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Energy calibration of a Rowland circle spectrometer for inverse photoemission
Nuclear Inst. and Methods in Physics Research, A 945 (2019) 162570
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Energy calibration of a Rowland circle spectrometer for inverse photoemission Rolando Esparza a , Samuel Hevia b , Jean F. Veyan c , Claudio Figueroa a , Robert Bartynski d , Valeria del Campo a , Ricardo Henríquez a , Patricio Häberle a ,∗ a
Physics Department, Universidad Técnica Federico Santa María, Valparaíso 2390123, Chile Facultad de Física, Pontificia Universidad Católica de Chile, Santiago, Chile c Department of Materials Science and Engineering, University of Texas at Dallas, TX 75080, USA d Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA b
ARTICLE Keywords: Inverse photoemission Grating spectrometer Bremsstrahlung
INFO
ABSTRACT Inverse photoemission remains the main spectroscopic technique to explore the unoccupied electronic states of materials for both solids and adsorbed molecules. It also allows collecting information regarding the kdependence of the electronic bands above the Fermi level. For spectrometers that consider the use of a diffraction grating as a way of analyzing the photon energy, the energy calibration of the collected spectra is a problem that needs to be addressed. In this paper we present results related to the application of an energy calibration procedure applied to a recently completed inverse photoemission spectrometer.
1. Introduction Characterizing the electronic structure of single crystal surfaces and nanoscale materials is a subject of continuous scientific interest, considering the permanent progress been made in different synthesis processes towards the search of novel applications of new materials. For example, the successful design of new devices that considers applications of phenomena such as spintronics [1] and valleytronics [2], requires a detailed characterization of the electronic structure of systems composed of few atomic layers of the material of interest. The occupied electronic states in these systems have been usually well described by photoemission, mainly by synchrotron radiation sources in a wide range of photon energies. Also, techniques available in a smaller lab. scale, such as vacuum ultraviolet photoemission (UPS) based on He or Ar lamps, combined with X-ray sources and electron energy analyzers (XPS), have been used to examine the density of states close to the valence band and also to obtain information from deeper bulk electronic states. In the case of unoccupied electronic states there is no equivalent to storage ring experimental techniques, as is the case for photoemission. Mainly two approaches have been used to examine states above the Fermi level, first using 2-photon photoemission (2PPE) [3], which provides some information regarding density of states and lifetime of excited states and second, inverse photoemission spectroscopy (IPES), which when operated in a momentum resolved mode, allows the determination of the unoccupied band structure of materials. ∗
The theoretical prediction by Pendry [4], on the possibility of implementing IPES as a viable experimental technique and the first report of an experimental spectrometer for IPES [5] included the use of a variable energy electron gun (e-gun) and a Geiger Müller band-pass filter detector [6]. The next instrumental improvement was the incorporation of an optical device with energy dispersion capabilities in order to obtain energy sensitivity. This would allow the spectrometer to operate in a similar way as electron energy analyzers do in photoemission, with the exchange of roles between photons and electrons. In this mode, the sample is bombarded with electrons of a fixed kinetic energy and the emerging photons, with different energies, are detected simultaneously. Considering the reduced cross section for optical transitions in IPES experiments, the angular acceptance for photons that constitute the spectroscopic signal should be maximized and at the same time a reduced number of optical element should be used, since each additional optical component absorbs part of the signal. The element of choice for this role is then a single concave grating, which includes both the energy dispersion and the necessary focusing properties to allow detection of vacuum ultra violet (VUV) photons through a position sensitive detector. The extensive experience of a few optical manufacturers, that have mastered the design and fabrication of spherical diffraction gratings (SDG) for handling synchrotron radiation light sources, makes the SDG the optimum element to incorporate into IPES spectrometers. The optical properties of the SDG are such that, in the so-called Rowland Circle (RC) [7] configuration, optimal focusing
Corresponding author. E-mail address: [email protected] (P. Häberle).
https://doi.org/10.1016/j.nima.2019.162570 Received 16 August 2018; Received in revised form 10 July 2019; Accepted 11 August 2019 Available online 14 August 2019 0168-9002/© 2019 Published by Elsevier B.V.
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Nuclear Inst. and Methods in Physics Research, A 945 (2019) 162570
Table 1 Optical efficiency of spherical grating. Energy range
Average efficiency
10–18 eV 18–31 eV 31–40 eV
3.7% 7.0% 2.0%
The RC configuration for a SDG spectrometer considers that both the entrance slit and the detector should be located along a circumference of diameter equal to the grating’s radius of curvature. In the case of IPES, the entrance slit is simply the spot illuminated by the e-beam on the sample being examined, since the photons to be analyzed only emerge from this point. As indicated in Fig. 1, the detector surface is located along the same circumference. A stepping motor, that rotates a couple of diametric rods on which the PSD support base is mounted, moves the detector along the RC. Changing the position of the detector, as described in Fig. 1, allows examining different photon energy ranges while keeping the detector in the RC. As mentioned above, in order to maximize photon counting, the design presented here considers near normal incidence (NI) of photons onto the grating. This choice immediately implies that the electron gun, of the type incorporated in this instrument, and the detector should be both located in the same vacuum chamber. In principle this is no problem, but since the PSD is also sensitive to charged particles, ions and electrons, the likelihood of having them reach the detector, and contributing to the signal, as unwanted noise, is fairly high if a hot filament is close by. This problem has been circumvented in the past by two different approaches, one of them has been to opt for a slightly off-RC configuration [16], keeping NI and moving away from the RC by displacing both sample and detector in opposite directions. In this geometry the detector and e-gun can then be located in different vacuum chambers, thus minimizing the shielding requirements necessary to assure proper PSD operation. An alternative design considered a strict RC mounting for both detector and photon source, but moving away from NI, thus reducing the effective solid angle for photon detection [11]. In the latter case, the separation between the sample and detector is large enough to allow mounting them in different vacuum chambers. Our NI-RC design considers instead, shielding the PSD, as effectively as possible, and keeping it in the same vacuum chamber together with the e-gun. A grounded metal plate was introduced to separate the sample section of the chamber from the PSD. In addition, a cylindrical metallic cover was used to surround the PSD and a grounded, gold covered, mesh was installed in front of the channel plates to avoid unwanted charged particles reaching the detector. The advantage of this design is that for a small area SDG a relatively high fraction of the emitted photon flux is collected (f /3.1 and 0.32 sr) while retaining at the same time the optimum focusing properties of the RC mounting. When a spectrum is collected in this type of detector, a 2D image of the photon intensities is generated as a function of the coordinates in the anode. A typical spectrum, collected from Au (111) bombarded with a 24.0 eV electron beam incident normal to the surface, is displayed in Fig. 2. Data appears as a stripe over the circular sensitive area of the detector. The wide segment is oriented perpendicular to the SDG ruling and as such, this is the energy dispersing direction. Even in the Rowland circle configuration the focusing in the transversal direction is not perfect and depends slightly on the photon energy. The front end of the data stripe, low channel numbers in the vertical direction (Fig. 2a), shows only the background intensity as expected, since for this particular detector position, the IPES onset is located close to channel 25. In order to circumvent the difficulty of mounting both the SDG and the detector perfectly aligned, the acquisition software can rotate the image of the data prior to summing them up in the direction perpendicular to the photon energy dispersion. For the electron gun (e-gun) we have used the design of Stoffel and Johnson [17], machined in a copper alloy (everdur), and polarized without the implementation of a contact potential compensation [18]. There are a few relevant aspects to consider while characterizing the gun under normal operation conditions (filament current: 0.95 A; sample current: 5 to 10 μA). The first one is the energy resolution. Despite the fact the cathode can be attached to a voltage supply with minimum ripple (<1 mV for a typical output of 20 V), the electrons are thermally emitted from a BaO cathode [19] , so they do acquire an
is obtained for different photon energies, along a circumference of diameter equal to the radius of curvature of the SDG (the Rowland circle). Despite the advantage of SDG based spectrometers of being able to detect different photon energy, it is not clear that the quantum efficiency of the diffraction based spectrometers is any better than the original Geiger Müller configuration. A few experimental setups based on diffraction gratings have been implemented [8–13] and used to examine various single crystal surfaces and overlayers. Even though IPES, has been around, as a functional experimental technique, for nearly 40 years, there are still no commercial IPES units among the handful of such systems currently operating around the world. 2. Description of the apparatus In the present paper we describe the calibration of an IPES spectrometer operating in a RC configuration. Considering the higher optical efficiency of the VUV-SDG under normal incidence (NI), a near-NI design was considered. This configuration has the problem of having almost overlapping positions for the sample, the actual photon source for the optical system, and the photon detector. This coincidence was avoided by displacing the sample a couple of degrees away from the normal direction. Fig. 1 shows a schematic diagram of the configuration of the present design, indicating the position of the SDG and the sample. The detector has been depicted located in two positions, one for the low photon energy end: 10 eV and the other located 13.2◦ away, to intercept the maximum photon energy (40 eV), diffracted from a point like source on the sample. The custom designed SDG [14] has a ruling of 2400 lines/mm, a diameter of 16 cm and a radius of curvature equal to 50 cm. It has a rectangular groove profile that optimizes the efficiency at first order over higher diffraction orders. The grating is supported in a NG5 black glass substrate, which is covered by 30 nm Pt with a 2 nm Cr binding layer. The optical efficiency, over the energy range of interest, provided by the manufacturer 14 is detailed in Table 1. The SDG, the electron gun and the detector are all held in place attached to a metallic frame inside the ultra high vacuum chamber. The sample is transferred from a preparation chamber and mounted on a xyz commercial translation stage (xy precision of 0.03 mm) with rotations around two orthogonal axes. A reference indicator, attached to the supporting frame, has been included in order to assist in the positioning of the sample surface in the RC circumference. A low energy electron diffraction system is used to orient the azimuthal angle of single crystal surfaces in a way in which a principal crystallographic direction and the momentum of the IPES e-beam are both contained in the same plane. The rotation of the sample around an axis perpendicular to this plane, changes the projection of the electronic momentum parallel to the surface of the sample (along the chosen crystallographic direction). In the case of single crystals, this characteristic of the spectrometer allows the collection of spectra for different parallel momentum, thus permitting the exploration of the unoccupied electronic bands of the material. The 2D-position sensitive photon detector (PSD) consists of a set of micro-channel plates, backed by a resistive anode encoded in two perpendicular axes, by an array of 256 × 256 channels over a circle of radius 25.4 mm [15]. Hence, in any of the two directions each channel corresponds roughly to 1/10 mm on the surface of the detector. This value finally limits the ultimate energy resolution of the spectrometer for a theoretical point like photon source. 2
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Nuclear Inst. and Methods in Physics Research, A 945 (2019) 162570
Fig. 1. Schematic representation of the spectrometer.
Fig. 2. (a) 2D Image of the IPES intensity as collected in the detector. (b) The same spectrum in (a), displayed as intensity vs. channel number. The intensity of a particular channel corresponds to the sum of the intensities in all active pixels along a direction perpendicular to the dispersion direction.
additional thermal energy distribution. This additional energy spread, together with the cathode potential define the energy profile of the electron beam and determines the ultimate energy resolution of the gun. There is a clear tradeoff between maximizing the current on the sample (typically 7 to 10 μA) by increasing the heating power delivered to the cathode, and the spectrometer energy resolution. A second ingredient in the e-gun performance is the actual energy the electron beam displays outside the e-gun, in vacuum. This is not simply the cathode potential energy since the electrons have to overcome the additional barrier of the cathode work function to become part of the electron beam. Since the effective cathode work function depends on its temperature, the kinetic energy of the e-beam has to be determined experimentally under standard conditions. Finally, the angular dispersion of the e-beam (<5◦ ) is also a relevant parameter [17]. It has an impact both in the energy resolution, by defining a finite spot size on the sample from which the bremsstrahlung photons emerge, and the momentum resolution of the electron beam. This latter parameter is significant for the operation of the spectrometer in a mode that can provide relevant band structure information from crystalline surfaces. It allows discriminating intensities between contiguous values of the electron momentum, a necessary requirement to operate the spectrometer in a k-resolving mode, denoted as k-RIPES [10,20]. It may be an important aspect of this particular design that the egun is not rigidly fixed to the multi-pin vacuum flange connector, which
attaches the e-gun to the vacuum chamber. It is simply supported by contact on a metal plate, fixed to the flange, and the flexible electrical wires that carry the different polarization voltages to the e-gun. This allows placing the e-gun, during installation, in a gondola like support piece secured to the frame that also holds the SDG and the PSD. This design feature minimizes the misalignments induced by the assembly procedure, thus decreasing the possibility of moving away from RC condition while moving either the sample or the detector. 3. Characterization of the e-gun A direct way to obtain an upper limit for the energy resolution of the e-gun is by measuring, at a fixed cathode potential (V 𝑐 ), the current on the sample (∼5 μA, Au(111)), as a function of a repulsive voltage (𝑉𝑟𝑒𝑝 ), applied to it. Since the sample presents a rather sharp potential barrier for incident electrons, one would expect, for a perfectly monochromatic electron beam, a step-like function behavior for the current on the sample, as a function of an applied retarding voltage, if space charge effects can be neglected (see Fig. 3). Since the electron beam has an energy distribution centered on the nominal beam energy, in part due to the thermal origin of the emission, the derivative of the current with respect to the retarding voltage around the onset is roughly proportional to this e-beam energy distribution. 3
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Nuclear Inst. and Methods in Physics Research, A 945 (2019) 162570
of the e-beam spot on the sample, up to some geometrical corrections that depends on the relative orientations of sample, the grating and the e-beam momentum. The shape of the spot behaves as expected with respect to sample rotations and also to changes in the focusing voltage. The actual dimensions of the spot in the detector can be obtained experimentally by comparing directly the white light image of a portion of the sample plate. Fig. 5 displays a 2D white light image of a set of e-beam profiles on the sample. The position of the detector was shifted slightly between each measurement, while the reflected beam was kept in a fixed position. The collection time was the same for each one of the spots. There is indeed a manifest nonlinearity in the detector (maximum nonlinearity: 0.5%/channel), which in part could be intrinsic or related to a non-uniform distribution of the voltages polarizing the microchannel-plates array, an effect, which is fairly evident at the detector‘s edge. A measurement like the one shown in Fig. 5b, could be used to compensate the measured intensities along the detector if required. The FWHM of the white light image of the e-beam profile on the sample is in the range between 1.5 mm to 1.3 mm for e-beam energies varying form 25 eV to 35 eV. Illuminating a section of the sample plate with a rather defocused e-beam, with a relatively high current (20 μA), allows collecting a white light image (Fig. 5d), displaying a fairly well recognizable shape of the sample plate. The resulting image has a unitary lateral magnification, as expected for a spherical reflector in a Rowland circle configuration.
Fig. 3. Energy diagram for the electrons emerging form the cathode and directed onto the Au sample during the repulsion measurement. For a monochromatic incident beam the current becomes zero for 𝑒𝑉 𝑟𝑒𝑝 > 𝐾𝐸 − 𝜙𝐴𝑢 . During standard operation, the samples are grounded together with the chamber.
4. Photon energy calibration procedure While assembling the optical components of the spectrometer, the detector’s angular position, along the Rowland circle, was calibrated against the stepping motor counter. The reading in the counter reproduces quite well the detector position, with an accuracy below 1/10 of a degree. The condition for constructive interference in a concave spherical grating is the same as for a flat grating, Fig. 4. (−)𝑑𝑖∕𝑑𝑉𝑟𝑒𝑝 calculated from the experimental repulsion curves for different cathode voltages as a function of 𝑉𝑟𝑒𝑝 . The kinetic energy of the electron beam (𝐾𝐸 ) for each value of 𝑉𝑐 , can be estimated from the value 𝑒𝑉 𝑟𝑒𝑝 *, for which (−)𝑑𝑖∕𝑑𝑉𝑟𝑒𝑝 is maximum, as: 𝐾𝐸 = 𝑒𝑉 𝑟𝑒𝑝 * +𝜙𝐴𝑢 . An estimation of the kinetic energy dispersion of the e-beam can be directly obtained from the FWHM of each peak (it varies from 350 meV to 480 meV.)
sin 𝛼 + sin 𝜃 = 𝑚𝜆∕𝑎
(1)
where 𝛼 and 𝜃 are the incidence angle and the diffraction angle for incoming and diffracted photons, both measured from the central grating normal, 𝑎, is the spacing of the grooves, 𝜆 is the wavelength of the light and m is the diffraction order. In order to obtain an expression relating the channels in the detector with the energy of the detected photons, we can differentiate Eq. (1), to get a relation between differentials:
Fig. 4 shows, in a single plot, the derivative of these repulsion curves for a set of different beam energies. Two important parameters describing the operation of the e-gun can be obtained; one of them is the FWHM of the e-beam energy distribution and the other is the kinetic energy (𝐾𝐸 ) of the e-beam in vacuum. 𝐾𝐸 can be estimated from the value of 𝑉𝑟𝑒𝑝 for which (−)𝑑𝑖∕𝑑𝑉𝑟𝑒𝑝 is maximum (𝑉𝑟𝑒𝑝 *), namely: 𝐾𝐸 = 𝑒𝑉 𝑟𝑒𝑝 * +𝜙𝐴𝑢 ; where 𝜙𝐴𝑢 is the work function of Au(111) (5.3 eV [21]).
𝛥𝜃 𝑚 = (2) 𝛥𝜆 𝑎 cos 𝜃 The change in 𝜃 can be expressed as a change in the channel number (Ch) in the detector along the dispersion direction of the grating. For this system: Ch ≈ −R𝜃, with R being an adimensional constant, proportional to the SDG-detector distance, so Eq. (2) can be rewritten as:
For these type of spectrometers the overall energy resolution, including both photons and electrons, is typically between 300 and 500 meV [10]. Considering that the size of the photon source on the sample is roughly 1.3 mm, the actual limitation for the spectrometer resolution is not due to the optical properties of the SDG, but rather, directly linked to the kinetic energy distribution of the incident e-beam. The characterization of the size and shape of the electron beam spot on the sample is usually inferred from measurements performed using a Faraday cup, to collect part of the e-beam current as a function of position. In the absence of such device, the IPES spectrometer itself can be used to determine the diameter of the e-beam. For this measurement, the position of the SDG can be modified slightly to fit the white light reflection onto the detector surface. This is a slightly offRowland configuration, but nonetheless it can be used to provide useful information of the e-gun focusing properties. Under this condition, the profile of the white light spot on the detector corresponds to an image
𝛥𝐶ℎ −𝑅𝑚 = (3) 𝛥𝜆 𝑎 cos 𝜃 By replacing the change in wavelength by a change in photon energy (E= hc/𝜆) in (3), this last eq. can be expressed as: 𝛥𝐶ℎ 𝛥𝐸 𝛥𝐶ℎ −𝐸 2 −𝑅𝑚 = = 𝛥𝐸 𝛥𝜆 𝛥𝐸 ℎ𝑐 𝑎 cos 𝜃 By further simplification, with 𝑚 = −1, (4) can be rewritten as:
(4)
𝛥𝐶ℎ −K = (5) 𝛥𝐸 𝐸2 with K being a positive and approximately constant number, independent of energy. This approximation is valid since, for a fixed detector position, over the range of interest (𝐶ℎ = 0 to 256), cos 𝜃 is essentially constant. From the integration of Eq. (5), we obtain a simple relation 4
R. Esparza, S. Hevia, J.F. Veyan et al.
Nuclear Inst. and Methods in Physics Research, A 945 (2019) 162570
Fig. 5. (a) 2D image of the bremsstrahlung white light, collected slightly out of the Rowland circle configuration, as seen in the detector for a 25.1 eV e-beam. The different spots correspond to different detector positions, for a fixed white light spot in space, collected for 30 s in each position. (b) Intensity as a function of channel number along the dispersion direction for all the spots in (a). (c) Graphic representation of the sample holding plate. (d) White light emitted from the sample plate under illumination by a high current and defocused e-beam.
between the channels in the detector, Ch, and the energy, E, of the detected photons: 𝐶ℎ = 𝑐 + K(1∕𝐸)
Fig. 6 shows a series of normal incidence spectra collected form Au(111) at a single detector position, the data is consistent with previous measurements showing a strong surface feature right at the Fermi level [22]. The difference among these spectra is simply a change in 𝐾𝐸 , which is increased by 1 eV, from one spectrum to the next, starting from right to left in Fig. 6. The nonlinear relation that exists between the energy scale and the channels in the detector is evident in Fig. 6, by the increments in both the width of the surface feature and the separation between maxima, which are indeed equidistant in energy between successive spectra. The detector edge effects are also apparent in this data set, as shown by the high counting rate, displayed roughly at 10 to 15 channels from the detector’s edge (channel 256). The detector channel (Ch), identified with a photon energy equals to E for each spectrum, was determined by finding the intersection between a horizontal line, going over the background data in front of the Fermi edge, and a linear fit to the front rise of the IPES intensity. A good estimate of the e-beam energy spread can be obtained from the FWHM displayed by the repulsion curves shown in Fig. 4. The average value of 𝛥KE , obtained for the spectra displayed in Fig. 6 is 366 meV. The actual value of E is then determined by the expression: E= 𝐾E+ 𝛥KE .
(6)
The next step is then to use a set of experimentally determined values of Ch and E to find the unknown constants (c and K) in Eq. (6). Both constants fully describe the energy calibration for this particular detector position. Apart from using electronic transitions in hydrogen [10] as a source of photons, there are not very many standard frequency light sources that can be easily used to calibrate a spectrometer for inverse photoemission, especially if the detector can be moved to collect higher energies than the characteristic emission lines from hydrogen. The standard alternative method to perform the energy calibration, has been to use the response of the spectrometer itself. A brief description follows: For an electrically grounded metallic sample (Au(111)), bombarded by a monochromatic electron beam, it turns out that the maximum energy of the photons emitted from the sample will correspond to the kinetic energy (𝐾𝐸 ) of the electron beam in vacuum. In practice, for nearly monochromatic electron beams, the onset for photon emission occurs at a slightly higher energy, namely at 𝐸 = 𝐾𝐸 + 𝛥𝐾𝐸 , with 𝛥𝐾𝐸 being the characteristic energy spread of the electron beam. Photons with this energy are then making optical transitions to a final state, right above the Fermi level of the sample. A set of IPES spectra from this sample can be collected for different applied cathode voltages, modifying in each case 𝐾𝐸 , hence changing the channel (Ch) at which the IPES intensity takes off (IPES onset) for each spectrum. This set of experimentally obtained values (Ch vs E) can then be used to determine the best adjustment for c and K, in Eq. (6), both parameters finally define the spectrometer energy calibration.
This set of paired values, channel numbers (Ch) and photon energies (E), can then be plotted as shown in Fig. 7. The linear fit to these data points is then used to define the energy calibration of the detector. In Fig. 8, we have used these calibration parameters to display two of the spectra shown in Fig. 6, but now as a function of the energy of the detected photons, instead of channel number. Both spectra were fitted with a Gaussian function to determine the central energy of the surface state. A difference of 4 eV in the e-beam energy, is not expected to imply a significant change in the cross section for optical transitions, 5
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Nuclear Inst. and Methods in Physics Research, A 945 (2019) 162570
Fig. 6. Set of IPES spectra collected from Au(111), with the energy of the electron beam changed in increments of 1 eV, from 𝐾e . = 19.0 eV to 25.1 eV. The lower channel numbers correspond to higher photon energies.
hence, these leading peaks in both spectra should have essentially the same shape, but displaced in energy by 4 eV. The comparison is good within 50 meV. Underlying this agreement, nonetheless, is the use of the correct nonlinear calibration between photon energies and channel numbers. This comparison cannot be considered as proof of an absolute calibration of the spectrometer, but rather a consistency check for the calibration procedure. 5. Conclusion As mentioned above, the energy calibration of grating spectrometers in the VUV range lacks the existence of standard monochromatic light sources. This is in contrast to what happens in the visible range, where many different gas discharge lamps can provide distinctive wavelength which could be used for calibration purposes over a wide spectral range. In IPES, only H transitions (Lyman 𝛼 and Lyman 𝛽) have been used as a standard light source [10]. This is a difficulty, especially when the detector has to be moved to a spectral region that does not include the Lyman series. The calibration procedure for the IPES spectrometer described in this work relies on two simple references: the work function of a single crystal metal surface (Au(111)) and the kinetic energy of a nearly monochromatic e-beam, as determined in an experiment that measures the stopping potential. The energy calibration for the photon flux is then derived from an analytical expression, based on the grating dispersion, and the reference voltages used to polarize the sample and the electron source. Using standard electronic equipment the consistency of the energy calibration is better than 100 meV for 20 eV photons.
Fig. 7. Channel number versus (1/E). This data set of correlated pairs of energy and channel number generated by optical transitions right above the Fermi level (from Fig. 6). The markers are the experimental data points and the straight line is the best fit to the data. The agreement between the linear fit and the data points is explained by the theoretical functional dependence between Ch and (1/E), shown in Eq. (6).
Acknowledgments Partial funding for this research has been provided by MECESUP grant 0108 and FONDECYT grant 1171584, Chile. References [1] Dmytro Pesin, Allan H. MacDonald, Spintronics and pseudospintronics in graphene and topological insulators, Nature Mater. 11 (2012) 409, http://dx. doi.org/10.1038/nmat3305. [2] John R. Schaibley, Hongyi Yu, Genevieve Clark, Pasqual Rivera, Jason S. Ross, Kyle L. Seyler, Wang Yao, Xiaodong Xu, Valleytronics in 2D materials, Nat. Rev. Mater. 1 (2016) 16055. [3] Thomas Fauster, Wulf Steinmann, Electromagnetic waves: Recent developments in research, in: P. Halevi (Ed.), Volume 2: Photonic Probes of Surfaces, Elsevier, Amsterdam, 1995, pp. 347–411, Chapter 8. [4] J.B. Pendry, New probe for unoccupied bands at surfaces, Phys. Rev. Lett. 45 (1980) 1356; Theory of inverse photoemission, J. Phys. C 14 (1981) 1381. [5] V. Dose, VUV isochromat spectroscopy, Appl. Phys. 14 (1977) 117, http://dx. doi.org/10.1007/BF00882639. [6] G. Denninger, V. Dose, H. Scheidt, A VUV isochromat spectrometer for surface analysis, Appl. Phys. 18 (1979) 375, http://dx.doi.org/10.1007/BF00899691. [7] H.G. Beutler, The theory of the concave grating, J. Opt. Amer. 35 (1945) 311. [8] Th. Fauster, D. Straub, J.J. Donelon, D. Grimm, A. Marx, F.J. Himpsel, Normalincidence grating spectrograph with large acceptance for inverse photoemission, Rev. Sci. Instrum. 56 (1985) 1212, http://dx.doi.org/10.1063/1.1137977.
Fig. 8. Energy calibrated spectra of the IPES intensity vs photon energy obtained from Au(111). The as collected spectra were presented in Fig. 6. The solid lines are Gaussian fits to the surface state [21] in both spectra. The difference in energy between both maxima exceeds the kinetic energy difference between both spectra by 50 meV. A value, which is consistent with the error margin introduced by the calibration (<100 meV)
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Nuclear Inst. and Methods in Physics Research, A 945 (2019) 162570 [16] P.D. Johnson, S.L. Hulbert, R.F. Garrett, M.R. Howells, Normal incidence grating spectrometer designed for inverse photoemission studies in the range 10–30 eV, Rev. Sci. Instrum. 57 (1986) 1324. [17] N.G. Stoffel, P.D. Johnson, A low-energy high-brightness electron gun for inverse photoemission, Nucl. Instrum. Methods A 234 (1984) 230. [18] M. Maniraj, Sudipta Roy Barman, A low-energy high-brightness electron gun for inverse photoemission, Rev. Sci. Instrum. 85 (2014) 033301, http://dx.doi.org/ 10.1063/1.4866650. [19] Heat Wave Labs., 195 Aviation Way, Suite 100, Watsonville, CA 95076-2069, USA. [20] A. Zumbülte, A.B. Schmidt, M. Donath, Momentum resolution in inverse photoemission, Rev. Sci. Instrum. 86 (2015) 013908, http://dx.doi.org/10.1063/1. 4906508. [21] D. Straub, F.J. Himpsel, Spectroscopy of image-potential states with inverse photoemission, Phys. Rev. B 33 (1986) 2256–2261. [22] D.P. Woodruff, W.A. Royer, N.V. Smith, Empty surface states, image states, and band edge on Au(111), Phys. Rev. B 34 (1986) 764–767.
[9] M. Sancrotti, L. Braicovich, C. Chemelli, F. Ciccacci, E. Puppin, G. Trezzi, E. Vescovo, Ultraviolet inverse photoemission spectrograph with parallel multichannel isochromat acquisition, Rev. Sci. Instrum. 62 (1991) 639, http://dx.doi.org/ 10.1063/1.1142062. [10] P.D. Johnson, S.L. Hulbert, Inverse photoemission, Rev. Sci. Instrum. 61 (1990) 2277, http://dx.doi.org/10.1063/1.1141352. [11] D.A. Arena, F.G. Curti, R.A. Bartynski, Momentum-dependent orbital character of unoccupied Cs-induced levels on Cu(100) and Cu(111), Surf. Sci. 369 (1996) L117, http://dx.doi.org/10.1016/S0039-6028(96)01127-2. [12] L. Kipp, M. Boehme, H. Carstensen, R. Claessen, M. Skiwoski, Low-energy inverse photoemission spectroscopy using a high-resolution grating spectrometer in the near ultraviolet range, Rev. Sci. Instrum. 68 (1997) 2144, http://dx.doi.org/10. 1063/1.1148077. [13] Hiroyuki Yoshida, Hiroyuki yoshida low-energy inverse photoemission spectroscopy using a high-resolution grating spectrometer in the near ultraviolet range, Rev. Sci. Instrum. 84 (2013) 103901. [14] Carl Zeiss Optronics GmbH, grating designed and characterized by R. Lenke and K. Heidemann, 2005. [15] Detector serial number: 3390-3510-CsI, Quantar Technology Incorporated, 2620 A Mission Street, Santa Cruz, CA 95060, USA.
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Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima
Energy calibration of a Rowland circle spectrometer for inverse photoemission Rolando Esparza a , Samuel Hevia b , Jean F. Veyan c , Claudio Figueroa a , Robert Bartynski d , Valeria del Campo a , Ricardo Henríquez a , Patricio Häberle a ,∗ a
Physics Department, Universidad Técnica Federico Santa María, Valparaíso 2390123, Chile Facultad de Física, Pontificia Universidad Católica de Chile, Santiago, Chile c Department of Materials Science and Engineering, University of Texas at Dallas, TX 75080, USA d Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA b
ARTICLE Keywords: Inverse photoemission Grating spectrometer Bremsstrahlung
INFO
ABSTRACT Inverse photoemission remains the main spectroscopic technique to explore the unoccupied electronic states of materials for both solids and adsorbed molecules. It also allows collecting information regarding the kdependence of the electronic bands above the Fermi level. For spectrometers that consider the use of a diffraction grating as a way of analyzing the photon energy, the energy calibration of the collected spectra is a problem that needs to be addressed. In this paper we present results related to the application of an energy calibration procedure applied to a recently completed inverse photoemission spectrometer.
1. Introduction Characterizing the electronic structure of single crystal surfaces and nanoscale materials is a subject of continuous scientific interest, considering the permanent progress been made in different synthesis processes towards the search of novel applications of new materials. For example, the successful design of new devices that considers applications of phenomena such as spintronics [1] and valleytronics [2], requires a detailed characterization of the electronic structure of systems composed of few atomic layers of the material of interest. The occupied electronic states in these systems have been usually well described by photoemission, mainly by synchrotron radiation sources in a wide range of photon energies. Also, techniques available in a smaller lab. scale, such as vacuum ultraviolet photoemission (UPS) based on He or Ar lamps, combined with X-ray sources and electron energy analyzers (XPS), have been used to examine the density of states close to the valence band and also to obtain information from deeper bulk electronic states. In the case of unoccupied electronic states there is no equivalent to storage ring experimental techniques, as is the case for photoemission. Mainly two approaches have been used to examine states above the Fermi level, first using 2-photon photoemission (2PPE) [3], which provides some information regarding density of states and lifetime of excited states and second, inverse photoemission spectroscopy (IPES), which when operated in a momentum resolved mode, allows the determination of the unoccupied band structure of materials. ∗
The theoretical prediction by Pendry [4], on the possibility of implementing IPES as a viable experimental technique and the first report of an experimental spectrometer for IPES [5] included the use of a variable energy electron gun (e-gun) and a Geiger Müller band-pass filter detector [6]. The next instrumental improvement was the incorporation of an optical device with energy dispersion capabilities in order to obtain energy sensitivity. This would allow the spectrometer to operate in a similar way as electron energy analyzers do in photoemission, with the exchange of roles between photons and electrons. In this mode, the sample is bombarded with electrons of a fixed kinetic energy and the emerging photons, with different energies, are detected simultaneously. Considering the reduced cross section for optical transitions in IPES experiments, the angular acceptance for photons that constitute the spectroscopic signal should be maximized and at the same time a reduced number of optical element should be used, since each additional optical component absorbs part of the signal. The element of choice for this role is then a single concave grating, which includes both the energy dispersion and the necessary focusing properties to allow detection of vacuum ultra violet (VUV) photons through a position sensitive detector. The extensive experience of a few optical manufacturers, that have mastered the design and fabrication of spherical diffraction gratings (SDG) for handling synchrotron radiation light sources, makes the SDG the optimum element to incorporate into IPES spectrometers. The optical properties of the SDG are such that, in the so-called Rowland Circle (RC) [7] configuration, optimal focusing
Corresponding author. E-mail address: [email protected] (P. Häberle).
https://doi.org/10.1016/j.nima.2019.162570 Received 16 August 2018; Received in revised form 10 July 2019; Accepted 11 August 2019 Available online 14 August 2019 0168-9002/© 2019 Published by Elsevier B.V.
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Table 1 Optical efficiency of spherical grating. Energy range
Average efficiency
10–18 eV 18–31 eV 31–40 eV
3.7% 7.0% 2.0%
The RC configuration for a SDG spectrometer considers that both the entrance slit and the detector should be located along a circumference of diameter equal to the grating’s radius of curvature. In the case of IPES, the entrance slit is simply the spot illuminated by the e-beam on the sample being examined, since the photons to be analyzed only emerge from this point. As indicated in Fig. 1, the detector surface is located along the same circumference. A stepping motor, that rotates a couple of diametric rods on which the PSD support base is mounted, moves the detector along the RC. Changing the position of the detector, as described in Fig. 1, allows examining different photon energy ranges while keeping the detector in the RC. As mentioned above, in order to maximize photon counting, the design presented here considers near normal incidence (NI) of photons onto the grating. This choice immediately implies that the electron gun, of the type incorporated in this instrument, and the detector should be both located in the same vacuum chamber. In principle this is no problem, but since the PSD is also sensitive to charged particles, ions and electrons, the likelihood of having them reach the detector, and contributing to the signal, as unwanted noise, is fairly high if a hot filament is close by. This problem has been circumvented in the past by two different approaches, one of them has been to opt for a slightly off-RC configuration [16], keeping NI and moving away from the RC by displacing both sample and detector in opposite directions. In this geometry the detector and e-gun can then be located in different vacuum chambers, thus minimizing the shielding requirements necessary to assure proper PSD operation. An alternative design considered a strict RC mounting for both detector and photon source, but moving away from NI, thus reducing the effective solid angle for photon detection [11]. In the latter case, the separation between the sample and detector is large enough to allow mounting them in different vacuum chambers. Our NI-RC design considers instead, shielding the PSD, as effectively as possible, and keeping it in the same vacuum chamber together with the e-gun. A grounded metal plate was introduced to separate the sample section of the chamber from the PSD. In addition, a cylindrical metallic cover was used to surround the PSD and a grounded, gold covered, mesh was installed in front of the channel plates to avoid unwanted charged particles reaching the detector. The advantage of this design is that for a small area SDG a relatively high fraction of the emitted photon flux is collected (f /3.1 and 0.32 sr) while retaining at the same time the optimum focusing properties of the RC mounting. When a spectrum is collected in this type of detector, a 2D image of the photon intensities is generated as a function of the coordinates in the anode. A typical spectrum, collected from Au (111) bombarded with a 24.0 eV electron beam incident normal to the surface, is displayed in Fig. 2. Data appears as a stripe over the circular sensitive area of the detector. The wide segment is oriented perpendicular to the SDG ruling and as such, this is the energy dispersing direction. Even in the Rowland circle configuration the focusing in the transversal direction is not perfect and depends slightly on the photon energy. The front end of the data stripe, low channel numbers in the vertical direction (Fig. 2a), shows only the background intensity as expected, since for this particular detector position, the IPES onset is located close to channel 25. In order to circumvent the difficulty of mounting both the SDG and the detector perfectly aligned, the acquisition software can rotate the image of the data prior to summing them up in the direction perpendicular to the photon energy dispersion. For the electron gun (e-gun) we have used the design of Stoffel and Johnson [17], machined in a copper alloy (everdur), and polarized without the implementation of a contact potential compensation [18]. There are a few relevant aspects to consider while characterizing the gun under normal operation conditions (filament current: 0.95 A; sample current: 5 to 10 μA). The first one is the energy resolution. Despite the fact the cathode can be attached to a voltage supply with minimum ripple (<1 mV for a typical output of 20 V), the electrons are thermally emitted from a BaO cathode [19] , so they do acquire an
is obtained for different photon energies, along a circumference of diameter equal to the radius of curvature of the SDG (the Rowland circle). Despite the advantage of SDG based spectrometers of being able to detect different photon energy, it is not clear that the quantum efficiency of the diffraction based spectrometers is any better than the original Geiger Müller configuration. A few experimental setups based on diffraction gratings have been implemented [8–13] and used to examine various single crystal surfaces and overlayers. Even though IPES, has been around, as a functional experimental technique, for nearly 40 years, there are still no commercial IPES units among the handful of such systems currently operating around the world. 2. Description of the apparatus In the present paper we describe the calibration of an IPES spectrometer operating in a RC configuration. Considering the higher optical efficiency of the VUV-SDG under normal incidence (NI), a near-NI design was considered. This configuration has the problem of having almost overlapping positions for the sample, the actual photon source for the optical system, and the photon detector. This coincidence was avoided by displacing the sample a couple of degrees away from the normal direction. Fig. 1 shows a schematic diagram of the configuration of the present design, indicating the position of the SDG and the sample. The detector has been depicted located in two positions, one for the low photon energy end: 10 eV and the other located 13.2◦ away, to intercept the maximum photon energy (40 eV), diffracted from a point like source on the sample. The custom designed SDG [14] has a ruling of 2400 lines/mm, a diameter of 16 cm and a radius of curvature equal to 50 cm. It has a rectangular groove profile that optimizes the efficiency at first order over higher diffraction orders. The grating is supported in a NG5 black glass substrate, which is covered by 30 nm Pt with a 2 nm Cr binding layer. The optical efficiency, over the energy range of interest, provided by the manufacturer 14 is detailed in Table 1. The SDG, the electron gun and the detector are all held in place attached to a metallic frame inside the ultra high vacuum chamber. The sample is transferred from a preparation chamber and mounted on a xyz commercial translation stage (xy precision of 0.03 mm) with rotations around two orthogonal axes. A reference indicator, attached to the supporting frame, has been included in order to assist in the positioning of the sample surface in the RC circumference. A low energy electron diffraction system is used to orient the azimuthal angle of single crystal surfaces in a way in which a principal crystallographic direction and the momentum of the IPES e-beam are both contained in the same plane. The rotation of the sample around an axis perpendicular to this plane, changes the projection of the electronic momentum parallel to the surface of the sample (along the chosen crystallographic direction). In the case of single crystals, this characteristic of the spectrometer allows the collection of spectra for different parallel momentum, thus permitting the exploration of the unoccupied electronic bands of the material. The 2D-position sensitive photon detector (PSD) consists of a set of micro-channel plates, backed by a resistive anode encoded in two perpendicular axes, by an array of 256 × 256 channels over a circle of radius 25.4 mm [15]. Hence, in any of the two directions each channel corresponds roughly to 1/10 mm on the surface of the detector. This value finally limits the ultimate energy resolution of the spectrometer for a theoretical point like photon source. 2
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Fig. 1. Schematic representation of the spectrometer.
Fig. 2. (a) 2D Image of the IPES intensity as collected in the detector. (b) The same spectrum in (a), displayed as intensity vs. channel number. The intensity of a particular channel corresponds to the sum of the intensities in all active pixels along a direction perpendicular to the dispersion direction.
additional thermal energy distribution. This additional energy spread, together with the cathode potential define the energy profile of the electron beam and determines the ultimate energy resolution of the gun. There is a clear tradeoff between maximizing the current on the sample (typically 7 to 10 μA) by increasing the heating power delivered to the cathode, and the spectrometer energy resolution. A second ingredient in the e-gun performance is the actual energy the electron beam displays outside the e-gun, in vacuum. This is not simply the cathode potential energy since the electrons have to overcome the additional barrier of the cathode work function to become part of the electron beam. Since the effective cathode work function depends on its temperature, the kinetic energy of the e-beam has to be determined experimentally under standard conditions. Finally, the angular dispersion of the e-beam (<5◦ ) is also a relevant parameter [17]. It has an impact both in the energy resolution, by defining a finite spot size on the sample from which the bremsstrahlung photons emerge, and the momentum resolution of the electron beam. This latter parameter is significant for the operation of the spectrometer in a mode that can provide relevant band structure information from crystalline surfaces. It allows discriminating intensities between contiguous values of the electron momentum, a necessary requirement to operate the spectrometer in a k-resolving mode, denoted as k-RIPES [10,20]. It may be an important aspect of this particular design that the egun is not rigidly fixed to the multi-pin vacuum flange connector, which
attaches the e-gun to the vacuum chamber. It is simply supported by contact on a metal plate, fixed to the flange, and the flexible electrical wires that carry the different polarization voltages to the e-gun. This allows placing the e-gun, during installation, in a gondola like support piece secured to the frame that also holds the SDG and the PSD. This design feature minimizes the misalignments induced by the assembly procedure, thus decreasing the possibility of moving away from RC condition while moving either the sample or the detector. 3. Characterization of the e-gun A direct way to obtain an upper limit for the energy resolution of the e-gun is by measuring, at a fixed cathode potential (V 𝑐 ), the current on the sample (∼5 μA, Au(111)), as a function of a repulsive voltage (𝑉𝑟𝑒𝑝 ), applied to it. Since the sample presents a rather sharp potential barrier for incident electrons, one would expect, for a perfectly monochromatic electron beam, a step-like function behavior for the current on the sample, as a function of an applied retarding voltage, if space charge effects can be neglected (see Fig. 3). Since the electron beam has an energy distribution centered on the nominal beam energy, in part due to the thermal origin of the emission, the derivative of the current with respect to the retarding voltage around the onset is roughly proportional to this e-beam energy distribution. 3
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of the e-beam spot on the sample, up to some geometrical corrections that depends on the relative orientations of sample, the grating and the e-beam momentum. The shape of the spot behaves as expected with respect to sample rotations and also to changes in the focusing voltage. The actual dimensions of the spot in the detector can be obtained experimentally by comparing directly the white light image of a portion of the sample plate. Fig. 5 displays a 2D white light image of a set of e-beam profiles on the sample. The position of the detector was shifted slightly between each measurement, while the reflected beam was kept in a fixed position. The collection time was the same for each one of the spots. There is indeed a manifest nonlinearity in the detector (maximum nonlinearity: 0.5%/channel), which in part could be intrinsic or related to a non-uniform distribution of the voltages polarizing the microchannel-plates array, an effect, which is fairly evident at the detector‘s edge. A measurement like the one shown in Fig. 5b, could be used to compensate the measured intensities along the detector if required. The FWHM of the white light image of the e-beam profile on the sample is in the range between 1.5 mm to 1.3 mm for e-beam energies varying form 25 eV to 35 eV. Illuminating a section of the sample plate with a rather defocused e-beam, with a relatively high current (20 μA), allows collecting a white light image (Fig. 5d), displaying a fairly well recognizable shape of the sample plate. The resulting image has a unitary lateral magnification, as expected for a spherical reflector in a Rowland circle configuration.
Fig. 3. Energy diagram for the electrons emerging form the cathode and directed onto the Au sample during the repulsion measurement. For a monochromatic incident beam the current becomes zero for 𝑒𝑉 𝑟𝑒𝑝 > 𝐾𝐸 − 𝜙𝐴𝑢 . During standard operation, the samples are grounded together with the chamber.
4. Photon energy calibration procedure While assembling the optical components of the spectrometer, the detector’s angular position, along the Rowland circle, was calibrated against the stepping motor counter. The reading in the counter reproduces quite well the detector position, with an accuracy below 1/10 of a degree. The condition for constructive interference in a concave spherical grating is the same as for a flat grating, Fig. 4. (−)𝑑𝑖∕𝑑𝑉𝑟𝑒𝑝 calculated from the experimental repulsion curves for different cathode voltages as a function of 𝑉𝑟𝑒𝑝 . The kinetic energy of the electron beam (𝐾𝐸 ) for each value of 𝑉𝑐 , can be estimated from the value 𝑒𝑉 𝑟𝑒𝑝 *, for which (−)𝑑𝑖∕𝑑𝑉𝑟𝑒𝑝 is maximum, as: 𝐾𝐸 = 𝑒𝑉 𝑟𝑒𝑝 * +𝜙𝐴𝑢 . An estimation of the kinetic energy dispersion of the e-beam can be directly obtained from the FWHM of each peak (it varies from 350 meV to 480 meV.)
sin 𝛼 + sin 𝜃 = 𝑚𝜆∕𝑎
(1)
where 𝛼 and 𝜃 are the incidence angle and the diffraction angle for incoming and diffracted photons, both measured from the central grating normal, 𝑎, is the spacing of the grooves, 𝜆 is the wavelength of the light and m is the diffraction order. In order to obtain an expression relating the channels in the detector with the energy of the detected photons, we can differentiate Eq. (1), to get a relation between differentials:
Fig. 4 shows, in a single plot, the derivative of these repulsion curves for a set of different beam energies. Two important parameters describing the operation of the e-gun can be obtained; one of them is the FWHM of the e-beam energy distribution and the other is the kinetic energy (𝐾𝐸 ) of the e-beam in vacuum. 𝐾𝐸 can be estimated from the value of 𝑉𝑟𝑒𝑝 for which (−)𝑑𝑖∕𝑑𝑉𝑟𝑒𝑝 is maximum (𝑉𝑟𝑒𝑝 *), namely: 𝐾𝐸 = 𝑒𝑉 𝑟𝑒𝑝 * +𝜙𝐴𝑢 ; where 𝜙𝐴𝑢 is the work function of Au(111) (5.3 eV [21]).
𝛥𝜃 𝑚 = (2) 𝛥𝜆 𝑎 cos 𝜃 The change in 𝜃 can be expressed as a change in the channel number (Ch) in the detector along the dispersion direction of the grating. For this system: Ch ≈ −R𝜃, with R being an adimensional constant, proportional to the SDG-detector distance, so Eq. (2) can be rewritten as:
For these type of spectrometers the overall energy resolution, including both photons and electrons, is typically between 300 and 500 meV [10]. Considering that the size of the photon source on the sample is roughly 1.3 mm, the actual limitation for the spectrometer resolution is not due to the optical properties of the SDG, but rather, directly linked to the kinetic energy distribution of the incident e-beam. The characterization of the size and shape of the electron beam spot on the sample is usually inferred from measurements performed using a Faraday cup, to collect part of the e-beam current as a function of position. In the absence of such device, the IPES spectrometer itself can be used to determine the diameter of the e-beam. For this measurement, the position of the SDG can be modified slightly to fit the white light reflection onto the detector surface. This is a slightly offRowland configuration, but nonetheless it can be used to provide useful information of the e-gun focusing properties. Under this condition, the profile of the white light spot on the detector corresponds to an image
𝛥𝐶ℎ −𝑅𝑚 = (3) 𝛥𝜆 𝑎 cos 𝜃 By replacing the change in wavelength by a change in photon energy (E= hc/𝜆) in (3), this last eq. can be expressed as: 𝛥𝐶ℎ 𝛥𝐸 𝛥𝐶ℎ −𝐸 2 −𝑅𝑚 = = 𝛥𝐸 𝛥𝜆 𝛥𝐸 ℎ𝑐 𝑎 cos 𝜃 By further simplification, with 𝑚 = −1, (4) can be rewritten as:
(4)
𝛥𝐶ℎ −K = (5) 𝛥𝐸 𝐸2 with K being a positive and approximately constant number, independent of energy. This approximation is valid since, for a fixed detector position, over the range of interest (𝐶ℎ = 0 to 256), cos 𝜃 is essentially constant. From the integration of Eq. (5), we obtain a simple relation 4
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Fig. 5. (a) 2D image of the bremsstrahlung white light, collected slightly out of the Rowland circle configuration, as seen in the detector for a 25.1 eV e-beam. The different spots correspond to different detector positions, for a fixed white light spot in space, collected for 30 s in each position. (b) Intensity as a function of channel number along the dispersion direction for all the spots in (a). (c) Graphic representation of the sample holding plate. (d) White light emitted from the sample plate under illumination by a high current and defocused e-beam.
between the channels in the detector, Ch, and the energy, E, of the detected photons: 𝐶ℎ = 𝑐 + K(1∕𝐸)
Fig. 6 shows a series of normal incidence spectra collected form Au(111) at a single detector position, the data is consistent with previous measurements showing a strong surface feature right at the Fermi level [22]. The difference among these spectra is simply a change in 𝐾𝐸 , which is increased by 1 eV, from one spectrum to the next, starting from right to left in Fig. 6. The nonlinear relation that exists between the energy scale and the channels in the detector is evident in Fig. 6, by the increments in both the width of the surface feature and the separation between maxima, which are indeed equidistant in energy between successive spectra. The detector edge effects are also apparent in this data set, as shown by the high counting rate, displayed roughly at 10 to 15 channels from the detector’s edge (channel 256). The detector channel (Ch), identified with a photon energy equals to E for each spectrum, was determined by finding the intersection between a horizontal line, going over the background data in front of the Fermi edge, and a linear fit to the front rise of the IPES intensity. A good estimate of the e-beam energy spread can be obtained from the FWHM displayed by the repulsion curves shown in Fig. 4. The average value of 𝛥KE , obtained for the spectra displayed in Fig. 6 is 366 meV. The actual value of E is then determined by the expression: E= 𝐾E+ 𝛥KE .
(6)
The next step is then to use a set of experimentally determined values of Ch and E to find the unknown constants (c and K) in Eq. (6). Both constants fully describe the energy calibration for this particular detector position. Apart from using electronic transitions in hydrogen [10] as a source of photons, there are not very many standard frequency light sources that can be easily used to calibrate a spectrometer for inverse photoemission, especially if the detector can be moved to collect higher energies than the characteristic emission lines from hydrogen. The standard alternative method to perform the energy calibration, has been to use the response of the spectrometer itself. A brief description follows: For an electrically grounded metallic sample (Au(111)), bombarded by a monochromatic electron beam, it turns out that the maximum energy of the photons emitted from the sample will correspond to the kinetic energy (𝐾𝐸 ) of the electron beam in vacuum. In practice, for nearly monochromatic electron beams, the onset for photon emission occurs at a slightly higher energy, namely at 𝐸 = 𝐾𝐸 + 𝛥𝐾𝐸 , with 𝛥𝐾𝐸 being the characteristic energy spread of the electron beam. Photons with this energy are then making optical transitions to a final state, right above the Fermi level of the sample. A set of IPES spectra from this sample can be collected for different applied cathode voltages, modifying in each case 𝐾𝐸 , hence changing the channel (Ch) at which the IPES intensity takes off (IPES onset) for each spectrum. This set of experimentally obtained values (Ch vs E) can then be used to determine the best adjustment for c and K, in Eq. (6), both parameters finally define the spectrometer energy calibration.
This set of paired values, channel numbers (Ch) and photon energies (E), can then be plotted as shown in Fig. 7. The linear fit to these data points is then used to define the energy calibration of the detector. In Fig. 8, we have used these calibration parameters to display two of the spectra shown in Fig. 6, but now as a function of the energy of the detected photons, instead of channel number. Both spectra were fitted with a Gaussian function to determine the central energy of the surface state. A difference of 4 eV in the e-beam energy, is not expected to imply a significant change in the cross section for optical transitions, 5
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Fig. 6. Set of IPES spectra collected from Au(111), with the energy of the electron beam changed in increments of 1 eV, from 𝐾e . = 19.0 eV to 25.1 eV. The lower channel numbers correspond to higher photon energies.
hence, these leading peaks in both spectra should have essentially the same shape, but displaced in energy by 4 eV. The comparison is good within 50 meV. Underlying this agreement, nonetheless, is the use of the correct nonlinear calibration between photon energies and channel numbers. This comparison cannot be considered as proof of an absolute calibration of the spectrometer, but rather a consistency check for the calibration procedure. 5. Conclusion As mentioned above, the energy calibration of grating spectrometers in the VUV range lacks the existence of standard monochromatic light sources. This is in contrast to what happens in the visible range, where many different gas discharge lamps can provide distinctive wavelength which could be used for calibration purposes over a wide spectral range. In IPES, only H transitions (Lyman 𝛼 and Lyman 𝛽) have been used as a standard light source [10]. This is a difficulty, especially when the detector has to be moved to a spectral region that does not include the Lyman series. The calibration procedure for the IPES spectrometer described in this work relies on two simple references: the work function of a single crystal metal surface (Au(111)) and the kinetic energy of a nearly monochromatic e-beam, as determined in an experiment that measures the stopping potential. The energy calibration for the photon flux is then derived from an analytical expression, based on the grating dispersion, and the reference voltages used to polarize the sample and the electron source. Using standard electronic equipment the consistency of the energy calibration is better than 100 meV for 20 eV photons.
Fig. 7. Channel number versus (1/E). This data set of correlated pairs of energy and channel number generated by optical transitions right above the Fermi level (from Fig. 6). The markers are the experimental data points and the straight line is the best fit to the data. The agreement between the linear fit and the data points is explained by the theoretical functional dependence between Ch and (1/E), shown in Eq. (6).
Acknowledgments Partial funding for this research has been provided by MECESUP grant 0108 and FONDECYT grant 1171584, Chile. References [1] Dmytro Pesin, Allan H. MacDonald, Spintronics and pseudospintronics in graphene and topological insulators, Nature Mater. 11 (2012) 409, http://dx. doi.org/10.1038/nmat3305. [2] John R. Schaibley, Hongyi Yu, Genevieve Clark, Pasqual Rivera, Jason S. Ross, Kyle L. Seyler, Wang Yao, Xiaodong Xu, Valleytronics in 2D materials, Nat. Rev. Mater. 1 (2016) 16055. [3] Thomas Fauster, Wulf Steinmann, Electromagnetic waves: Recent developments in research, in: P. Halevi (Ed.), Volume 2: Photonic Probes of Surfaces, Elsevier, Amsterdam, 1995, pp. 347–411, Chapter 8. [4] J.B. Pendry, New probe for unoccupied bands at surfaces, Phys. Rev. Lett. 45 (1980) 1356; Theory of inverse photoemission, J. Phys. C 14 (1981) 1381. [5] V. Dose, VUV isochromat spectroscopy, Appl. Phys. 14 (1977) 117, http://dx. doi.org/10.1007/BF00882639. [6] G. Denninger, V. Dose, H. Scheidt, A VUV isochromat spectrometer for surface analysis, Appl. Phys. 18 (1979) 375, http://dx.doi.org/10.1007/BF00899691. [7] H.G. Beutler, The theory of the concave grating, J. Opt. Amer. 35 (1945) 311. [8] Th. Fauster, D. Straub, J.J. Donelon, D. Grimm, A. Marx, F.J. Himpsel, Normalincidence grating spectrograph with large acceptance for inverse photoemission, Rev. Sci. Instrum. 56 (1985) 1212, http://dx.doi.org/10.1063/1.1137977.
Fig. 8. Energy calibrated spectra of the IPES intensity vs photon energy obtained from Au(111). The as collected spectra were presented in Fig. 6. The solid lines are Gaussian fits to the surface state [21] in both spectra. The difference in energy between both maxima exceeds the kinetic energy difference between both spectra by 50 meV. A value, which is consistent with the error margin introduced by the calibration (<100 meV)
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