Higher Ionization Energies from Sequential Vacuum-Ultraviolet

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Higher Ionization Energies from Sequential Vacuum-Ultraviolet Multiphoton Ionization of Size-Selected Silicon Cluster Cations Christian Kasigkeit, Konstantin Hirsch, Andreas Langenberg, Thomas Moller, Jürgen Probst, Jochen Rittmann, Marlene Vogel, Jörg Wittich, Vicente Zamudio-Bayer, Bernd von Issendorff, and J. Tobias Lau J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp511928m • Publication Date (Web): 09 Feb 2015 Downloaded from http://pubs.acs.org on February 18, 2015

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The Journal of Physical Chemistry

Higher Ionization Energies from Sequential Vacuum-Ultraviolet Multiphoton Ionization of Size-Selected Silicon Cluster Cations Christian Kasigkeit,†,‡ Konstantin Hirsch,‡ Andreas Langenberg,‡,§ Thomas Möller,† Jürgen Probst,† Jochen Rittmann,‡,∥ Marlene Vogel,‡,† Jörg Wittich,† Vicente Zamudio-Bayer,‡,¶ Bernd von Issendorff,¶ and J. Tobias Lau∗,‡ Institut f¨ ur Optik und Atomare Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany, Institut f¨ ur Methoden und Instrumentierung der Forschung mit Synchrotronstrahlung, Helmholtz-Zentrum Berlin, Albert-Einstein-Straße 15, 12489 Berlin, Germany, and Physikalisches Institut, Universität Freiburg, Stefan-Meier-Straße 21, 79104 Freiburg, Germany E-mail: [email protected]

∗

To whom correspondence should be addressed Technische Universit¨ at Berlin ‡ Helmholtz-Zentrum Berlin ¶ Universität Freiburg § Current address: Max Planck Institut f¨ ur Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany ∥ Current address: Faculté des sciences de base, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland †

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Abstract The second to fifth ionization energies and the appearance sizes of the higher charge states of silicon clusters with 6-92 atoms are determined by sequential vacuumultraviolet multiphoton ionization of size-selected cluster ions in a cryogenic ion trap. The higher ionization energies are well described by the charging energy in a spherical droplet model. In contrast to the electron affinity and the first ionization energy of silicon clusters, the higher ionization energy seem to change less abruptly at the prolate-to-spherical shape transition.

Keywords Ion trap, Silicon, Ionization energies, Multiphoton Processes, Ion yield, Charging energy, Structural transition, Synchrotron radiation

Introduction Silicon clusters are among the most widely studied semiconductor clusters. Ionization energies and electron affinities were determined by ultraviolet and visible laser spectroscopy, 1–3 while ion mobility and infrared photodissociation studies have been performed to investigate their geometric structure. 4–8 The polarizabilities of Sin have been studied in electrical beam deflection studies 9,10 and their valence electronic structure by normal photoelectron spectroscopy 11–13 or angle-resolved velocity map imaging photoelectron spectroscopy. 14 Photoabsorption 15 and photodissociation 16,17 spectroscopy have been performed to investigate optical and geometrical properties of silicon clusters. Many of these experiments have revealed a structural transition from prolate to spherical structures in the size range around 25 atoms per cluster, that is also predicted by theory. 18–25 This structural transition leads to significant changes in the electron affinity and first ionization energy of silicon clusters. Higher ionization energies of clusters were so far only accessible 2 ACS Paragon Plus Environment

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via multiphoton absorption of very large particles in the ultraviolet and visible range as for the case of alkaline 26 or aluminum clusters. 27 The combination of vacuum-ultraviolet and soft-x-ray spectroscopy with ion traps has only recently been pursued successfully at synchrotron radiation sources. 28–36 These offer the possibility to study the electronic properties of size-selected ionic clusters, molecules, or complexes at photon energies that can address states well below the vacuum level. With this technique, valence and 2p core-level binding energy of doped silicon clusters have been determined. Furthermore, core-level binding energies of size-selected silicon clusters have helped to elucidate the geometric structure of Si+ 12 and have shown that the same charging energy applies to valence and core level photoionization. 34 Here, we extend these studies to the vacuum-ultraviolet spectral range to access the second to fifth ionization energy of size-selected silicon clusters. We show that the charging energy for the removal of one elementary charge is independent of the initial charge state of the cluster within the experimental error bars.

Experimental methods Experimental setup Silicon cluster cations were produced by DC magnetron sputtering of p-doped silicon sputter targets with argon ions in a mixed helium-argon flow. Details of the experimental setup are given elsewhere. 30,37 In brief, a size distribution of silicon cluster ions was transferred from the cluster source through a hexapole collision cell into a linear quadrupole mass filter. Size-selected Si+ n clusters where then guided into a liquid-nitrogen cooled quadrupole ion trap in the presence of helium buffer gas. Cluster size distributions and size-selected clusters were analyzed with a reflectron time-of-flight mass spectrometer that is mounted perpendicular to the ion trap axis. Ion bunches are guided into the acceleration region of the mass spectrometer via a quadrupole deflector behind the ion trap exit aperture.



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Spectroscopic technique Vacuum-ultraviolet photoionization spectroscopy in the 5-20 eV photon energy range was performed at BESSY II U125/2-NIM beamline. This undulator beamline with a normal incidence monochromator provides a photon flux on the order of 1010 − 1013 photons per second in the photon energy range of 5-30 eV and is therefore well adapted to valence photoionization studies of small clusters 31,34 and molecules. Photoionization efficiency studies were performed on size-selected cluster cations Si+ n by scanning the incident photon energy while monitoring the Siq+ n product ion yield with q ≥ 2. The irradiation time at a given photon energy is 8 s, and the storage time of the parent ions in the ion trap is of the same order of magnitude. With the mass resolution of m/∆m ≥ 1200 of the + compact reflectron time-of-flight mass spectrometer, Siq+ n could be distinguished from Sin/q

for integer values of n/q by the distribution of natural isotopologues in the relevant size and charge range. This is necessary to separate multiple photoionization from photodissociation events that also take place in this photon energy range. All photoionization spectra were normalized to the incident photon flux that was monitored with a GaAsP photo diode.

Determination of ionization energies The q th ionization energy of a given silicon cluster with size n was determined as the smallest + photon energy where a Siq+ n product ion was detected for a Sin parent ion in a photoionization

efficiency spectrum. This ionization energy was derived by differentiating the Siq+ n ion yield curve with respect to the photon energy, giving a measure of the electronic density of states referenced to the vacuum level. A Gaussian distribution curve was fit to the peak at lowest photon energy to determine the first turning point of the photoionization efficiency curve. A line fit was then done with the slope around this turning point, and its intersection with the baseline at lower photon energy is taken as the ionization energy. This is illustrated in Fig. 1 for the second ionization energy of Si23 . For higher ionization energies, where the 4 ACS Paragon Plus Environment

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signal-to-noise ratio does not allow for differentiation of the ionization efficiency curve, line

Si232+ ion yield Y (arb. units)

fits were performed manually. Si23+ → Si232+ photoioniza"on efficiency curve

2nd IP

dY/dE (arb. units)

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6

7

8 9 10 11 photon energy E (eV)

12

13

Figure 1: Photoionization efficiency curve of the Si2+ 23 product ion and its derivative with respect to the photon energy. From these curves the second ionization energy of Si23 is determined as 8.9 ± 0.1 eV.

Results and discussion Photon-flux dependence of multiple ionization Sequential multiple photoionization of free silicon clusters in the ion trap occurs if the photon energy is higher than the mth ionization energy because the parent ion is successively charged by +e upon absorption of a single photon above threshold. This sequential multiple photoionization occurs already at relatively low photon flux of 1011 − 1012 photons per second because of the large photoabsorption cross section on the order of 0.05 ˚ A2 per valence electron and because product ions are efficiently stored in the ion trap for 1-10 s. To verify the generation of multiply charged ions by multiple photoionization, the dependence of the intensity I(q) of q-fold charged product ions on the incident photon flux Φph 5 ACS Paragon Plus Environment


Si83q+ q=2 k = 1.12 ± 0.05

q=3 k = 2.8 ± 0.2

q=4 k = 3.1 ± 0.3

q=5 k = 3.8 ± 0.3

1010

2

exponent k

log intensity (arb. units)

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4 3 2 1 0

1 2 3 4 5 product ion charge q (e)

3 4 5 6 789 11 2 3 4 5 6 7 89 12 10 10 photon flux Фph (photons s-1)

Figure 2: Photon flux dependence of the Siq+ 83 product ion yield for q = 2 − 5 generated from Si+ parent ions at 16 eV photon energy on a log-log scale. The ion yield follows an 83 (k) exponential dependence on the photon flux with Iq ∝ Φph with k ≈ (q − 1) as can be seen from the fits (dotted lines) to the data. The exponent k is given for each product ion charge state and is plotted versus q in the inset. The dotted line in the inset represents the expected dependence for sequential multiphoton ionization.


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th was investigated for the Si+ 83 parent ion at 16.0 eV photon energy, which is above the 5

ionization energy of Si83 of 13.7 ± 0.3 eV. To decrease the photon flux at otherwise identical beam parameters, the undulator gap was detuned from its optimum value while keeping the exit slit and monochromator settings fixed. The resulting intensity of Siq+ 83 , (q = 2 − 5) and exponential fits ∝ Φkph to the data are plotted in Fig. 2 on a log-log scale. The exponent k, which is extracted from the fit functions for different final charge states q is plotted versus q in the inset. The graph shows the expected Iq ∝ Φkph dependence with k ≈ (q − 1) except for q = 3 where the exponent is overestimated, possibly related to the larger scatter in the data. It can also be seen that the ion yield of Si2+ 83 decreases for a photon flux Φph above 3+ 3 × 1011 photons per second because of increasing ionization of Si2+ 83 to Si83 . Because of the

multiphoton process, the relative intensity of the ion yield signal for charge q + 1 is smaller by a factor of 10-100 than for charge q, which results in increased error bars of the higher ionization energies of up to ±300 meV.

Higher ionization energies of silicon clusters The second to fifth ionization energies of silicon clusters are shown in Fig. 3 along with the first ionization energies 1,3 by Fuke et al. and Kostko et al. as well as the electron affinities 2 by Astruc Hoffmann. Additionally indicated is the 4.85 eV work function of polycrystalline silicon by Michaelson. 38 Where possible, the mean value of second ionization energy and electron affinity, which roughly corresponds to the first ionization energy, is also given. At least for the larger sizes the data are fairly well described by a spherical droplet model for the ionization energies

IE(Z) = WF + (Z + α)

e2 4πε0 (n−1/3 rW S + δ)

with the following parameters: workfunction WF = 5.05 eV, asymmetry parameter α = 0.3, spillout δ = 0˚ A, and Wigner-Seitz-radius rW S = 1.57˚ A. The model ionization energies are



indicated by the broken lines. bulk 103 100 18 16

cluster size (n) 20 10 5 4 3

2

1

EA (Astruc Hoffman 2001) 1st IP (Fuke 1993) 1st IP (Kostko 2010) (2nd IP + EA) / 2 2nd IP 3rd IP 4th IP 5th IP WF (Michaelson 1977)

Sin

14 energy (eV)

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12 10 8 6 4 2 0 0.0

0.2 0.4 0.6 0.8 inverse cluster radius (n-1/3)

1.0

Figure 3: 2nd (Si6 to Si77 ), 3rd (Si8 to Si81 ), 4th (Si25 to Si94 ), and 5th (Si70 to Si92 ) ionization energy (IE) of this work along with reported 1st ionization energy 1,3 and electron affinity 2 1 (EA) plotted versus R−1 ∝ n− 3 . Dotted lines are fits to the data, using a simple spherical droplet model (see text). Experimental error bars of the higher ionization energies are smaller than the symbols. There is a sudden change in the ionization energy of Sin in the data of Fuke et al. around n ≈ 23, which is also, though less pronounced, present in the Sin electron affinity, 2 as well as in the second and third ionization energies. This is commonly interpreted as the result of a structural transition from prolate to spherical shape that was observed in ion mobility studies 5 and reproduced in theoretical work. 18–20,24,25 Here, we do not observe as strong a change in the higher ionization energies. For the higher charge states this structural transition could be masked, e.g., if the clusters studied here were rather liquid than rigid as a result of large internal energy because of sequential multiphoton absorption. Even though photoabsorption will prepare the cluster in an excited state, this will not be long-lived on the time scale of the experiment. At the present conditions of photon flux, helium buffer gas pressure, ion trap temperature, and photoabsorption cross section, the photoexcited clusters either dissociate or cool down by collisions with the helium buffer gas. The cooling takes place on a time scale of a few ten milliseconds; the cluster ions will therefore typically have relaxed between sequential photoionization events, which occur with intervals of a few 0.1-1 8 ACS Paragon Plus Environment

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s. Moreover we do not see a strong change in the ionization potentials of the singly charged cations, which have not undergone any excitation before ionization. For silicon cluster cations the structural transition has been clearly observed in mobility measurements; 5 it is therefore an interesting question whether this transition has a smaller influence on the ionization energies of higher charge states than on that of the neutral state. Another possibility is that the data of Fuke et al. somewhat overestimates the change in ionization energy. The deviation between this data and our rough estimate of the ionization energies of the neutrals (taking the average of electron affinity and second ionization energy) seems to indicate this. Some deviation in fact is to be expected. While the difference between first and the second ionization energy of the cluster is just its charging energy (assuming a similar geometric structure), the difference between the first ionization potential and the electron affinity is the charging energy plus the bandgap of the cluster (the energy difference between the lowest unoccupied and highest occupied orbital of the neutral). Therefore the average of electron affinity and second ionization energy will deviate by half the bandgap from the first ionization energy, so by something like 0.2 eV. 12 Nevertheless this is not sufficient to explain the deviation between the two data sets; it would be therefore very helpful if calculations could clarify the relation between the ionization energies of the different charge states.

Charging energy and critical sizes of silicon clusters Charging energy From the experimental photoionization data, the charging energy 39,40 for a given cluster size was determined as the difference of its (q + 1)th and q th ionization energy, corresponding to ∆q = 1. This charging energy is plotted versus the inverse cluster radius R−1 ∝ n− 3 in Fig. 1

4 and is quite well described by a spherical droplet model as

e2 1 4πε0 R+δ

with unit charge e,

cluster radius R, and electron spill-out δ. From the Si77 charging energy of 2.18 ± 0.03 eV, a Wigner-Seitz radius of 1.55 ± 0.02 ˚ A can be estimated if the spill-out δ is neglected, which is very close to the value used for the lines in Fig.3. Interestingly, this is significantly smaller 9 ACS Paragon Plus Environment


bulk 103 100 6

cluster size (n) 20 10 5 4 3

2

1

5 charging energy (eV)

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4 3

1. IP - EA; 2. IP - 1. IP 3. IP - 2. IP 4. IP - 3. IP 5. IP - 4. IP line fit through zero

2 1 0

0.0

0.2 0.4 0.6 0.8 inverse cluster radius (n-1/3)

1.0

Figure 4: Charging energy of silicon clusters plotted versus the inverse radius R−1 ∝ n− 3 . As expected, the charging energy does not depend on the final charge of the ion but only on its inverse radius. Literature values were used for the first ionization energy 1,3 and the electron affinity 2 of silicon clusters. 1

than the value for diamond silicon (rWS = 1.69 ˚ A), but very close to that of its high pressure β-tin phase (rWS = 1.55 ˚ A) 41 . This seems to indicate that silicon clusters in this size range might adopt compact structures with atomic packing pattern closer to that of the bulk high pressure form.

Critical sizes of multiply charged silicon clusters The critical size nc against Coulomb dissociation of Siq+ n , (q = 3 − 5) cluster cations was determined as the appearance size in the ion yield spectrum. Because of the long storage time of 1-10 s and because of buffer gas cooling in the cryogenic ion trap, the appearance size, which depends on the experimental parameters, is given here for charge states with a lifetime of > 0.1 − 1 s and therefore corresponds to the critical size in our case. Table 1: Critical size nc for the stability of q-fold charged silicon cluster cations q nc

2 ≤ 6a

3 4 8 25

5 70

a

Si+ 6 is smallest parent cluster investigated here.

The smallest cluster size investigated here, Si+ 6 , is already stable as a dication, which sets 10 ACS Paragon Plus Environment

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an upper limit of nc ≤ 6 as the critical size for q = 2. The critical size limits the number of charge states that can be observed for a given cluster size and is summarized in Table 1. For q = 3 − 5 the dependence of the critical size on the charge state can be fitted by an equation nc = 0.05 ∗ q 4.50 , so with an exponent significantly higher than the value of 2.3 measured for alkaline clusters. 26 This might be due to the fact that the clusters studied here are cold and therefore solid, while the alkaline clusters studied by Näher et al. 26 were liquid. The strong increase of the critical size with size seems to indicate that the smaller silicon clusters are more rigid than the larger ones, so less prone to undergo a deformation which then develops into the Coulomb dissociation. It would be very interesting to study critical sizes for cold metal clusters as well; it might well be that they are similarly different to the critical sizes of the liquid clusters. The fit of the critical sizes suggests that n = 2 is the critical size for q = 2. In the size range investigated here Siq+ n cluster ions with q ≥ 6 should not stable and indeed have not been observed. Because the charging energy is independent of the initial charge state but the critical size increases with charge, all higher ionization energies could be obtained in the photon energy range below 20 eV. For n ≥ 103 − 104 with higher ionization energies below 6-8 eV, conventional laser spectroscopy could be applied. 27

Conclusion In summary, we have demonstrated that higher ionization energies of size-selected clusters can be obtained by sequential multiple photoionization with tunable vacuum-ultraviolet radiation in a linear ion trap. Long parent ion storage times of ≈ 10 s and typical photoabsorption cross sections of 0.05 ˚ A2 per electron facilitate the observation of multiphoton processes even for the typical photon flux of ≈ 1012 photons per second of undulator radiation at synchrotron storage rings. The silicon clusters with more than about 20 atoms exhibit ionization energies which are in good agreement with a simple spherical droplet model, if



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a density slightly higher than the bulk density of silicon is assumed. For smaller sizes the ionization energies of the singly and multiply positively charged clusters deviate from this model, but far less strongly than the ionization energies of neutral silicon clusters as measured by the Fuke et al. 1 The critical sizes against Coulomb dissociation exhibit a much stronger dependence on the charge state than predicted by liquid drop models and observed for liquid metal clusters, which might be due to the fact that the silicon clusters studied here are cold and solid.

Acknowledgement This work was supported by grant LA2398/5 from Deutsche Forschungsgemeinschaft within the FOR1282 research unit. Beam time for this project at BESSY II beamline U125/2-NIM, operated by Helmholtz-Zentrum Berlin, is gratefully acknowledged. The authors thank Ingo Packe and Peter Baumgärtel for technical support. BvI acknowledges travel support by HZB.

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(22) Jackson, K. A.; Horoi, M.; Chaudhuri, I.; Frauenheim, T.; Shvartsburg, A. A. Unraveling the Shape Transformation in Silicon Clusters. Phys. Rev. Lett. 2004, 93, 013401. (23) Jackson, K. A.; Yang, M.; Chaudhuri, I.; Frauenheim, T. Shape, Polarizability, and Metallicity in Silicon Clusters. Phys. Rev. A 2005, 71, 033205. (24) Hellmann, W.; Hennig, R. G.; Goedecker, S.; Umrigar, C. J.; Delley, B.; Lenosky, T. Questioning the Existence of a Unique Ground-State Structure for Si Clusters. Phys. Rev. B 2007, 75, 085411. (25) Qin, W.; Lu, W.-C.; Zhao, L.-Z.; Zang, Q.-J.; Wang, C. Z.; Ho, K. M. Stabilities and Fragmentation Energies of Sin Clusters (n = 2 − 33). J. Phys. Chem. Ref. Data 2009, 21, 455501. (26) Näher, U.; Frank, S.; Malinowski, N.; Zimmermann, U.; Martin, T. Fission of Highly Charged Alkali Metal Clusters. ZPD Atoms, Molecules and Clusters 1994, 31, 191–197. (27) Astruc Hoffmann, M.; Wrigge, G.; Issendorff, B. v. Photoelectron Spectroscopy of Al− 32000 : Observation of a “Coulomb Staircase” in a Free Cluster. Phys. Rev. B 2002, 66, 041404. (28) Grimm, M.; Langer, B.; Schlemmer, S.; Lischke, T.; Becker, U.; Widdra, W.; Gerlich, D.; Flesch, R.; R¨ uhl, E. Charging Mechanisms of Trapped Element-Selectively Excited Nanoparticles Exposed to Soft X Rays. Phys. Rev. Lett. 2006, 96, 066801. (29) Thissen, R.; Bizau, J. M.; Blancard, C.; Coreno, M.; Dehon, C.; Franceschi, P.; Giuliani, A.; Lemaire, J.; Nicolas, C. Photoionization Cross Section of Xe+ Ion in the Pure 5p5 2 P3/2 Ground Level. Phys. Rev. Lett. 2008, 100, 223001. (30) Lau, J. T.; Rittmann, J.; Zamudio-Bayer, V.; Vogel, M.; Hirsch, K.; Klar, P.; Lofink, F.; Möller, T.; v. Issendorff, B. Size Dependence of L2,3 Branching Ratio and 2p Core-Hole Screening in X-Ray Absorption of Metal Clusters. Phys. Rev. Lett. 2008, 101, 153401. 15 ACS Paragon Plus Environment


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Sin+

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5+ 4+ 3+ 2+ 1+

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Higher Ionization Energies from Sequential Vacuum-Ultraviolet

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