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Experimental determination of energy resolution and transmission characteristics of an electrostatic toroidal spectrometer adapted to a standard scanning electron microscope
Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119–127 www.elsevier.nl / locate / elspec
Experimental determination of energy resolution and transmission characteristics of an electrostatic toroidal spectrometer adapted to a standard scanning electron microscope a, b a b a D. Berger *, M. Filippov , H. Niedrig , E.I. Rau , F. Schlichting a
Technical University Berlin, Optical Institute, Sekr. P 1 -1, Strasse des 17. Juni 135, D-10623 Berlin, Germany b Moscow State University, Department of Physics, 119899 Moscow, Russia Received 4 January 1999; received in revised form 31 May 1999; accepted 8 June 1999
Abstract The main characteristics of sectorial toroidal energy analyzer for a new electrostatic electron spectrometer adapted to a standard scanning electron microscope are defined and determined experimentally. These transfer characteristics, i.e. intensity-energy response and transmission functions, energy resolution and coupling constant, are needed for spectrometer calibration, registration and energy correction of measured backscattered electron spectra and microtomographic analysis of multilayered structures. The spectrometer response to a monoenergetic primary electron beam and to a continuous energy distribution is discussed. Detector response functions for energy independent and linear energy dependent detectors are considered. For aperture slits of the spectrometer which allow reasonable electron intensities at the detector an energy resolution of about 2.5% is obtained. 1999 Elsevier Science B.V. All rights reserved. Keywords: Toroidal energy analyzer; BSE spectroscopy in SEM; Spectrometer calibration; Spectrometer characteristics; BSE spectra correction
1. Introduction The analysis of solid surfaces is of great importance in recent scientific and technological studies. Electron spectroscopy, i.e. measurements of the energy distribution of emitted electrons, yields detailed information about the sample surface [1,2]. For measuring the energy distribution, different energy analyzers are used, partly in combination with a
*Corresponding author.
scanning electron microscope (SEM) for surface imaging [3–6]. As shown in previous publications [7–11] backscattered electron (BSE) spectroscopy is an excellent method for microtomographic analysis of multilayered structures and depth selective measurements. By evaluating the shape of the electron spectra quantitative results of the structures under investigation can be obtained, e.g. layer thickness and build-in depth. The shape of the spectra does not only depend on the specimen structure but is also explicitly correlated to the spectrometer’s geometry and its transfer characteristics [10–13].
0368-2048 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S0368-2048( 99 )00036-5
120
D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127
Here we must note the main differences between our geometry of toroidal analyzer and those considered and developed previously [13–19]. We have chosen the basic electron optical parameters with polar geometry of the toroidal analyzer as required for optimum adaptation to a commercial SEM [7,8]:
1. The analyzer has to be axially-symmetrical with respect to the electron–optical axis of the SEM in order to obtain an azimuthal acceptance angle w 52p. 2. In order to obtain a reasonable SEM working distance, the spectrometer size along the SEM optical axis should be as small as possible. These two requirements lead to a toroidal scale factor R /r 0 .1 (see Fig. 1) and a polar start angle u 5208. The basic spectrometer characteristics are the response function of the energy analyzer R(E1 , E) and the corresponding transmission function T(E1 ) [20-24] where E is the energy of analyzed electrons and E1 is the spectrometer set energy (pass energy). In this paper we define R(E1 , E) as the response function of the spectrometer to a monoenergetic incident electron beam and T(E1 ) as the integral of all R(E1 , E) over all occurring incident calibration energies E [24]. In order to clarify terminology we like to point out that the term ‘energy analyzer’ refers only to the toroidal deflecting electrodes including slits while the expression ‘energy spec-
trometer’ comprises the energy analyzer and the detector. Accurate theoretical calculations of R(E1 , E) and T(E1 ) are difficult to apply due to various parameters concerning the spectrometer configuration. In most cases the transmission functions and the response functions are different not only for different types of spectrometers but also for each particular spectrometer. Therefore the experimental determination of R(E1 , E) and T(E1 ) is preferred over theoretical calculations. Hence individual measurements of such characteristics are required for each spectrometer [24].
2. Design of the toroidal spectrometer In [7,8,10] a novel toroidal sectorial spectrometer was described, which has been incorporated into a commercial SEM for BSE microtomography [9]. This spectrometer consists of an electrostatic sectorial toroidal condenser in axial symmetry with the SEM’s optical axis combined with a suitable electron detector, e.g. scintillation or planar semiconductor detector (Fig. 1). Backscattered electrons (BSE) entering the spectrometer through a ring slit of width S1 at an angle u 5208 with respect to the SEM axis are deflected by an electric field generated between two electrodes with curvature radii r 1 and r 2 , respectively. Therefore only electrons with a specific energy determined by the symmetrical potential difference DV 5 uV1 u 1 uV2 u can exit the deflector through a ring slit of width S2 .
Table 1 Main parameters of used spectrometers [7–11]
Sector angle w (8) Inner electrode radius r 1 (mm) Outer electrode radius r 2 (mm) Toroidal radius R (mm) Distance h (sample – input slit plane) (mm) Starting angle u (8) Spectrometer size with housing (mm 2 ) Typ. energy resolution (see Section 4.2) (%) k exp (see Section 3.1) k theor (see Section 3.1)
Spectrometer 1
Spectrometer 2
115 21 23 26.9 10.8 20 [ 125330 4.2 6.2 5.5
90 16 18 20 8 20 [ 100325 2.5 4.8 4.2
D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127
121
Fig. 1. Schematic design of BSE-spectrometer adapted to a commercial SEM.
Two types of spectrometer (Table 1) are currently used differing in sector angle f, curvature radii r 1 , r 2 , toroidal radius R and distance h resulting in a different energy resolution and coupling constant k (see Section 3.1). Spectrometer 2 contains Herzog electrodes H to prevent fringing field effects (Figs. 1 and 2).
3. Spectrometer transmission characteristics
3.1. Spectrometer response, transmission functions and coupling constant k The energy filtering characteristics of the energy analyzer are most adequately characterized by two functions: the response function R(E1 , E) and the transmission function T(E1 ). R(E1 , E) is determined as the response of the toroidal deflector to a monoenergetic electron beam with energy E. In this case the observable broadening of the detected signal is caused by imperfect properties of the deflector: aberrations, finite width of slits and electron scattering by surfaces inside the spectrometer. The transmission function T(E1 ) is defined as the integral of R(E1 , E) over the energy E of all incident electrons `
E
T(E1 ) 5 R(E1 , E)dE
(1)
0
Fig. 2. Set-up for calibration of the sectorial toroidal spectrometer.
This function can be interpreted as the response of the toroidal deflector to a continuous energy spectrum of incident electrons with constant intensity for all energies. The output signal of the spectrometer i reg (E1 ) can be described as
D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127
122 `
E
i reg (E1 ) 5 n 0 D(E) R(E1 , E) N(E) dE
(2)
0
monoenergetic electron beam. Inserting d (E 2 E0 ) into (2) yields i reg (E1 ) 5 n 0 D(E0 ) R(E1 ,E0 )
where E1 is the set spectrometer energy (pass energy) given by the applied deflecting potential, E and N(E) are the energy and the normalized energy distribution of the electrons at the entrance of the spectrometer dnsEd NsEd 5 ]] n dE
(3)
(6)
By using a monoenergetic electron beam it is possible to determine the spectrometer’s energy resolution: DE /E is obtained as the full width at half maximum (FWHM) DE1 divided by the energy at the peak position E max of the R(E1 , E)-function at 1 the given primary energy E
0
dn(E) is the number of electrons having an energy between E and E 1 dE, n 0 the number of electrons at the entrance of the spectrometer and D(E) the detector response function, which is the ratio of the detector signal to the number of incident electrons. The set energy E1 directly depends on the potential difference DV applied to the toroidal electrodes causing the deflecting field E1 5 ke DV
(4)
where the coupling constant of the spectrometer k is a function of the geometry and dimensions of the device [1,5]. The constant k can be used for the calibration of the energy axis of recorded BSEspectra. According to [13] k can be calculated by
F
r 2 (p R 1 2r 1 ) 1 pR k theor 5 ] ]]] ln]]]] 2 p R 1 2r 0 r 1 (p R 1 2r 2 )
G
-1
r0 ¯ ]] 2Dr
Dr
(5) Experimental and theoretical values for the coupling constant k are shown in Table 1. Due to constructional variations, the calculated values of k theor differ from experimental data. Hence it is necessary to determine the coupling constant k experimentally for each particular spectrometer.
3.2. Spectrometer response to a monoenergetic beam and energy resolution For the examination of the response function R(E1 , E) a monoenergetic electron beam with an energy spread of a few electronvolts is used [24] (see Section 4.1). Hence the energy distribution N(E) of initial electrons can be assumed as Dirac’s d -function d (E2E0 ), where E0 is the energy of the
DE1 DE ] 5 ]] E E max 1
(7)
Further it is possible to calibrate the energy axis of the spectrometer with monoenergetic electron beams by measuring R(E1 , E) for various primary energies E. The energy differences of the R(E1 , E) peak positions can be related to the corresponding energy differences of the taken primary energies (see Section 5.1).
3.3. Registration of BSE spectra In the BSE-registration mode backscattered electrons with an energy distribution N(E) are incident into the solid angle DV, defined by the entrance slit S1 of the spectrometer and its distance h to the target. N(E) is given by N(E) 5
E f(E, V ) dV \ f
DV
(E)
(8)
DV
with the twofold differential backscattering coefficient f(E, V ) dn BSE (E) f(E, V ) 5 ]]] N0 dE dV
(9)
where n BSE (E) is the number of scattered electrons with energies between E and E 1dE within the solid angle interval dV. N0 is the number of primary electrons impinging on the specimen. The function f(E, V ) is normalized in such a way that integration over the whole range of energies and over the solid angle in the upper hemisphere yields the integral backscattering coefficient h. The relation between the registered signal and the energy angular distribution of BSE is given according to Eq. (2)
D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127 `
E
i reg (E1 ) 5 n 0 D(E) R(E1 , E) fD V (E) dE
(10)
0
Eq. (10) is applicable in general for this kind of spectrometer: if the functions R(E1 , E) and D(E) are known and i reg (E1 ) is measured it is possible to determine the function fD V (E). In our spectrometer design the BSE acceptance angle intervals are: q [[188, 228] and w [[0, 2p]. Using Monte-Carlo simulations it was shown that the form of the distribution of fD V (E) taken at the interval q [[188, 228] is proportional to the energy distribution of BSE averaged over the whole upper hemisphere fE (E). Substituting fD V (E) ¯ gfE (E) into Eq. (10) we obtain `
i reg (E1 ) 5 g N0
E D(E) R(E , E) f (E) dE 1
E
(11)
0
where g is an energy independent constant. The integral Eq. (11) gives the relation between the BSE energy spectrum fE (E) and the detected signal i reg (E1 ). Assuming a relatively weak change of fE (E) and D(E) within the energy interval E and E 1dE and a non-vanishing R(E1 , E)-function only in the neighbourhood of E (ideal response function) a simplified method for fE (E) extraction is carried out: applying the mean value theorem to fE (E) and D(E) in (11) and taking (1) into consideration yields
i reg (E1 ) fE (E1 ) 5 ]]]]] g N0 D(E1 )T(E1 )
123
(12)
4. Energy resolution and calibration factor of toroidal spectrometer
4.1. Experimental calibration set-up The determination of the response function R(E1 , E) for various incident calibration energies E was accomplished over an energy range E1 53 to 30 keV both with energy independent (Faraday cup) and energy dependent (scintillator or semiconductor) detectors. For calibration the spectrometer was reversely mounted on the specimen holder of the SEM [24] so that the electron beam is incident directly into the input slit S1 (Fig. 2). The spectrometer inclination angle is u 5208 with respect to the SEM’s optical axis. The SEM electron beam was used as a source of divergent spray of electrons with negligible energy spread. In order to simulate the BSE distribution in working mode the primary electron beam was focused on the plane F with distance h to the spectrometer corresponding to the target position in working mode. It is essential that the beam aperture a1 exceeds the spectrometer acceptance angle a2 , i.e. the beam diameter is larger than the input slit width S1 . To acquire the response functions for monoenergetic electrons the deflecting voltage DV is scanned, i.e. sweeping the pass energy E1 . The SEM’s electron beam current was measured for all primary energies E by means of a separate Faraday cup.
4.2. Determination of energy resolution DE /E
Fig. 3. Energy resolution for different modes of beam focusing.
With the SEM electron beam being focused on the plane F as described in Section 4.1 and S1 5S2 5 200 mm an energy resolution of 2–3% is obtained. If, however, the SEM beam is focused on the entrance slit S1 the energy resolution can be improved to 0.7–1.0%. The change in resolution is due to different conditions of entrance slit illumination: with a defocused beam a considerable number of entrance electrons has a starting point placed off the central trajectory at the entrance slit S1 (‘off axis’
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D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127
electrons). Since this way of focusing simulates the condition in BSE spectra registration mode the prior setup is used (see Section 4.1) despite a worse energy resolution as can be seen in Fig. 3: curve 1 represents the broader i reg (E1 )-function for an incident beam focused at the distance h and curve 2 describes the case of a beam focused on the entrance slit. In both cases of focusing the energy resolution can be improved by reducing the slit widths S1 and S2 . For a successful use of the BSE spectrometer in SEM, however, not only a high resolution, but also a high transmission intensity is desirable in order to obtain microtomographic images of high quality [7– 9]. Therefore a suitable compromise between resolution and transmission intensity has to be chosen by optimizing the slit widths.
5. Experimental determination of transmission characteristics and BSE-spectra
5.1. Experimental determination of D( E) and R( E1 , E) Figs. 4 and 5 show typical experimental data for the determination of R(E1 , E) as a function of E and E1 : in Fig. 4 an energy dependent semiconductor detector in current mode was used. The maximum heights of the recorded response functions depend linearly on the primary energy E due to the linear energy dependence D(E) of the used detector which was measured separately. For a scintillator-photomultiplier detector in current mode a similar dependence for D(E) was obtained. This function is well fitted by a linear function of the form
Fig. 4. Functions i reg (E1 ) of different monoenergetic divergent electron beams recorded with a semiconductor detector.
D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127
125
`
ER(E , E) dE ~ E 1
1
(15)
0
Fig. 5. Function i reg (E1 ) of different monoenergetic divergent electron beams recorded with a Faraday cup detector.
D(E) 5 a(E 2 Ethresh )
(13)
where a is the linear amplification coefficient of the detector system and Ethresh the threshold energy of the semiconductor or the metal film coated scintillator. For the semiconductor detector used Ethresh was measured to be around 0.5 keV. Experimentally it was only possible to determine the combined function R(E1 , E)*D(E) for these detectors. If the functions i reg (E1 ) and D(E) are measured separately the function R(E1 , E) can be calculated according to formula (6). For energy independent detectors such as Faraday cups or detector systems in pulse counting mode the detector energy response function D(E) is constant. In this case, for a monoenergetic beam, the response function R(E1 , E) is proportional to the recorded signal (Fig. 5) i reg (E1 ) | R(E1 , E)
The line profiles of the transmission characteristics show extra ‘wings’ both above and below the primary energy peak and a ‘tail’ of lower energy electrons extending down to energies of a few keV, as illustrated in Fig. 6. In this graph the dependence of R(E1 , E) on E1 for two primary energies E510 keV and 20 keV is shown. These parasitic ‘wing’ and background contributions are typical for all electrostatic energy analyzers [20,25–27]. Background and ‘wing’ effects result from electrons backscattered and multiply scattered from the electrode surfaces, at the Herzog electrodes and aperture slits. The number of scattered electrons that are detected increases with increasing width of the exit slit S2 . The shape of the wings and the background of the response functions R(E1 , E) are different for all spectrometers and all widths of the exit slit. Therefore R(E1 , E) has to be measured separately for every particular spectrometer and exit slit adjustment.
5.2. Measured energy spectra of BSE The background and ‘wing’ effects of the response functions R(E1 , E) for this type of spectrometer lead to certain problems in data interpretation of regis-
(14)
From the response functions R(E1 , E) (Figs. 4 and 5) the FWHM DE can be derived: DE increases proportional with increasing E, i.e. DE /E0 5 const in both cases. The DE /E0 5 const dependence implies that the number of electrons transmitted through the toroidal energy analyzer depends linearly on the energy E. This number of electrons is correlated to the area under the response functions R(E1 , E) that increases proportionally to the energy E as well:
Fig. 6. Illustration of the ‘wings’ appearing in the spectra recorded by means of deflector type energy analyzers for monoenergetic electron beams.
126
D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127
tered BSE-spectra. The signal i reg (E1 ) for a chosen energy E1 contains not only electrons with the set energy E1 but also scattered electrons with deviating energies. In addition the energy resolution DE /E of the spectrometer has to be taken into account for the spectrum analysis. In Fig. 7 typical examples are shown for the recorded signals i reg (E1 ) (curves 2 and 4) and their corresponding extracted BSE-spectra fE (E) (curves 1 and 3) for bulk Au and Cu. The extraction of the fE (E)-function is based on the simplified model described above (see Section 3.3). Since a linear energy dependent detector was used, the integral of R(E1 , E)*D(E) is proportional to E1 *(E1 2Ethresh ). Therefore the experimentally obtained signal was divided by the latter term. This model does not correct the background and ‘wing’ effects, and due to the division by E1 *(E1 2Ethresh ) the deviation from the true spectrum in the region of high energy losses is even more evident in the corrected spectra fE (E1 ). Fig. 7 shows that the deformation of spectra on the left hand side of the maximum and the shift of the position of the maximum to lower energies increase with atomic number Z. The background and ‘wing’ effects contributes at least 10–20% to the total curve area of R(E1 , E) for optimized spectrometers. Essential improvement can be reached however by using corrugated electrodes which minimize the electron reflection [28]. In order to make use of the smaller backscattering coefficient of low Z elements on rough surfaces the electrodes were spray coated with graphite. As an example Fig.
Fig. 7. Measured and energy corrected BSE-spectra of Au and Cu (bulk specimens).
Fig. 8. Reduction of ‘wing’-effects by carbon-coating of spectrometer electrodes.
8 shows measured BSE-spectra for Au with coated and uncoated electrodes leading to a significant reduction of those artefacts by a factor of at least 0.1.
6. Conclusions The main metrological characteristics such as response and transmission functions, coupling constant and energy resolution for a toroidal electrostatic energy analyzer adapted to a standard SEM have been studied. The techniques of correct determination of these characteristics for this kind of spectrometer were discussed. For aperture slits of the spectrometer allowing reasonable electron intensities at the detector, an energy resolution of about 2.5% was obtained. The energy spectra of transmitted electrons have been studied for linear-energy-dependent and energyindependent detectors in the energy range 3–30 keV. It is shown that in order to obtain absolute energy spectra the experimental spectra have to be divided
D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127
by E1 *(E1 2 Ethresh ) in the case of energy-dependent detectors and by E1 only for energy-independent detectors. The influence of the background and ‘wing’ effects on the measured BSE spectra has been analyzed. The parasitic contribution of this factor in BSE-spectra is significant, especially in the low energy region. These artefacts can significantly be reduced by carbon spray-coating of the electrodes.
Acknowledgements This work was supported by the Volkswagen foundation. Thanks are due to A. Gostev for the development of data acquisition hard- and software.
References [1] H. Ibach, Electron spectroscopy for surface analysis, in: Topics in Current Physics, Vol. 4, Springer, Berlin, 1977. [2] M.P. Seah, Surface and Interface Analysis 2 (1980) 222. [3] W. Steckelmacher, J. Physics E: Sci. Instrum. 6 (1973) 1061. [4] H. Seiler, Ultramicroscopy 17 (1985) 1. [5] R.C.G. Leckey, J. Elect. Spectros. Rel. Phenom. 43 (1987) 183. [6] D. Roy, D. Tremblay, Rep. Prog. Phys. 53 (1990) 1623. [7] E.I. Rau, V.N.E. Robinson, Scanning 18 (1996) 556. [8] H. Niedrig, E.I. Rau, Nucl. Instrum. Methods Phys Res. B 142 (1998) 523. [9] V.V. Aristov, E.I. Rau, E.B. Yakimov, Phys. Stat. Sol.(a) 150 (1995) 675. [10] F. Schlichting, D. Berger, H. Niedrig, E.I. Rau, in: Electron Microscopy 1996 (Proc. 11th EUREM, Dublin), CESM, Brussels, 1998, pp. I–279.
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[11] F. Schlichting, D. Berger, H. Niedrig, in: H.A. Calderon, M.J. Yacaman (Eds.), Electron Microscopy 1998 (Proc. 14th ICEM, Cancun), Inst. Phys. Publishing, Bristol, 1998, pp. II–349. [12] E.I. Rau, B. Schindler, L. Reimer, in: Electron Microscopy 1996 (Proc. 11th EUREM, Dublin), CESM, Brussels, 1998, pp. I–336. [13] F. Toffoletto, R.C.G. Leckey, J.D. Riley, Nucl. Instrum. Methods Phys Res.: B 12 (1985) 282. [14] R.G. Smeenk, R.M. Tromp, H.H. Kersten, A.J.H. Boerboom, F.W. Saris, Nucl. Instrum. Methods 195 (1982) 581. [15] G.J.A. Hellings, H. Ottevanger, C. Knibbeler, J. van Engelshoven, H. Brongersma, J. Elect. Spectros. Rel. Phenom. 49 (1989) 359. [16] A. Ghielmetti, E. Shelley, Nucl. Instrum. Methods Phys. Res. A 298 (1990) 181. [17] M.I. Yavor, H. Wollnik, M. Nappi, B. Hartman, Nucl. Instrum. Methods Phys. Res. A 311 (1992) 448. [18] H.A. Engelhardt, W. Back, D. Menzel, H. Liebl, Rev. Sci. Instrum. 52 (1981) 835. [19] R.C.G. Leckey, J.D. Riley, Appl. Surf. Sci. 22–23 (1985) 196. [20] D. Roy, J.D. Carette, J. Appl. Phys. 42 (1971) 3601. [21] G.G. Kurbatov, V.I. Zaporozchenko, J. Elect. Spectros. Rel. Phenom. 53 (1990) 29. [22] L.T. Weng, G. Vereecke, M.J. Genet, P. Bertrand, W. Stone, Surface Interface Anal. 20 (1993) 179. [23] C.S. Hemminger, T.A. Land, A. Christie, J.C. Hemminger, Surface Interface Anal. 15 (1990) 323. [24] D. Berger, M. Filippov, H. Niedrig, E.I. Rau, F. Schlichting, in: H.A. Calderon, M.J. Yacaman (Eds.), Electron Microscopy 1998 (Proc. 14th ICEM, Cancun), Inst. Phys. Publishing, Bristol, 1998, pp. IV–449. [25] H.D. Bauer, Exp. Technik Physik 27 (1979) 331. [26] H.H. Hubbel, W.J. McConnel, R.D. Birkhoff, Nucl. Instrum. Methods 31 (1964) 331. [27] D. Roy, J.D. Carette, Appl. Phys. Lett. 16 (1970) 413. [28] H. Froitzheim, H. Ibach, S. Lehwald, Rev. Sci. Instrum. 46 (1975) 1325.
Experimental determination of energy resolution and transmission characteristics of an electrostatic toroidal spectrometer adapted to a standard scanning electron microscope a, b a b a D. Berger *, M. Filippov , H. Niedrig , E.I. Rau , F. Schlichting a
Technical University Berlin, Optical Institute, Sekr. P 1 -1, Strasse des 17. Juni 135, D-10623 Berlin, Germany b Moscow State University, Department of Physics, 119899 Moscow, Russia Received 4 January 1999; received in revised form 31 May 1999; accepted 8 June 1999
Abstract The main characteristics of sectorial toroidal energy analyzer for a new electrostatic electron spectrometer adapted to a standard scanning electron microscope are defined and determined experimentally. These transfer characteristics, i.e. intensity-energy response and transmission functions, energy resolution and coupling constant, are needed for spectrometer calibration, registration and energy correction of measured backscattered electron spectra and microtomographic analysis of multilayered structures. The spectrometer response to a monoenergetic primary electron beam and to a continuous energy distribution is discussed. Detector response functions for energy independent and linear energy dependent detectors are considered. For aperture slits of the spectrometer which allow reasonable electron intensities at the detector an energy resolution of about 2.5% is obtained. 1999 Elsevier Science B.V. All rights reserved. Keywords: Toroidal energy analyzer; BSE spectroscopy in SEM; Spectrometer calibration; Spectrometer characteristics; BSE spectra correction
1. Introduction The analysis of solid surfaces is of great importance in recent scientific and technological studies. Electron spectroscopy, i.e. measurements of the energy distribution of emitted electrons, yields detailed information about the sample surface [1,2]. For measuring the energy distribution, different energy analyzers are used, partly in combination with a
*Corresponding author.
scanning electron microscope (SEM) for surface imaging [3–6]. As shown in previous publications [7–11] backscattered electron (BSE) spectroscopy is an excellent method for microtomographic analysis of multilayered structures and depth selective measurements. By evaluating the shape of the electron spectra quantitative results of the structures under investigation can be obtained, e.g. layer thickness and build-in depth. The shape of the spectra does not only depend on the specimen structure but is also explicitly correlated to the spectrometer’s geometry and its transfer characteristics [10–13].
0368-2048 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S0368-2048( 99 )00036-5
120
D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127
Here we must note the main differences between our geometry of toroidal analyzer and those considered and developed previously [13–19]. We have chosen the basic electron optical parameters with polar geometry of the toroidal analyzer as required for optimum adaptation to a commercial SEM [7,8]:
1. The analyzer has to be axially-symmetrical with respect to the electron–optical axis of the SEM in order to obtain an azimuthal acceptance angle w 52p. 2. In order to obtain a reasonable SEM working distance, the spectrometer size along the SEM optical axis should be as small as possible. These two requirements lead to a toroidal scale factor R /r 0 .1 (see Fig. 1) and a polar start angle u 5208. The basic spectrometer characteristics are the response function of the energy analyzer R(E1 , E) and the corresponding transmission function T(E1 ) [20-24] where E is the energy of analyzed electrons and E1 is the spectrometer set energy (pass energy). In this paper we define R(E1 , E) as the response function of the spectrometer to a monoenergetic incident electron beam and T(E1 ) as the integral of all R(E1 , E) over all occurring incident calibration energies E [24]. In order to clarify terminology we like to point out that the term ‘energy analyzer’ refers only to the toroidal deflecting electrodes including slits while the expression ‘energy spec-
trometer’ comprises the energy analyzer and the detector. Accurate theoretical calculations of R(E1 , E) and T(E1 ) are difficult to apply due to various parameters concerning the spectrometer configuration. In most cases the transmission functions and the response functions are different not only for different types of spectrometers but also for each particular spectrometer. Therefore the experimental determination of R(E1 , E) and T(E1 ) is preferred over theoretical calculations. Hence individual measurements of such characteristics are required for each spectrometer [24].
2. Design of the toroidal spectrometer In [7,8,10] a novel toroidal sectorial spectrometer was described, which has been incorporated into a commercial SEM for BSE microtomography [9]. This spectrometer consists of an electrostatic sectorial toroidal condenser in axial symmetry with the SEM’s optical axis combined with a suitable electron detector, e.g. scintillation or planar semiconductor detector (Fig. 1). Backscattered electrons (BSE) entering the spectrometer through a ring slit of width S1 at an angle u 5208 with respect to the SEM axis are deflected by an electric field generated between two electrodes with curvature radii r 1 and r 2 , respectively. Therefore only electrons with a specific energy determined by the symmetrical potential difference DV 5 uV1 u 1 uV2 u can exit the deflector through a ring slit of width S2 .
Table 1 Main parameters of used spectrometers [7–11]
Sector angle w (8) Inner electrode radius r 1 (mm) Outer electrode radius r 2 (mm) Toroidal radius R (mm) Distance h (sample – input slit plane) (mm) Starting angle u (8) Spectrometer size with housing (mm 2 ) Typ. energy resolution (see Section 4.2) (%) k exp (see Section 3.1) k theor (see Section 3.1)
Spectrometer 1
Spectrometer 2
115 21 23 26.9 10.8 20 [ 125330 4.2 6.2 5.5
90 16 18 20 8 20 [ 100325 2.5 4.8 4.2
D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127
121
Fig. 1. Schematic design of BSE-spectrometer adapted to a commercial SEM.
Two types of spectrometer (Table 1) are currently used differing in sector angle f, curvature radii r 1 , r 2 , toroidal radius R and distance h resulting in a different energy resolution and coupling constant k (see Section 3.1). Spectrometer 2 contains Herzog electrodes H to prevent fringing field effects (Figs. 1 and 2).
3. Spectrometer transmission characteristics
3.1. Spectrometer response, transmission functions and coupling constant k The energy filtering characteristics of the energy analyzer are most adequately characterized by two functions: the response function R(E1 , E) and the transmission function T(E1 ). R(E1 , E) is determined as the response of the toroidal deflector to a monoenergetic electron beam with energy E. In this case the observable broadening of the detected signal is caused by imperfect properties of the deflector: aberrations, finite width of slits and electron scattering by surfaces inside the spectrometer. The transmission function T(E1 ) is defined as the integral of R(E1 , E) over the energy E of all incident electrons `
E
T(E1 ) 5 R(E1 , E)dE
(1)
0
Fig. 2. Set-up for calibration of the sectorial toroidal spectrometer.
This function can be interpreted as the response of the toroidal deflector to a continuous energy spectrum of incident electrons with constant intensity for all energies. The output signal of the spectrometer i reg (E1 ) can be described as
D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127
122 `
E
i reg (E1 ) 5 n 0 D(E) R(E1 , E) N(E) dE
(2)
0
monoenergetic electron beam. Inserting d (E 2 E0 ) into (2) yields i reg (E1 ) 5 n 0 D(E0 ) R(E1 ,E0 )
where E1 is the set spectrometer energy (pass energy) given by the applied deflecting potential, E and N(E) are the energy and the normalized energy distribution of the electrons at the entrance of the spectrometer dnsEd NsEd 5 ]] n dE
(3)
(6)
By using a monoenergetic electron beam it is possible to determine the spectrometer’s energy resolution: DE /E is obtained as the full width at half maximum (FWHM) DE1 divided by the energy at the peak position E max of the R(E1 , E)-function at 1 the given primary energy E
0
dn(E) is the number of electrons having an energy between E and E 1 dE, n 0 the number of electrons at the entrance of the spectrometer and D(E) the detector response function, which is the ratio of the detector signal to the number of incident electrons. The set energy E1 directly depends on the potential difference DV applied to the toroidal electrodes causing the deflecting field E1 5 ke DV
(4)
where the coupling constant of the spectrometer k is a function of the geometry and dimensions of the device [1,5]. The constant k can be used for the calibration of the energy axis of recorded BSEspectra. According to [13] k can be calculated by
F
r 2 (p R 1 2r 1 ) 1 pR k theor 5 ] ]]] ln]]]] 2 p R 1 2r 0 r 1 (p R 1 2r 2 )
G
-1
r0 ¯ ]] 2Dr
Dr
(5) Experimental and theoretical values for the coupling constant k are shown in Table 1. Due to constructional variations, the calculated values of k theor differ from experimental data. Hence it is necessary to determine the coupling constant k experimentally for each particular spectrometer.
3.2. Spectrometer response to a monoenergetic beam and energy resolution For the examination of the response function R(E1 , E) a monoenergetic electron beam with an energy spread of a few electronvolts is used [24] (see Section 4.1). Hence the energy distribution N(E) of initial electrons can be assumed as Dirac’s d -function d (E2E0 ), where E0 is the energy of the
DE1 DE ] 5 ]] E E max 1
(7)
Further it is possible to calibrate the energy axis of the spectrometer with monoenergetic electron beams by measuring R(E1 , E) for various primary energies E. The energy differences of the R(E1 , E) peak positions can be related to the corresponding energy differences of the taken primary energies (see Section 5.1).
3.3. Registration of BSE spectra In the BSE-registration mode backscattered electrons with an energy distribution N(E) are incident into the solid angle DV, defined by the entrance slit S1 of the spectrometer and its distance h to the target. N(E) is given by N(E) 5
E f(E, V ) dV \ f
DV
(E)
(8)
DV
with the twofold differential backscattering coefficient f(E, V ) dn BSE (E) f(E, V ) 5 ]]] N0 dE dV
(9)
where n BSE (E) is the number of scattered electrons with energies between E and E 1dE within the solid angle interval dV. N0 is the number of primary electrons impinging on the specimen. The function f(E, V ) is normalized in such a way that integration over the whole range of energies and over the solid angle in the upper hemisphere yields the integral backscattering coefficient h. The relation between the registered signal and the energy angular distribution of BSE is given according to Eq. (2)
D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127 `
E
i reg (E1 ) 5 n 0 D(E) R(E1 , E) fD V (E) dE
(10)
0
Eq. (10) is applicable in general for this kind of spectrometer: if the functions R(E1 , E) and D(E) are known and i reg (E1 ) is measured it is possible to determine the function fD V (E). In our spectrometer design the BSE acceptance angle intervals are: q [[188, 228] and w [[0, 2p]. Using Monte-Carlo simulations it was shown that the form of the distribution of fD V (E) taken at the interval q [[188, 228] is proportional to the energy distribution of BSE averaged over the whole upper hemisphere fE (E). Substituting fD V (E) ¯ gfE (E) into Eq. (10) we obtain `
i reg (E1 ) 5 g N0
E D(E) R(E , E) f (E) dE 1
E
(11)
0
where g is an energy independent constant. The integral Eq. (11) gives the relation between the BSE energy spectrum fE (E) and the detected signal i reg (E1 ). Assuming a relatively weak change of fE (E) and D(E) within the energy interval E and E 1dE and a non-vanishing R(E1 , E)-function only in the neighbourhood of E (ideal response function) a simplified method for fE (E) extraction is carried out: applying the mean value theorem to fE (E) and D(E) in (11) and taking (1) into consideration yields
i reg (E1 ) fE (E1 ) 5 ]]]]] g N0 D(E1 )T(E1 )
123
(12)
4. Energy resolution and calibration factor of toroidal spectrometer
4.1. Experimental calibration set-up The determination of the response function R(E1 , E) for various incident calibration energies E was accomplished over an energy range E1 53 to 30 keV both with energy independent (Faraday cup) and energy dependent (scintillator or semiconductor) detectors. For calibration the spectrometer was reversely mounted on the specimen holder of the SEM [24] so that the electron beam is incident directly into the input slit S1 (Fig. 2). The spectrometer inclination angle is u 5208 with respect to the SEM’s optical axis. The SEM electron beam was used as a source of divergent spray of electrons with negligible energy spread. In order to simulate the BSE distribution in working mode the primary electron beam was focused on the plane F with distance h to the spectrometer corresponding to the target position in working mode. It is essential that the beam aperture a1 exceeds the spectrometer acceptance angle a2 , i.e. the beam diameter is larger than the input slit width S1 . To acquire the response functions for monoenergetic electrons the deflecting voltage DV is scanned, i.e. sweeping the pass energy E1 . The SEM’s electron beam current was measured for all primary energies E by means of a separate Faraday cup.
4.2. Determination of energy resolution DE /E
Fig. 3. Energy resolution for different modes of beam focusing.
With the SEM electron beam being focused on the plane F as described in Section 4.1 and S1 5S2 5 200 mm an energy resolution of 2–3% is obtained. If, however, the SEM beam is focused on the entrance slit S1 the energy resolution can be improved to 0.7–1.0%. The change in resolution is due to different conditions of entrance slit illumination: with a defocused beam a considerable number of entrance electrons has a starting point placed off the central trajectory at the entrance slit S1 (‘off axis’
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electrons). Since this way of focusing simulates the condition in BSE spectra registration mode the prior setup is used (see Section 4.1) despite a worse energy resolution as can be seen in Fig. 3: curve 1 represents the broader i reg (E1 )-function for an incident beam focused at the distance h and curve 2 describes the case of a beam focused on the entrance slit. In both cases of focusing the energy resolution can be improved by reducing the slit widths S1 and S2 . For a successful use of the BSE spectrometer in SEM, however, not only a high resolution, but also a high transmission intensity is desirable in order to obtain microtomographic images of high quality [7– 9]. Therefore a suitable compromise between resolution and transmission intensity has to be chosen by optimizing the slit widths.
5. Experimental determination of transmission characteristics and BSE-spectra
5.1. Experimental determination of D( E) and R( E1 , E) Figs. 4 and 5 show typical experimental data for the determination of R(E1 , E) as a function of E and E1 : in Fig. 4 an energy dependent semiconductor detector in current mode was used. The maximum heights of the recorded response functions depend linearly on the primary energy E due to the linear energy dependence D(E) of the used detector which was measured separately. For a scintillator-photomultiplier detector in current mode a similar dependence for D(E) was obtained. This function is well fitted by a linear function of the form
Fig. 4. Functions i reg (E1 ) of different monoenergetic divergent electron beams recorded with a semiconductor detector.
D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127
125
`
ER(E , E) dE ~ E 1
1
(15)
0
Fig. 5. Function i reg (E1 ) of different monoenergetic divergent electron beams recorded with a Faraday cup detector.
D(E) 5 a(E 2 Ethresh )
(13)
where a is the linear amplification coefficient of the detector system and Ethresh the threshold energy of the semiconductor or the metal film coated scintillator. For the semiconductor detector used Ethresh was measured to be around 0.5 keV. Experimentally it was only possible to determine the combined function R(E1 , E)*D(E) for these detectors. If the functions i reg (E1 ) and D(E) are measured separately the function R(E1 , E) can be calculated according to formula (6). For energy independent detectors such as Faraday cups or detector systems in pulse counting mode the detector energy response function D(E) is constant. In this case, for a monoenergetic beam, the response function R(E1 , E) is proportional to the recorded signal (Fig. 5) i reg (E1 ) | R(E1 , E)
The line profiles of the transmission characteristics show extra ‘wings’ both above and below the primary energy peak and a ‘tail’ of lower energy electrons extending down to energies of a few keV, as illustrated in Fig. 6. In this graph the dependence of R(E1 , E) on E1 for two primary energies E510 keV and 20 keV is shown. These parasitic ‘wing’ and background contributions are typical for all electrostatic energy analyzers [20,25–27]. Background and ‘wing’ effects result from electrons backscattered and multiply scattered from the electrode surfaces, at the Herzog electrodes and aperture slits. The number of scattered electrons that are detected increases with increasing width of the exit slit S2 . The shape of the wings and the background of the response functions R(E1 , E) are different for all spectrometers and all widths of the exit slit. Therefore R(E1 , E) has to be measured separately for every particular spectrometer and exit slit adjustment.
5.2. Measured energy spectra of BSE The background and ‘wing’ effects of the response functions R(E1 , E) for this type of spectrometer lead to certain problems in data interpretation of regis-
(14)
From the response functions R(E1 , E) (Figs. 4 and 5) the FWHM DE can be derived: DE increases proportional with increasing E, i.e. DE /E0 5 const in both cases. The DE /E0 5 const dependence implies that the number of electrons transmitted through the toroidal energy analyzer depends linearly on the energy E. This number of electrons is correlated to the area under the response functions R(E1 , E) that increases proportionally to the energy E as well:
Fig. 6. Illustration of the ‘wings’ appearing in the spectra recorded by means of deflector type energy analyzers for monoenergetic electron beams.
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tered BSE-spectra. The signal i reg (E1 ) for a chosen energy E1 contains not only electrons with the set energy E1 but also scattered electrons with deviating energies. In addition the energy resolution DE /E of the spectrometer has to be taken into account for the spectrum analysis. In Fig. 7 typical examples are shown for the recorded signals i reg (E1 ) (curves 2 and 4) and their corresponding extracted BSE-spectra fE (E) (curves 1 and 3) for bulk Au and Cu. The extraction of the fE (E)-function is based on the simplified model described above (see Section 3.3). Since a linear energy dependent detector was used, the integral of R(E1 , E)*D(E) is proportional to E1 *(E1 2Ethresh ). Therefore the experimentally obtained signal was divided by the latter term. This model does not correct the background and ‘wing’ effects, and due to the division by E1 *(E1 2Ethresh ) the deviation from the true spectrum in the region of high energy losses is even more evident in the corrected spectra fE (E1 ). Fig. 7 shows that the deformation of spectra on the left hand side of the maximum and the shift of the position of the maximum to lower energies increase with atomic number Z. The background and ‘wing’ effects contributes at least 10–20% to the total curve area of R(E1 , E) for optimized spectrometers. Essential improvement can be reached however by using corrugated electrodes which minimize the electron reflection [28]. In order to make use of the smaller backscattering coefficient of low Z elements on rough surfaces the electrodes were spray coated with graphite. As an example Fig.
Fig. 7. Measured and energy corrected BSE-spectra of Au and Cu (bulk specimens).
Fig. 8. Reduction of ‘wing’-effects by carbon-coating of spectrometer electrodes.
8 shows measured BSE-spectra for Au with coated and uncoated electrodes leading to a significant reduction of those artefacts by a factor of at least 0.1.
6. Conclusions The main metrological characteristics such as response and transmission functions, coupling constant and energy resolution for a toroidal electrostatic energy analyzer adapted to a standard SEM have been studied. The techniques of correct determination of these characteristics for this kind of spectrometer were discussed. For aperture slits of the spectrometer allowing reasonable electron intensities at the detector, an energy resolution of about 2.5% was obtained. The energy spectra of transmitted electrons have been studied for linear-energy-dependent and energyindependent detectors in the energy range 3–30 keV. It is shown that in order to obtain absolute energy spectra the experimental spectra have to be divided
D. Berger et al. / Journal of Electron Spectroscopy and Related Phenomena 105 (1999) 119 – 127
by E1 *(E1 2 Ethresh ) in the case of energy-dependent detectors and by E1 only for energy-independent detectors. The influence of the background and ‘wing’ effects on the measured BSE spectra has been analyzed. The parasitic contribution of this factor in BSE-spectra is significant, especially in the low energy region. These artefacts can significantly be reduced by carbon spray-coating of the electrodes.
Acknowledgements This work was supported by the Volkswagen foundation. Thanks are due to A. Gostev for the development of data acquisition hard- and software.
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