An accurate semi-empirical equation for sputtering yields, II: for neon, argon and xenon ions

doi:10.1016/j.nimb.2004.12.129

Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms

Volume 229, Issues 3–4, April 2005, Pages 348-358

https://doi.org/10.1016/j.nimb.2004.12.129 Get rights and content

Abstract

A new general, predictive semi-empirical equation for the sputtering yields of mono-elemental solids, using 250–10,000 eV ions incident normally on the surface, has been developed. This equation is based on the approach of Matsunami et al. but includes a new atomic density term and avoids their arbitrary Q term. By analysing published experimental data for Ne, Ar and Xe sputtering yields, the accuracy of this approach may be evaluated. The standard deviations of the data for Ne, Ar and Xe are 14%, 9% and 14%, respectively and represent a very significant improvement on the semi-empirical approaches of Matsunami et al. and of Yamamura and Tawara. General predictive relationships are established to allow the approach to be used for any incident ions, however, it is expected that accuracies for low reactivity (inert gas) incident ions with masses in the range from Ne to Xe will be comparable to the above figures but extrapolation to lighter elements than Ne or heavier than Xe, or to reactive primary ions, should be treated with considerable caution.

Introduction

Sputtering yields have been extensively studied since the 1960s originally for their relevance to effects in gas filled valves but more latterly related to the design of fusion reactors, for space research and for composition-depth profiling using ion sputtering in surface analysis instruments [1], [2]. In sputter-depth profiling to determine compositions, the depth sputtered, D, and the sputtering yield, Y are directly related via $D = \frac{{JYr}^{3} t}{e_{0}},$ where J is the beam current density, t is the time of sputtering, r³ is the volume of an atom of the sample and e₀ the charge on the electron. Uncertainties in Y lead directly to uncertainties in the thickness scale, D.

Over the years there have been a number of predictive relations to enable Y to be calculated, based on Sigmund’s theory [3] and developments to cover threshold sputtering, etc. Most important for depth profiling using Auger electron spectroscopy (AES) or X-ray photoelectron spectroscopy (XPS) is sputtering using ions of the noble gases, Ne, Ar or Xe. Generally Ar is preferred but Ne or Xe are also used where the Auger or photoelectron emission lines from Ar may cause unwanted signals during analysis. Xenon has also been popular in secondary ion mass spectrometry to generate higher yields with lower damage levels [4].

Elsewhere [5] we have analysed the extensive published data for argon ion sputtering, reviewed the two main semi-empirical approaches for predicting sputtering yields and provided a new method and data for the experimental measurement of sputtering yields. The two essential approaches used are those of Matsunami et al. [6] and the later development by Yamamura and Tawara [7]. These are very popular for calculating sputtering yields [5]. In both of these approaches there is a factor, Q, that is uniquely evaluated for each elemental target solid by fitting their equations over very many measured data sets. Unfortunately, the Q values range from 0.47 to 4.6 in Matsunami et al.’s study and 0.54–2.62 in Yamamura and Tawara’s analysis. These were determined for 34 elements but for other elements Q is recommended to be set to unity. In view of the range of values where a non-unity Q is given, a value of unity could be significantly in error.

The approach followed in both studies [6], [7] involved assessing the parameter α which was a dimensionless factor providing the proportion of the energy from the incident ion, back-reflected to contribute to the sputtering. In their assessments, very many experimental measurements were involved using both heavy and light incident ions in many targets. Sigmund’s approach implied that α would depend on the ratio of the target atom’s mass, M₂ to the incident ion mass, M₁ with a certain dependence that was, broadly, upheld. However, our analysis for argon ions [5] showed that this dependence is, when using Matsunami et al.’s approach [6], in fact, highly structured. It appears that α, or rather αQ, is a function of the product of both a term in M₂/M₁ and a term in M₂ alone. By plotting α as a function of M₂/M₁ the structure in M₂ for each different incident ion was displaced to a different extent on the abscissa leading to a blurred distribution of points. By studying the large volume of data for argon sputtering this structure becomes clear [5]. However, the predictions and formulae that we then obtained were no longer general but were specific to argon ion sputtering. There is also a large volume of sputtering data for neon and xenon and so here we adopt the earlier approach and test how this may be generalised to these other ions. In the next section we review the essential equations from the previous analysis, showing how they are generalised.

Section snippets

The semi-empirical sputtering approaches of Matsunami et al. [6] and of Yamamura and Tawara [7]

At normal incidence, the generalised development of Sigmund’s theory [3] gives $Y = \frac{0.042 Q α^{*}}{U_{0}} \frac{S_{n} (E)}{1 + {As}_{e} (ε)} {(1 - {(\frac{E_{th}}{E})}^{1 / 2})}^{s},$ where S_n(E) is the nuclear stopping power per atom and U₀ the surface binding energy per atom. The heat of sublimation per atom sputtered is often equated to U₀ and new calculations for this term have been provided [5]. The coefficient 0.042 has units of Å⁻² and should include 10⁻²⁰ for SI units.

Here we use the nuclear stopping power given by [8] $S_{n} (E) = 4 π Z_{1} Z_{2} \frac{e_{0}^{2}}{4 π ε_{0}} a_{12} \frac{M_{1}}{M_{1} + M_{2}} s_{n} (ε),$

Analysis of Ne and Xe ion sputtering data

In addition to the data of [10] to [15], which contain data for Ne and Xe ions as well as Ar, is the study of Rosenberg and Wehner [18]. We analyse all of these data, here, to compute Q_eff using either Matsunami et al.’s [6] or Yamamura and Tawara’s [7] approaches. As before, Q_eff is evaluated, for each incident ion, from a least squares fit of the measured sputtering yield divided by that calculated with Q set to unity.

These data are mostly for significant levels of sputtering of bulk solids

Implantation of beam ions

In the above, the theories of sputtering on which the calculations are based are valid for the first ion entering the solid. In practice, of course, as sputtering proceeds, the bombarding ions enter the solid and accumulate until a steady state is reached in which their rate of arrival is matched by their rate of removal by the sputtering or other processes. The inert gas ions are unusual in that they are used for cleaning samples and also for depth profiling in surface analysis studies. In

Conclusions

The previous analyses of the semi-empirical approaches for sputtering using argon ions has been extended to neon and xenon to evaluate the systematics for the new Q values for sputtering by any incident ion to be used with Matsunami et al.’s approach [6]. The general behaviour between all of the noble gases is very similar and the equations developed for argon are also applicable to neon and xenon with relevant changes to five of the six coefficients. However, these changes have relatively

Acknowledgement

The author would like to thank S.J. Spencer for preparation of many of the Figures for publication and I.S. Gilmore for comments. This work is supported by the National Measurement System of the UK Department of Trade and Industry through the Valid Analytical Measurements Programme.

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An accurate semi-empirical equation for sputtering yields, II: for neon, argon and xenon ions

Abstract

Introduction

Section snippets

The semi-empirical sputtering approaches of Matsunami et al. [6] and of Yamamura and Tawara [7]

Analysis of Ne and Xe ion sputtering data

Implantation of beam ions

Conclusions

Acknowledgement

Atom. Data Nucl. Data Tables

Atom. Data Nucl. Data Tables

Nucl. Instr. and Meth. B

Thin Solid Films

J. Electron Spectrosc.

Phys. Rev.

Mat. Fys. Medd. Dan. Vid. Selsk.

Radiat. Eff. Lett.

J. Appl. Phys.

Philips Res. Rep.

Appl. Phys.

J. Appl. Phys.