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Determination of effective electron inelastic mean free paths in SiO2 and Si3N4 using a Si reference
Surface Science 543 (2003) 153–161 www.elsevier.com/locate/susc
Determination of effective electron inelastic mean free paths in SiO2 and Si3N4 using a Si reference R. Jung a, J.C. Lee a, G.T. Orosz b, A. Sulyok b, G. Zsolt b, M. Menyhard b
b,*
a Samsung Advanced Institute of Technology, 440-600 South Korea Department of Surface Physics, Research Institute for Technical Physics and Materials Sciences, P.O. Box 49, H-1525 Budapest, Hungary
Received 24 March 2003; accepted for publication 1 August 2003
Abstract Elastic peak electron spectroscopy (EPES) provides inelastic mean free path (IMFP) values in the near-surface region. Such values, which will be called effective IMFPs, might be different from these derived from bulk parameters. In this work we derive effective IMFP values from EPES measurements in the range of 300–2000 eV for SiO2 and Si3 N4 using a Si reference. Corrections for surface excitation are applied. Our effective IMFP values agree well with those calculated from optical data in the case of SiO2 ; that is, the ion sputtering does not alter the SiO2 surface significantly. On the other hand, systematic deviations between our data and those provided by a predictive formula were found in the case of sputtered Si3 N4 . These differences are attributed to alteration in the surface layer caused by sputtering. 2003 Elsevier B.V. All rights reserved. Keywords: Surface electrical transport (surface conductivity, surface recombination, etc.); Silicon oxides; Silicon nitride; Sputtering
1. Introduction If one wants either to calculate the surface concentration from the measured AES or XPS spectra [1], or to reconstruct the original concentration distribution with depth from measured Auger spectroscopic depth profiling [2,3], one must to understand the transport of signal electrons in the near-surface region. An important part of the transport is the inelastic scattering of the electrons. The inelastic processes during transport are taken into account through the use of the inelastic mean
*
Corresponding author. Tel.: +36-139-22688; fax: +36-12754996. E-mail address: [email protected] (M. Menyhard).
free path (IMFP). The most commonly used IMFP values [4,5] are based on optical data and represent inelastic scattering in the bulk. In the following these values will be referred to as bulk IMFPs. The IMFP valid for the actual surface layer of interest will be called the effective IMFP. The effective IMFP is not necessarily equal to the bulk IMFP since (a) the bulk IMFP does not consider the ‘‘extra’’ inelastic processes appearing when the electron crosses the surface (b) the surface layer might be different from the bulk for various reasons, e.g. ion bombardment, a common operation in surface analysis, alters the near-surface region. There are several analyses, which deals with the loss processes in the vicinity of the surface [6–18] (and references cited therein). Obviously there are no calculations to describe the effect of the
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alteration of the near-surface layer on the IMFP since even the alteration itself is badly defined. On the other hand elastic peak electron spectroscopy (EPES) [19,20] automatically provides the effective IMFPs. Applying this method one measures the ratio of the elastic peak intensities (EP) of two homogeneous specimens, one of the sample of interest and the other a suitable reference material. Using this value as input parameter in a Monte Carlo (MC) calculation [21] for EPES, one can determine the IMFP of one of the specimens provided the IMFP of the other specimen is known [21]. The most important advantage of EPES method is that the measured intensity originates from the same region of the sample as the signal electrons in the case of AES or XPS, if the energy of the EP is roughly half of the energy of the AES or XPS signal electrons. Consequently the intensity of the signal electrons and the elastically reflected electrons is affected in the same way in the studied region; that is, the effective IMFP is determined. In this communication we report on EPES measurement of SiO2 and Si3 N4 in the electron energy range of 300–2000 eV at two angles of excitation with Si as a reference material. The effective IMFP values are derived from the EPES measurements after applying a correction for surface excitations. Using some of the available correction factors [10,11,14], the effective IMFPs will be compared with the corresponding bulk IMFPs. Two different behaviors were observed. In the case of SiO2 the bulk IMFP values seem to be correct in our sample; that is, they agree with the effective IMFP for electron energies above some hundred eV. In the case of Si3 N4 , the effective IMFPs differ from the ÔbulkÕ values. This difference will be explained by alteration of the sample surface due to ion bombardment.
2. Experimental 2.1. Samples The measurements were carried out on silicon dioxide and silicon nitride thin-film (single or
multilayer) structures. They were prepared by remote nitrogen plasma treatment after thermal oxidation. All of them were of high-quality semiconductor-industry-related thin films on silicon wafers. The thicknesses of the films were in the range of 6–100 nm. The silicon nitride films always contained some percentage, generally less than 5%, of oxygen. 2.2. Elastic peak and reflected electron loss spectrum (REELS) measurements The measurements were carried out in the depth-profiling mode with sequential ion sputtering and EP and REELS measurements. This way we could make many measurements of the EP intensity of a sample (silicon dioxide or silicon nitride) and, after crossing the substrate interface, for the silicon (reference) as well. In this way the scatter in the measurements was considerably reduced. For ion sputtering, Arþ ions with various energies (300–1000 eV) were used. The angle of incidence was 82 (with respect to the surface normal). The ion current was about 7 and 30 lA for 0.3 and 1 keV ion energies, respectively. The shape of the ion beam was a Gaussian with FWHM of about 0.5 mm. The specimen was rotated during sputtering to avoid surface roughening when removal of a thicker layer was required [22]. The EP intensities did not depend on the sputtering condition except in the interface region, which was excluded from this analysis. REELS spectra were measured in the counting mode by a pre-retarded cylindrical mirror analyzer (DESA 100, STAIB) in the range of [Ep to (Ep 50 eV)], where Ep is the primary energy of the electron beam. The current of the electron beam was between 20 and 50 nA with a diameter of about 20 lm. The energy resolution of the analyzer could be adjusted electronically, and it was thus possible to measure all spectra with the same energy resolution. The shapes of EPs of the sample and reference were identical, and we therefore only needed to measure and compare the peak heights of EPs. Two geometrical arrangements were used for the measurements. In both cases the sample plane was perpendicular to the axis of the analyzer. The
R. Jung et al. / Surface Science 543 (2003) 153–161
polar acceptance angle of the analyzer was between 19 and 31. Thus, in both cases, the average emission angle for the detected electrons, aout , were 25. For excitation, two electron guns with angles of incidences (ain ) of 0 and 55 (with respect to the surface normal) were used. 2.3. Evaluation procedure IMFPs were derived from the measured EPs by means of our novel MC code (see details in Ref. [18]), by applying the usual routine [21]. According to this procedure, it is assumed that the samples and reference are homogeneous and semi-infinite. The EP intensity of the reference, silicon, was calculated with IMFP values from by the calculation of Tanuma et al. [4]. Similarly, the EP intensity of the compound sample was calculated using an arbitrary starting value for the IMFP. Then this IMFP value was varied until the ratio of calculated EPs was equal to the experimentally determined ratio of EP intensities. These IMFP values, to be referred to as non-corrected, were found by applying a simple search algorithm. The input parameters of the MC calculation were the following: • Measurement geometry for DESA 100 is: angles of incidence 0 and 55, angular range of acceptance 19–31; all angles are measured with respect to the surface normal. • Relativistic differential elastic scattering cross sections were taken from the NIST Database 64 [23]. • IMFP values of Si were taken from Ref. [5]. • Density values were taken as 2.32, 2.33 and 3.44 g/cm3 for Si, SiO2 and Si3 N4 , respectively.
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3. Results The experimentally measured EPs of SiO2 and Si3 N4 with respect to Si as a function of electron energy are shown in Table 1 and in Fig. 1. The scatter of the above values is less than 4%. Based on these measured ratios, the effective IMFP values were calculated applying the evaluation routine; these non-corrected values are shown in Tables 2 and 3 for SiO2 and Si3 N4 , respectively. It is clear that for both materials (a) there are deviations between the non-corrected values and those calculated from optical data [4] or predicted IMFPs for bulk solids [5], (b) the IMFP values determined at the two angles of incidence agree well. 4. Discussion Disagreements between measured and calculated IMFPs have been known for some time (see
Fig. 1. Ratios of experimentally measured peak heights of SiO2 and Si3 N4 with respect to Si at the indicated primary energies and angles of incidence.
Table 1 Ratios of experimentally measured peak heights of SiO2 and Si3 N4 with respect to Si at the indicated primary energies and angles of incidence Energy (eV)
SiO2 /Si ain ¼ 0
SiO2 /Si ain ¼ 55
300 500 1000 1500 2000
1.14 1.11 1.02 1.02
1.48 1.38 1.21 1.13 1.09
Si3 N4 /Si ain ¼ 0 1.14 1.01 0.96
Si3 N4 /Si ain ¼ 55 0.87 0.82 1.02 1.00 0.95
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Table 2 IMFP values for SiO2 as a function of electron energy derived from our measurements at ain ¼ 0 and ain ¼ 55 Energy (eV)
Non-corr. ain ¼ 0
Non-corr. ain ¼ 55
300 500 1000 1500 2000
23.5 35.5 47.1 55.8
16.8 24.1 36.3 48.7 59.3
Corr. Chen ain ¼ 0
Corr. Chen ain ¼ 55
Corr. Chen + Kwei ain ¼ 0
Corr. Chen + Kwei ain ¼ 55
Corr. Werner ain ¼ 0
Corr. Werner ain ¼ 55
TPP optical data
18.5 30.5 42.0 50.3
10.8 17.5 29.4 41.2 51.3
20.2 32.4 44.0 52.6
12.6 19.7 32.0 44.0 54.5
16.5 27.9 39.0 47.0
9.8 15.8 26.8 37.8 47.4
12.6 17.7 29.3 40.1 50.4
Without surface correction (columns 2, 3), using correction for surface excitation for the intensity of EPSi using ChenÕs (columns 4, 5), and WernerÕs (columns 8, 9) data, respectively. In columns 6, 7 we show IMFPs when the correction for surface excitation to the EP intensity of both materials was applied using ChenÕs and KweiÕs data. The last column shows the IMFPs of Tanuma et al. [4].
Table 3 IMFP values of Si3 N4 derived from EPES measurements for two geometrical arrangements, without surface correction, and applying the correction for surface excitations to the intensity of EPSi using the data of Chen, and IMFP values calculated from the TPP-2M predictive formula [5] using default parameters Energy (eV)
Non-corr. ain ¼ 0
Non-corr. ain ¼ 55
Corr. Chen ain ¼ 0
Corr. Chen ain ¼ 55
TPP-2M
300 500 1000 1500 2000
15.3 21.6 27 34.8
13 15.3 19.9 29.4 34.1
12.0 18.5 23.9 31.3
9.2 11.1 16.0 25.0 29.5
10.2 14.2 23.6 32.3 40.6
details in Ref. [24]). There are many factors that can cause such disagreements, and we will mention only some of them. One class of uncertainties concerns the conditions of the specimen. The MC calculation is based on the assumption that the surface composition and density are the same as the bulk, there is no surface roughness, the structure at the surface region is ideally amorphous, and there is no contamination on the surface, etc. If one or more of these conditions are not met, deviations can occur between the calculated and measured IMFPs. Another class of problems concerns measurement conditions, such as the proper measurement of the elastic peak intensity (background subtraction) and the accuracy and stability of the experimental configuration. A final class of problems is more basic. The usual MC simulation considers only bulk inelastic processes. Since the sample is semi-infinite surface excitations can also affect the intensity of the EP. In the present case, the studied surface (as is generally the case in EPES, and for depth profil-
ing) is bombarded by ions. The near-surface layer after ion bombardment is always altered with respect to the bulk to some extent. The alteration might appear as a change of composition, density and the electronic structure. Additionally surface roughness might also develop. Our ion-sputtering conditions resulted in a roughness of less than 1 nm (rms) [22] that did not change during sputtering. Contamination on the surface was not detected by AES. In the case of SiO2 , we did not see changes in the Auger peak shapes and heights (no ion or electron-beam-induced decomposition was observed) and the REELS showed the expected gap. On the other hand the Auger peak shapes of Si3 N4 did not change during sputtering, and were not affected by the change of ion energy, but the REELS did not show a gap. This result means that the near-surface layer was different from that of the bulk. The inelastic-excitation processes in the three materials are strongly different. This is demon-
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it is vital to make a correction for surface excitation to the intensity of the EP of Si the reference material.
4.1. Correction for surface excitation in Si
Fig. 2. The REELS spectra of Si, SiO2 and Si3 N4 (Ipr ¼ 25 nA). The spectra are normalized to unit area of the elastic peak. SP stands for surface plasmon.
strated by Fig. 2, which shows the corresponding REELS spectra. The REELS spectrum can be used for rough estimation of the IMFP; high and weak loss intensities indicate low and high IMFPs, respectively. For better comparison, the elastic peaks in Fig. 2 are normalized to unit area. It is clear that the loss intensities are strongest for Si and weakest for SiO2 . The magnitude of the surface plasmon can be used to give a rough estimate of the strength of the energy loss due to the presence of the surface. There is a well defined surface plasmon loss in the case of Si (denoted by SP in Fig. 2). In contrast, we cannot identify in Fig. 2 any signs of surface excitations in the cases of SiO2 and Si3 N4 . To support this observation, we compared the REELS spectra taken at 0.5 and 2 keV energies. Because the surface/bulk contribution should change with energy, the spectra would change if the surface contribution were measurable. Though we find sometimes weak features representative of surface excitation their intensity never increased by decreasing the excitation energy. Our result is in agreement with the work of Yubero et al. [25], for SiO2 . They found a broad and weak feature at the expected surface plasmon energy using 2 keV excitation energy (see Fig. 7 in Ref. [25]). The intensity of this feature, however, decreased when the excitation energy was decreased to 0.6 keV, contrary to expectation for a surface plasmon. Since the surface-excitation probabilities for the reference and studied materials are very different,
Ritchie [6] pointed out first the role of surface excitations when an electron crosses a surface. The surface excitation takes place in a relatively extended space around the geometrical surface, inside and outside the specimen, and its intensity strongly varies with depth [7–10,14–16]. The total surface excitation probability is given by an integral quantity, the surface excitation parameter (SEP), which is the number of surface excitations occurring when an electron crosses the surface [7,11,12]. The surface-loss statistics obeys the Poisson law. The zeroth term of the series (the no-scattering term) is expðPs Þ where Ps is the SEP value. Since the electron crosses the surface twice in EPES, the probability of no scattering, that is, the surface correction factor, is fs ¼ expðPs ðinÞÞ expðPs ðoutÞÞ. Obviously, EP values calculated by MC simulation should be multiplied by fs to be compared to the measured EPs. To make this correction, one must know the Ps values as a function of electron energy and of the angles of incidence and emission at the surface. The presence of a surface causes not only additional loss processes (by the surface losses) but also influences the bulk loss intensity in a region near the surface. Inside the target, the reduction of the bulk excitation is approximately compensated by the increasing intensity of the surface excitation. Simply stated, the correction factor need consider only the surface excitations taking place outside of the target [9,10,15,16]. By integrating over the electron path outside the surface, a similar correction for surface excitations Cs has be derived [10,16]. (Note: this latter definition is different from the one cited above [11,12].) The attenuation of the EP intensity due to presence of the surface is calculated, as previously, by fs ¼ expðCs ðinÞÞ expðCs ðoutÞÞ. A formula for Cs and the necessary constants for some materials were published by Chen [11]; his expression is
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Cs ða; EÞ ¼
R. Jung et al. / Surface Science 543 (2003) 153–161
a cos a E1=2
ð1Þ
where a is the angle of emission or incidence for an electron with energy E crossing the surface, and a is a material constant; aSi ¼ 2:51. From Eq. (1) fs values were calculated. Werner et al. provided a formula and parameters for the calculation of Ps for Si as well [12]: Ps ða; EÞ ¼
1 a cos a E1=2 þ 1
ð2Þ
In Eq. (2) the material parameter a, for Si is 0.171. This formula and the corresponding parameters do not consider, however, the coupling between the surface and bulk plasmons. Using the Chen [10] and Werner et al. [11] data, we calculated the correction factors fs for Si for our energies and angular conditions. The two sets of values are systematically different; ChenÕs values are higher than those of WernerÕs. This difference is maintained during the calculation of the IMFP. It follows that the IMFP values based on WernerÕs works are lower than those from ChenÕs results. 4.2. IMFP in SiO2 Let us consider first the REELS spectrum of SiO2 (shown in Fig. 2), which gives some rough information on its electronic structure. In Fig. 2 we can see that the band gap (which appears as a low plateau near the elastic peak) is about 7 eV and the plasmon energy is 21.5 eV. (The intensity in the band gap region in principle should be zero since there is no excitation into the band gap. In our case a non-zero constant intensity appears because of the transfer function of the analyzer.) Experimentally, we could not observe surface losses. On the other hand the theoretical calculation of Kwei et al. [14] indicates that the surface excitation in SiO2 is small but not negligible. They provide Cs values for a series of energies for ain ¼ aout ¼ 0. Assuming that the angular dependence of Cs can be described by a 1= cos a factor [10,11], the Cs and corresponding fs values were calculated for SiO2 . Using MC simulation, we derived effective IMFPs from the measured peak-height ratios of
SiO2 and Si making various assumptions. First, we neglected the effect of surface excitations for both materials. These IMFPs values are designated as non-corrected. Second, based on the experimental finding, we neglected the effect of surface excitation in SiO2 , but corrected the intensity of the EPSi for surface excitation using ChenÕs and WernerÕs correction factors. Finally, we corrected the intensity of EPs of both materials using ChenÕs and KweiÕs correction factors. All derived IMFPs derived and the corresponding bulk values [4] are shown in Table 2. Fig. 3 shows effective IMFPs derived from the use only of ChenÕs correction factors for Si and the bulk IMFPs [4]. The agreement between these two data sets is excellent. A closer look at Table 2 allows us to make some remarks. First, the IMFP values derived by applying the surface correction at two angles of incidences agree remarkably well. Let us recall that the non-corrected IMFPs measured at the two different angles (columns 2 and 3) also agree closely. This means that the MC calculation accounts properly for the measurement configuration. Since the correction for surface excitation does not affect this agreement, we conclude that the angular dependence of the surface correction factor is reliable. We note as well that IMFP values using WernerÕs corrections are systematically lower than those found after applying ChenÕs results. It is also clear that applying a correction for the surface
Fig. 3. IMFP values in SiO2 as a function of electron energy. ( ) Calculated values from optical data [4], () and (D) derived values from our measurements using ChenÕs surface correction for Si at ain ¼ 0 and ain ¼ 55, respectively.
R. Jung et al. / Surface Science 543 (2003) 153–161
excitation in SiO2 as well results in an increase of the deviations between the effective and bulk IMFPs. The IMFPs derived by correcting the EP of Si using ChenÕs data agree well with the bulk values except at 300 eV (where the deviation is 17%). To explain the latter difference, one might speculate, that the correction factor provided by Chen is slightly inaccurate at 300 eV. The other most likely explanation is that the actual surface excitation is not the same as for an ideal surface. It is well known that the intensity of the surface plasmon and even its energy depend on the condition of the surface [26]. This also means that, in principle, fs should also depend on the condition of the surface; this dependence is obviously missing in the present descriptions. It might also happen that some defect accumulation occurs in the SiO2 layer due to the ion bombardment. These defects might affect the electron transport at low energies. We conclude that the effective IMFP in SiO2 (subjected to ion sputtering) is very close to the bulk IMFP, which means that the bulk values can be safely used for this case. 4.3. IMFP in Si3 N4 Fig. 2 also shows the REELS spectrum of Si3 N4 . The shape of the REELS spectrum of Si3 N4 deviates from that expected. First there is no band gap. This observation is in contradiction with the finding of Pic et al. [27], but agrees with the similar observation of Holgado et al. [28] for SiOx samples. It should be also added that, allowing some slight contamination after ion bombardment, the band gap appeared again in the spectrum [29]. On the other hand, it is known that the band gap of this material strongly depends on its stoichiometry [30], which might be altered by ion sputtering. The energy of the bulk plasmon is about 22 eV. This value is in good agreement with that found by Samano et al. [31] who measured the plasmon energy to be 22 eV for a Si3 N4 layer produced by laser ablation. Gritsenko et al. [32] measured 23.5 eV for plasmon energy in amorphous Si3 N4 made by chemical vapor deposition. The different plasmon energies found in layers produced by different techniques suggest that the electronic structures of
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the above layers are different, and that such differences could affect the IMFP as well. The REELS spectrum (Fig. 2) shows a broad loss peak. As a result, it is not possible to prove that there is no measurable surface excitation. To test for the presence of surface excitations we carried out the same procedure that was used for SiO2 . We compared the REELS spectra measured at high (2000 eV) and low (300 eV) excitation energies but we could not find any difference characteristic of any surface excitation. Thus we will assume that fs (Si3 N4 ) ¼ 1, and will apply a correction only for the intensity EPSi . Table 3 shows IMFPs for Si3 N4 derived from MC simulations ignoring the correction for surface excitations for both materials (non-corrected), correcting the intensity of EPSi using ChenÕs correction factors, and IMFPs calculated by the TPP-2M predictive formula [5]. (In this case, the correction of Werner [12] was not applied since it increases the deviations.) The following default values were used for the TPP-2M formula: number of valence electrons (Nv ) is 32, energy gap, Eg , is 5.4 eV, and the density q ¼ 3:44 g/cm3 . The effective IMFPs derived from our measurements using ChenÕs correction for Si, and those calculated from the TPP-2M formula are shown in Fig. 4. While there is a reasonable agreement at low energies, the deviations at higher energies are appreciable. We have examined whether reasonable variation of the input parameters of the TPP-2M formula could provide better agreement with the
Fig. 4. The same as Fig. 3 but Si3 N4 . ( ) Calculated values from the TPP-2M predictive formula [5].
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Table 4 IMFP values of Si3 N4 for an assumed density of 3.0 g/cm3 Energy (eV)
Corr. Chen
TPP-2M
300 500 1000 1500 2000
10.4 12.9 20.3 27 38
10.4 14.6 24.3 33.3 41.9
Column 2 derived from our EPES measurements applying the correction for surface excitations to the intensity of EPSi using the data of Chen. The IMFPs in column 3 were derived from the TPP-2M formula assuming the bulk parameters for Nv and Eg and an assumed density of 3.0 g/cm3 .
Acknowledgements This work was carried out in the frame of Technical Collaboration Agreement # RFP 2002109 between Samsung Ltd and the Research Institute for Technical Physics and Materials Science. The development of the MC code was supported by the Hungarian Fund for Scientific Research (OTKA) through grant T 030430 (M.M.).
References effective IMFPs. The parameters used in the TPP2M formula for bulk Si3 N4 Nv , Eg and q, could be different from the values applicable to our sample. Eg can be changed to the experimentally found 0 eV, but this change weakly affects the IMFPs. Since Nv is fixed by the sum rule [5], only q can be varied. Thus IMFPs were also derived for one configuration (ain ¼ 55 and aout ¼ 25) from our measurements using ChenÕs data for the surface correction of the Si intensity and from the formula TPP-2M assuming that the density of the material was 3.0 g/ cm3 . These results are shown in Table 4. We see now that the agreement between the IMFPs from TPP-2M and from our measurements is much better. Unfortunately, we have no any independent test of whether the density of the surface layer deviated from the nominal bulk value. 5. Conclusions EPES measurements were carried out for SiO2 and Si3 N4 using a Si reference in the energy range of 300–2000 eV. We derived effective IMFPs from MC simulations after correcting the intensity of the Si elastic peak for surface excitations from the data of Chen [10]. For SiO2 and Si3 N4 , surface excitations were neglected. 1. The effective IMFPs of SiO2 were found to be similar to bulk IMFPs except at 300 eV. 2. Si3 N4 did not show a band gap. A systematic difference between the effective IMFPs and the bulk values were found assuming the nominal bulk density of Si3 N4 .
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Determination of effective electron inelastic mean free paths in SiO2 and Si3N4 using a Si reference R. Jung a, J.C. Lee a, G.T. Orosz b, A. Sulyok b, G. Zsolt b, M. Menyhard b
b,*
a Samsung Advanced Institute of Technology, 440-600 South Korea Department of Surface Physics, Research Institute for Technical Physics and Materials Sciences, P.O. Box 49, H-1525 Budapest, Hungary
Received 24 March 2003; accepted for publication 1 August 2003
Abstract Elastic peak electron spectroscopy (EPES) provides inelastic mean free path (IMFP) values in the near-surface region. Such values, which will be called effective IMFPs, might be different from these derived from bulk parameters. In this work we derive effective IMFP values from EPES measurements in the range of 300–2000 eV for SiO2 and Si3 N4 using a Si reference. Corrections for surface excitation are applied. Our effective IMFP values agree well with those calculated from optical data in the case of SiO2 ; that is, the ion sputtering does not alter the SiO2 surface significantly. On the other hand, systematic deviations between our data and those provided by a predictive formula were found in the case of sputtered Si3 N4 . These differences are attributed to alteration in the surface layer caused by sputtering. 2003 Elsevier B.V. All rights reserved. Keywords: Surface electrical transport (surface conductivity, surface recombination, etc.); Silicon oxides; Silicon nitride; Sputtering
1. Introduction If one wants either to calculate the surface concentration from the measured AES or XPS spectra [1], or to reconstruct the original concentration distribution with depth from measured Auger spectroscopic depth profiling [2,3], one must to understand the transport of signal electrons in the near-surface region. An important part of the transport is the inelastic scattering of the electrons. The inelastic processes during transport are taken into account through the use of the inelastic mean
*
Corresponding author. Tel.: +36-139-22688; fax: +36-12754996. E-mail address: [email protected] (M. Menyhard).
free path (IMFP). The most commonly used IMFP values [4,5] are based on optical data and represent inelastic scattering in the bulk. In the following these values will be referred to as bulk IMFPs. The IMFP valid for the actual surface layer of interest will be called the effective IMFP. The effective IMFP is not necessarily equal to the bulk IMFP since (a) the bulk IMFP does not consider the ‘‘extra’’ inelastic processes appearing when the electron crosses the surface (b) the surface layer might be different from the bulk for various reasons, e.g. ion bombardment, a common operation in surface analysis, alters the near-surface region. There are several analyses, which deals with the loss processes in the vicinity of the surface [6–18] (and references cited therein). Obviously there are no calculations to describe the effect of the
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alteration of the near-surface layer on the IMFP since even the alteration itself is badly defined. On the other hand elastic peak electron spectroscopy (EPES) [19,20] automatically provides the effective IMFPs. Applying this method one measures the ratio of the elastic peak intensities (EP) of two homogeneous specimens, one of the sample of interest and the other a suitable reference material. Using this value as input parameter in a Monte Carlo (MC) calculation [21] for EPES, one can determine the IMFP of one of the specimens provided the IMFP of the other specimen is known [21]. The most important advantage of EPES method is that the measured intensity originates from the same region of the sample as the signal electrons in the case of AES or XPS, if the energy of the EP is roughly half of the energy of the AES or XPS signal electrons. Consequently the intensity of the signal electrons and the elastically reflected electrons is affected in the same way in the studied region; that is, the effective IMFP is determined. In this communication we report on EPES measurement of SiO2 and Si3 N4 in the electron energy range of 300–2000 eV at two angles of excitation with Si as a reference material. The effective IMFP values are derived from the EPES measurements after applying a correction for surface excitations. Using some of the available correction factors [10,11,14], the effective IMFPs will be compared with the corresponding bulk IMFPs. Two different behaviors were observed. In the case of SiO2 the bulk IMFP values seem to be correct in our sample; that is, they agree with the effective IMFP for electron energies above some hundred eV. In the case of Si3 N4 , the effective IMFPs differ from the ÔbulkÕ values. This difference will be explained by alteration of the sample surface due to ion bombardment.
2. Experimental 2.1. Samples The measurements were carried out on silicon dioxide and silicon nitride thin-film (single or
multilayer) structures. They were prepared by remote nitrogen plasma treatment after thermal oxidation. All of them were of high-quality semiconductor-industry-related thin films on silicon wafers. The thicknesses of the films were in the range of 6–100 nm. The silicon nitride films always contained some percentage, generally less than 5%, of oxygen. 2.2. Elastic peak and reflected electron loss spectrum (REELS) measurements The measurements were carried out in the depth-profiling mode with sequential ion sputtering and EP and REELS measurements. This way we could make many measurements of the EP intensity of a sample (silicon dioxide or silicon nitride) and, after crossing the substrate interface, for the silicon (reference) as well. In this way the scatter in the measurements was considerably reduced. For ion sputtering, Arþ ions with various energies (300–1000 eV) were used. The angle of incidence was 82 (with respect to the surface normal). The ion current was about 7 and 30 lA for 0.3 and 1 keV ion energies, respectively. The shape of the ion beam was a Gaussian with FWHM of about 0.5 mm. The specimen was rotated during sputtering to avoid surface roughening when removal of a thicker layer was required [22]. The EP intensities did not depend on the sputtering condition except in the interface region, which was excluded from this analysis. REELS spectra were measured in the counting mode by a pre-retarded cylindrical mirror analyzer (DESA 100, STAIB) in the range of [Ep to (Ep 50 eV)], where Ep is the primary energy of the electron beam. The current of the electron beam was between 20 and 50 nA with a diameter of about 20 lm. The energy resolution of the analyzer could be adjusted electronically, and it was thus possible to measure all spectra with the same energy resolution. The shapes of EPs of the sample and reference were identical, and we therefore only needed to measure and compare the peak heights of EPs. Two geometrical arrangements were used for the measurements. In both cases the sample plane was perpendicular to the axis of the analyzer. The
R. Jung et al. / Surface Science 543 (2003) 153–161
polar acceptance angle of the analyzer was between 19 and 31. Thus, in both cases, the average emission angle for the detected electrons, aout , were 25. For excitation, two electron guns with angles of incidences (ain ) of 0 and 55 (with respect to the surface normal) were used. 2.3. Evaluation procedure IMFPs were derived from the measured EPs by means of our novel MC code (see details in Ref. [18]), by applying the usual routine [21]. According to this procedure, it is assumed that the samples and reference are homogeneous and semi-infinite. The EP intensity of the reference, silicon, was calculated with IMFP values from by the calculation of Tanuma et al. [4]. Similarly, the EP intensity of the compound sample was calculated using an arbitrary starting value for the IMFP. Then this IMFP value was varied until the ratio of calculated EPs was equal to the experimentally determined ratio of EP intensities. These IMFP values, to be referred to as non-corrected, were found by applying a simple search algorithm. The input parameters of the MC calculation were the following: • Measurement geometry for DESA 100 is: angles of incidence 0 and 55, angular range of acceptance 19–31; all angles are measured with respect to the surface normal. • Relativistic differential elastic scattering cross sections were taken from the NIST Database 64 [23]. • IMFP values of Si were taken from Ref. [5]. • Density values were taken as 2.32, 2.33 and 3.44 g/cm3 for Si, SiO2 and Si3 N4 , respectively.
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3. Results The experimentally measured EPs of SiO2 and Si3 N4 with respect to Si as a function of electron energy are shown in Table 1 and in Fig. 1. The scatter of the above values is less than 4%. Based on these measured ratios, the effective IMFP values were calculated applying the evaluation routine; these non-corrected values are shown in Tables 2 and 3 for SiO2 and Si3 N4 , respectively. It is clear that for both materials (a) there are deviations between the non-corrected values and those calculated from optical data [4] or predicted IMFPs for bulk solids [5], (b) the IMFP values determined at the two angles of incidence agree well. 4. Discussion Disagreements between measured and calculated IMFPs have been known for some time (see
Fig. 1. Ratios of experimentally measured peak heights of SiO2 and Si3 N4 with respect to Si at the indicated primary energies and angles of incidence.
Table 1 Ratios of experimentally measured peak heights of SiO2 and Si3 N4 with respect to Si at the indicated primary energies and angles of incidence Energy (eV)
SiO2 /Si ain ¼ 0
SiO2 /Si ain ¼ 55
300 500 1000 1500 2000
1.14 1.11 1.02 1.02
1.48 1.38 1.21 1.13 1.09
Si3 N4 /Si ain ¼ 0 1.14 1.01 0.96
Si3 N4 /Si ain ¼ 55 0.87 0.82 1.02 1.00 0.95
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Table 2 IMFP values for SiO2 as a function of electron energy derived from our measurements at ain ¼ 0 and ain ¼ 55 Energy (eV)
Non-corr. ain ¼ 0
Non-corr. ain ¼ 55
300 500 1000 1500 2000
23.5 35.5 47.1 55.8
16.8 24.1 36.3 48.7 59.3
Corr. Chen ain ¼ 0
Corr. Chen ain ¼ 55
Corr. Chen + Kwei ain ¼ 0
Corr. Chen + Kwei ain ¼ 55
Corr. Werner ain ¼ 0
Corr. Werner ain ¼ 55
TPP optical data
18.5 30.5 42.0 50.3
10.8 17.5 29.4 41.2 51.3
20.2 32.4 44.0 52.6
12.6 19.7 32.0 44.0 54.5
16.5 27.9 39.0 47.0
9.8 15.8 26.8 37.8 47.4
12.6 17.7 29.3 40.1 50.4
Without surface correction (columns 2, 3), using correction for surface excitation for the intensity of EPSi using ChenÕs (columns 4, 5), and WernerÕs (columns 8, 9) data, respectively. In columns 6, 7 we show IMFPs when the correction for surface excitation to the EP intensity of both materials was applied using ChenÕs and KweiÕs data. The last column shows the IMFPs of Tanuma et al. [4].
Table 3 IMFP values of Si3 N4 derived from EPES measurements for two geometrical arrangements, without surface correction, and applying the correction for surface excitations to the intensity of EPSi using the data of Chen, and IMFP values calculated from the TPP-2M predictive formula [5] using default parameters Energy (eV)
Non-corr. ain ¼ 0
Non-corr. ain ¼ 55
Corr. Chen ain ¼ 0
Corr. Chen ain ¼ 55
TPP-2M
300 500 1000 1500 2000
15.3 21.6 27 34.8
13 15.3 19.9 29.4 34.1
12.0 18.5 23.9 31.3
9.2 11.1 16.0 25.0 29.5
10.2 14.2 23.6 32.3 40.6
details in Ref. [24]). There are many factors that can cause such disagreements, and we will mention only some of them. One class of uncertainties concerns the conditions of the specimen. The MC calculation is based on the assumption that the surface composition and density are the same as the bulk, there is no surface roughness, the structure at the surface region is ideally amorphous, and there is no contamination on the surface, etc. If one or more of these conditions are not met, deviations can occur between the calculated and measured IMFPs. Another class of problems concerns measurement conditions, such as the proper measurement of the elastic peak intensity (background subtraction) and the accuracy and stability of the experimental configuration. A final class of problems is more basic. The usual MC simulation considers only bulk inelastic processes. Since the sample is semi-infinite surface excitations can also affect the intensity of the EP. In the present case, the studied surface (as is generally the case in EPES, and for depth profil-
ing) is bombarded by ions. The near-surface layer after ion bombardment is always altered with respect to the bulk to some extent. The alteration might appear as a change of composition, density and the electronic structure. Additionally surface roughness might also develop. Our ion-sputtering conditions resulted in a roughness of less than 1 nm (rms) [22] that did not change during sputtering. Contamination on the surface was not detected by AES. In the case of SiO2 , we did not see changes in the Auger peak shapes and heights (no ion or electron-beam-induced decomposition was observed) and the REELS showed the expected gap. On the other hand the Auger peak shapes of Si3 N4 did not change during sputtering, and were not affected by the change of ion energy, but the REELS did not show a gap. This result means that the near-surface layer was different from that of the bulk. The inelastic-excitation processes in the three materials are strongly different. This is demon-
R. Jung et al. / Surface Science 543 (2003) 153–161
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it is vital to make a correction for surface excitation to the intensity of the EP of Si the reference material.
4.1. Correction for surface excitation in Si
Fig. 2. The REELS spectra of Si, SiO2 and Si3 N4 (Ipr ¼ 25 nA). The spectra are normalized to unit area of the elastic peak. SP stands for surface plasmon.
strated by Fig. 2, which shows the corresponding REELS spectra. The REELS spectrum can be used for rough estimation of the IMFP; high and weak loss intensities indicate low and high IMFPs, respectively. For better comparison, the elastic peaks in Fig. 2 are normalized to unit area. It is clear that the loss intensities are strongest for Si and weakest for SiO2 . The magnitude of the surface plasmon can be used to give a rough estimate of the strength of the energy loss due to the presence of the surface. There is a well defined surface plasmon loss in the case of Si (denoted by SP in Fig. 2). In contrast, we cannot identify in Fig. 2 any signs of surface excitations in the cases of SiO2 and Si3 N4 . To support this observation, we compared the REELS spectra taken at 0.5 and 2 keV energies. Because the surface/bulk contribution should change with energy, the spectra would change if the surface contribution were measurable. Though we find sometimes weak features representative of surface excitation their intensity never increased by decreasing the excitation energy. Our result is in agreement with the work of Yubero et al. [25], for SiO2 . They found a broad and weak feature at the expected surface plasmon energy using 2 keV excitation energy (see Fig. 7 in Ref. [25]). The intensity of this feature, however, decreased when the excitation energy was decreased to 0.6 keV, contrary to expectation for a surface plasmon. Since the surface-excitation probabilities for the reference and studied materials are very different,
Ritchie [6] pointed out first the role of surface excitations when an electron crosses a surface. The surface excitation takes place in a relatively extended space around the geometrical surface, inside and outside the specimen, and its intensity strongly varies with depth [7–10,14–16]. The total surface excitation probability is given by an integral quantity, the surface excitation parameter (SEP), which is the number of surface excitations occurring when an electron crosses the surface [7,11,12]. The surface-loss statistics obeys the Poisson law. The zeroth term of the series (the no-scattering term) is expðPs Þ where Ps is the SEP value. Since the electron crosses the surface twice in EPES, the probability of no scattering, that is, the surface correction factor, is fs ¼ expðPs ðinÞÞ expðPs ðoutÞÞ. Obviously, EP values calculated by MC simulation should be multiplied by fs to be compared to the measured EPs. To make this correction, one must know the Ps values as a function of electron energy and of the angles of incidence and emission at the surface. The presence of a surface causes not only additional loss processes (by the surface losses) but also influences the bulk loss intensity in a region near the surface. Inside the target, the reduction of the bulk excitation is approximately compensated by the increasing intensity of the surface excitation. Simply stated, the correction factor need consider only the surface excitations taking place outside of the target [9,10,15,16]. By integrating over the electron path outside the surface, a similar correction for surface excitations Cs has be derived [10,16]. (Note: this latter definition is different from the one cited above [11,12].) The attenuation of the EP intensity due to presence of the surface is calculated, as previously, by fs ¼ expðCs ðinÞÞ expðCs ðoutÞÞ. A formula for Cs and the necessary constants for some materials were published by Chen [11]; his expression is
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Cs ða; EÞ ¼
R. Jung et al. / Surface Science 543 (2003) 153–161
a cos a E1=2
ð1Þ
where a is the angle of emission or incidence for an electron with energy E crossing the surface, and a is a material constant; aSi ¼ 2:51. From Eq. (1) fs values were calculated. Werner et al. provided a formula and parameters for the calculation of Ps for Si as well [12]: Ps ða; EÞ ¼
1 a cos a E1=2 þ 1
ð2Þ
In Eq. (2) the material parameter a, for Si is 0.171. This formula and the corresponding parameters do not consider, however, the coupling between the surface and bulk plasmons. Using the Chen [10] and Werner et al. [11] data, we calculated the correction factors fs for Si for our energies and angular conditions. The two sets of values are systematically different; ChenÕs values are higher than those of WernerÕs. This difference is maintained during the calculation of the IMFP. It follows that the IMFP values based on WernerÕs works are lower than those from ChenÕs results. 4.2. IMFP in SiO2 Let us consider first the REELS spectrum of SiO2 (shown in Fig. 2), which gives some rough information on its electronic structure. In Fig. 2 we can see that the band gap (which appears as a low plateau near the elastic peak) is about 7 eV and the plasmon energy is 21.5 eV. (The intensity in the band gap region in principle should be zero since there is no excitation into the band gap. In our case a non-zero constant intensity appears because of the transfer function of the analyzer.) Experimentally, we could not observe surface losses. On the other hand the theoretical calculation of Kwei et al. [14] indicates that the surface excitation in SiO2 is small but not negligible. They provide Cs values for a series of energies for ain ¼ aout ¼ 0. Assuming that the angular dependence of Cs can be described by a 1= cos a factor [10,11], the Cs and corresponding fs values were calculated for SiO2 . Using MC simulation, we derived effective IMFPs from the measured peak-height ratios of
SiO2 and Si making various assumptions. First, we neglected the effect of surface excitations for both materials. These IMFPs values are designated as non-corrected. Second, based on the experimental finding, we neglected the effect of surface excitation in SiO2 , but corrected the intensity of the EPSi for surface excitation using ChenÕs and WernerÕs correction factors. Finally, we corrected the intensity of EPs of both materials using ChenÕs and KweiÕs correction factors. All derived IMFPs derived and the corresponding bulk values [4] are shown in Table 2. Fig. 3 shows effective IMFPs derived from the use only of ChenÕs correction factors for Si and the bulk IMFPs [4]. The agreement between these two data sets is excellent. A closer look at Table 2 allows us to make some remarks. First, the IMFP values derived by applying the surface correction at two angles of incidences agree remarkably well. Let us recall that the non-corrected IMFPs measured at the two different angles (columns 2 and 3) also agree closely. This means that the MC calculation accounts properly for the measurement configuration. Since the correction for surface excitation does not affect this agreement, we conclude that the angular dependence of the surface correction factor is reliable. We note as well that IMFP values using WernerÕs corrections are systematically lower than those found after applying ChenÕs results. It is also clear that applying a correction for the surface
Fig. 3. IMFP values in SiO2 as a function of electron energy. ( ) Calculated values from optical data [4], () and (D) derived values from our measurements using ChenÕs surface correction for Si at ain ¼ 0 and ain ¼ 55, respectively.
R. Jung et al. / Surface Science 543 (2003) 153–161
excitation in SiO2 as well results in an increase of the deviations between the effective and bulk IMFPs. The IMFPs derived by correcting the EP of Si using ChenÕs data agree well with the bulk values except at 300 eV (where the deviation is 17%). To explain the latter difference, one might speculate, that the correction factor provided by Chen is slightly inaccurate at 300 eV. The other most likely explanation is that the actual surface excitation is not the same as for an ideal surface. It is well known that the intensity of the surface plasmon and even its energy depend on the condition of the surface [26]. This also means that, in principle, fs should also depend on the condition of the surface; this dependence is obviously missing in the present descriptions. It might also happen that some defect accumulation occurs in the SiO2 layer due to the ion bombardment. These defects might affect the electron transport at low energies. We conclude that the effective IMFP in SiO2 (subjected to ion sputtering) is very close to the bulk IMFP, which means that the bulk values can be safely used for this case. 4.3. IMFP in Si3 N4 Fig. 2 also shows the REELS spectrum of Si3 N4 . The shape of the REELS spectrum of Si3 N4 deviates from that expected. First there is no band gap. This observation is in contradiction with the finding of Pic et al. [27], but agrees with the similar observation of Holgado et al. [28] for SiOx samples. It should be also added that, allowing some slight contamination after ion bombardment, the band gap appeared again in the spectrum [29]. On the other hand, it is known that the band gap of this material strongly depends on its stoichiometry [30], which might be altered by ion sputtering. The energy of the bulk plasmon is about 22 eV. This value is in good agreement with that found by Samano et al. [31] who measured the plasmon energy to be 22 eV for a Si3 N4 layer produced by laser ablation. Gritsenko et al. [32] measured 23.5 eV for plasmon energy in amorphous Si3 N4 made by chemical vapor deposition. The different plasmon energies found in layers produced by different techniques suggest that the electronic structures of
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the above layers are different, and that such differences could affect the IMFP as well. The REELS spectrum (Fig. 2) shows a broad loss peak. As a result, it is not possible to prove that there is no measurable surface excitation. To test for the presence of surface excitations we carried out the same procedure that was used for SiO2 . We compared the REELS spectra measured at high (2000 eV) and low (300 eV) excitation energies but we could not find any difference characteristic of any surface excitation. Thus we will assume that fs (Si3 N4 ) ¼ 1, and will apply a correction only for the intensity EPSi . Table 3 shows IMFPs for Si3 N4 derived from MC simulations ignoring the correction for surface excitations for both materials (non-corrected), correcting the intensity of EPSi using ChenÕs correction factors, and IMFPs calculated by the TPP-2M predictive formula [5]. (In this case, the correction of Werner [12] was not applied since it increases the deviations.) The following default values were used for the TPP-2M formula: number of valence electrons (Nv ) is 32, energy gap, Eg , is 5.4 eV, and the density q ¼ 3:44 g/cm3 . The effective IMFPs derived from our measurements using ChenÕs correction for Si, and those calculated from the TPP-2M formula are shown in Fig. 4. While there is a reasonable agreement at low energies, the deviations at higher energies are appreciable. We have examined whether reasonable variation of the input parameters of the TPP-2M formula could provide better agreement with the
Fig. 4. The same as Fig. 3 but Si3 N4 . ( ) Calculated values from the TPP-2M predictive formula [5].
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Table 4 IMFP values of Si3 N4 for an assumed density of 3.0 g/cm3 Energy (eV)
Corr. Chen
TPP-2M
300 500 1000 1500 2000
10.4 12.9 20.3 27 38
10.4 14.6 24.3 33.3 41.9
Column 2 derived from our EPES measurements applying the correction for surface excitations to the intensity of EPSi using the data of Chen. The IMFPs in column 3 were derived from the TPP-2M formula assuming the bulk parameters for Nv and Eg and an assumed density of 3.0 g/cm3 .
Acknowledgements This work was carried out in the frame of Technical Collaboration Agreement # RFP 2002109 between Samsung Ltd and the Research Institute for Technical Physics and Materials Science. The development of the MC code was supported by the Hungarian Fund for Scientific Research (OTKA) through grant T 030430 (M.M.).
References effective IMFPs. The parameters used in the TPP2M formula for bulk Si3 N4 Nv , Eg and q, could be different from the values applicable to our sample. Eg can be changed to the experimentally found 0 eV, but this change weakly affects the IMFPs. Since Nv is fixed by the sum rule [5], only q can be varied. Thus IMFPs were also derived for one configuration (ain ¼ 55 and aout ¼ 25) from our measurements using ChenÕs data for the surface correction of the Si intensity and from the formula TPP-2M assuming that the density of the material was 3.0 g/ cm3 . These results are shown in Table 4. We see now that the agreement between the IMFPs from TPP-2M and from our measurements is much better. Unfortunately, we have no any independent test of whether the density of the surface layer deviated from the nominal bulk value. 5. Conclusions EPES measurements were carried out for SiO2 and Si3 N4 using a Si reference in the energy range of 300–2000 eV. We derived effective IMFPs from MC simulations after correcting the intensity of the Si elastic peak for surface excitations from the data of Chen [10]. For SiO2 and Si3 N4 , surface excitations were neglected. 1. The effective IMFPs of SiO2 were found to be similar to bulk IMFPs except at 300 eV. 2. Si3 N4 did not show a band gap. A systematic difference between the effective IMFPs and the bulk values were found assuming the nominal bulk density of Si3 N4 .
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