Sputtering of dimers off a silicon surface

Nuclear Instruments and Methods in Physics Research B 289 (2012) 97–99

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Short Communication

Sputtering of dimers off a silicon surface Maureen L. Nietiadi a,b, Yudi Rosandi a,b,c, Michael Kopnarski a,b,d, Herbert M. Urbassek a,b,⇑ a

Physics Department, University Kaiserslautern, Erwin-Schrödinger-Straße, D-67663 Kaiserslautern, Germany Research Center OPTIMAS, University Kaiserslautern, Erwin-Schrödinger-Straße, D-67663 Kaiserslautern, Germany c Department of Physics, Universitas Padjadjaran, Jatinangor, Sumedang 45363, Indonesia d Institut für Oberflächen- und Schichtanalytik IFOS GmbH, Trippstadter Straße 120, D-67663 Kaiserslautern, Germany b

a r t i c l e

i n f o

Article history: Received 25 July 2012 Received in revised form 29 July 2012 Available online 10 August 2012 Keywords: Molecular dynamics Sputtering Silicon

a b s t r a c t We present experimental and molecular-dynamics simulation results of the sputtering of a Si surface by 2 keV Ar ions. Results on both the monomer and dimer distributions are presented. In simulation, these distributions follow a generalized Thompson law with power exponent n ¼ 2 and n ¼ 3, respectively. The experimental data, obtained via plasma post-ionization in an SNMS (secondary neutral mass spectrometry) apparatus, show good agreement with respect to the dimer fraction, and the relative energy distributions of dimers and monomers. The consequences for the dimer sputtering mechanism are discussed. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Silicon is arguably the most important material used in surface characterization techniques. For ion-irradiation based methods, such as secondary-ion mass spectrometry (SIMS) or secondaryneutral mass spectrometry (SNMS), hence a considerable amount of information about the basic sputtering process has been produced over the years, and sputter yields and sputtered particle energy distributions have become reliably known [1–4]. Besides monatomic species, as a rule also dimers and larger clusters are found in the sputtered flux. An understanding of the properties of sputtered molecules is necessary for a reliable interpretation of sputtered-particle mass spectra and surface analysis. In sputter theory, various mechanisms for the sputtering of dimers have been analyzed and discussed [5–7]; these include the socalled direct-emission mechanism [8,9], in which close neighbors are emitted, and the so-called recombination mechanism [10], in which previously unbound atoms are associated during the emission process to form a dimer. These two different mechanisms give rise to distinctly different energy distributions of emitted dimers. Sputtering of a Si surface by keV ions has been studied repeatedly by molecular-dynamics simulation. We mention in particular the early work by Stansfield et al. [11] and by Smith et al. [12], in which the sputtering of both a reconstructed and a non-reconstructed Si (1 0 0) surface by 6 1:5 keV Ar ions was examined. ⇑ Corresponding author at: Physics Department, University Kaiserslautern, Erwin-Schrödinger-Straße, D-67663 Kaiserslautern, Germany. Fax: +49 631 205 3907. E-mail address: [email protected] (H.M. Urbassek). URL: http://www.physik.uni-kl.de/urbassek/ (H.M. Urbassek). 0168-583X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nimb.2012.07.037

These studies used a Stillinger–Weber [13] and a Tersoff [14] interatomic interaction potential, respectively. Their results on the energy distribution and the depth of origin of sputtered monomers are comparable, while small differences in the angular emission distributions show up. No results on sputtered dimers were reported. In the present paper, we study dimer emission from a Si surface induced by 2 keV Ar impact. We compare energy distributions obtained from an SNMS apparatus with those obtained by moleculardynamics simulation. Our results will allow to draw conclusions on the dimer sputtering mechanism.

2. Method 2.1. Simulation We employ a standard molecular-dynamics code for the sputtering simulation. Our target crystallite consists of 5407 Si atoms arranged in 30 monolayers. The surface is a (1 0 0) surface in 2  1 reconstruction. Apart from the free surface, the outermost atoms at the other five boundaries were kept fixed, surrounded by an energy-damping zone [15]. We checked with the help of a larger simulation target (270,504 atoms with a depth of 100 layers) that our simulation results reproduce sputtering reliably. Ar atoms impinge with an energy of 2 keV on the Si surface, with perpendicular incidence direction. In total, we simulate 50,000 individual Ar impacts. For each impact, the exact impact point has been varied randomly within the irreducible surface impact cell [16,17]; this gives us a statistically reliable overview over all possible impact conditions. Note that each impact occurs on a

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fresh 2  1 Si (1 0 0) surface; we thus simulate static irradiation conditions. We follow the events up to 3 ps after impact. Si atoms interact via the Stillinger–Weber potential [13]. The potential is cut off at rcut ¼ 3:77 Å. We note that the cohesive energy of SW-Si amounts to U ¼ 4:34 eV, in reasonable agreement with the experimental value, 4.67 eV [18]. For small interaction distances the potential is fitted to the Ziegler–Biersack–Littmark (ZBL) potential [19]. Ar and Si atoms interact via the purely repulsive ZBL potential. Atoms are considered sputtered if they left the interaction zone of the target, i.e., if they feel no longer an attractive interaction with the target. Sputtered molecules are identified by a cluster detector [20].

0.6 0.5

f(Y)

0.4 0.3 0.2 0.1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Y Fig. 1. Frequency distribution f ðYÞ of sputter yield Y for 2 keV Ar ion bombardment of the Si 2  1 (1 0 0) surface.

(a)

1

monomers fit

0.1 0.01 f(E)

For the experimental determination of monomer and dimer yields we used the plasma-based sputtered neutral mass spectrometry SNMS which is established as a common method in surface and thin-film analysis [21]. Here the so called direct bombardment mode DBM was applied and a Si (1 0 0) surface was bombarded by 2 keV Ar+ plasma ions with perpendicular incidence and an ion current density of about 1 mA cm2. The sputterreleased neutrals undergo collisions by electron impact while traveling some centimeters through a hot Maxwellian electron gas which is also delivered by the low pressure plasma excited by electron cyclotron wave resonance ECWR. The electron temperature lies in the range of T e ¼ 105 K and an electron density of up to 1011 cm3 is obtained. With a collision frequency of some kHz and a dwell time Dt ¼ 10 ls in the plasma, post-ionization probabilities in the range of some 102 are achieved. The post-ionized  neutrals are collected under an oblique take-off angle of 30 and, leaving the plasma, they are guided into the quadrupole mass filter  by means of electro-static lenses and a 45 energy analyzer. The energy- and mass-filtered SNMS signals at 28 and 56 amu were detected by single ion counting and are used to monitor the monomer and dimer yields.

0.001 0.0001 1e-05 1e-06 1e-07 0.1

1

10

100

energy E (eV)

(b)

1

dimers fit

0.1 0.01 f(E)

2.2. Experiment

0.001 0.0001 1e-05

3. Results

1e-06

Fig. 1 shows the frequency distribution for sputtering for the case of 2 keV Ar impact on a Si 2  1 (1 0 0) surface at perpendicular incidence, as obtained by molecular dynamics simulation. The average sputter yield is hYi ¼ 0:920  0:007. Note that in 57% of all cases, no atom is sputtered. The second most probable situation is that exactly one atom is sputtered, Y ¼ 1; this happens in 20.3% of all impacts. 3.1. Energy distributions Since we performed 50,000 ion impacts, we obtained in total 45,986 sputtered particles. This allows us to present their energy distributions. Fig. 2 displays the energy distribution of all ejected atoms and dimers (Si2). We fit the atom distribution with a law,

f ðEÞ /

E ðE þ UÞnþ1

;

ð1Þ

where U ¼ 4:34 eV is the cohesive energy of Si in our potential. The well-known Thompson law predicts n ¼ 2 [22–24], and is often found in the analysis of sputtered atoms, both in experiment and in simulation [25,26]. Our comparison in Fig. 2(a) shows that Eq. (1) with n ¼ 2 describes our data well in the energy interval of 2–50 eV. Note that in this comparison no parameter was fitted. The steeper decay

1e-07 0.01

0.1

1 10 energy E (eV)

100

Fig. 2. Normalized energy distributions of sputtered (a) monomers and (b) dimers. Data are compared to a simple analytical law, Eq. (1), with n ¼ 2 for monomers and n ¼ 3 for dimers.

for E > 50 eV is typical for keV impact and is due to the fact that the approximation E  E0 is no longer valid at high energies E [27]. We also observe sputtered dimers in our simulation: 2.0% of all sputtered atoms are emitted as dimers. This can be compared to the dimer to monomer intensity ratio observed by Secondary Neutral Mass Spectrometry SNMS [21]. For 2 keV Ar+ bombardment on Si the SNMS dimer intensity is 4.1% of the corresponding monomer signal. The signal ratio of the post-ionized neutrals has to be corrected for the different post-ionization probabilities for dimers and monomers which are caused by (i) the different dwell time of the sputtered neutral particles in the post ionizing electron gas and (ii) the different cross sections for electron impact ionization. Using the energy distribution, Eq. (1), with n ¼ 2 for the monomers and n ¼ 3 for the dimers we calculate the average inverse velocity of the dimers to be a factor of 2 higher compared to the monomers and following Ref. [28] the ionization cross section of the dimers counts 1.87 times the monomer ionization cross section. Hence, dividing the measured SNMS intensity ratio by 3.7

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1000

simulation experiment fit

fd(E)/fm(E)

100 10 1 0.1 0.01 0.01

0.1

1 10 energy E (eV)

100

1000

Fig. 3. Ratio of the dimer to the monomer energy distributions: comparison of simulation with experimental data. The fit line denotes a proportionality to E0:9 .

bound to each other in the solid. In fact, Fig. 4 demonstrates that more than 40% of the emitted dimers consist of atoms which were originally bound on the surface as first- or second-nearest neighbors. Note that dimer emission is exceptionally active for 8th nearest neighbors; these are originally at a distance of 1.3 lattice constants. We checked that these dimersare formed by a particular emission mechanism in the crystalline target; a 4th layer atom is ejected via a <110> channel towards the surface where it hits a surface atom and combines with it to a dimer. Dimer emission has been studied for Ge under 5 keV Ar impact  at 45 incidence angle [31]. It was found that the energy distribution decays very softly (power exponent n ¼ 2); this soft decay is not understood. 4. Conclusions We study monomer and dimer emission induced by 2 keV Ar impact on the Si 2  1 (1 0 0) surface. In simulation, both distributions follow a Thompson-like law with power exponents 2 and 3 for monomers and dimers, respectively. Experimental data for these distributions agree with the measured distributions. Our results are compatible with a direct-emission mechanism of dimers; in fact our simulations find that > 40% of all dimer atoms were bound on the surface as first- or second-nearest neighbors before emission.

0.3 0.25 frequency

99

0.2 0.15 0.1 0.05

Acknowledgement 0 1

2

3 4 5 6 7 8 nearest neighbor shell

9

10

Fig. 4. Frequency distribution of the distance (measured in nearest-neighbor shells) which the two atoms of the sputtered dimer originally had.

This work has been supported by the Deutsche Forschungsgemeinschaft via the Research Unit 845 Self-organized nanostructures induced by low-energy ion beam erosion. References

we arrive at an experimental dimer yield of 1.1% of the partial monomer sputter yield which compares reasonably well with our simulation. In Fig. 2(b), we compare the dimer energy spectrum with Eq. (1); in this case we use n as a fit parameter. Choosing n ¼ 3 leads to a valid description of our simulation data for energies in 0:2  20 eV. Experimental energy distributions are obtained by post-ionization of emitted monomers and dimers in an Ar plasma. The energy distributions are therefore strongly influenced by the plasma: when leaving the plasma the ions are accelerated by the electric field of the Langmuir sheath, and since the exact position where the ionization occurred is unknown, also the extra acceleration in the plasma presheath is unknown. Although there exist procedures to correct for this effect [29], we consider the safest way to present our data consists in showing the ratio of dimer to monomer energy distributions. Since for a given energy the trajectories of the postionized monomers and dimers are determined by electrostatic fields only, it can be assumed that the corrections due to the plasma acceleration cancel. We plot the ratio of the energy distributions of monomer and dimer data in Fig. 3; between 1 and 100 eV they follow well a 1=E0:9 fall-off. We compare this with the experimental results obtained in our SNMS experiment. Good agreement is observed. Energy distributions of sputtered dimers have been reviewed in [5,26]. Both in experiment and simulation, a power exponent of n ffi 3 is often found for dimers; as a careful experimental study we mention the work by Wucher and Wahl on Ag2 emission [30]. Such a slow decay rules out the so-called ‘recombination model’ of dimer formation [10] which assumes independent emission of two atoms from the solid and predicts a power exponent of n ¼ 5. The slower decay is hence usually attributed to the concerted emission of nearby surface atoms, which were already

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