In-situ analysis on the initial growth of ultra-thin ruthenium films with atomic layer deposition

Microelectronic Engineering 107 (2013) 151–155

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In-situ analysis on the initial growth of ultra-thin ruthenium films with atomic layer deposition Marion Geidel ⇑, Marcel Junige, Matthias Albert, Johann W. Bartha Technische Universität Dresden, Institute of Semiconductors and Microsystems (IHM), 01062 Dresden, Germany

a r t i c l e

i n f o

Article history: Available online 20 September 2012 Keywords: In-situ XPS In-vacuo XPS In-situ AFM In-vacuo AFM Initial growth Initial reaction mechanism Thermal ALD of Ru ECPR

a b s t r a c t The initial growth behavior of ruthenium during the thermal-activated atomic layer deposition (ALD) using [(ethylcyclopentadienyl)(pyrrolyl)ruthenium(II)] (ECPR) and molecular oxygen was investigated in a cluster tool combining an ALD reactor with a surface analysis unit under high vacuum conditions. A direct qualification and quantification of the chemical surface composition by X-ray photoelectron spectroscopy (XPS) and a determination of the surface topography by atomic force microscopy (AFM) were conducted in the course of the ALD cycles without vacuum break. XPS revealed a substrate-inhibited Ru growth on a hydrogen-terminated silicon surface, which was preceded by an incubation period of 20 ALD cycles. The Si surface oxidized during the first 50 cycles. AFM measurements showed a roughness maximum around the 40th ALD cycle, which suggested an island growth mode and thus corresponded with the substrate inhibition. As verified from the AFM data with an analytical model by Nilsen et al. the Ru islands coalesced between the 40th and 50th ALD cycle. The ALD growth initiation of Ru was also investigated on aluminum oxide and tantalum nitride. XPS revealed a similarly inhibited growth behavior on all the investigated substrates. However, the ECPR adsorption during the very first Ru precursor pulse differed as the amount of chemisorbed Ru on the NHy-terminated TaNx(O, C) surface was much higher compared to the OH-terminated Al2O3 and the H-terminated Si surface. Summarizing, we demonstrated that in-vacuo XPS and AFM as well as the combination of both are ideally suited for studying the ALD growth initiation of Ru. Furthermore, we provided important chemical information about the initial Ru precursor adsorption on several foreign substrate materials, which will direct further investigations towards a non-inhibited Ru growth. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Atomic layer deposition (ALD) has emerged as a key enabling technology for the miniaturization of advanced integrated circuits and also for the implementation of new device concepts. An excellent uniformity and conformity as well as a good thickness control characterize the outstanding features of ALD [1]. Much progress has been achieved in the development of adequate ALD processes by a though time-consuming screening of various precursors behaving in dependence on the most important process parameters. However, due to technical challenges in the combination of processing and surface analysis, a fundamental understanding of the physico-chemical as well as structural surface mechanisms during the ALD has lagged behind the empirically developed ALD processes, especially in the case of ultra-thin metallic films [2]. This study intends to close this gap for the example of ruthenium’s thermal-activated ALD. Aaltonen et al. [3] as well as Elliot [4] have already pointed out a special reaction mechanism during ⇑ Corresponding author. E-mail address: [email protected] (M. Geidel). 0167-9317/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.mee.2012.08.026

the linear Ru-on-Ru film growth regime for a variety of organometallic precursors in conjunction with molecular oxygen. They have suggested the penetration of oxygen into the sub-surface region of the as-deposited Ru film during O2 exposures; and the subsequent complete consumption of this superficially incorporated oxygen during Ru precursor pulses. However, the initial ALD growth of Ru on foreign substrate materials has been reported to occur non-spontaneously with a substantial incubation period [5]. Thus, the growth initiation and the transition to the linear Ru-on-Ru film growth regime are in the focus of this paper, also concerning the adsorption of the Ru precursor molecule on different initial substrate materials. 2. Experimental details We investigated the thermal-activated ALD of Ru from [(ethylcyclopentadienyl)(pyrrolyl)ruthenium(II)], abbreviated as ECPR, and molecular oxygen. An ALD process from the same Ru precursor on HF-etched Si, SiO2, ZrO2, and TiN substrates has already been reported by Kukli et al. [6]. However, we developed our corresponding Ru ALD process by in-situ real-time spectroscopic ellipsometry

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Table 1 Process parameter set for the thermal-activated ALD of Ru from ECPR and O2, which was especially optimized in terms of the linear Ru-on-Ru film growth regime[7] and which was applied in this study for the initial ALD growth as well. ECPR bubbler temperature ECPR pulsing time Ar carrier gas flow O2 pulsing time O2 gas flow Ar purging time Ar purging gas flow Substrate temperature Total process pressure

80 °C 5/7 s 50 sccm 10 s 200 sccm 20 s each 1000 sccm 255 °C 200 Pa

(SE) as recently described in Ref. [7]. There, any non-ideal effects from the starting substrate material were prevented by coating a closed Ru film prior to the process parameter variations. Thus, we ensured a process optimization in terms of the linear Ru-onRu film growth regime. Table 1 summarizes the corresponding process conditions, which were applied in this study for ALD growth initiation as well. The Ru films were deposited in a top-injection ALD reactor from FHR Anlagenbau GmbH that can be evacuated to a base pressure in the range of 104 Pa. During the ALD processes, the total pressure was controlled to 200 Pa and the samples were heated to a surface temperature around 255 °C as determined by spectroscopic ellipsometry [8]. The production of pure Ru films without any oxygen incorporation in the bulk film was verified both by an absence of the O 1s signal and by a well-defined Ru 3d double peak when performing XPS after Ru precursor pulses (data not shown here). The ALD growth of Ru was investigated on three different initial substrates: bulk silicon, an 20 nm aluminum oxide film and a 30 nm tantalum nitride film. These foreign substrate materials differed in their functional groups, which terminated the surface after a pre-treatment procedure or after the production of the respective film. The preparation and the associated surface properties of the starting substrates are summarized in Table 2. The monocrystalline Si was pre-cleaned by dipping in VLSIgrade acetone, dipping in VLSI-grade isopropanol and rinsing with deionized water for two minutes each. Afterwards, the Si sample was etched in 0.5% hydrofluoric acid for two minutes, rinsed with deionized water again and blown dry by pure nitrogen. No fluoric residues, but ambient carbon contaminations were found at the initial Si surface by X-ray photoelectron spectroscopy (XPS). The Al2O3(C) film was deposited by ALD from [trimethylaluminium] and water in an attached ALD-chamber ending with a water pulse. Thus, the Al2O3(C) surface was assumed to be terminated by hydroxyl groups [9]. The following transfer of the sample into the Ru reactor proceeded under a high vacuum of 105 Pa. The TaNx(O, C) film was deposited in-situ prior to the Ru experiments by ALD from [tertiarybutylimino,tris(diethylamino)tantalum] and ammonia [10] ending with an ammonia pulse. Hence, the TaNx(O, C) surface was assumed to be terminated by amino groups [11]. Sufficient argon purging separated the TaN from the subsequent Ru ALD process. The in-vacuo preparation of the Al2O3(C) and TaNx(O, C) films enabled a Ru deposition on functionalized surfaces without any ambient contamination. A possible influence of carbon contaminations inside the in-vacuo-prepared ALD films had to be neglected for this study. As previously described by Schmidt et al. [10] and Strehle et al. [12], our ALD-tool is attached to an ultra-high vacuum surface analytic system MultiprobeÒ from Omicron Nanotechnology GmbH with the possibility of X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM) among others. Like in a similar study [13], we transferred an investigated sample between the

Table 2 Preparation and surface properties of the investigated initial substrate materials. Substrate

Preparation

Surface properties

Si

ex-situ: 2 min in acetone; 2 min in isopropanol; rinse with deionized water; drying with N2; 2 min in 0.5% hydrofluoric acid; rinse with deionized water; drying with N2

H-terminated; with ambient contamination

Al2O3(C)

in-vacuo: in an attached ALD chamber; 180 ALD cycles with TMA and H2O at 250 °C; on silicon with native dioxide

OH-terminated; without ambient contamination

TaNx(O, C)

in-situ: in the same deposition chamber; 500 ALD cycles with TBTDET and NH3 at 300 °C[9]; on silicon with native dioxide

NHy-terminated; without ambient contamination

deposition chamber and the surface analysis system without breaking a high vacuum in the range of 105 Pa and thus with negligible alteration of the sample after applying one ALD half-reaction or a number of cycles (quasi-in-situ or in-vacuo analysis). XPS was used to analyze chemical states and the composition of the surface. The present XPS investigations were operated with a non-monochromatic Al-Ka X-ray source. Thus, the photoelectrons were excited by a radiation of 1486.6 eV. Those photoelectrons that were emitted from the sample surface under an angle of 45° were detected in a hemispherical analyzer according to their kinetic energy. The constant analyzer pass energy (CAE) was set to 30/50 eV. The evaluation and synthesis of the acquired XP spectra were performed with the XPS analyses software UNIFIT 2011 [14]. The satellites and a Shirley background were subtracted from the measured spectra. UNIFIT 2011 uses the curve fitting algorithm of Marquardt for peak synthesis. The surface roughness was determined over an area of 500  500 nm with a non-contact AFM.

3. Results 3.1. Ruthenium growth on a hydrogen-terminated silicon surface In this first part, we focus on the ALD growth of Ru starting on a H-terminated Si surface. Fig. 1a shows the original XP spectra in a range of the binding energy from 456 to 468 eV indicating an arising Ru 3p3/2 signal for progressing ALD cycle numbers. After subtraction of a Shirley background, the increasing area under the Ru peak is plotted over the cycle number in Fig. 2a as the green curve with triangles. This graph shows three distinct growth regimes: an incubation period of about 20 cycles, where only a very slight Ru nucleation occurred; a transition period until around the 100th ALD cycle; and the homogeneous Ru-on-Ru film growth regime, where the Ru 3p3/2 XPS signal saturates as the film thickness exceeded the mean free path of the emitted photoelectrons. In the latest regime, no signal from the Si substrate was detected and a homogeneous ALD growth was assumed. According to Puurunen et al. [15], this division into three distinct growth regions indicated a substrateinhibited ALD growth. Fig. 1b prints the spectra of X-ray-excited O 1s photoelectrons measured after O2 pulses in the progress of the ALD cycle number. This also pointed out the incubation time until the 20th ALD cycle; and it revealed the emersion of two different oxygen binding states in the transition regime (between the 20th and around 100th ALD cycle). For an exemplary XP spectrum after the 50th ALD cycle, Fig. 1c demonstrates the deconvolution of the O 1s peak into its two components: The first binding state is located at a binding en-

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Fig. 1c. XP spectrum of O 1s electrons after the 50th Ru ALD cycle onto HF-etched Si with fitted components that were assigned to O–Si and O–Ru bonds. (pass energy 30 eV; fit parameters are summarized in Table 3).

Fig. 1a. Original XP spectra of Ru 3p3/2 photoelectrons over the number of Ru ALD cycles onto HF-etched Si. (pass energy 30 eV).

Fig. 1b. Original XP spectra of O 1s photoelectrons over the number of Ru ALD cycles onto HF-etched Si. (pass energy 30 eV).

ergy of about 532.3 eV and was referred to an oxygen–silicon bond [16] (superimposed by a small amount of an oxygen–carbon bond [16]); and the second binding state at 530.2 eV was assigned to an oxygen–metal bond (i.e., to a superficial ruthenium oxide) [16,17]. The corresponding peak fit parameters are summarized in Table 3. The integrated areas under these two O 1s components are plotted over the cycle number in Fig. 2a as a blue line with diamonds and as a red curve with squares, respectively. An increase of the O–Si signal during the first 30 cycles disclosed an oxidation of the silicon substrate. This silicon oxide signal remained fairly constant between the 30th and the 50th ALD cycle. Possibly, the Si surface was further oxidized during this O– Si intensity plateau, but the corresponding O–Si signal increase might be superimposed by a signal attenuation due to the growth of Ru onto the silicon (oxide) surface which was indicated by a rising Ru 3p3/2 signal after the 30th ALD cycle. Up to now it remained unclear whether the Ru nucleation occurred on pure silicon and the surrounding silicon was oxidized or on silicon dioxide.

The Ru 3p3/2 signal in Fig. 2a increases until its saturation at around the 100th ALD cycle. A corresponding O–Ru signal saturates around the 80th cycle, indicating a limited amount of oxygen that penetrated into the Ru sub-surface of a closed film, and thus confirmed the assumed homogeneous Ru-on-Ru growth regime. As the O–Ru signal component in Fig. 1c was not observed when performing XPS after ECPR pulses (data not shown here), the formation of a metallic Ru film without any oxygen contamination was verified. Rather, the alternating absence and presence of the O–Ru component after Ru precursor pulses and O2 exposures, respectively, confirmed the suggested reaction mechanism of Aaltonen et al. [3] and Elliott [4], where a very narrow range of the Ru surface is oxidized during O2 exposures. This reactive ruthenium oxide at the surface is substantial for the ECPR adsorption in the subsequent Ru precursor pulses [4]. It is worth to mention here, that this formation of the intrinsic RuOx overlayer was observed during both the homogeneous Ru-on-Ru film growth regime and also the transitional region. Consequently, not only a closed Ru film but also separate Ru islands were oxidized at the surface during O2 exposures. Fig. 2b contains the root-mean-squared (RMS) surface roughness derived from AFM measurements in the course of the ALD cycle number. During the incubation period, where almost no ruthenium growth occurred, the surface roughness remained constant at 0.2 nm. In the following transient region, the surface roughness increased up to a maximum of 0.55 nm around the 40th ALD cycle and then decreased to a plateau around 0.4 nm. According to Nilsen et al. [19], this characteristic course of the surface roughness clarified an substrate-inhibited growth of type 2. And their analytical island growth model [19] points out the island coalescence a few cycles after the roughness maximum. In our case, the Ru islands apparently merged after the 40th ALD cycle and formed a closed film until the 50th ALD cycle. This formation of a closed Ru film corresponded to the decreasing silicon oxide signal after the 50thALD cycle in Fig. 2a due to the attenuation of the O–Si photoelectrons by the growing Ru film. In summary, our in-vacuo XPS and AFM results revealed a substrate-inhibited island growth mode for the Ru ALD process from ECPR and O2 on an H-terminated Si surface. After an incubation period of about 20 cycles and the oxidation of the Si substrate, Ru islands grew until their coalescence between the 40th and 50th ALD cycle. A homogeneous Ru-on-Ru film growth seemed to occur just after the 100th ALD cycle. Not only a closed Ru film as previously suggested [3,4], but also the Ru islands were superficially oxidized during O2 exposures, which was confirmed by an O–Ru XPS signal even during the transitional region.

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Table 3 Fit parameters for the deconvolution of XP sectra. Binding state[16,17] O1s: O–Si (Fig. 1c, 2a) O–Si (O–C) O1s: O–Ru (Fig. 1c, 2a) O–Ru C1s (Figs. 3 and 4) C–H Ru3d (Figs. 3 and 4) Metallic Ru !    h i2 1 h i2  EE0 EE0 f ðEÞ ¼ h M 1 þ 1FWHM þ ð1  MÞexp ln2 1FWHM 2

E0 (eV)

FWHM (eV)

M

532.3 ± 0.3 530.2 ± 0.3 284.4 ± 0.4 280.3 ± 0.4

2.1 ± 0.3

0.1 ± 0.1

2.1 ± 0.4 1.6 ± 0.5

0.5 ± 0.1 0.3 ± 0.1 [18]

2

f . . . fit function h . . . peak hight E . . . binding energy (eV) E0 . . . peak position (eV) M . . . Lorentz/Gauß mix ratio FWHM . . . full width at half maximum (eV)

160 120 80

linear growthh regime

incubation/nuucleation period

XPS intensity (a. u.)

transition regime

0.4 0.3

transition regime

0.2 0.1

linear growth regime

200

0.5

coalescende of the islands

RMS roughness (nm)

×10e3

incubation/nucleation period

0.6

O1s(532.3 eV): O-Si O1s (530.2 eV): O-Ru Ru3p3/2 (462 eV)

0 0

20

40

60

80

100

120

140

Cycle number

40

Fig. 2b. RMS surface roughness measured by AFM over the number of Ru ALD cycles onto HF-etched Si.

0 0

20

40

60

80

100

120

140

Cycle number Fig. 2a. XPS intensity (integrated peak area after Shirley background subtraction and peak synthesis) of the Ru 3p3/2 signal and of the deconvoluted O 1s components over the number of Ru ALD cycles onto HF-etched Si. (pass energy 30 eV; fit parameters are summarized in Table 3).

3.2. Comparison of the ruthenium growth initiation on hydrogenterminated silicon, hydroxyl-terminated aluminum oxide and aminoterminated tantalum nitride In this second part, the ALD growth initiation of Ru is compared for the three starting materials H-terminated Si, OH-terminated Al2O3(C) and NHy-terminated TaNx(O, C). Due to a very little Ru signal during the very first five ALD cycles, the most intense Ru 3d peak had to be taken into account. Fig. 3 shows the Ru 3d XPS signal (black area), which is superimposed by a C 1s XPS signal (grey area), after the very first ECPR pulsing. The corresponding peak fit parameters are summarized in Table 3. In the case of the Si substrate, an ambient carbon contamination of the surface caused a C 1s signal despite the absence of adsorbed ECPR molecules (no Ru signal was observed). In the case of the two in-vacuo substrates, the C 1s signal originated from both carbon impurities in the initial ALD films and ligands of the adsorbed ECPR molecules. While only a little Ru signal appeared on OH-terminated Al2O3(C), a clear Ru 3d double peak emerged on NHy-terminated TaNx(O, C). As the amount of Ru precursor molecules on the NHy-terminated TaNx(O, C) surface was much higher compared to the OHterminated Al2O3 and the H-terminated Si surface (cf. the Ru signal in Fig. 3), the ECPR adsorption during the very first Ru precursor

Fig. 3. XP spectrum (after background subtraction and peak synthesis) of the Ru 3d doublet peak superimposed by a C 1s signal after the very first ECPR pulse on the three foreign substrate materials HF-cleaned Si, Al2O3(C), and TaNx(O, C). (pass energy 50 eV; fit parameters are summarized in Table 3).

M. Geidel et al. / Microelectronic Engineering 107 (2013) 151–155

25 ×10e3

Si Al2O3(C)

XPS intensity (a. u.)

20

TaNx(O, C)

15 10 5 0 0

1

2

3

4

5

Cycle number Fig. 4. XPS intensity (integrated peak area after Shirley background subtraction and peak synthesis) of the Ru 3d doublet peak excluding the C 1s signal component in the course of the first five ALD cycles comparing the three foreign substrate materials HF-cleaned Si, Al2O3(C), and TaNx(O, C). (pass energy 50 eV; fit parameters are summarized in Table 3).

155

island growth caused an undesired increase in surface roughness as the arising Ru nuclei in the very first ALD cycles were superficially oxidized during O2 exposures and thus served as preferred adsorption sites for the subsequently delivered Ru precursor molecules. Another unintended effect was the oxidation of the initial substrate material until the Ru islands coalesced. In a second part, we studied the Ru precursor adsorption on the three starting materials Si, Al2O3(C) and TaNx(O, C). Our results will direct further investigations towards a non-inhibited Ru growth. One approach could be the provision of additional nitrogen at the starting surface (e.g., in the form of amino groups) by employing an ECPR–O2–NH3 pulsing sequence during the very first ALD cycles. Another approach could be the enhancement of an assumed statistical adsorption mechanism by a variation of the process parameters, in particular adjusted to the initial growth period. For example, a longer ECPR pulsing time or a higher substrate temperature might increase the amount of adsorbed precursor molecules on the initial substrate surface. This knowledge might be transferable wherever similar organometallic Ru precursors are employed in conjunction with molecular oxygen. Acknowledgements

pulse differed significantly. This observation corresponded with a report by Yim et al. [5] regarding the nucleation kinetics of a slightly different organometallic Ru precursor: On silicon nitride surfaces and on NH3-plasma-nitrided SiO2, the deposited amount of Ru has been much larger than on a SiO2 surface. Likewise, Kukli et al. [6] have observed an increase in the resulting Ru film thicknesses on TiN compared to SiO2 substrates after applying a fixed number of deposition cycles with the ECPR precursor at set point temperatures above 300 °C. Consequently, we concluded that a nitrogen-rich starting surface promotes the adsorption of Ru precursor molecules. Fig. 4 displays the integrated area under the Ru 3d double peak in the course of the first five ALD cycles comparing the three above-mentioned starting substrates. However, the growth of the Ru 3d signal intensities approximated already after the second ALD cycle revealing a similar inhibition for all the investigated hetero substrates. Accordingly, two different adsorption mechanisms had to be taken into account: On the one hand, nitrogen or amino surface groups seemed to provide a much higher sticking coefficient for the Ru precursor adsorption than other surface groups. Nevertheless, a delayed Ru growth occurred on the Al2O3(C) and Si surfaces irrespective of a lack of nitrogen. Thus on the other hand, a statistical (possibly thermally induced) adsorption mechanism seemed to exist, which dominated the ECPR adsorption even on the TaNx(O, C) surface after the completion of the first ALD cycle, i. e. after the consumption of all the amino adsorption sites. 4. Conclusion In summary, a combination of in-vacuo XPS and AFM measurements provided important chemical as well as structural information about the ALD growth mechanisms of Ru from the organometallic precursor ECPR and molecular oxygen. We revealed a substrate-inhibited growth of type 2 characterized by the formation of islands during the growth initiation on HF-etched Si. This

The authors thank Volker Neumann for fruitful discussions. Marion Geidel and Marcel Junige are grateful to their funding by the European Social Fund (ESF) and the Free State of Saxony of the Federal Republic of Germany (Contract No. 080942435 and 100077335). References [1] H. Kim, H.-B.-R. Lee, W.-J. Maeng, Thin Solid Films, 2008. [2] H. Kim, J. Vac. Sci. Technol. B21 (2003) 2231. [3] T. Aaltonen, A. Rahtu, M. Ritala, M. Leskelä, Electrochem. Solid-State Lett. 6 (2003) C130. [4] S.D. Elliott, Langmuir 26 (2010) 9179. [5] S.-S. Yim, D.-J. Lee, K.-S. Kim, S.-H. Kim, T.-S. Yoon, K.-B. Kim, J. Appl. Phys. 103 (2008) 113509. [6] K. Kukli, M. Kemell, E. Puukilainen, J. Aarik, A. Aidla, T. Sajavaara, M. Laitinen, M. Tallarida, J. Sundqvist, M. Ritala, M. Leskelä, J. Electrochem. Soc. 158 (2011) D158. [7] M. Knaut, M. Junige, M. Albert, J.W. Bartha, J. Vac. Sci. Technol. A30 (1) (2012). [8] M. Junige, M. Geidel, M. Knaut, M. Albert, J.W. Bartha, IEEE Semiconductor Conference Dresden 2011 (Dresden, 2011), pp. 1–4. http://dx.doi.org/10.1109/ SCD.2011.6068739. [9] R.L. Puurunen, Appl. Phys. 97 (2005) 121301. [10] D. Schmidt, S. Strehle, M. Albert, W. Hentsch, J.W. Bartha, Microelectron. Eng. 85 (2008) 527. [11] C. Hossbach, M. Drees, D. Seiffert, M.Junige, V. Neumann, S. Strehle, M. Geidel, M. Knaut, H. Wojcik, M. Albert, J.W. Bartha, AVS 12th International Conference on Atomic Layer Deposition, Dresden, 2012. [12] S. Strehle, H. Schumacher, D. Schmidt, M. Knaut, M. Albert, J.W. Bartha, Microelectron. Eng. 85 (2008) 2064. [13] M. Geidel, M. Knaut, M. Junige, M. Albert, J.W. Bartha, IEEE Semiconductor Conference Dresden 2011, Dresden, 2011, pp. 1–4. http://dx.doi.org/10.1109/ SCD.2011.6068753. [14] R. Hesse, T. Chassé, R. Szargan, Fresenius, J. Anal. Chem. 365 (1999) 48–54. [15] R.L. Puurunen, J. Appl. Phys. 96 (2004) 7686. [16] J.F. Moulder, W.F. Stickle, P. E. Sobol, K.D. Bomben, Handbook of X-ray Photoelectron Spectroscopy, Physical Electronics, Inc., USA, p. 45 (1992, 1995). [17] S. Bhaskar, P.S. Dobal, S.B. Majumder, R.S. Katiyar, J. Appl. Phys. 89 (2001) 5. [18] R. Hesse, P. Streubel, R. Szargan, Surf. Interface Anal. 39 (2007) 381–391. [19] O. Nilsen, C.E. Mohn, A. Kjekshus, H. Fjellvag, J. Appl. Phys. 102 (2007) 024906.