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Charge transfer rates for xenon Rydberg atoms at metal and semiconductor surfaces
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 258 (2007) 61–67 www.elsevier.com/locate/nimb
Charge transfer rates for xenon Rydberg atoms at metal and semiconductor surfaces F.B. Dunning a
a,*
, S. Wethekam b, H.R. Dunham a, J.C. Lancaster
a
Department of Physics and Astronomy, Rice University, MS 61, 6100 Main Street, Houston, TX 77005-1892, USA b Institut fu¨r Physik der Humboldt-Universita¨t zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany Available online 22 December 2006
Abstract Recent progress in the study of charge exchange between xenon Rydberg atoms and surfaces is reviewed. Experiments using Au(1 1 1) surfaces show that under appropriate conditions each incident atom can be detected as an ion. The ionization dynamics, however, are strongly influenced by the perturbations in the energies and structure of the atomic states that occur as the ion collection field is applied and as the atom approaches the surface. These lead to avoided crossings between different atomic levels causing the atom to successively assume the character of a number of different states and lose much of its initial identity. The effects of this mixing are discussed. Efficient surface ionization is also observed at Si(1 0 0) surfaces although the ion signal is influenced by stray fields present at the surface. 2007 Elsevier B.V. All rights reserved. PACS: 34.70.+e; 34.60.+z Keywords: Charge transfer; Tunneling; Surface ionization
1. Introduction Charge exchange between atoms and surfaces is an important precursor to many surface reactions. It forms the basis of a number of practical surface spectroscopies and determines the charge state of particles scattered from a surface making it important, for example, when discussing plasma–wall interactions. Because of their large physical size and weak binding, Rydberg atoms in which one electron is excited to a state of large principal quantum number n provide a particularly sensitive probe of atom– surface interactions and of charge exchange. Even relatively far from the surface, the motion of the excited electron is strongly influenced by image charge interactions which shift the atomic energy levels and distort the electronic wavefunctions leading to strong hybridization and formation of ‘‘Stark-like’’ states. For some of these the electron probability densities are maximal towards surface, *
Corresponding author. Tel.: +1 713 348 3544; fax: +1 713 348 4150. E-mail address: [email protected] (F.B. Dunning).
0168-583X/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.12.094
others towards vacuum. Ionization can occur through resonant tunneling into a vacant level in the surface. This reduces the lifetime of the excited states which, close to the surface, can become very broad. The first experimental estimate of the atom–surface separation at which ionization occurs, i.e., the ionization distance, was obtained by measuring the transmission of Na(nd) Rydberg atoms through micrometer-sized slits [1]. However, subsequent experiments using fine-mesh grids suggested that transmission might also be affected by localized electric fields produced by adsorbed surface layers [2]. The first direct observations of ions produced by surface ionization were made by directing K(nd) Rydberg atoms at near grazing incidence onto a gold surface [3]. Again, alkali deposition lead to the appearance of localized surface fields which complicated interpretation of the data. Subsequent experiments have used xenon Rydberg atoms which do not stick to or react chemically with the target surface [4–8]. Measurements of surface ionization have now been extended to include hydrogen Rydberg molecules [9].
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F.B. Dunning et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 61–67
Rydberg atom–surface interactions allow for detailed quantitative comparisons between theory and experiment. Tunneling occurs far from the surface where the lateral corrugation of the surface is unimportant and can be neglected. In addition, the kinetic energy of the incident atoms is small allowing almost exact solution of the dynamical part of the charge transfer problem. Initial theoretical studies focussed on hydrogen Rydberg atoms and used perturbation methods [10]. More recently, non-perturbative techniques have been employed [11–18]. The predicted tunneling rates, which depend critically on the overlap between the electronic wavefunction and the surface, vary widely from state to state and are many orders of magnitude larger for states oriented towards the surface. Calculations have been extended to xenon Rydberg atoms. These show that energy level shifts induced by the surface can lead to avoided crossings between neighboring levels as the surface is approached. If these are traversed adiabatically, and if the states involved have very different spatial characteristics, this can result in dramatic changes in the tunneling rate as the atom successively assumes the character of states oriented towards and away from the surface [7,18]. Here we discuss recent developments in the area of Rydberg atom–surface interactions.
2. Experimental techniques The same basic approach is used to probe Rydberg atom– and Rydberg molecule–surface interactions and can be understood by reference to Fig. 1 which shows the apparatus employed in studies with xenon Rydberg atoms [4,8]. The Rydberg atoms are directed at near grazing incidence onto the target surface. Ions formed by tunneling are attracted to the surface by their image charge fields. These are large and rapidly accelerate the ions to the surface where they are (typically) neutralized by an Auger process. To prevent this, an ion collection field is applied perpendic-
ular to the surface. Since the initial image-charge field experienced by an ion, and thus the external field required to counteract it, depends on the atom–surface separation at which ionization occurs this can be inferred from measurements of the surface ionization signal as a function of ion collection field. The xenon Rydberg atoms are created by photoexciting 3 P0 atoms contained in a beam of Xe(3P0, 2) metastable atoms that is produced by electron impact excitation of ground-state xenon atoms contained in a supersonic expansion. The atoms are excited close to the surface by the crossed output of an extracavity-doubled Ti:sapphire laser. Excitation occurs in the presence of a weak dc field to permit creation of selected red-shifted or blue-shifted Stark states which are initially oriented towards or away from the surface, respectively. Experiments are conducted in a pulsed mode by forming the output of the (cw) laser into a train of pulses of 1 ls duration and 4 kHz repetition frequency. Immediately following each laser pulse a strong pulsed ion collection field of 1 ls risetime and 20 ls duration is applied. Ions that escape the surface are detected by a bell-mouthed channeltron. Time-of-flight techniques coupled with arrival time gating are used to identify those ions produced in atom–surface interactions. If tunneling occurs at an atom–surface separation Zi, the minimum external field (in a.u.) that must be applied to prevent the ion striking the surface and being lost is (for a dielectric surface) pffiffiffi rffiffiffiffiffiffi2 b T? Emin ðZ i ; T ? Þ ¼ þ ; ð1Þ Zi 2Z i where T ? mv2? =2 is the initial kinetic energy of the atom perpendicular to the surface and b = (e 1)/(e + 1), where e is the dielectric constant. (For a metal surface b = 1.) Thus by measuring the surface ionization signal as a function of ion collection field the range of ionization distances can be deduced. To obtain the absolute efficiency with which Rydberg atoms striking the surface are detected as ions the number of incident atoms must be determined. This is accomplished by measuring the number of Rydberg atoms initially created using field ionization induced by a large pulsed field applied immediately after the laser pulse. This number is then corrected for radiative decay during transit to the surface using the known (field-dependent) Rydberg atom lifetimes [8]. 3. Theory In the presence of an external electric field the (one-electron) potential can be written as V eff ðq; z; ZÞ ¼ V A ðq; z; ZÞ þ V s0 ðzÞ þ DV A ðq; z; ZÞ þ V E ðzÞ: ð2Þ
Fig. 1. Schematic diagram of the apparatus.
Here cylindrical coordinates are assumed with the cylinder axis perpendicular to the surface and passing through the core ion. The electron coordinates are denoted (q, z, /)
F.B. Dunning et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 61–67
and the atom–surface separation by Z. VA describes the interaction with the atomic core ion. For hydrogen, VA is given by the Coulomb potential 1/r, where r is the distance from the nucleus. (Unless otherwise noted, atomic units are used throughout.) For xenon, VA (q, z; Z) is represented by an ‘-dependent pseudopotential. V s0 ðzÞ describes the bare electron–surface interaction. For metals this must smoothly join an image potential interaction in vacuum to a constant potential inside the bulk. Since ionization occurs far from the surface where V s0 ðzÞ is dominated by the image charge interaction, ionization distances are not strongly dependent on the metal parameters. The term DVA(q, z; Z) describes the interaction with the electrical image of the core ion. The final term VE(z) (Ez for z P 0 and zero elsewhere) includes the effect of the external field E. Qualitative insights into the shifts in atomic energy levels induced by a nearby surface are obtained by considering the perturbation introduced by the surface (and external field) given by DV ðq; z; ZÞ ¼ V s0 ðzÞ þ DV A ðq; z; ZÞ þ V E ðzÞ:
ð3Þ
This is shown in Fig. 2 along a surface normal through the core ion for three values of E. The assumed atom–surface separation is Z = 200 a.u. DV changes sign at some critical value of z, zc, being negative for z < zc and positive for z > zc. With no external field zc = Z/3, and DV has a maximum at z = Z and vanishes as z ! 1. An external field changes the shape of DV which near the core ion can be dominated by this field. Because DV is positive for z > zc, excited states localized near the core ion or towards vacuum will tend to move up in energy, In contrast, states oriented towards the surface with large probability densities at z < zc (which also correspond to the shortest lived states) can be lowered in energy. As noted earlier, the widths and energies of atomic states near a surface have been calculated non-perturbat-
Fig. 2. Perturbation DV(q, z; Z) in the electron potential due to the presence of a surface and an external field E versus the electron–surface separation z for (—) E = 0, (– – –) E = 2 · 106 a.u., and (- - -) E = 4 · 106 a.u. This is evaluated along a surface normal through the core ion, which is located Z = 200 a.u. from the surface.
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ively using a number of different approaches. Initial studies used the complex scaling method in which a complex variable substitution in the atomic radial coordinate, r ! rexp[ih], is introduced [6,11–13]. This changes the resonance boundary conditions into a simpler form allowing the resulting Hamiltonian to be diagonalized using a normalizable basis. The imaginary part of the complex eigenenergies give the widths of the states, i.e. their ionization rates, the real part their energies. Ionization distances can then be calculated from the ionization rates. The etalon equation method [17] focuses on electron tunneling in the vicinity of the potential barrier between the surface and core ion exploiting the fact that such tunneling occurs at large atom–surface separations. The tunneling dynamics are described by a decaying state that represents an eigenfunction of the Hamiltonian subject to the boundary condition of an outgoing wave directed towards the surface. The corresponding complex eigenenergies give the widths and energies of the states. Close-coupling techniques have been employed to solve the time-dependent Schro¨dinger equation [14–16]. The wavefunction is expanded in terms of adiabatic resonance states that depend parametrically on time via the changing atom–surface separation. Inserting this expansion into the Schro¨dinger equation yields a set of coupled equations whose solution provides the ionization probability as a function of atom–surface separation. In the wavepacket propagation approach [18] the time evolution of the electron wavefunction associated with the (classical) motion of the core ion is obtained by direct solution of the time-dependent Schro¨dinger equation, the wavefunction being discretized on a grid of points. Ionization distances are computed from the time dependence of the electron flux through a detector plane located beneath the surface.
4. Results and discussion Fig. 3 shows the applied field dependence of the surface ion signal observed when xenon atoms initially prepared in the red-most and blue-most states in the Xe (n = 17) m = 0 Stark manifold are incident (at h 4) on a near atomically-flat Au(1 1 1) surface. The data are normalized to the number of incident atoms that strike the surface. Both data sets display very similar behavior. The ion signals have sharp onsets and then build up steadily with increasing field until, at the highest fields, essentially every incident atom is detected as an ion. The sudden decrease in the surface ion signal at large fields is due to direct field ionization of the Rydberg atoms in vacuum before they reach the surface. The variation of the ionization rate with atom–surface separation is inferred by analysis of the data. The probability that an incident atom will survive passage to a distance Z from the surface can be written [8] Z 1 CðZ 0 ; EÞ 0 P ðZ; E; m? Þ ¼ exp dZ ; ð4Þ jm? j Z
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assuming that, on average, the tunneling rate increases exponentially as the surface is approached and can be written Z 0 ð1 kE0 Þ 0 ; ð8Þ CðZ ; EÞ ¼ C0 exp Z decay
APPLIED FIELD (kV/cm) 0
1
2
3
4
5
6
0.8
where E0 n4E is the ion collection field classically scaled to n, and C0, Zdecay and k are constants. The factor (1 kE0) recognizes that the presence of the collection field increases the ionization rate at a particular atom–surface separation by lowering the potential barrier between the atom and surface. (The value of k can be derived from calculations of the field dependence of the tunneling rates for selected hydrogenic states.) The optimum fit to the data for the red-most Stark state is included in Fig. 3 and the corresponding ionization rates are shown in the inset for representative values of E. In zero field (E = 0) the most probable ionization distance
0.6
-7
0.4
10
RATE (a.u.)
NORMALIZED ION SIGNAL
1
0.2
E = 4 kV/cm
E=0 -8
10
0 500
1000
1500
2000
DISTANCE (a.u.) Fig. 3. Applied field dependence of the surface ion signal observed when xenon atoms initially prepared in the red-most (s) and blue-most (d) states in the Xe (n = 17) m = 0 Stark manifold are incident on a Au(1 1 1) surface (—), optimum fit to the experimental data for the red-most state (see text). The inset shows the inferred ionization rates as a function of atom–surface separation Z for the values of applied field E indicated.
where C(Z 0 , E) is the tunneling rate, which is influenced by the presence of the ion collection field E. Taking into account the (known) distribution, f(m?), of atomic velocities perpendicular to the surface, the fraction of incident atoms that will be detected as ions using a collection field E is given by Z 1 F ðEÞ ¼ f ðm? Þf1 P ðZ crit ; E; m? Þg dm? ; ð5Þ 0
where {1 P(Zcrit, E, m?)} is the fraction of incident atoms that undergo ionization before reaching some critical distance Zcrit. Substitution yields Z 1 F ðEÞ ¼ 1 f ðm? Þ 0 ( Z ) 1 CðZ 0 ; EÞ 0 dZ dm? ; ð6Þ exp jm? j Z crit ðE;m? Þ
Z ¼ Z decay ln
jm? j Z decay C0
ð9Þ
is 875 a.u., i.e. 3n2 which is in reasonable agreement with hydrogenic predictions (for surface-oriented states) of 3.4n2. However, the characteristic decay length Zdecay 230 a.u. is much larger than the value, 30 a.u., suggested by the same theory. Furthermore, the onset fields for the red-most and blue-most Stark states are similar. This appears surprising as the blue-most state is initially strongly oriented towards vacuum and according to hydrogenic theory is not expected to ionize until much closer to the surface leading to a substantially higher threshold field. These differences can be understood in terms of the mixing of xenon Rydberg states induced by application of the ion collection field and by interactions with the surface. The calculated Stark structure for xenon m = 0 states in the vicinity of n = 14, 15 is shown in Fig. 4 [7]. This is complicated by the large quantum defects associated with the low-‘ states and by the appearance of avoided crossings
where Z crit
8 9 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffi 2 T? < 2 bE= 1þ 1þ ¼ : 4E : T? ;
ð7Þ
Tests using a ‘‘steplike’’ function for C(Z 0 , E) {C(Z 0 , E) = 0 for Z 0 > Zs and infinity for Z 0 6 Zs} showed that the broad onset in the ion signal can not be accounted for by the distribution of m?. Rather ionization must occur over a range of atom–surface separations. The data can be well fit by
Fig. 4. Calculated Stark structure for xenon m = 0 Stark states in the vicinity of n = 14, 15. The solid lines show the adiabatic evolution of the neighboring extreme blue- and red-shifted states in the n = 14 and n = 15 manifolds.
F.B. Dunning et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 61–67
when neighboring levels converge. The red-shifted (blueshifted) states that move down (up) in energy with increasing field are localized towards (away from) the surface, behavior that is readily explained by considering the classical dipole potential energy ~ p ~ E, where ~ p is the induced atomic dipole moment and the applied field ~ E is directed away from the surface. As E increases, states in adjacent manifolds undergo avoided crossings which for these n begin at fields less than the critical value required for ion collection. The effect of this is illustrated in Fig. 4 which highlights the adiabatic evolution of the neighboring extreme blue- and red-shifted states. Each state successively assumes the character of a number of adjacent Stark states with different spatial orientations and loses much of its initial identity. Their final states are determined by E as well as by whether the avoided crossings are traversed wholly or partially adiabatically. As demonstrated in Fig. 5, surface-induced perturbations lead to further energy level shifts as the surface is approached [7]. A large number of avoided crossings are evident whose locations are governed by the applied field. Many occur far from the surface and can lead to dramatic changes in the ionization rate as shown in the inset for the extreme Stark states considered above. The calculated widths of both levels depend strongly on atom–surface separation and increase dramatically when adjacent levels begin to cross. For small values of m?, once the width increases to 104 eV the atom will travel at most a few atomic units closer to the surface before ionization occurs suggesting that both initial states should ionize at similar atom–surface separations. The strong mixing induced by the applied field and by the surface prevents direct mea-
65
surement of the true ionization distance for vacuum-oriented states because once such states mix with strongly surface-oriented states they rapidly ionize at atom–surface separations characteristic of surface-oriented states. Furthermore, as seen in Fig. 5, the widths of individual states can vary dramatically with atom–surface separation and do not simply increase steadily as the surface is approached. If that for the red-shifted state is ‘‘averaged’’ by an exponential, the resulting decay length Cdecay 100 a.u. (for n = 15) is in better accord with the measured values. Measurements of charge transfer have been extended to dielectric surfaces, specifically Si(1 0 0) [19]. For such a narrow-electronic-band-gap material the bottom of the conduction band lies below the vacuum level and tunneling is possible. Fig. 6 shows the applied field dependence of the observed surface ion signals when xenon atoms prepared in the red-most n = 17 m = 0. Stark state are incident on hydrogen-passivated n- and p-type Si(1 0 0) surfaces. (Small differences in behavior were seen from sample to sample and the data represent ‘‘typical’’ behavior.) Although the steady growth of the ion signal with increasing field parallels that for Au(1 1 1), significant differences are apparent. In particular, for Si(1 0 0) measurable ion signals are observed even for quite small collection fields. A number of possible explanations have been considered. The first is that some tunneling does indeed occur far from the surface. However, the ionization distances required to see ion signals at the onset near 300 V cm1 are 2600 a.u., i.e. 9n2, and appear physically unreasonable. Another possibility is that some of the ions striking the surface are not neutralized but rather reflect and are
NORMALIZED ION SIGNAL
1
0.8
0.6
0.4
0.2
0 0
1
2
3
4
5
6
APPLIED FIELD (kV/cm) Fig. 5. Calculated energies of xenon m = 0 Rydberg states as a function of atom–surface separation Z for an applied field of 1.0 · 106 a.u. The solid lines show the evolution of the red-shifted n = 15 and blue-shifted n = 14 states featured in Fig. 4. The widths of these states are shown by the dashed and solid lines, respectively, in the inset as a function of Z.
Fig. 6. Applied field dependence of the surface ion signals observed when xenon atoms initially prepared in the red-most state in the Xe (n = 17) m = 0 Stark manifold are incident on hydrogen-passivated n-type (s) and p-type (h) Si(1 0 0) surfaces. For comparison, data for Au(1 1 1) (n) are also included.
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F.B. Dunning et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 61–67
collected. Such behavior, however, would increase the surface ion signal relative to that from Au(1 1 1) at all fields, which is not what is seen experimentally. The observed behavior can be explained by the presence of localized stray fields at the surface. These broaden the range of fields experienced by different ions allowing some to escape even with relatively weak applied fields. Stray fields might result from surface charging or from surface inhomogenities caused by damage from metastable atom impact. Hydrogen passivation was used to remove the native oxide layer in an attempt to produce a stable surface. Metastable atom impact, however, removes the passivation layer [19] allowing growth of an adsorbate layer through reactions with background gas. The effects of stray fields are difficult to quantify because ionization occurs over a range of atom–surface separations. Since stray ‘‘patch’’ fields decrease rapidly with distance from the surface, ions formed closer to the surface will, on average, experience greater stray fields than those formed further away. An estimate of their size can be obtained by assuming that the ionization rate at any given atom–surface separation is the same as that inferred for Au(1 1 1) (see Fig. 4.) The simple over-the-barrier model suggests that this is reasonable as the predicted shift in the ionization distance for Si(1 0 0) relative to that for Au(1 1 1) is small compared to the characteristic decay length, Zdecay. The calculated field dependence of the resulting ion signal is shown in Fig. 7 using the value e = 11.7 for Si(1 0 0). The decrease in image charge attrac-
NORMALIZED ION SIGNAL
1
0.8
tion at the dielectric surface leads to a reduction in the required ion collection fields but the shift is insufficient to account for the signal observed at the lowest fields. To illustrate the effect of stray fields the predicted onset is convoluted with a Gaussian function and results are included in Fig. 7 for different assumed standard deviations r. The results indicate that the experimental observations are consistent with the presence of stray fields with values of ±1 kV cm1. Such fields are not unreasonable and correspond to potential variations of 0.1 V over length scales of 1 lm. (As noted earlier, ‘‘patch’’ fields resulting from such local variations decrease rapidly with distance from the surface and thus do not broaden the cut off in the surface ion signal, which is due to field ionization well removed from the surface.) Fig. 7 includes results recorded at an unpassivated surface. Although the pronounced increase in ion signal seen at low collection fields would be consistent with the presence of larger stray fields due to charging of the thick (1 nm) robust native oxide layer, the shape of the onset, i.e. a rapid rise to a ‘‘plateau,’’ is difficult to explain in terms of stray fields. It is, however, consistent with the behavior that might be expected if the presence of the oxide layer inhibits ion neutralization allowing a significant fraction of those ions that strike the surface to reflect. The component of ion kinetic energy perpendicular to the surface is then directed outwards allowing their collection in much weaker applied fields. Such reflection merits further study but could form the basis of an efficient detector for low-n Rydberg atoms. Recent work has improved understanding of charge transfer during atom–surface interactions and of the importance of surface-induced perturbations in the energies and structure of the atomic states. Nonetheless, many interesting questions remain to be explored. For example, theory suggests that for tunneling into very thin (1– 10 nm) conducting films grown on insulating substrates quantum size effects become important and can strongly influence ionization rates [15,16].
0.6
Acknowledgments 0.4
The research by the authors discussed here was supported by the National Science Foundation under Grant PHY0353424 and by the Robert A. Welch Foundation. S.W. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG Grant Wi1336).
0.2
0
0
1
2
3
4
5
6
APPLIED FIELD (kV/cm) Fig. 7. Calculated applied field dependence of the surface ion signal for Xe (n = 17) atoms assuming e = 11.7 and that the ionization rate at a given atom–surface separation is the same as for Au(1 1 1). Results are included both with no stray field present (—) and assuming a Gaussian distribution of such fields with standard deviations r of 0.5 kV cm1 (- - -) and 1.0 kV cm1 (– – –) (see text). Representative data for passivated (d) and unpassivated (s) n-type surfaces are included for comparison.
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[13] P. Nordlander, F.B. Dunning, Nucl. Instr. and Meth. B 125 (1997) 300. [14] P. Ku¨rpick, U. Thumm, U. Wille, Phys. Rev. A 57 (1998) 1920. [15] B. Bahrim, P. Ku¨rpick, U. Thumm, U. Wille, Nucl. Instr. and Meth. B 164–165 (2000) 614. [16] U. Thumm, P. Ku¨rpick, U. Wille, Phys. Rev. B 61 (2000) 3067. [17] N.N. Nedeljkovic, Lj. D. Nedeljkovic, Phys. Rev. A 72 (2005) 032901. [18] J. Sjakste, A.G. Borisov, J.P. Gauyacq, Phys. Rev. A 73 (2006) 042903. [19] H.R. Dunham, S. Wethekam, J.C. Lancaster, F.B. Dunning, Nucl. Instr. and Meth. B, in press, doi:10.1016/j.nimb.2006.11.091.
Nuclear Instruments and Methods in Physics Research B 258 (2007) 61–67 www.elsevier.com/locate/nimb
Charge transfer rates for xenon Rydberg atoms at metal and semiconductor surfaces F.B. Dunning a
a,*
, S. Wethekam b, H.R. Dunham a, J.C. Lancaster
a
Department of Physics and Astronomy, Rice University, MS 61, 6100 Main Street, Houston, TX 77005-1892, USA b Institut fu¨r Physik der Humboldt-Universita¨t zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany Available online 22 December 2006
Abstract Recent progress in the study of charge exchange between xenon Rydberg atoms and surfaces is reviewed. Experiments using Au(1 1 1) surfaces show that under appropriate conditions each incident atom can be detected as an ion. The ionization dynamics, however, are strongly influenced by the perturbations in the energies and structure of the atomic states that occur as the ion collection field is applied and as the atom approaches the surface. These lead to avoided crossings between different atomic levels causing the atom to successively assume the character of a number of different states and lose much of its initial identity. The effects of this mixing are discussed. Efficient surface ionization is also observed at Si(1 0 0) surfaces although the ion signal is influenced by stray fields present at the surface. 2007 Elsevier B.V. All rights reserved. PACS: 34.70.+e; 34.60.+z Keywords: Charge transfer; Tunneling; Surface ionization
1. Introduction Charge exchange between atoms and surfaces is an important precursor to many surface reactions. It forms the basis of a number of practical surface spectroscopies and determines the charge state of particles scattered from a surface making it important, for example, when discussing plasma–wall interactions. Because of their large physical size and weak binding, Rydberg atoms in which one electron is excited to a state of large principal quantum number n provide a particularly sensitive probe of atom– surface interactions and of charge exchange. Even relatively far from the surface, the motion of the excited electron is strongly influenced by image charge interactions which shift the atomic energy levels and distort the electronic wavefunctions leading to strong hybridization and formation of ‘‘Stark-like’’ states. For some of these the electron probability densities are maximal towards surface, *
Corresponding author. Tel.: +1 713 348 3544; fax: +1 713 348 4150. E-mail address: [email protected] (F.B. Dunning).
0168-583X/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.12.094
others towards vacuum. Ionization can occur through resonant tunneling into a vacant level in the surface. This reduces the lifetime of the excited states which, close to the surface, can become very broad. The first experimental estimate of the atom–surface separation at which ionization occurs, i.e., the ionization distance, was obtained by measuring the transmission of Na(nd) Rydberg atoms through micrometer-sized slits [1]. However, subsequent experiments using fine-mesh grids suggested that transmission might also be affected by localized electric fields produced by adsorbed surface layers [2]. The first direct observations of ions produced by surface ionization were made by directing K(nd) Rydberg atoms at near grazing incidence onto a gold surface [3]. Again, alkali deposition lead to the appearance of localized surface fields which complicated interpretation of the data. Subsequent experiments have used xenon Rydberg atoms which do not stick to or react chemically with the target surface [4–8]. Measurements of surface ionization have now been extended to include hydrogen Rydberg molecules [9].
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Rydberg atom–surface interactions allow for detailed quantitative comparisons between theory and experiment. Tunneling occurs far from the surface where the lateral corrugation of the surface is unimportant and can be neglected. In addition, the kinetic energy of the incident atoms is small allowing almost exact solution of the dynamical part of the charge transfer problem. Initial theoretical studies focussed on hydrogen Rydberg atoms and used perturbation methods [10]. More recently, non-perturbative techniques have been employed [11–18]. The predicted tunneling rates, which depend critically on the overlap between the electronic wavefunction and the surface, vary widely from state to state and are many orders of magnitude larger for states oriented towards the surface. Calculations have been extended to xenon Rydberg atoms. These show that energy level shifts induced by the surface can lead to avoided crossings between neighboring levels as the surface is approached. If these are traversed adiabatically, and if the states involved have very different spatial characteristics, this can result in dramatic changes in the tunneling rate as the atom successively assumes the character of states oriented towards and away from the surface [7,18]. Here we discuss recent developments in the area of Rydberg atom–surface interactions.
2. Experimental techniques The same basic approach is used to probe Rydberg atom– and Rydberg molecule–surface interactions and can be understood by reference to Fig. 1 which shows the apparatus employed in studies with xenon Rydberg atoms [4,8]. The Rydberg atoms are directed at near grazing incidence onto the target surface. Ions formed by tunneling are attracted to the surface by their image charge fields. These are large and rapidly accelerate the ions to the surface where they are (typically) neutralized by an Auger process. To prevent this, an ion collection field is applied perpendic-
ular to the surface. Since the initial image-charge field experienced by an ion, and thus the external field required to counteract it, depends on the atom–surface separation at which ionization occurs this can be inferred from measurements of the surface ionization signal as a function of ion collection field. The xenon Rydberg atoms are created by photoexciting 3 P0 atoms contained in a beam of Xe(3P0, 2) metastable atoms that is produced by electron impact excitation of ground-state xenon atoms contained in a supersonic expansion. The atoms are excited close to the surface by the crossed output of an extracavity-doubled Ti:sapphire laser. Excitation occurs in the presence of a weak dc field to permit creation of selected red-shifted or blue-shifted Stark states which are initially oriented towards or away from the surface, respectively. Experiments are conducted in a pulsed mode by forming the output of the (cw) laser into a train of pulses of 1 ls duration and 4 kHz repetition frequency. Immediately following each laser pulse a strong pulsed ion collection field of 1 ls risetime and 20 ls duration is applied. Ions that escape the surface are detected by a bell-mouthed channeltron. Time-of-flight techniques coupled with arrival time gating are used to identify those ions produced in atom–surface interactions. If tunneling occurs at an atom–surface separation Zi, the minimum external field (in a.u.) that must be applied to prevent the ion striking the surface and being lost is (for a dielectric surface) pffiffiffi rffiffiffiffiffiffi2 b T? Emin ðZ i ; T ? Þ ¼ þ ; ð1Þ Zi 2Z i where T ? mv2? =2 is the initial kinetic energy of the atom perpendicular to the surface and b = (e 1)/(e + 1), where e is the dielectric constant. (For a metal surface b = 1.) Thus by measuring the surface ionization signal as a function of ion collection field the range of ionization distances can be deduced. To obtain the absolute efficiency with which Rydberg atoms striking the surface are detected as ions the number of incident atoms must be determined. This is accomplished by measuring the number of Rydberg atoms initially created using field ionization induced by a large pulsed field applied immediately after the laser pulse. This number is then corrected for radiative decay during transit to the surface using the known (field-dependent) Rydberg atom lifetimes [8]. 3. Theory In the presence of an external electric field the (one-electron) potential can be written as V eff ðq; z; ZÞ ¼ V A ðq; z; ZÞ þ V s0 ðzÞ þ DV A ðq; z; ZÞ þ V E ðzÞ: ð2Þ
Fig. 1. Schematic diagram of the apparatus.
Here cylindrical coordinates are assumed with the cylinder axis perpendicular to the surface and passing through the core ion. The electron coordinates are denoted (q, z, /)
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and the atom–surface separation by Z. VA describes the interaction with the atomic core ion. For hydrogen, VA is given by the Coulomb potential 1/r, where r is the distance from the nucleus. (Unless otherwise noted, atomic units are used throughout.) For xenon, VA (q, z; Z) is represented by an ‘-dependent pseudopotential. V s0 ðzÞ describes the bare electron–surface interaction. For metals this must smoothly join an image potential interaction in vacuum to a constant potential inside the bulk. Since ionization occurs far from the surface where V s0 ðzÞ is dominated by the image charge interaction, ionization distances are not strongly dependent on the metal parameters. The term DVA(q, z; Z) describes the interaction with the electrical image of the core ion. The final term VE(z) (Ez for z P 0 and zero elsewhere) includes the effect of the external field E. Qualitative insights into the shifts in atomic energy levels induced by a nearby surface are obtained by considering the perturbation introduced by the surface (and external field) given by DV ðq; z; ZÞ ¼ V s0 ðzÞ þ DV A ðq; z; ZÞ þ V E ðzÞ:
ð3Þ
This is shown in Fig. 2 along a surface normal through the core ion for three values of E. The assumed atom–surface separation is Z = 200 a.u. DV changes sign at some critical value of z, zc, being negative for z < zc and positive for z > zc. With no external field zc = Z/3, and DV has a maximum at z = Z and vanishes as z ! 1. An external field changes the shape of DV which near the core ion can be dominated by this field. Because DV is positive for z > zc, excited states localized near the core ion or towards vacuum will tend to move up in energy, In contrast, states oriented towards the surface with large probability densities at z < zc (which also correspond to the shortest lived states) can be lowered in energy. As noted earlier, the widths and energies of atomic states near a surface have been calculated non-perturbat-
Fig. 2. Perturbation DV(q, z; Z) in the electron potential due to the presence of a surface and an external field E versus the electron–surface separation z for (—) E = 0, (– – –) E = 2 · 106 a.u., and (- - -) E = 4 · 106 a.u. This is evaluated along a surface normal through the core ion, which is located Z = 200 a.u. from the surface.
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ively using a number of different approaches. Initial studies used the complex scaling method in which a complex variable substitution in the atomic radial coordinate, r ! rexp[ih], is introduced [6,11–13]. This changes the resonance boundary conditions into a simpler form allowing the resulting Hamiltonian to be diagonalized using a normalizable basis. The imaginary part of the complex eigenenergies give the widths of the states, i.e. their ionization rates, the real part their energies. Ionization distances can then be calculated from the ionization rates. The etalon equation method [17] focuses on electron tunneling in the vicinity of the potential barrier between the surface and core ion exploiting the fact that such tunneling occurs at large atom–surface separations. The tunneling dynamics are described by a decaying state that represents an eigenfunction of the Hamiltonian subject to the boundary condition of an outgoing wave directed towards the surface. The corresponding complex eigenenergies give the widths and energies of the states. Close-coupling techniques have been employed to solve the time-dependent Schro¨dinger equation [14–16]. The wavefunction is expanded in terms of adiabatic resonance states that depend parametrically on time via the changing atom–surface separation. Inserting this expansion into the Schro¨dinger equation yields a set of coupled equations whose solution provides the ionization probability as a function of atom–surface separation. In the wavepacket propagation approach [18] the time evolution of the electron wavefunction associated with the (classical) motion of the core ion is obtained by direct solution of the time-dependent Schro¨dinger equation, the wavefunction being discretized on a grid of points. Ionization distances are computed from the time dependence of the electron flux through a detector plane located beneath the surface.
4. Results and discussion Fig. 3 shows the applied field dependence of the surface ion signal observed when xenon atoms initially prepared in the red-most and blue-most states in the Xe (n = 17) m = 0 Stark manifold are incident (at h 4) on a near atomically-flat Au(1 1 1) surface. The data are normalized to the number of incident atoms that strike the surface. Both data sets display very similar behavior. The ion signals have sharp onsets and then build up steadily with increasing field until, at the highest fields, essentially every incident atom is detected as an ion. The sudden decrease in the surface ion signal at large fields is due to direct field ionization of the Rydberg atoms in vacuum before they reach the surface. The variation of the ionization rate with atom–surface separation is inferred by analysis of the data. The probability that an incident atom will survive passage to a distance Z from the surface can be written [8] Z 1 CðZ 0 ; EÞ 0 P ðZ; E; m? Þ ¼ exp dZ ; ð4Þ jm? j Z
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assuming that, on average, the tunneling rate increases exponentially as the surface is approached and can be written Z 0 ð1 kE0 Þ 0 ; ð8Þ CðZ ; EÞ ¼ C0 exp Z decay
APPLIED FIELD (kV/cm) 0
1
2
3
4
5
6
0.8
where E0 n4E is the ion collection field classically scaled to n, and C0, Zdecay and k are constants. The factor (1 kE0) recognizes that the presence of the collection field increases the ionization rate at a particular atom–surface separation by lowering the potential barrier between the atom and surface. (The value of k can be derived from calculations of the field dependence of the tunneling rates for selected hydrogenic states.) The optimum fit to the data for the red-most Stark state is included in Fig. 3 and the corresponding ionization rates are shown in the inset for representative values of E. In zero field (E = 0) the most probable ionization distance
0.6
-7
0.4
10
RATE (a.u.)
NORMALIZED ION SIGNAL
1
0.2
E = 4 kV/cm
E=0 -8
10
0 500
1000
1500
2000
DISTANCE (a.u.) Fig. 3. Applied field dependence of the surface ion signal observed when xenon atoms initially prepared in the red-most (s) and blue-most (d) states in the Xe (n = 17) m = 0 Stark manifold are incident on a Au(1 1 1) surface (—), optimum fit to the experimental data for the red-most state (see text). The inset shows the inferred ionization rates as a function of atom–surface separation Z for the values of applied field E indicated.
where C(Z 0 , E) is the tunneling rate, which is influenced by the presence of the ion collection field E. Taking into account the (known) distribution, f(m?), of atomic velocities perpendicular to the surface, the fraction of incident atoms that will be detected as ions using a collection field E is given by Z 1 F ðEÞ ¼ f ðm? Þf1 P ðZ crit ; E; m? Þg dm? ; ð5Þ 0
where {1 P(Zcrit, E, m?)} is the fraction of incident atoms that undergo ionization before reaching some critical distance Zcrit. Substitution yields Z 1 F ðEÞ ¼ 1 f ðm? Þ 0 ( Z ) 1 CðZ 0 ; EÞ 0 dZ dm? ; ð6Þ exp jm? j Z crit ðE;m? Þ
Z ¼ Z decay ln
jm? j Z decay C0
ð9Þ
is 875 a.u., i.e. 3n2 which is in reasonable agreement with hydrogenic predictions (for surface-oriented states) of 3.4n2. However, the characteristic decay length Zdecay 230 a.u. is much larger than the value, 30 a.u., suggested by the same theory. Furthermore, the onset fields for the red-most and blue-most Stark states are similar. This appears surprising as the blue-most state is initially strongly oriented towards vacuum and according to hydrogenic theory is not expected to ionize until much closer to the surface leading to a substantially higher threshold field. These differences can be understood in terms of the mixing of xenon Rydberg states induced by application of the ion collection field and by interactions with the surface. The calculated Stark structure for xenon m = 0 states in the vicinity of n = 14, 15 is shown in Fig. 4 [7]. This is complicated by the large quantum defects associated with the low-‘ states and by the appearance of avoided crossings
where Z crit
8 9 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffi 2 T? < 2 bE= 1þ 1þ ¼ : 4E : T? ;
ð7Þ
Tests using a ‘‘steplike’’ function for C(Z 0 , E) {C(Z 0 , E) = 0 for Z 0 > Zs and infinity for Z 0 6 Zs} showed that the broad onset in the ion signal can not be accounted for by the distribution of m?. Rather ionization must occur over a range of atom–surface separations. The data can be well fit by
Fig. 4. Calculated Stark structure for xenon m = 0 Stark states in the vicinity of n = 14, 15. The solid lines show the adiabatic evolution of the neighboring extreme blue- and red-shifted states in the n = 14 and n = 15 manifolds.
F.B. Dunning et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 61–67
when neighboring levels converge. The red-shifted (blueshifted) states that move down (up) in energy with increasing field are localized towards (away from) the surface, behavior that is readily explained by considering the classical dipole potential energy ~ p ~ E, where ~ p is the induced atomic dipole moment and the applied field ~ E is directed away from the surface. As E increases, states in adjacent manifolds undergo avoided crossings which for these n begin at fields less than the critical value required for ion collection. The effect of this is illustrated in Fig. 4 which highlights the adiabatic evolution of the neighboring extreme blue- and red-shifted states. Each state successively assumes the character of a number of adjacent Stark states with different spatial orientations and loses much of its initial identity. Their final states are determined by E as well as by whether the avoided crossings are traversed wholly or partially adiabatically. As demonstrated in Fig. 5, surface-induced perturbations lead to further energy level shifts as the surface is approached [7]. A large number of avoided crossings are evident whose locations are governed by the applied field. Many occur far from the surface and can lead to dramatic changes in the ionization rate as shown in the inset for the extreme Stark states considered above. The calculated widths of both levels depend strongly on atom–surface separation and increase dramatically when adjacent levels begin to cross. For small values of m?, once the width increases to 104 eV the atom will travel at most a few atomic units closer to the surface before ionization occurs suggesting that both initial states should ionize at similar atom–surface separations. The strong mixing induced by the applied field and by the surface prevents direct mea-
65
surement of the true ionization distance for vacuum-oriented states because once such states mix with strongly surface-oriented states they rapidly ionize at atom–surface separations characteristic of surface-oriented states. Furthermore, as seen in Fig. 5, the widths of individual states can vary dramatically with atom–surface separation and do not simply increase steadily as the surface is approached. If that for the red-shifted state is ‘‘averaged’’ by an exponential, the resulting decay length Cdecay 100 a.u. (for n = 15) is in better accord with the measured values. Measurements of charge transfer have been extended to dielectric surfaces, specifically Si(1 0 0) [19]. For such a narrow-electronic-band-gap material the bottom of the conduction band lies below the vacuum level and tunneling is possible. Fig. 6 shows the applied field dependence of the observed surface ion signals when xenon atoms prepared in the red-most n = 17 m = 0. Stark state are incident on hydrogen-passivated n- and p-type Si(1 0 0) surfaces. (Small differences in behavior were seen from sample to sample and the data represent ‘‘typical’’ behavior.) Although the steady growth of the ion signal with increasing field parallels that for Au(1 1 1), significant differences are apparent. In particular, for Si(1 0 0) measurable ion signals are observed even for quite small collection fields. A number of possible explanations have been considered. The first is that some tunneling does indeed occur far from the surface. However, the ionization distances required to see ion signals at the onset near 300 V cm1 are 2600 a.u., i.e. 9n2, and appear physically unreasonable. Another possibility is that some of the ions striking the surface are not neutralized but rather reflect and are
NORMALIZED ION SIGNAL
1
0.8
0.6
0.4
0.2
0 0
1
2
3
4
5
6
APPLIED FIELD (kV/cm) Fig. 5. Calculated energies of xenon m = 0 Rydberg states as a function of atom–surface separation Z for an applied field of 1.0 · 106 a.u. The solid lines show the evolution of the red-shifted n = 15 and blue-shifted n = 14 states featured in Fig. 4. The widths of these states are shown by the dashed and solid lines, respectively, in the inset as a function of Z.
Fig. 6. Applied field dependence of the surface ion signals observed when xenon atoms initially prepared in the red-most state in the Xe (n = 17) m = 0 Stark manifold are incident on hydrogen-passivated n-type (s) and p-type (h) Si(1 0 0) surfaces. For comparison, data for Au(1 1 1) (n) are also included.
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collected. Such behavior, however, would increase the surface ion signal relative to that from Au(1 1 1) at all fields, which is not what is seen experimentally. The observed behavior can be explained by the presence of localized stray fields at the surface. These broaden the range of fields experienced by different ions allowing some to escape even with relatively weak applied fields. Stray fields might result from surface charging or from surface inhomogenities caused by damage from metastable atom impact. Hydrogen passivation was used to remove the native oxide layer in an attempt to produce a stable surface. Metastable atom impact, however, removes the passivation layer [19] allowing growth of an adsorbate layer through reactions with background gas. The effects of stray fields are difficult to quantify because ionization occurs over a range of atom–surface separations. Since stray ‘‘patch’’ fields decrease rapidly with distance from the surface, ions formed closer to the surface will, on average, experience greater stray fields than those formed further away. An estimate of their size can be obtained by assuming that the ionization rate at any given atom–surface separation is the same as that inferred for Au(1 1 1) (see Fig. 4.) The simple over-the-barrier model suggests that this is reasonable as the predicted shift in the ionization distance for Si(1 0 0) relative to that for Au(1 1 1) is small compared to the characteristic decay length, Zdecay. The calculated field dependence of the resulting ion signal is shown in Fig. 7 using the value e = 11.7 for Si(1 0 0). The decrease in image charge attrac-
NORMALIZED ION SIGNAL
1
0.8
tion at the dielectric surface leads to a reduction in the required ion collection fields but the shift is insufficient to account for the signal observed at the lowest fields. To illustrate the effect of stray fields the predicted onset is convoluted with a Gaussian function and results are included in Fig. 7 for different assumed standard deviations r. The results indicate that the experimental observations are consistent with the presence of stray fields with values of ±1 kV cm1. Such fields are not unreasonable and correspond to potential variations of 0.1 V over length scales of 1 lm. (As noted earlier, ‘‘patch’’ fields resulting from such local variations decrease rapidly with distance from the surface and thus do not broaden the cut off in the surface ion signal, which is due to field ionization well removed from the surface.) Fig. 7 includes results recorded at an unpassivated surface. Although the pronounced increase in ion signal seen at low collection fields would be consistent with the presence of larger stray fields due to charging of the thick (1 nm) robust native oxide layer, the shape of the onset, i.e. a rapid rise to a ‘‘plateau,’’ is difficult to explain in terms of stray fields. It is, however, consistent with the behavior that might be expected if the presence of the oxide layer inhibits ion neutralization allowing a significant fraction of those ions that strike the surface to reflect. The component of ion kinetic energy perpendicular to the surface is then directed outwards allowing their collection in much weaker applied fields. Such reflection merits further study but could form the basis of an efficient detector for low-n Rydberg atoms. Recent work has improved understanding of charge transfer during atom–surface interactions and of the importance of surface-induced perturbations in the energies and structure of the atomic states. Nonetheless, many interesting questions remain to be explored. For example, theory suggests that for tunneling into very thin (1– 10 nm) conducting films grown on insulating substrates quantum size effects become important and can strongly influence ionization rates [15,16].
0.6
Acknowledgments 0.4
The research by the authors discussed here was supported by the National Science Foundation under Grant PHY0353424 and by the Robert A. Welch Foundation. S.W. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG Grant Wi1336).
0.2
0
0
1
2
3
4
5
6
APPLIED FIELD (kV/cm) Fig. 7. Calculated applied field dependence of the surface ion signal for Xe (n = 17) atoms assuming e = 11.7 and that the ionization rate at a given atom–surface separation is the same as for Au(1 1 1). Results are included both with no stray field present (—) and assuming a Gaussian distribution of such fields with standard deviations r of 0.5 kV cm1 (- - -) and 1.0 kV cm1 (– – –) (see text). Representative data for passivated (d) and unpassivated (s) n-type surfaces are included for comparison.
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