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Instrumental function of the SPECS XPS system
Nuclear Instruments and Methods in Physics Research B xxx (2017) xxx–xxx
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Instrumental function of the SPECS XPS system Maja Popovic´, Jelena Potocˇnik, Nenad Bundaleski ⇑, Zlatko Rakocˇevic´ University of Belgrade, INS VINCˇA, Mike Petrovic´a Alasa 12-14, 11351 Belgrade, Serbia
a r t i c l e
i n f o
Article history: Received 23 January 2017 Received in revised form 24 February 2017 Accepted 24 February 2017 Available online xxxx Keywords: XPS Electron spectroscopy Instrumental function Energy resolution Deconvolution Valence band maximum
a b s t r a c t A simple method for the energy resolution measurement of a spectrometer, working in the fixed analyser transmission mode, is proposed and used to determine the resolution of a SPECS Phoibos 100 spectrometer, being a part of an X-ray Photoelectron Spectroscopy (XPS) setup. The spectrometer resolution was obtained from the O 1s photoelectron line profiles, taken from the oxidized boron-doped silicon single crystal vs. the analyzer pass energy. The measurements were performed for two entrance slits having respective widths of 1 mm and 7 mm. An excellent agreement with the theoretical expectations was obtained for the narrower slit, showing linear dependence on the pass energy. As for the wider slit, agreement with theory is achieved only for lower pass energies. At higher pass energies, the resolution shows non-linear behaviour and even saturation, while the analyzer transmission continues to grow. The instrumental function of the whole XPS system is determined as a convolution of the spectrometer instrumental function and the X-ray energy profile. The usefulness of the total instrumental function for the analysis of valence band spectra was also tested. For that purpose, a novel deconvolution procedure is introduced, giving a possibility to analytically calculate the position of the valence band maximum, providing excellent agreement in the case of high resolution spectra. When the valence band spectra are taken in lower resolution, deconvolution efficiently reduces the spectrum deviations due to the lower resolution, although the valence band maximum determination is less precise. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction X-ray Photoelectron Spectroscopy (XPS) is nowadays probably the most widely used surface sensitive analytical technique. Due to its unique property to provide both quantitative composition analysis and information on the chemical bonds even for the non-conductive and biological samples, it became equally popular as a common tool for material characterization [1,2]. However, the interpretation of XPS spectra, based on the fitting of characteristic photoelectron lines, is far from straight forward. Although there are some attempts to make an expert system for the XPS data analysis (cf. [3] for instance), this complicated task is still mainly done by specialists, being strongly dependent on their overall skills and knowledge. Regardless the way of performing XPS spectra analysis, knowing energy resolution and other instrumental effects (detector linearity, transmission function, to mention the most important) is essential for proper data interpretation, just as it is
⇑ Corresponding author at: CEFITEC, Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, P-2829-516, Campus de Caparica, Caparica, Portugal. E-mail address: [email protected] (N. Bundaleski).
for the optimal choice of the spectrometer parameters during the spectra acquisition. Spectra acquisition in modern XPS systems is performed by hemispherical energy analyser operated in the fixed analyser transmission (FAT) mode. In this working mode of the spectrometer, the energy of electrons Ee is being decreased along the trajectory towards the detector: their kinetic energy is Ek at the moment of emission, and then becomes reduced to Ee = Epass while travelling along the optical axis of the analyser. Choice of the pass energy Epass is a common way of tuning the spectrometer energy resolution. Information on instrument properties, mainly energy resolution, is necessary for making XPS measurements efficient: there is no point in increasing the energy resolution (by reducing Epass) and consequently decreasing the analyser transmission if the lines are significantly broader than the instrumental function. Additionally, concerning the data analysis when a photoelectron line is resolved in several contributions by a fitting procedure, the instrumental function width should be used as a lower limit for the width of any contribution. Knowledge of the instrumental function is particularly important when XPS is used to measure valence band with the main goal to determine the position of the valence band maximum [4]. In these measurements instrumental effects introduce a broadening and thereby shift the apparent valence band onset
http://dx.doi.org/10.1016/j.nimb.2017.02.071 0168-583X/Ó 2017 Elsevier B.V. All rights reserved.
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towards lower binding energies. The only way to partially overcome this systematic error would be to deconvolute the instrumental function from the measured spectra. Instrumental function of an XPS system represents a convolution of the instrumental function of an electron spectrometer, which can be very well described as a Gaussian [5], and the energy line profile of the X-ray source. The latter is typically considered to be Lorentzian, so that the instrumental function is expected to have Voigt profile. This is most probably the historical reason why pseudo-Voigt profiles are typically used for the fitting of photoelectron lines, apart from the fact that they work very well in practice. On the other hand, X-ray line profile in a SPECS XPS instrument with the monochromatic Al Ka X-ray source is actually a Gaussian, with a Full Width at Half Maximum (FWHM) equal to 167 meV [6]. Consequently, the instrumental function of this XPS system should also be a Gaussian with FWHM wXPS equal to the square root of the sum of squares of the FWHMs of the X-ray beam profile (wX) and the spectrometer instrumental function (wS):
wXPS ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w2X þ w2S :
ð1Þ
In this paper, we measure wS of the SPECS Phoibos 100 spectrometer for different pass energies and two entrance slits, with widths of 1 mm and 7 mm, respectively. This allows us to calculate the instrumental function of the whole XPS system, using the expression (1). Theoretical background and the corresponding experimental procedure for the measurement of wS are presented in the forthcoming section. The experimental results, which include determination of the overall resolution of the XPS system and their discussion, are given in Section 3. Finally, a simple deconvolution procedure is introduced and employed for the data processing of valence band spectra taken from an air exposed silicon single crystal in order to demonstrate the usefulness of the determined XPS instrumental function. 2. Energy resolution of a hemispherical energy analyser operated in FAT mode Relative energy resolution DE/E of a hemispherical energy analyser having the equilibrium trajectory radius R, and entrance and exit slit widths s1 and s2, is expressed in the frame of the 2nd order approximation as
DE s 1 þ s 2 a 2 ¼ þ ; E 4R 4
ð2Þ
where a is the analyser acceptance angle in the dispersive plane, and E is the energy of electrons travelling along the optical axis of the energy analyser [7]. The absolute resolution DE corresponds to FWHM of the spectrometer instrumental function, assuming it has triangular profile. However, the expression (2) works equally well for the Gaussian profile [8]. Therefore, it is still valid to a very good approximation for an analyser operating in FAT regime when E and DE are replaced by Epass and wS, respectively. Let us now consider a photoelectron line taken by the SPECS XPS system that can be fitted to a single Voigt profile, the latter being a convolution of a Lorentzian and a Gaussian with respective widths wL and wG. Lorentzian component would then originate exclusively from the energy distribution, whilst the Gaussian is a convolution of the energy distribution component and the instrumental function of the XPS system having FWHMs wN and wXPS, respectively. Therefore, the Gaussian component of the measured line represents a convolution of three Gaussians having widths wN, wX and wS. Our Phoibos spectrometer does not have the exit slit. Its SPECS 2D CCD detector system consists of two multi-channel plates mounted in a chevron assembly, a fast P43 phosphor screen and
a 12 bit CCD camera. Since the magnitude s2 represents the camera resolution, being about 0.04 mm [9], its value in expression (2) can be readily neglected. In this case wS EpassS, where S = s1/(4R) + a2/4. Finally, the width of the Gaussian component wG can be expressed as wG = (w2N + w2X + E2passS2)1/2. Therefore, w2G should be directly proportional to E2pass, with the slope S2:
w2G ¼ C þ S2 E2pass ;
ð3Þ
where C = w2N + w2X does not depend on Epass. Even if, due to any circumstance, the dependence in some range of Epass is not linear, the change of wG with Epass would still correspond only to wS. In that case, S can be readily calculated as
S¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w2G C Epass
;
ð4Þ
where C is obtained from fitting of the w2G(E2pass) linear part dependence to the Eq. (3). In any case, once S is known, the instrumental function of the XPS system will be fully determined. It was assumed so far that s1 equals the entrance slit width, which is generally not correct. The process of electron transport from the sample to the entrance in the energy analyser is schematically presented in Fig. 1. A spectrometer working in the FAT mode is tuned to pass through along the analyser optical axis only electrons emitted with an energy Ee = Ek. The sample area from which the photoelectrons that can reach the detector are emitted, here denoted as emitting area, represents a cross-section of the area irradiated by X-rays and the acceptance area of the spectrometer (cf. Fig. 1a). The size of the emitting area is characterized by its characteristic dimension r0. A solid angle in which the electrons with the kinetic energy Ek have to be emitted in order to reach the detector is determined by the opening angle a0. The emitting area is an object for the electron-optical column situated between the sample and the entrance slit of the energy analyser, as shown in Fig. 1b. The electron optics decelerates electrons from their initial energy Ek to Epass, and forms an image onto the entrance slit plane (cf. Fig. 1c). This image is characterized by its size i.e. linear dimension r, and the maximum opening angle of trajectories of electrons reaching the detector. The latter is actually the analyser acceptance angle, a. One of the main characteristics of the electron-optical system are its linear Mr = r/r0 and angular Ma = a/a0 magnifications. If the image size is larger than the entrance slit width, we may safely consider s1 as the entrance slit width; otherwise, s1 = Mrr0 [10,11]. According to the Liouville’s theorem applied to the beam of charged particles, the product of the linear and the angular magnification equals the square root of the retardation ratio: MrMa = (Ek/ Epass)1/2 [10–12]. Hence, the change of the retardation ratio could strongly influence the image size, r. In that case, s1 in Eq. (2) will not be a constant when the retardation ratio is sufficiently low. Consequently, the parameter S will not be independent on Epass either; its value will be lower than expected (under the assumption s1 equals the entrance slit width), and the spectrometer resolution wS = SEpass will be improved. At the same time, the angular magnification will not affect the energy resolution since the acceptance angle is independent on Epass i.e. a const. Reduction of Ma will actually increase a0, and therefore enhance the spectrometer transmission. The theoretical considerations presented so far imply that experimental determination of the parameter S is straight forward: one should measure a profile of a photoelectron line for different FAT modes and perform the above described data analysis. However, there are several conditions that a convenient photoelectron line has to fulfil:
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Fig. 1. General scheme of the electron transport from the sample to the entrance slit in a XPS setup: (a) details in the vicinity of the sample surface; (b) overall view; (c) details in the vicinity of the entrance slit plane.
(1) The line has to be intensive, symmetric, narrow, and perfectly fitted to a single Voigt profile. This condition automatically eliminates metallic samples, having asymmetric photoelectron lines. Choice of a narrow line will increase sensitivity to the instrumental broadening. (2) Knowing that the background removal in XPS is not very well established, the change of the line background should be as small as possible with respect to the line intensity. In that case influence of the background definition on the fitting result would be negligible. (3) The sample should be conductive i.e. the line profile should not be affected by the charging effects. (4) There should not be any additional lines in the spectrum close to the considered line. (5) The sample should be flat, with low roughness, which potentially introduces line broadening and consequently reduces the sensitivity to the instrumental broadening. Although some of the above stated conditions contradict each other, there are samples and corresponding photoelectron lines that fulfil very well all of them. One excellent example appears to be O 1s line measured from the naturally oxidized, doped Si sample. The oxide layer is very thin, so that the background does not change much in the vicinity of the O 1s line. Due to the same reason, eventual charging effects should be negligible. Since the O 1s line is not very sensitive to different Si-oxide phases, it should be situated at about 532.8 eV [13], the line consists practically of a single symmetric contribution that should very well fit to a Voigt profile. Ion sputtering should be avoided when preparing the sample, since it will most probably introduce surface roughness and dramatically reduce the oxygen signal.
3. Experimental determination of the instrumental function The experimental determination of the instrumental function was performed from the measurements of the O 1s line taken from the as-received boron-doped Si(100) single crystal sample manu-
factured by Wafer Works Corp. Helitek Company Ltd. The sample was cleaned with acetone in ultrasonic bath and rinsed with 18.2 MO deionised water. The crystal was then dried, and introduced into the fast-entry load lock of the XPS setup. The most important parts of the SPECS XPS system are the dual Al Ka/Ag La X-ray source XR 50 with Focus 500 monochromator, PHOIBOS 100 hemispherical energy analyser with the electronoptical column for electron retardation, FG 15/40 electron flood gun for the charge compensation and IQE 12/38 sputter ion gun. All measurements have been performed in the medium area transmission mode (acceptance area of about 2 mm in diameter and the estimated analyser acceptance angle a 8°), using two entrance slits with the respective widths of 1 mm and 7 mm [14]. The spectra of the O 1 s line were taken with pass energies in the range from 3 eV to 100 eV. Since eventual non-linearity could affect the influence of the line profile measured for different Epass, the dynamic properties of the detection system were previously experimentally studied. It appeared that the signal is perfectly linear in the intensity range of interest i.e. up to 80,000 cps. The main lines of silicon, oxygen and carbon, the latter being a surface impurity, were observed in the survey XPS spectrum. According to the quantitative composition analysis, the sample surface consists of 46% of Si, 30% of O and 24% of C. The binding energy shift due to modest charging, equal to 0.2 eV, was determined from the position of the Si 2p3/2 line of the pure silicon contribution, assuming it is situated at 99.4 eV [13]. Apart from the dominant silicon contribution, another one with Si 2p3/2 at 102.8 eV was attributed to SiOx (x 1.5) [15]. Although most of the carbon can be attributed to saturated hydrocarbons at about 284.8 eV, there is some amount of carbon bound as C-OH. Fortunately, C-OH contribution in the O 1s line is also expected to be situated very close to that of SiOx, at about 532.7 eV [16] (after a correction for the C 1s reference position), which implies that this line should be most likely well described by a single Voigt line. Detailed XPS spectrum of the O 1s line taken in FAT 30 mode (Epass = 30 eV) with the 7 mm entrance slit is shown in Fig. 2. As expected, the background change in the vicinity of the line is very small with respect to its intensity. After the background removal
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Fig. 2. XPS spectrum of the O 1s line taken from the B-doped Si(100) single crystal in FAT 30 mode with the 7 mm entrance slit, and the best fit to the Voigt profile.
using the Shirley algorithm, the line was fitted to a single Voigt profile having FWHMs of the Gaussian and Lorentzian components equal to wG = 1.49 eV and wL = 0.69 eV, respectively. It can be seen from Fig. 2 that an excellent agreement is obtained, which is also confirmed by the square of the correlation parameter R2 = 0.999. As a matter of fact, such small fitting errors were obtained for all pass energies and both entrance slits. As already discussed, putting wL as a fitting parameter is unphysical. Therefore, wL was treated as a free parameter only during the initial fitting of all spectra, performed in order to get its average value. The latter appears to be 0.52 eV. Then, the fittings were repeated while keeping wL fixed at 0.52 eV, which negligibly reduced the fitting quality. The shape of the O 1s line and the quality of fittings allow measuring the dependence of wG vs. Epass for both slits. The square of the Gaussian component FWHM w2G vs. E2pass in the case of the 1 mm slit is presented in Fig. 3. This dependence can be readily fitted to a linear function, with the exception of the points corresponding to the pass energies below 30 eV. From the slope of the fitting result, shown in the figure, the value of parameter S was found to be 0.00654. The calculated S using the Eq. (2), assuming that the angular spread is a = 8° and s1 = 1 mm, is 0.00737, being quite close to the experimental value. The result suggests that
Fig. 3. w2G vs. E2pass measured for the 1 mm entrance slit. Linear fit, presented as the dashed line, was performed for Epass > 20 eV.
the actual angular spread is somewhat lower, more precisely, around 7.3°. The fact that the points corresponding to Epass < 30 eV are below the line obtained by the linear fit, suggests that the angular spread is even smaller in the case of lower pass energies. Nevertheless, the obtained linear dependence and very good general agreement of the slope with the expected value is a clear confirmation that the proposed concept for the spectrometer resolution measurement is correct and applicable. In Fig. 4 we present w2G vs. E2pass dependence for the 7 mm slit (sample biasing voltage Ub = 0 V), having striking difference as compared to the one obtained for the 1 mm slit. Excellent linear dependence is achieved only for the 5–55 eV pass energy range. These points were used to perform a linear fit, also shown in the figure. For higher pass energies the width of the Gaussian component becomes saturated up to 90 eV, and then increases again. Similarly to the low pass energies in the case of the 1 mm slit, the experimental point for Epass = 3 eV also lies below the line obtained from the fit. The value of the parameter S, obtained from the line slope in Fig. 4, is 0.02514. This is in excellent agreement with the expected value 0.02544, obtained using Eq. (2) with a = 8° and s1 = 7 mm. Significant reduction of wG with respect to the expected linear dependence at higher pass energies is most probably related to the decrease of the emitting surface image in the entrance slit plane for smaller retardation ratios, as already elaborated in the previous section. Linear magnification of the electron-optical column is reduced with the retardation ratio, according to the Liouville’s theorem, so that the image of the emitting surface becomes smaller than the entrance slit. Consequently, the analyser resolution is higher than expected. This interpretation is supported by the fact that this effect did not take place for the much narrower 1 mm entrance slit. Influence of the retardation ratio on the energy resolution actually means that wS can depend on the kinetic energy of emitted electrons Ek even when it is measured in the FAT mode. The result in Fig. 4 is therefore not universal: it is only valid for Ek = 954 eV, corresponding to the O 1s photoelectrons excited by Al Ka Xrays. The energy resolution is directly proportional to Epass only for the retardation ratios greater than b = 954 eV/55 eV 17.3. The spectrometer resolution for lower retardation ratio depends on the focusing properties of the electron-optical column.
Fig. 4. w2G vs. E2pass measured for the 7 mm entrance slit when the sample is biased to 0 V, 300 V and +200 V. Linear fit, performed only for Epass 55 eV for the grounded sample, is presented by the dashed line.
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An apparently straight forward way for proving that the spectrometer resolution is Ek dependent would be to perform a similar set of measurements for a photoelectron line having different kinetic energy. Unfortunately, finding another suitable sample and line, fulfilling the conditions stated in Section 2, is not an easy task. Therefore, we performed two more sets of measurements on the same line with the sample biased to 200 V and 300 V. The biasing voltage Ub changes the kinetic energy of detected electrons. At the same time, the intensity of Ub was not too high in order to suppress eventual distortions of trajectories in-between the sample and the entrance into the electron-optical column. The fitting was performed in exactly the same way as for other measurements. The results, which are also presented in Fig. 4, clearly confirm the influence of the kinetic energy on the energy resolution. All three w2G(E2pass) sets of data follow the same linear dependence for low Epass. For the photoelectron kinetic energy increased to 1255 eV (Ub = 300 V), the Epass range in which the linear dependence is kept is increased up to 70 eV. This corresponds to b 17.9. In the case of electrons decelerated to 755 eV (Ub = 200 V), the linear dependence is preserved for Epass up to about 40 eV i.e. b 18.9. These measurements were performed with an Epass step of 10 eV, and here applied approach to determine b will always yield overestimated values. Therefore, we may safely state that the critical retardation ratio at which wS(Epass) dependence stops to be linear is around b 17.3, being independent of the electron kinetic energy in the frame of the experimental error. When the retardation ratio is below the critical one, w2G(E2pass) has a qualitative behaviour independent of the kinetic energy: the resolution reaches saturation for Epass Ek/b, and then increases further for the highest pass energies. The saturation of the spectrometer resolution as a function of the pass energy will be reached already at Epass = 27 eV in the case of the Zn 2p3/2 line and even at Epass = 11 eV in the case of the Mg 1 s line (here we assumed that Al Ka line is used for the photoelectron excitation). Of course, it is not clear whether the linear dependence of wS(Ek) in the saturation region is valid for very small retardation ratio, in particular below 1, when the emitted electrons should be accelerated instead of decelerated. But, anyway, working in this regime is not of a wide interest, and it will not be further considered. The number of counts per second detected at the maximum of O 1s line vs. the pass energy, in the case of the wider entrance slit, is presented in Fig. 5. Since the X-ray power was kept constant, the
5
count rate growth is caused by the spectrometer transmission function increase with Epass for Ek = 954 eV. In spite of the energy resolution saturation at higher pass energies, the transmission monotonically increases with Epass. Experimentally observed non-linear dependence of wS on Epass contradicts one of the basic assumptions in the XPS instrumentation: when working in FAT regime the resolution is independent of the kinetic energy. When taking an energy spectrum in the FAT mode using the 7 mm slit, the energy resolution of the spectrometer will be constant and equal SEpass (S is obtained from the slope in Fig. 4) as long as Ek > bEpass. For lower kinetic energies, the resolution is approximately proportional to Ek: wS = SEk/b, unless Epass is too high. At the same time, the transmission of the spectrometer increases with the pass energy, as shown in Fig. 5. Therefore, this effect provides an opportunity to increase Epass and therefore increase the instrument sensitivity without considerable loss in energy resolution. This may be significant when analysing trace elements having characteristic photoelectron lines at low kinetic energies. Besides, it can be even more important when a very similar spectrometer Phoibos 150 is used in synchrotrons (cf. [17–19] for instance), where the photon energy is tuneable and frequently reduced to increase both photoelectron emission cross section and the surface sensitivity. Then, much wider part of the spectrum can be taken with the non-constant energy resolution although Epass is kept fixed. From the measured S (using the slope in the case of the linear dependence in Figs. 3 and 4, or Eq. (4)) the spectrometer instrumental function can be obtained as wS = SEpass. Then, the instrumental function of the whole XPS system is a Gaussian with FWHM calculated by Eq. (1) with wX = 0.167 eV. The result of the wXPS vs. Epass for both slits is shown in Fig. 6. For Epass < 30 eV in the case of the 1 mm slit we also assumed linear dependence, which somewhat overestimates wS. However, in this Epass range the instrumental function width is dominated by wX, so that the introduced error is minor. While the presented wXPS is correct for any kinetic energy when 1 mm entrance slit is used, the result corresponds solely to Ek = 954 eV in the case of the 7 mm slit. However, since the saturation of wXPS for higher pass energies always takes place at Epass = Ek/b, wXPS (Epass) can be simply estimated for any kinetic energy. If S does not depend on the pass energy and wX is negligible, wXPS would be directly proportional to Epass. This linear dependence is also presented in Fig. 6 for both slits. As expected, the width of the XPS instrumental function is dominated by the spectrometer function at higher pass energies, while the relative contribution of wX becomes more significant for low Epass. This is observed as the deviation from the linear dependence for low Epass, which becomes noticeable for Epass < 15 eV for the 7 mm slit, but even at Epass < 70 eV for the 1 mm slit. Knowing that the photoelectron lines practically never have widths smaller than 0.5 eV, it is clear that 1 mm slit provides ‘too good’ resolution and consequently, unnecessary low transmission for the XPS measurements. As for the 7 mm slit, working with Epass = 20 eV appears to be a good first choice for the high resolution spectroscopy of photoelectron lines, which fully supports the usual experimental practice by different workers. As for the survey XPS spectra, working with the pass energy of 40 eV, providing the resolution of about 1 eV, seems to be suitable.
4. Deconvolution of the valence band
Fig. 5. O 1s line height, taken with the 7 mm entrance slit, as a function of the pass energy.
Once the instrumental function of the XPS system is known, it can be used to determine the actual energy distribution of emitted photoelectrons by its deconvolution from the spectrum. As already discussed, this task is particularly significant in the case of the
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Fig. 6. Instrumental function width of the whole XPS instrument for entrance slits widths of (a) 1 mm and (b) 7 mm. The result for the 7 mm slit is valid only for the O 1s line i.e. for Ek = 954 eV. Dashed line corresponds to the spectrometer contribution to the overall width wXPS, assuming wS Epass.
valence band maximum determination. Valence band spectra are typically measured on a similar setup, using UV photons. An efficient deconvolution procedure could allow similar kind of measurements on XPS systems, which are much more common. Since in most cases deconvolution cannot be performed analytically, numerical processing of the raw data has to be performed, which is far from straight forward. Here we introduce a simple deconvolution procedure, which can be implemented to any spectrum when the instrumental function has a Gaussian profile. It is based on two well-known properties of the convolution operation: its linearity and the fact that a convolution of two Gaussians of widths w1 and w2 is a Gaussian having width w = (w21 + w22)1/2. The proposed algorithm consists of two steps. Firstly, a spectrum is fitted to an arbitrary sum of Gaussians Gi, after the background removal. These Gaussians do not have any physical meaning. Since the only aim is to get a good fit of the experimental data, the overall number of Gaussians is irrelevant. Moreover, some of them can even have negative intensity. The only condition each Gaussian in the sum has to fulfil is that its width wi is greater than the width of the corresponding instrumental function wXPS. In the second step, the deconvolution is performed by deconvoluting the instrumental function from each of the superimposed Gaussians in the sum. That way, each Gaussian Gi is transformed into Gaussian G0i , having width w0i = (w2i w2XPS)1/2. The position and intensity (area) of the Gaussians are unchanged. The deconvoluted spectrum is the superposition of the newly formed Gaussians, G0i . Once the deconvolution is performed, the valence band maximum with respect to the Fermi level Ev, can be determined from the width w0m , and the position Em of the Gaussian G0m closest to the Fermi level. Ev should correspond to the energy at which G0m drops to zero, which may be written to a very good approximation as
Ev ¼ Em 3 r0m :
ð5Þ
The parameter r0m = w0m /(8ln2)1/2 w0m /2.355 is the standard deviation of the Gaussian G0m . The valence band of the as-received silicon sample was measured in FAT 20 and FAT 60 modes using 7 mm wide entrance slit, in order to test usefulness of the XPS instrumental functions and of the proposed deconvolution procedure. Since the retardation ratio for the valence band measurements significantly exceeds the critical one (b 17.3) for both FAT modes, wS is directly proportional to Epass, with the proportionality constant S experimentally determined in the previous section. The valence band spectrum taken in FAT 20 mode, and its fit to the sum of 9 Gaussians, are shown in Fig. 7. The background was calculated using the Shirley algorithm. These Gaussians are then transformed into narrower ones after deconvoluting the XPS instrumental function. The superposi-
Fig. 7. XPS spectrum of the valence band of as-received boron-doped Si(100) single crystal taken in the FAT 20 mode: raw experimental data, fit to the sum of Gaussians, and the deconvolution result.
tion of the narrowed Gaussians represents the deconvoluted spectrum, also shown in the figure. The deconvoluted spectrum practically overlaps with the measured one, which is due to the FWHMs of Gaussians used to fit the spectrum. Their widths in the range 1.3–3.7 eV are too large to be significantly affected by a deconvolution with the instrumental function having wXPS = 0.53 eV. Position of the valence band maximum Ev was determined from 0 the position and the width of the Gaussian Gm with the position closest to EF, using the expression (5). The procedure for determining the position of the valence band maximum is summarized in Table 1. The valence band maximum appears to be at Ev 0 eV, which is fully in accordance with the expectations: since the doped silicon sample is of P-type, the valence band maximum is expected to be almost at the Fermi level. Therefore, small discrepancy between the deconvoluted spectrum and the raw data, observed
Table 1 Calculation of the valence band maximum position from the deconvoluted valence band spectra. Epass (eV)
Em (eV)
wm (eV)
wXPS (eV)
w0m (eV)
r0m (eV)
Ev (eV)
20 60
1.651 2.398
1.408 2.701
0.530 1.436
1.304 2.289
0.554 0.972
0.011 0.518
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Fig. 8. Normalized XPS spectra of the valence band of as-received boron-doped Si(100) single crystal taken in the FAT 20 and FAT 60 modes: (a) raw experimental data and (b) after the deconvolution.
in Fig. 7, is justified. It also shows that the measured spectrum practically corresponds to the electron energy distribution. In contrast to the result obtained in FAT 20 mode, the valence band spectrum measured with pass energy of 60 eV is expected to be much more influenced by the deconvolution procedure, since wXPS = 1.44 eV. In Fig. 8, we compare the normalized valence band spectra taken in FAT 20 and FAT 60 modes (a) before, and (b) after deconvoluting the instrumental functions. The discrepancy between the two spectra in Fig. 8a is mainly due to the low energy resolution in the FAT 60 mode. In theory, the disagreement should be suppressed by the deconvolution of the instrumental function. As can be seen from Fig. 8b, this was actually achieved: the general agreement between the deconvoluted spectra is excellent with the exception of the feature at about 15 eV. The latter could be due to its proximity to the boundary of the range considered for fitting, or related to the background removal. This is an indirect proof that the width of the instrumental function determined in the previous section and the proposed deconvolution procedure are both sound and very useful, although generally approximate. The latter is manifested from the calculation of Ev from the deconvoluted spectrum measured in FAT 60 mode (cf. Table 1). The obtained result, Ev = 0.45 eV, which can be also seen from Fig. 8b, is unphysical and points out that the procedure is of limited reliability when speaking of spectrum details. The result can be certainly improved by modifying the fitting procedure, such as increasing the number of Gaussians and reducing their widths. But our aim here is to emphasize the strong points of the procedure in its present form, as well as its weaknesses.
5. Conclusion A simple experimental procedure to measure the instrumental function width of the SPECS XPS system operating in fixed analyser transmission mode is introduced and validated. The key point in the proposed approach is the choice of the photoelectron line and the sample. O1s line originating from a thin oxide layer of doped silicon single crystal appears to be highly suitable for this purpose. While the spectrometer resolution measurements for the 1 mm entrance slit are in accordance with expectations, this was definitely not the case for the 7 mm slit. Saturation of wS at higher Epass, which means that the energy resolution is higher than expected, can be qualitatively explained from the basic principles of electron optics by applying Louiville’s theorem. The direct consequence of this saturation is that the resolution is generally not constant even when the spectrometer is operated in FAT mode: in the case of kinetic energies lower than bEpass, it is roughly proportional to Ek. It should be stressed that, while the resolution is
saturated, the transmission continues to grow with the pass energy. This is potentially of interest when detecting low intensity lines (of trace elements, for instance) having low Ek, but also in the case of photoelectron measurements with tuneable X-ray sources i.e. in synchrotrons. In order to test the usefulness of the determined instrumental functions, we applied them to the deconvolution of valence band spectra. For that purpose we propose a simple deconvolution scheme providing analytical result in the form of a set of superimposed Gaussians. Therefore, the Gaussian situated closest to the Fermi level can be used to calculate the position of the valence band maximum. The deconvolution procedure with the predetermined instrumental functions gives very good results: the shapes of the deconvoluted spectra are apparently identical. However, when the spectra are measured with low resolution, the procedure in its present form is not reliable enough to provide a precise value of Ev. Acknowledgement This work was financially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia; project no. III 45005. References [1] J.F. Watts, J. Wolstenhome, An Introduction to Surface Analysis by XPS and AES, John Wiley & Sons Ltd., Chichester UK, 2003. [2] A. Jablonski, Quantification of surface-sensitive electron spectroscopies, Surf. Sci. 603 (2009) 1342–1352. [3] M. Mohai, XPS MultiQuant for Windows Users’ Manual, Version 7.0, http://aki. ttk.mta.hu/XMQpages/XMQhome.htm, 2011 (accessed February 2017). [4] E.A. Kraut, R.W. Grant, J.R. Waldrop, S.P. Kowalczyk, Semiconductor core-level to valence-band maximum binding-energy differences: precise determination by x-ray photoelectron spectroscopy, Phys. Rev. B 28 (1983) 1965–1977. [5] F.R. Paolini, G.C. Theodoridis, Charged particle transmission through spherical plate electrostatic analyzers, Rev. Sci. Instrum. 38 (1967) 579–588. [6] X-ray Source for Focus 500, XR-50 M, SPECS User Manual, 2014. [7] H. Wollnik, Electrostatic prisms, in: A. Septier (Ed.), Focusing of Charged Particles, vol. 2, Academic press, New York, 1967, ch. 4.1. [8] N. Bundaleski, Z. Ristic´, M. Radovic´, Z. Rakocˇevic´, Influence of the primary ion beam profile and the energy analyzer optics to the LEIS spectra: the analytical study, Nucl. Instrum. Methods Phys. Res. B 237 (2005) 613–622. [9] 2D CCD Detector, Version 2.0, SPECS User Manual, 2014. [10] E.H.A. Granneman, M.J. van der Wiel, Transport, dispersion and detection of electrons, ions and neutrals, in: D.E. Eastman, Y. Farge, E.E. Koch (Eds.), Handbook on Synchrotron Radiation, vol. 1, FOM, Amsterdam, 1979 (Ch. 6). [11] M. Yavor, Optics of Charged Particle Analyzers, Elsevier, 2009. [12] S. Humphries Jr., Charged Particle Beams, John Wiley & Sons Inc., 2002. [13] C.D. Wagner, A.V. Naumkin, A. Kraut-Vass, J.W. Allison, C.J. Powell, J.R.Jr. Rumble, NIST Standard Reference Database 20, Version 3.4, http://srdata. nist.gov/xps/, 2012 (Accessed December 2016). [14] PHOIBOS 100/150 – Hemispherical Energy Analyzer, Version 4.0, SPECS User Manual, 2014. [15] R. Alfonsetti, L. Lozzi, M. Passacantando, P. Picozzi, S. Santucci, XPS studies on SiOx thin films, Appl. Surf. Sci. 70 (71) (1993) 222–225.
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[16] G. Beamson, D. Briggs, High Resolution XPS of Organic Polymers – The Scienta ESCA300 Database, Wiley Interscience, New York, 1992. [17] J. Schnadt, J. Knudsen, J.N. Andersen, H. Siegbahn, A. Pietzsch, F. Hennies, N. Johansson, N. Mårtensson, G. Öhrwall, S. Bahr, S. Mähl, O. Schaff, The new ambient-pressure X-ray photoelectron spectroscopy instrument at MAX-lab, J. Synchrotron Radiat. 19 (2012) 701–704.
[18] Australian synchrotron soft X-ray technical information, available at http:// www.synchrotron.org.au/aussyncbeamlines/soft-x-ray-spectroscopy/ technical-information (accessed December 2016). [19] D.E. Starr, Z. Liu, M. Hävecker, A. Knop-Gericke, H. Bluhm, Investigation of solid/vapor interfaces using ambient pressure X-ray photoelectron spectroscopy, Chem. Soc. Rev. 42 (2013) 5833–5857.
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Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Instrumental function of the SPECS XPS system Maja Popovic´, Jelena Potocˇnik, Nenad Bundaleski ⇑, Zlatko Rakocˇevic´ University of Belgrade, INS VINCˇA, Mike Petrovic´a Alasa 12-14, 11351 Belgrade, Serbia
a r t i c l e
i n f o
Article history: Received 23 January 2017 Received in revised form 24 February 2017 Accepted 24 February 2017 Available online xxxx Keywords: XPS Electron spectroscopy Instrumental function Energy resolution Deconvolution Valence band maximum
a b s t r a c t A simple method for the energy resolution measurement of a spectrometer, working in the fixed analyser transmission mode, is proposed and used to determine the resolution of a SPECS Phoibos 100 spectrometer, being a part of an X-ray Photoelectron Spectroscopy (XPS) setup. The spectrometer resolution was obtained from the O 1s photoelectron line profiles, taken from the oxidized boron-doped silicon single crystal vs. the analyzer pass energy. The measurements were performed for two entrance slits having respective widths of 1 mm and 7 mm. An excellent agreement with the theoretical expectations was obtained for the narrower slit, showing linear dependence on the pass energy. As for the wider slit, agreement with theory is achieved only for lower pass energies. At higher pass energies, the resolution shows non-linear behaviour and even saturation, while the analyzer transmission continues to grow. The instrumental function of the whole XPS system is determined as a convolution of the spectrometer instrumental function and the X-ray energy profile. The usefulness of the total instrumental function for the analysis of valence band spectra was also tested. For that purpose, a novel deconvolution procedure is introduced, giving a possibility to analytically calculate the position of the valence band maximum, providing excellent agreement in the case of high resolution spectra. When the valence band spectra are taken in lower resolution, deconvolution efficiently reduces the spectrum deviations due to the lower resolution, although the valence band maximum determination is less precise. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction X-ray Photoelectron Spectroscopy (XPS) is nowadays probably the most widely used surface sensitive analytical technique. Due to its unique property to provide both quantitative composition analysis and information on the chemical bonds even for the non-conductive and biological samples, it became equally popular as a common tool for material characterization [1,2]. However, the interpretation of XPS spectra, based on the fitting of characteristic photoelectron lines, is far from straight forward. Although there are some attempts to make an expert system for the XPS data analysis (cf. [3] for instance), this complicated task is still mainly done by specialists, being strongly dependent on their overall skills and knowledge. Regardless the way of performing XPS spectra analysis, knowing energy resolution and other instrumental effects (detector linearity, transmission function, to mention the most important) is essential for proper data interpretation, just as it is
⇑ Corresponding author at: CEFITEC, Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, P-2829-516, Campus de Caparica, Caparica, Portugal. E-mail address: [email protected] (N. Bundaleski).
for the optimal choice of the spectrometer parameters during the spectra acquisition. Spectra acquisition in modern XPS systems is performed by hemispherical energy analyser operated in the fixed analyser transmission (FAT) mode. In this working mode of the spectrometer, the energy of electrons Ee is being decreased along the trajectory towards the detector: their kinetic energy is Ek at the moment of emission, and then becomes reduced to Ee = Epass while travelling along the optical axis of the analyser. Choice of the pass energy Epass is a common way of tuning the spectrometer energy resolution. Information on instrument properties, mainly energy resolution, is necessary for making XPS measurements efficient: there is no point in increasing the energy resolution (by reducing Epass) and consequently decreasing the analyser transmission if the lines are significantly broader than the instrumental function. Additionally, concerning the data analysis when a photoelectron line is resolved in several contributions by a fitting procedure, the instrumental function width should be used as a lower limit for the width of any contribution. Knowledge of the instrumental function is particularly important when XPS is used to measure valence band with the main goal to determine the position of the valence band maximum [4]. In these measurements instrumental effects introduce a broadening and thereby shift the apparent valence band onset
http://dx.doi.org/10.1016/j.nimb.2017.02.071 0168-583X/Ó 2017 Elsevier B.V. All rights reserved.
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towards lower binding energies. The only way to partially overcome this systematic error would be to deconvolute the instrumental function from the measured spectra. Instrumental function of an XPS system represents a convolution of the instrumental function of an electron spectrometer, which can be very well described as a Gaussian [5], and the energy line profile of the X-ray source. The latter is typically considered to be Lorentzian, so that the instrumental function is expected to have Voigt profile. This is most probably the historical reason why pseudo-Voigt profiles are typically used for the fitting of photoelectron lines, apart from the fact that they work very well in practice. On the other hand, X-ray line profile in a SPECS XPS instrument with the monochromatic Al Ka X-ray source is actually a Gaussian, with a Full Width at Half Maximum (FWHM) equal to 167 meV [6]. Consequently, the instrumental function of this XPS system should also be a Gaussian with FWHM wXPS equal to the square root of the sum of squares of the FWHMs of the X-ray beam profile (wX) and the spectrometer instrumental function (wS):
wXPS ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w2X þ w2S :
ð1Þ
In this paper, we measure wS of the SPECS Phoibos 100 spectrometer for different pass energies and two entrance slits, with widths of 1 mm and 7 mm, respectively. This allows us to calculate the instrumental function of the whole XPS system, using the expression (1). Theoretical background and the corresponding experimental procedure for the measurement of wS are presented in the forthcoming section. The experimental results, which include determination of the overall resolution of the XPS system and their discussion, are given in Section 3. Finally, a simple deconvolution procedure is introduced and employed for the data processing of valence band spectra taken from an air exposed silicon single crystal in order to demonstrate the usefulness of the determined XPS instrumental function. 2. Energy resolution of a hemispherical energy analyser operated in FAT mode Relative energy resolution DE/E of a hemispherical energy analyser having the equilibrium trajectory radius R, and entrance and exit slit widths s1 and s2, is expressed in the frame of the 2nd order approximation as
DE s 1 þ s 2 a 2 ¼ þ ; E 4R 4
ð2Þ
where a is the analyser acceptance angle in the dispersive plane, and E is the energy of electrons travelling along the optical axis of the energy analyser [7]. The absolute resolution DE corresponds to FWHM of the spectrometer instrumental function, assuming it has triangular profile. However, the expression (2) works equally well for the Gaussian profile [8]. Therefore, it is still valid to a very good approximation for an analyser operating in FAT regime when E and DE are replaced by Epass and wS, respectively. Let us now consider a photoelectron line taken by the SPECS XPS system that can be fitted to a single Voigt profile, the latter being a convolution of a Lorentzian and a Gaussian with respective widths wL and wG. Lorentzian component would then originate exclusively from the energy distribution, whilst the Gaussian is a convolution of the energy distribution component and the instrumental function of the XPS system having FWHMs wN and wXPS, respectively. Therefore, the Gaussian component of the measured line represents a convolution of three Gaussians having widths wN, wX and wS. Our Phoibos spectrometer does not have the exit slit. Its SPECS 2D CCD detector system consists of two multi-channel plates mounted in a chevron assembly, a fast P43 phosphor screen and
a 12 bit CCD camera. Since the magnitude s2 represents the camera resolution, being about 0.04 mm [9], its value in expression (2) can be readily neglected. In this case wS EpassS, where S = s1/(4R) + a2/4. Finally, the width of the Gaussian component wG can be expressed as wG = (w2N + w2X + E2passS2)1/2. Therefore, w2G should be directly proportional to E2pass, with the slope S2:
w2G ¼ C þ S2 E2pass ;
ð3Þ
where C = w2N + w2X does not depend on Epass. Even if, due to any circumstance, the dependence in some range of Epass is not linear, the change of wG with Epass would still correspond only to wS. In that case, S can be readily calculated as
S¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w2G C Epass
;
ð4Þ
where C is obtained from fitting of the w2G(E2pass) linear part dependence to the Eq. (3). In any case, once S is known, the instrumental function of the XPS system will be fully determined. It was assumed so far that s1 equals the entrance slit width, which is generally not correct. The process of electron transport from the sample to the entrance in the energy analyser is schematically presented in Fig. 1. A spectrometer working in the FAT mode is tuned to pass through along the analyser optical axis only electrons emitted with an energy Ee = Ek. The sample area from which the photoelectrons that can reach the detector are emitted, here denoted as emitting area, represents a cross-section of the area irradiated by X-rays and the acceptance area of the spectrometer (cf. Fig. 1a). The size of the emitting area is characterized by its characteristic dimension r0. A solid angle in which the electrons with the kinetic energy Ek have to be emitted in order to reach the detector is determined by the opening angle a0. The emitting area is an object for the electron-optical column situated between the sample and the entrance slit of the energy analyser, as shown in Fig. 1b. The electron optics decelerates electrons from their initial energy Ek to Epass, and forms an image onto the entrance slit plane (cf. Fig. 1c). This image is characterized by its size i.e. linear dimension r, and the maximum opening angle of trajectories of electrons reaching the detector. The latter is actually the analyser acceptance angle, a. One of the main characteristics of the electron-optical system are its linear Mr = r/r0 and angular Ma = a/a0 magnifications. If the image size is larger than the entrance slit width, we may safely consider s1 as the entrance slit width; otherwise, s1 = Mrr0 [10,11]. According to the Liouville’s theorem applied to the beam of charged particles, the product of the linear and the angular magnification equals the square root of the retardation ratio: MrMa = (Ek/ Epass)1/2 [10–12]. Hence, the change of the retardation ratio could strongly influence the image size, r. In that case, s1 in Eq. (2) will not be a constant when the retardation ratio is sufficiently low. Consequently, the parameter S will not be independent on Epass either; its value will be lower than expected (under the assumption s1 equals the entrance slit width), and the spectrometer resolution wS = SEpass will be improved. At the same time, the angular magnification will not affect the energy resolution since the acceptance angle is independent on Epass i.e. a const. Reduction of Ma will actually increase a0, and therefore enhance the spectrometer transmission. The theoretical considerations presented so far imply that experimental determination of the parameter S is straight forward: one should measure a profile of a photoelectron line for different FAT modes and perform the above described data analysis. However, there are several conditions that a convenient photoelectron line has to fulfil:
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Fig. 1. General scheme of the electron transport from the sample to the entrance slit in a XPS setup: (a) details in the vicinity of the sample surface; (b) overall view; (c) details in the vicinity of the entrance slit plane.
(1) The line has to be intensive, symmetric, narrow, and perfectly fitted to a single Voigt profile. This condition automatically eliminates metallic samples, having asymmetric photoelectron lines. Choice of a narrow line will increase sensitivity to the instrumental broadening. (2) Knowing that the background removal in XPS is not very well established, the change of the line background should be as small as possible with respect to the line intensity. In that case influence of the background definition on the fitting result would be negligible. (3) The sample should be conductive i.e. the line profile should not be affected by the charging effects. (4) There should not be any additional lines in the spectrum close to the considered line. (5) The sample should be flat, with low roughness, which potentially introduces line broadening and consequently reduces the sensitivity to the instrumental broadening. Although some of the above stated conditions contradict each other, there are samples and corresponding photoelectron lines that fulfil very well all of them. One excellent example appears to be O 1s line measured from the naturally oxidized, doped Si sample. The oxide layer is very thin, so that the background does not change much in the vicinity of the O 1s line. Due to the same reason, eventual charging effects should be negligible. Since the O 1s line is not very sensitive to different Si-oxide phases, it should be situated at about 532.8 eV [13], the line consists practically of a single symmetric contribution that should very well fit to a Voigt profile. Ion sputtering should be avoided when preparing the sample, since it will most probably introduce surface roughness and dramatically reduce the oxygen signal.
3. Experimental determination of the instrumental function The experimental determination of the instrumental function was performed from the measurements of the O 1s line taken from the as-received boron-doped Si(100) single crystal sample manu-
factured by Wafer Works Corp. Helitek Company Ltd. The sample was cleaned with acetone in ultrasonic bath and rinsed with 18.2 MO deionised water. The crystal was then dried, and introduced into the fast-entry load lock of the XPS setup. The most important parts of the SPECS XPS system are the dual Al Ka/Ag La X-ray source XR 50 with Focus 500 monochromator, PHOIBOS 100 hemispherical energy analyser with the electronoptical column for electron retardation, FG 15/40 electron flood gun for the charge compensation and IQE 12/38 sputter ion gun. All measurements have been performed in the medium area transmission mode (acceptance area of about 2 mm in diameter and the estimated analyser acceptance angle a 8°), using two entrance slits with the respective widths of 1 mm and 7 mm [14]. The spectra of the O 1 s line were taken with pass energies in the range from 3 eV to 100 eV. Since eventual non-linearity could affect the influence of the line profile measured for different Epass, the dynamic properties of the detection system were previously experimentally studied. It appeared that the signal is perfectly linear in the intensity range of interest i.e. up to 80,000 cps. The main lines of silicon, oxygen and carbon, the latter being a surface impurity, were observed in the survey XPS spectrum. According to the quantitative composition analysis, the sample surface consists of 46% of Si, 30% of O and 24% of C. The binding energy shift due to modest charging, equal to 0.2 eV, was determined from the position of the Si 2p3/2 line of the pure silicon contribution, assuming it is situated at 99.4 eV [13]. Apart from the dominant silicon contribution, another one with Si 2p3/2 at 102.8 eV was attributed to SiOx (x 1.5) [15]. Although most of the carbon can be attributed to saturated hydrocarbons at about 284.8 eV, there is some amount of carbon bound as C-OH. Fortunately, C-OH contribution in the O 1s line is also expected to be situated very close to that of SiOx, at about 532.7 eV [16] (after a correction for the C 1s reference position), which implies that this line should be most likely well described by a single Voigt line. Detailed XPS spectrum of the O 1s line taken in FAT 30 mode (Epass = 30 eV) with the 7 mm entrance slit is shown in Fig. 2. As expected, the background change in the vicinity of the line is very small with respect to its intensity. After the background removal
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Fig. 2. XPS spectrum of the O 1s line taken from the B-doped Si(100) single crystal in FAT 30 mode with the 7 mm entrance slit, and the best fit to the Voigt profile.
using the Shirley algorithm, the line was fitted to a single Voigt profile having FWHMs of the Gaussian and Lorentzian components equal to wG = 1.49 eV and wL = 0.69 eV, respectively. It can be seen from Fig. 2 that an excellent agreement is obtained, which is also confirmed by the square of the correlation parameter R2 = 0.999. As a matter of fact, such small fitting errors were obtained for all pass energies and both entrance slits. As already discussed, putting wL as a fitting parameter is unphysical. Therefore, wL was treated as a free parameter only during the initial fitting of all spectra, performed in order to get its average value. The latter appears to be 0.52 eV. Then, the fittings were repeated while keeping wL fixed at 0.52 eV, which negligibly reduced the fitting quality. The shape of the O 1s line and the quality of fittings allow measuring the dependence of wG vs. Epass for both slits. The square of the Gaussian component FWHM w2G vs. E2pass in the case of the 1 mm slit is presented in Fig. 3. This dependence can be readily fitted to a linear function, with the exception of the points corresponding to the pass energies below 30 eV. From the slope of the fitting result, shown in the figure, the value of parameter S was found to be 0.00654. The calculated S using the Eq. (2), assuming that the angular spread is a = 8° and s1 = 1 mm, is 0.00737, being quite close to the experimental value. The result suggests that
Fig. 3. w2G vs. E2pass measured for the 1 mm entrance slit. Linear fit, presented as the dashed line, was performed for Epass > 20 eV.
the actual angular spread is somewhat lower, more precisely, around 7.3°. The fact that the points corresponding to Epass < 30 eV are below the line obtained by the linear fit, suggests that the angular spread is even smaller in the case of lower pass energies. Nevertheless, the obtained linear dependence and very good general agreement of the slope with the expected value is a clear confirmation that the proposed concept for the spectrometer resolution measurement is correct and applicable. In Fig. 4 we present w2G vs. E2pass dependence for the 7 mm slit (sample biasing voltage Ub = 0 V), having striking difference as compared to the one obtained for the 1 mm slit. Excellent linear dependence is achieved only for the 5–55 eV pass energy range. These points were used to perform a linear fit, also shown in the figure. For higher pass energies the width of the Gaussian component becomes saturated up to 90 eV, and then increases again. Similarly to the low pass energies in the case of the 1 mm slit, the experimental point for Epass = 3 eV also lies below the line obtained from the fit. The value of the parameter S, obtained from the line slope in Fig. 4, is 0.02514. This is in excellent agreement with the expected value 0.02544, obtained using Eq. (2) with a = 8° and s1 = 7 mm. Significant reduction of wG with respect to the expected linear dependence at higher pass energies is most probably related to the decrease of the emitting surface image in the entrance slit plane for smaller retardation ratios, as already elaborated in the previous section. Linear magnification of the electron-optical column is reduced with the retardation ratio, according to the Liouville’s theorem, so that the image of the emitting surface becomes smaller than the entrance slit. Consequently, the analyser resolution is higher than expected. This interpretation is supported by the fact that this effect did not take place for the much narrower 1 mm entrance slit. Influence of the retardation ratio on the energy resolution actually means that wS can depend on the kinetic energy of emitted electrons Ek even when it is measured in the FAT mode. The result in Fig. 4 is therefore not universal: it is only valid for Ek = 954 eV, corresponding to the O 1s photoelectrons excited by Al Ka Xrays. The energy resolution is directly proportional to Epass only for the retardation ratios greater than b = 954 eV/55 eV 17.3. The spectrometer resolution for lower retardation ratio depends on the focusing properties of the electron-optical column.
Fig. 4. w2G vs. E2pass measured for the 7 mm entrance slit when the sample is biased to 0 V, 300 V and +200 V. Linear fit, performed only for Epass 55 eV for the grounded sample, is presented by the dashed line.
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An apparently straight forward way for proving that the spectrometer resolution is Ek dependent would be to perform a similar set of measurements for a photoelectron line having different kinetic energy. Unfortunately, finding another suitable sample and line, fulfilling the conditions stated in Section 2, is not an easy task. Therefore, we performed two more sets of measurements on the same line with the sample biased to 200 V and 300 V. The biasing voltage Ub changes the kinetic energy of detected electrons. At the same time, the intensity of Ub was not too high in order to suppress eventual distortions of trajectories in-between the sample and the entrance into the electron-optical column. The fitting was performed in exactly the same way as for other measurements. The results, which are also presented in Fig. 4, clearly confirm the influence of the kinetic energy on the energy resolution. All three w2G(E2pass) sets of data follow the same linear dependence for low Epass. For the photoelectron kinetic energy increased to 1255 eV (Ub = 300 V), the Epass range in which the linear dependence is kept is increased up to 70 eV. This corresponds to b 17.9. In the case of electrons decelerated to 755 eV (Ub = 200 V), the linear dependence is preserved for Epass up to about 40 eV i.e. b 18.9. These measurements were performed with an Epass step of 10 eV, and here applied approach to determine b will always yield overestimated values. Therefore, we may safely state that the critical retardation ratio at which wS(Epass) dependence stops to be linear is around b 17.3, being independent of the electron kinetic energy in the frame of the experimental error. When the retardation ratio is below the critical one, w2G(E2pass) has a qualitative behaviour independent of the kinetic energy: the resolution reaches saturation for Epass Ek/b, and then increases further for the highest pass energies. The saturation of the spectrometer resolution as a function of the pass energy will be reached already at Epass = 27 eV in the case of the Zn 2p3/2 line and even at Epass = 11 eV in the case of the Mg 1 s line (here we assumed that Al Ka line is used for the photoelectron excitation). Of course, it is not clear whether the linear dependence of wS(Ek) in the saturation region is valid for very small retardation ratio, in particular below 1, when the emitted electrons should be accelerated instead of decelerated. But, anyway, working in this regime is not of a wide interest, and it will not be further considered. The number of counts per second detected at the maximum of O 1s line vs. the pass energy, in the case of the wider entrance slit, is presented in Fig. 5. Since the X-ray power was kept constant, the
5
count rate growth is caused by the spectrometer transmission function increase with Epass for Ek = 954 eV. In spite of the energy resolution saturation at higher pass energies, the transmission monotonically increases with Epass. Experimentally observed non-linear dependence of wS on Epass contradicts one of the basic assumptions in the XPS instrumentation: when working in FAT regime the resolution is independent of the kinetic energy. When taking an energy spectrum in the FAT mode using the 7 mm slit, the energy resolution of the spectrometer will be constant and equal SEpass (S is obtained from the slope in Fig. 4) as long as Ek > bEpass. For lower kinetic energies, the resolution is approximately proportional to Ek: wS = SEk/b, unless Epass is too high. At the same time, the transmission of the spectrometer increases with the pass energy, as shown in Fig. 5. Therefore, this effect provides an opportunity to increase Epass and therefore increase the instrument sensitivity without considerable loss in energy resolution. This may be significant when analysing trace elements having characteristic photoelectron lines at low kinetic energies. Besides, it can be even more important when a very similar spectrometer Phoibos 150 is used in synchrotrons (cf. [17–19] for instance), where the photon energy is tuneable and frequently reduced to increase both photoelectron emission cross section and the surface sensitivity. Then, much wider part of the spectrum can be taken with the non-constant energy resolution although Epass is kept fixed. From the measured S (using the slope in the case of the linear dependence in Figs. 3 and 4, or Eq. (4)) the spectrometer instrumental function can be obtained as wS = SEpass. Then, the instrumental function of the whole XPS system is a Gaussian with FWHM calculated by Eq. (1) with wX = 0.167 eV. The result of the wXPS vs. Epass for both slits is shown in Fig. 6. For Epass < 30 eV in the case of the 1 mm slit we also assumed linear dependence, which somewhat overestimates wS. However, in this Epass range the instrumental function width is dominated by wX, so that the introduced error is minor. While the presented wXPS is correct for any kinetic energy when 1 mm entrance slit is used, the result corresponds solely to Ek = 954 eV in the case of the 7 mm slit. However, since the saturation of wXPS for higher pass energies always takes place at Epass = Ek/b, wXPS (Epass) can be simply estimated for any kinetic energy. If S does not depend on the pass energy and wX is negligible, wXPS would be directly proportional to Epass. This linear dependence is also presented in Fig. 6 for both slits. As expected, the width of the XPS instrumental function is dominated by the spectrometer function at higher pass energies, while the relative contribution of wX becomes more significant for low Epass. This is observed as the deviation from the linear dependence for low Epass, which becomes noticeable for Epass < 15 eV for the 7 mm slit, but even at Epass < 70 eV for the 1 mm slit. Knowing that the photoelectron lines practically never have widths smaller than 0.5 eV, it is clear that 1 mm slit provides ‘too good’ resolution and consequently, unnecessary low transmission for the XPS measurements. As for the 7 mm slit, working with Epass = 20 eV appears to be a good first choice for the high resolution spectroscopy of photoelectron lines, which fully supports the usual experimental practice by different workers. As for the survey XPS spectra, working with the pass energy of 40 eV, providing the resolution of about 1 eV, seems to be suitable.
4. Deconvolution of the valence band
Fig. 5. O 1s line height, taken with the 7 mm entrance slit, as a function of the pass energy.
Once the instrumental function of the XPS system is known, it can be used to determine the actual energy distribution of emitted photoelectrons by its deconvolution from the spectrum. As already discussed, this task is particularly significant in the case of the
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Fig. 6. Instrumental function width of the whole XPS instrument for entrance slits widths of (a) 1 mm and (b) 7 mm. The result for the 7 mm slit is valid only for the O 1s line i.e. for Ek = 954 eV. Dashed line corresponds to the spectrometer contribution to the overall width wXPS, assuming wS Epass.
valence band maximum determination. Valence band spectra are typically measured on a similar setup, using UV photons. An efficient deconvolution procedure could allow similar kind of measurements on XPS systems, which are much more common. Since in most cases deconvolution cannot be performed analytically, numerical processing of the raw data has to be performed, which is far from straight forward. Here we introduce a simple deconvolution procedure, which can be implemented to any spectrum when the instrumental function has a Gaussian profile. It is based on two well-known properties of the convolution operation: its linearity and the fact that a convolution of two Gaussians of widths w1 and w2 is a Gaussian having width w = (w21 + w22)1/2. The proposed algorithm consists of two steps. Firstly, a spectrum is fitted to an arbitrary sum of Gaussians Gi, after the background removal. These Gaussians do not have any physical meaning. Since the only aim is to get a good fit of the experimental data, the overall number of Gaussians is irrelevant. Moreover, some of them can even have negative intensity. The only condition each Gaussian in the sum has to fulfil is that its width wi is greater than the width of the corresponding instrumental function wXPS. In the second step, the deconvolution is performed by deconvoluting the instrumental function from each of the superimposed Gaussians in the sum. That way, each Gaussian Gi is transformed into Gaussian G0i , having width w0i = (w2i w2XPS)1/2. The position and intensity (area) of the Gaussians are unchanged. The deconvoluted spectrum is the superposition of the newly formed Gaussians, G0i . Once the deconvolution is performed, the valence band maximum with respect to the Fermi level Ev, can be determined from the width w0m , and the position Em of the Gaussian G0m closest to the Fermi level. Ev should correspond to the energy at which G0m drops to zero, which may be written to a very good approximation as
Ev ¼ Em 3 r0m :
ð5Þ
The parameter r0m = w0m /(8ln2)1/2 w0m /2.355 is the standard deviation of the Gaussian G0m . The valence band of the as-received silicon sample was measured in FAT 20 and FAT 60 modes using 7 mm wide entrance slit, in order to test usefulness of the XPS instrumental functions and of the proposed deconvolution procedure. Since the retardation ratio for the valence band measurements significantly exceeds the critical one (b 17.3) for both FAT modes, wS is directly proportional to Epass, with the proportionality constant S experimentally determined in the previous section. The valence band spectrum taken in FAT 20 mode, and its fit to the sum of 9 Gaussians, are shown in Fig. 7. The background was calculated using the Shirley algorithm. These Gaussians are then transformed into narrower ones after deconvoluting the XPS instrumental function. The superposi-
Fig. 7. XPS spectrum of the valence band of as-received boron-doped Si(100) single crystal taken in the FAT 20 mode: raw experimental data, fit to the sum of Gaussians, and the deconvolution result.
tion of the narrowed Gaussians represents the deconvoluted spectrum, also shown in the figure. The deconvoluted spectrum practically overlaps with the measured one, which is due to the FWHMs of Gaussians used to fit the spectrum. Their widths in the range 1.3–3.7 eV are too large to be significantly affected by a deconvolution with the instrumental function having wXPS = 0.53 eV. Position of the valence band maximum Ev was determined from 0 the position and the width of the Gaussian Gm with the position closest to EF, using the expression (5). The procedure for determining the position of the valence band maximum is summarized in Table 1. The valence band maximum appears to be at Ev 0 eV, which is fully in accordance with the expectations: since the doped silicon sample is of P-type, the valence band maximum is expected to be almost at the Fermi level. Therefore, small discrepancy between the deconvoluted spectrum and the raw data, observed
Table 1 Calculation of the valence band maximum position from the deconvoluted valence band spectra. Epass (eV)
Em (eV)
wm (eV)
wXPS (eV)
w0m (eV)
r0m (eV)
Ev (eV)
20 60
1.651 2.398
1.408 2.701
0.530 1.436
1.304 2.289
0.554 0.972
0.011 0.518
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Fig. 8. Normalized XPS spectra of the valence band of as-received boron-doped Si(100) single crystal taken in the FAT 20 and FAT 60 modes: (a) raw experimental data and (b) after the deconvolution.
in Fig. 7, is justified. It also shows that the measured spectrum practically corresponds to the electron energy distribution. In contrast to the result obtained in FAT 20 mode, the valence band spectrum measured with pass energy of 60 eV is expected to be much more influenced by the deconvolution procedure, since wXPS = 1.44 eV. In Fig. 8, we compare the normalized valence band spectra taken in FAT 20 and FAT 60 modes (a) before, and (b) after deconvoluting the instrumental functions. The discrepancy between the two spectra in Fig. 8a is mainly due to the low energy resolution in the FAT 60 mode. In theory, the disagreement should be suppressed by the deconvolution of the instrumental function. As can be seen from Fig. 8b, this was actually achieved: the general agreement between the deconvoluted spectra is excellent with the exception of the feature at about 15 eV. The latter could be due to its proximity to the boundary of the range considered for fitting, or related to the background removal. This is an indirect proof that the width of the instrumental function determined in the previous section and the proposed deconvolution procedure are both sound and very useful, although generally approximate. The latter is manifested from the calculation of Ev from the deconvoluted spectrum measured in FAT 60 mode (cf. Table 1). The obtained result, Ev = 0.45 eV, which can be also seen from Fig. 8b, is unphysical and points out that the procedure is of limited reliability when speaking of spectrum details. The result can be certainly improved by modifying the fitting procedure, such as increasing the number of Gaussians and reducing their widths. But our aim here is to emphasize the strong points of the procedure in its present form, as well as its weaknesses.
5. Conclusion A simple experimental procedure to measure the instrumental function width of the SPECS XPS system operating in fixed analyser transmission mode is introduced and validated. The key point in the proposed approach is the choice of the photoelectron line and the sample. O1s line originating from a thin oxide layer of doped silicon single crystal appears to be highly suitable for this purpose. While the spectrometer resolution measurements for the 1 mm entrance slit are in accordance with expectations, this was definitely not the case for the 7 mm slit. Saturation of wS at higher Epass, which means that the energy resolution is higher than expected, can be qualitatively explained from the basic principles of electron optics by applying Louiville’s theorem. The direct consequence of this saturation is that the resolution is generally not constant even when the spectrometer is operated in FAT mode: in the case of kinetic energies lower than bEpass, it is roughly proportional to Ek. It should be stressed that, while the resolution is
saturated, the transmission continues to grow with the pass energy. This is potentially of interest when detecting low intensity lines (of trace elements, for instance) having low Ek, but also in the case of photoelectron measurements with tuneable X-ray sources i.e. in synchrotrons. In order to test the usefulness of the determined instrumental functions, we applied them to the deconvolution of valence band spectra. For that purpose we propose a simple deconvolution scheme providing analytical result in the form of a set of superimposed Gaussians. Therefore, the Gaussian situated closest to the Fermi level can be used to calculate the position of the valence band maximum. The deconvolution procedure with the predetermined instrumental functions gives very good results: the shapes of the deconvoluted spectra are apparently identical. However, when the spectra are measured with low resolution, the procedure in its present form is not reliable enough to provide a precise value of Ev. Acknowledgement This work was financially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia; project no. III 45005. References [1] J.F. Watts, J. Wolstenhome, An Introduction to Surface Analysis by XPS and AES, John Wiley & Sons Ltd., Chichester UK, 2003. [2] A. Jablonski, Quantification of surface-sensitive electron spectroscopies, Surf. Sci. 603 (2009) 1342–1352. [3] M. Mohai, XPS MultiQuant for Windows Users’ Manual, Version 7.0, http://aki. ttk.mta.hu/XMQpages/XMQhome.htm, 2011 (accessed February 2017). [4] E.A. Kraut, R.W. Grant, J.R. Waldrop, S.P. Kowalczyk, Semiconductor core-level to valence-band maximum binding-energy differences: precise determination by x-ray photoelectron spectroscopy, Phys. Rev. B 28 (1983) 1965–1977. [5] F.R. Paolini, G.C. Theodoridis, Charged particle transmission through spherical plate electrostatic analyzers, Rev. Sci. Instrum. 38 (1967) 579–588. [6] X-ray Source for Focus 500, XR-50 M, SPECS User Manual, 2014. [7] H. Wollnik, Electrostatic prisms, in: A. Septier (Ed.), Focusing of Charged Particles, vol. 2, Academic press, New York, 1967, ch. 4.1. [8] N. Bundaleski, Z. Ristic´, M. Radovic´, Z. Rakocˇevic´, Influence of the primary ion beam profile and the energy analyzer optics to the LEIS spectra: the analytical study, Nucl. Instrum. Methods Phys. Res. B 237 (2005) 613–622. [9] 2D CCD Detector, Version 2.0, SPECS User Manual, 2014. [10] E.H.A. Granneman, M.J. van der Wiel, Transport, dispersion and detection of electrons, ions and neutrals, in: D.E. Eastman, Y. Farge, E.E. Koch (Eds.), Handbook on Synchrotron Radiation, vol. 1, FOM, Amsterdam, 1979 (Ch. 6). [11] M. Yavor, Optics of Charged Particle Analyzers, Elsevier, 2009. [12] S. Humphries Jr., Charged Particle Beams, John Wiley & Sons Inc., 2002. [13] C.D. Wagner, A.V. Naumkin, A. Kraut-Vass, J.W. Allison, C.J. Powell, J.R.Jr. Rumble, NIST Standard Reference Database 20, Version 3.4, http://srdata. nist.gov/xps/, 2012 (Accessed December 2016). [14] PHOIBOS 100/150 – Hemispherical Energy Analyzer, Version 4.0, SPECS User Manual, 2014. [15] R. Alfonsetti, L. Lozzi, M. Passacantando, P. Picozzi, S. Santucci, XPS studies on SiOx thin films, Appl. Surf. Sci. 70 (71) (1993) 222–225.
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Please cite this article in press as: M. Popovic´ et al., Instrumental function of the SPECS XPS system, Nucl. Instr. Meth. B (2017), http://dx.doi.org/10.1016/j. nimb.2017.02.071