The spectra were acquired from the surface and 21 deeper layers of the specimen. Each of the 21 deeper layers was reached by sputtering the specimen for 18 seconds using $Ar^+$ ion beam of 7.06mA current, 0.110 keV energy and 2 $\upmu$m diameter, rastered over an area of 100 $\upmu$m width. The photoelectrons were collected from a square area of width $10\; \upmu$m. The XPS spectra showed the predominant presence of the elements zirconium, oxygen and nitrogen. SIMS shows dominant intensities for zirconium, oxygen, nitrogen, fluorine, chlorine and hydrogen and a little of aluminium. Hence, the peaks corresponding to fluorine, chlorine and aluminium in the XPS spectra were also analysed. Since hydrogen cannot be detected by XPS, it is absent in XPS analysis. The XPS spectra were analyzed using CASA XPS software to quantify the peaks of Zr 3p, N 1s, O 1s, F 1s, and Cl 2s orbitals. The elemental depth profiles so obtained by XPS are shown in Fig. 2. The total concentration is normalized to 100%. Carbon is detected only at the surface (about 49 at. %), and not at deeper levels. The main carbon complex in SIMS, Cs2C, has a mass number of 278u. SIMS takes  445 s to reach 278u from 1u of the mass spectrum, by which time a depth of  35 nm is sputtered. At this depth, XPS shows zero carbon concentration, making Cs₂C intensity undetectable in the SIMS mass spectrum and thus not included in SIMS depth profiling. The concentrations of zirconium, oxygen and nitrogen dominate the rest of the depth in the XPS profiles. The XPS depth profiles are observed to have a noise of around 1%. Unlike with SIMS, the XPS depth profiles of fluorine, chlorine and aluminium don’t show any feature discernible from its noisy background as seen in Fig. 2b.

Figure 2

Depth profiles of elements obtained by XPS.

Results and discussion

Cluster counting

The conventional way of representing each element by a Cs complex is presented in Fig. 3a. The SIMS intensities are plotted against the left vertical axis with the sputtering time along the bottom horizontal axis. The XPS depth profiles of elemental concentrations are also plotted in the figure for comparison. The XPS concentrations are plotted against the right vertical axis with the XPS sputtering time along the top horizontal axis. The XPS data are corrected for relative sensitivity factors and the composition is normalized to 100%. The maximum of SIMS sputtering time axis is chosen to be 4000 seconds so that the sputtered depths by SIMS and XPS correlate with each other. The SIMS depth profiles differ from the XPS depth profiles not only quantitatively but also qualitatively in terms of the profile shapes.

The cluster counted elemental depth profiles obtained using Eq. (5) and (6) (or Eqs. (7) and (8) with $\varepsilon$ values equal to 1) counting all the Cs complex profiles in Fig. 1 is shown in Fig. 3b . There are totally seven elements contributed by those eighteen species. The nitrogen depth profile has improved drastically well while comparing the $Cs_2N$ profile in Fig. 3a . Nitrogen in Fig. 3b is computed as the sum of the intensities of CsN, CsZrN, $Cs_2N$, CsZrN, $Cs_2ZrON$, $CsN_2*2$, and $CsN_4*4$. The intensities of the last two species are multiplied by two and four since they contain two and four nitrogen atoms respectively. The relative intensities of zirconium, nitrogen and oxygen with respect to those of the impurities fluorine and chlorine, which are supposed to be at trace level, are more accurate in Fig. 3b than in Fig. 3a . The relative intensity of zirconium with respect to that of oxygen is also more accurate in Fig. 3b .

Figure 3

Comparing single Cs complex representation and cluster counted elemental depth profiles. XPS depth profiles of elemental concentrations are plotted against the right vertical axes.

The nitrogen profile in Fig. 3b has a surface peak whereas the $Cs_2N$ profile in Fig. 3a (the $Cs_2N$ profile in Fig. 1b can be seen for a better clarity) doesn’t show such a peak. This is caused by the strong surface peaks of the species $CsN_4$, $CsN_2$, and a milder one of CsN (Fig. 1c ), which contribute to the nitrogen profile in Fig. 3b . The Al peak in Fig. 1d also shows a surface peak. Carbon is the most dominant element in the surface as revealed by XPS. Hence, the surface peaks measured by SIMS could be due to some carbon containing clusters. The mass spectral analysis of the peaks around the masses of CsAl and $CsN_2$ reveals the presence of CsCNH, $CsN_2$ CsOC..., as shown in Fig. 4. The wider bar at every mass number seen behind the stacked species bars shows the measured intensity. The inversion process had to be regularized since the initial solution had negative values as shown in Table 2. Regularization shows that the species at 160u is $^{133}Cs^{12}C^{14}N^{1}H$ instead of $^{133}Cs^{27}Al$ as originally thought of. CsAl received an intensity of just 2.E-04 c/s that is to be considered as zero. Interestingly, CsCN is not considerable since the measured intensity was just 8 c/s at mass 159u.

Figure 4

Mass spectral analysis showing the presence of CsOC and $CsN_2$ at mass 161u. The species name labels in the bars represent the corresponding monoisotopic species such as CsN2 representing $^{133}Cs^{14}N_2$.

Table 2 Negative (non-physical) intensities in the initial solution and the physically meaningful intensities after regularization of the mass spectral analysis around mass 160u.

Thus, the depth profile acquired at mass number 161u is a composite of a sharp CsOC surface peak followed by a broad and short $CsN_2$ peak. Since the intensity of the surface CsOC peak appears to become negligible above around 540 s (labelled $CsN_2$ in Fig. 1c), the $Cs^{14}N_2$ component in the surface region must be obtained by extrapolating the profile measured below this depth. The polynomial $-3.548\times 10^{-8}t^3-5.093\times 10^{-5}t^2+0.4905t-1.8241$ (t representing the sputtered time), fits the measured profile from the sputtered time of around 540 s to 2100 s. The $Cs^{14}N_2$ profile below the sputtering time of 540 s is obtained by extrapolating the implantation peak using this polynomial. The $Cs^{16}O^{12}C$ component is obtained by subtracting the $Cs^{14}N_2$ profile from the measured profile. The $Cs^{14}N_2$, $Cs^{16}O^{12}C$ and the measured profiles are plotted in Fig. 5.

Figure 5

Decomposition of the $CsN_2$ profile.

Similarly, the depth profile acquired at mass 189u can be a composite of a sharp surface peak of a carbon containing species like $CsO_2C_2$ followed by a broad and short nitrogen containing implantation peak like $CsN_4$. The mass spectral analysis of the spectrum around 189u is shown in Fig. 6. The species seen at mass 189u, in the order of their stack in the graph are, (the sum of three isotopic combinations of) $Zr_2H$ (11.9 c/s), $^{133}Cs\,^{16}O_2\,^{12}C_2$ (7.1 c/s), $^{133}Cs\,^{14}N_4$ (7.3 c/s) and $^{133}Cs\,^{16}O\,^{14}N_2\,^{12}C$ (471 c/s). The depth profile measured at mass 189u (Fig. 1c) has a background intensity of around 200 c/s at the end of the profile, which could be due to $Zr_2H$. The tail region of the measured profile fits to the linear expression $-0.1t+214.4$ and the $Zr_2H$ profile is obtained by extrapolating this line until the surface. This is a very rough approximation since the depth trend of $Zr_2H$ is expected to be correlated with those of the Zr and H profiles. However, the subtraction of this profile is expected to cause the measured profile to be closer to the actual $CsN_4$ profile than leaving without the subtraction. The profile obtained by subtracting the $Zr_2H$ profile from the measured profile is expected to be the composite of implanted $^{133}Cs\,^{14}N_4$, surface $^{133}Cs\,^{16}O_2\,^{12}C_2$, and an in-between $^{133}Cs\,^{16}O^{14}N_2\,^{12}C$ profiles. The surface carbon containing peak appears to become negligible after around 850 seconds of sputtering. The polynomial $-7.705\times 10^{-8}t^3 + 1.942\times 10^{-4}t^2 + 3.947\times 10^{-2}t - 0.3896$, fits the composite profile from the depth of around 860 s to around 1900 s. The $^{133}Cs\,^{14}N_4$ component below 860 s of sputtering is obtained using this polynomial. The $^{133}Cs\,^{14}N_4$ component subtracted from the composite profile gives the surface peak constituted by $^{133}Cs\,^{16}O_2\,^{12}C_2$ and a sub-surface narrow $^{133}Cs\,^{16}O\,^{14}N_2\,^{12}C$ peak. The surface peak, the implantation $^{133}Cs\,^{14}N_4$ peak and the $ZrH_2$ background decomposed from the measured profile are shown in Fig. 7. Since the guiding principle to construct the $CsON_2C$ peak is not available, the surface peak is considered as from $CsO_2C_2$ alone.

Figure 6

Spectral analysis showing the presence of $Zr_2H$ (the composite of three possible isotopic combinations), $^{133}Cs\,^{16}O_2\,^{12}C_2$, $^{133}Cs\,^{14}N_4$ and $^{133}Cs\,^{16}O\,^{14}N_2\,^{12}C$ at mass 189u.

Figure 7

Decomposition of the profile measured at mass 189u.

The cluster counted depth profiles (Fig. 3b) after the decomposition of the $CsN_2$ and $CsN_4$ profiles, as shown in Figs. 5 and 7 respectively, are shown in Fig. 8. The artefact of surface nitrogen peak in Fig. 3b has been corrected in this figure. Element carbon is included, and aluminium is removed in Fig. 8 since it is found absent by the mass spectral analysis. Concentration of carbon is computed as the sum of the intensities of CsCNH, CsOC, and $Cs O_2 C_2$. Fluorine and chlorine are measured to be very high by SIMS, due to the high sensitivities for the $Cs_2F$ and $Cs_2Cl$ species. They will show the impact on the composition estimate when the intensities are normalized to get the elemental composition as discussed in “Methods”.

Figure 8

The cluster counted depth profiles after decomposing the $CsN_2$ and $CsN_4$ profiles from the measured profiles.

The depth profiles after normalizing the total intensity to 100% and calibrating the depth as discussed in “Depth calibration” are shown in Fig. 9. The last depth by XPS sputtering was chosen to be 60.3 nm such that the end of nitrogen depth profile matches with that of nitrogen depth profile by SIMS. The depth reached by the $i^{th}$ sputtering of XPS is determined as the SIMS depth at the time value, $\frac{t_{i_{XPS}}}{T_{XPS}}t_{SIMS}^{D_{XPS}}$. Here, $t_{i_{XPS}}$ and $T_{XPS}$ are the XPS sputtering time until the $i^{th}$ layer and the last layer ($21^{st}$) respectively. $t_{SIMS}^{D_{XPS}}$ is the time taken by SIMS to reach the crater depth by XPS ($D_{xps}$). By this way, the dynamic sputter rate trend of SIMS is transferred to the sputtering by XPS. The right vertical axes in Fig. 9 present the sputter rate, which was calculated as a function of depth based on the described calibration method..

As anticipated, the high intensities of fluorine and chlorine signals distort the profiles of other elements in Fig. 9 because of the total intensity normalization. The depth profiles of nitrogen are skewed, and the zirconium profiles are also distorted in a similar way.

Figure 9

The SIMS depth profiles after normalizing the total intensity to 100% and depth calibrated as discussed in “Depth calibration”.

Hydrogen cannot be detected by XPS. However, it is present in considerable amount as measured by SIMS. Hence, the hydrogen concentration must be taken from the SIMS measurement. Consequently, the sum of elemental concentration estimates by XPS in Fig. 10 is normalized to $100\%-C_H$, where $C_H$ is the percentage of hydrogen estimated by SIMS.

Figure 10

The sum of concentration by XPS normalized to $100\% - c_H$ ($C_H$ is the concentration estimate for hydrogen by SIMS).

Fluorine and chlorine measured by XPS are below detection limit due to their trace levels. SIMS sensitivity ($\varepsilon$) for $Cs_2X$ (where X is a halogen) is orders of magnitude higher than for CsX. Values of 40 and 10 for $\varepsilon$ of $Cs_2F$ and $Cs_2Cl$ yield the cluster counted profiles in Fig. 11b . For single CsX, values of 50 and 20 are used in Fig. 11a . These $\varepsilon$ values lead to fluorine and chlorine concentrations around 1%, matching XPS limits. Actual values are likely lower, suggesting higher $\varepsilon$ estimates for $Cs_2F$ and $Cs_2Cl$. Increasing $\varepsilon$ further does not significantly affect other element estimates, so these minimum $\varepsilon$ values are selected.

Figure 11

Depth profiles with $Cs_2F$ and $Cs_2Cl$ corrected for sensitivity factors and the sum of concentrations by XPS normalized to $100\%-C_H$ ($C_H$ is the concentration estimate for hydrogen by SIMS).

The match between the SIMS and XPS profiles is significantly better in Fig. 11b than that in Fig. 11a . Thus, it is verified that cluster counting of Cs complexes does produce significant improvements over the use of single CsX per element. In the analysis so far resulting in Figs. 3, 9, 10 and 11, the XPS results have been used just for a comparison purpose to weigh the efficacy of cluster counting over the use of single Cs complex per element. They are not used to tailor the SIMS quantification process. Similar treatments can be done, in general, on the SIMS data of any system to get similar quantifications of SIMS data.

In Fig. 11, the oxygen profile is similar to but scaled up in comparison with that by XPS. The mismatch between the nitrogen profiles in Fig. 3b at the end portion appears to be due to higher hydrogen estimate than it should be. Concentration estimate for zirconium is less by SIMS than that by XPS. These differences are due to the sensitivity factor values for many species being different from 1. We could make an estimate for only $Cs_2F$ and $Cs_2Cl$ without using the XPS data, using a minimum required value approach mentioned above. This approach is good enough when the concentration estimate of the major elements is of particular importance and not that of such impurities. However, we will make an estimate of the sensitivity factor values for all the species using the XPS data as the reference, in the next section, for academic interest.

An estimate for sensitivity factors

A set of sensitivity factor ($\varepsilon$) values was determined through a trial-and-error approach to align the cluster-counted SIMS profiles with the XPS profiles, as shown in Table 3. The resulting cluster-counted profiles are presented in Fig. 12b . Similarly, values for single CsX species, obtained using the same method, are listed in Table 4, with their corresponding SIMS profiles shown in Fig. 12a . The match achieved by the cluster-counted profiles with the XPS data is significantly more accurate than that obtained using the single CsX profiles, underscoring the necessity of including cluster species in the analysis.

The sputter rate at the surface is higher due to the transient regime of sputtering. The next broad peak in the sputter rate profile comes before the nitrogen implantation profile, and the two profiles overlap. This increase could be due to the defect distribution that usually precedes the implantation profile. If sputtering during implantation is negligible, the implantation profile is expected to be narrower. However, since the implantation energy of 10 keV used here causes considerable sputtering, the target surface recedes due to sputter erosion. As a result, the implantation profile is effectively carried deeper along with the receding surface. Therefore, the actual implantation profile observed is the convolution ($\circledast$) of the static implantation profile (in the absence of sputtering) and the surface recession profile. Assuming the specimen’s density to be $6.49 {\text {g/cm}}^3$ (corresponding to bulk zirconium, or $4.28 \times 10^{22}$ ${\text {atoms/cm}}^3)$, the retained nitrogen dose is estimated to be $3.6 \times 10^{16}$ ${\text {atoms/cm}}^2$. This is significantly lower than the implanted dose, which may be attributed to loss by sputtering during implantation.

To achieve an optimal match across all elements shown in Fig. 12b , the sensitivity factor values for $Cs_2F$ and $Cs_2Cl$ were adjusted to 75 and 25, respectively. This kind of estimation of sensitivity values is feasible only when the target composition is known, as is the case here. Nevertheless, when such information is available, the exercise is valuable-it facilitates the development of a database of sensitivity factors. Over time, such a database could help reveal correlations between sensitivity factors and the physical properties of the system, such as ionization potential, electron affinity, polarizability, etc., of the participating atoms or clusters. These insights could ultimately support the development of a predictive model for estimating sensitivity factor values in systems with unknown composition or unknown sensitivity data.

Table 3 Set of sensitivity factor values of all the species, optimized to match the cluster counted profiles with the XPS profiles, producing the results in Fig. 12b.

Table 4 Set of sensitivity factor values for the single CsX species to match them with the XPS profiles, producing the results in Fig. 12a.

Figure 12

Elemental depth profiles with sensitivity factors ($\varepsilon$) applied for all the species.

Conclusion

This study has demonstrated the efficacy of the cluster counting method in providing a significantly better composition estimate for nitrogen-implanted zirconium specimens compared to the single Cs complex approach. By incorporating the intensities of multiple Cs complexes, the cluster counting method effectively mitigates the matrix effects and dynamic sputter rate variations, leading to more accurate elemental depth profiles. The sensitivity factor values for various Cs complexes were estimated, which can be useful for academic research. These findings underscore the potential of the cluster counting method as a robust tool for SIMS data quantification, offering valuable insights for future studies on secondary ion and cluster formation. The improved accuracy in composition estimates achieved through this method can facilitate more precise material characterization and contribute to advancements in surface and thin film studies.