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Reneutralization bottleneck in Auger initiated desorption
Surface Science 102 (1981) L5!-L53 © North-Holland Publishing Company
SURFACE SCIENCE LETTERS RENEUTRALIZATION BOTTLENECK IN AUGER INITIATED DESORPTION Peter J. FEIBELMAN Sandia Laboratories *, Albuquerque, New Mexico 87185, USA
Received 11 August 1980; accepted for publication 16 September 1980
The rate of reneutralization of a doubly ionized surface species is shown to be 10-100 times slower than that of a singly ionized one, due to localization and orbital shrinkage effects associated with intra-atomic hole-hole interaction. Thus reneutralization is much less probable in Auger induced desorption than in single-hold initiated desorption.
The recognition [1-4] that electron and photon stimulated desorption (ESD and PSD respectively) are core-hole initiated phenomena, for many interesting surface systems, has led to widespread interest in using these experiments to analyze surface bonding. On the other hand it has long been evident that the phenomena following the initial excitation event, in stimulated desorption, are potentially as complicated as in any dissociation reaction, involving complex ion motions and possible electron-transfer. These phenomena can have a profound influence on ESD and PSD partial and total cross-sections and accordingly much of the theoretical attention that has been given to desorption has focussed on them [ 5 - 9 ] . The dominant theme in considering the escape of an initially excited positive surface ion (neutrals have not been detected directly and negatives have only been of interest recently [ 10]) has been that the probability of its leaving a surface without being reneutralized is low, since the time scale for electron motion is of the order of 1 0 - I s - 1 0 -16 s, corresponding to a typical band width of a few eV, whereas that for ions is ~10 -14 s corresponding to phonon energies of a few tens of meV. In this note I would like to draw attention to the fact that this comparison of time scales can be drastically altered in the case of Auger initiated desorption in which the first step in the desorption process is the creation of two or three holes on the desorbate species [1]. The argument stems from two key concepts, twohole localization due to hole-hole repulsion and orbital shrinkage due to reduced screening in a multi-hole state. One proceeds from the recognition that reneutralization and hole-motion off an ion are simply two different descriptions of the same phenomenon. The motion * A US DOE facility. L51
L5 2
P.J. Feibehnan / Reneutralization bottleneck in Auger initiated desorption
therefore becomes relevant to reneutralization phenomena that two valence holes on the same site are bound to one another if their Coulomb repulsion U is large compared to an appropriate single particle band width Art [ 1 1 - 1 4 ] , where t is a hopping matrix element and N a coordination number. Because of this binding, elastic reneutralization will occur only via two-hole hopping, which proceeds at a rate which is a factor ~ N t / U slower than the one-hole hopping rate which is of O(Nt) [15]. This agreement has been shown to explain the atomic-like Auger spectra of Idled band materials like Cu [16], and can account for an increase of a factor >~5 in reneutralization times, assuming N to be small, t < 1 eV as in typical band structure and U = 1 0 - 2 0 eV. In desorption from single coordination site (i.e. N = 1) this effect is particularly important. However, let us now consider whether it is correct to use a value of t which is characteristic of usual band structures. Here the important concept is that due to the substantial reduction in intra-site screening when two electrons are removed from a single atom, the lowest unfilled orbitals have a considerably reduced spatial extent. As a consequence their overlap with wave-functions on neighboring sites is exponentially diminished and the hopping time is correspondingly increased. Consider for example the desorption of an adsorbed C1. In the initial state the C1 is adsorbed as a C1- and is at a distance d = r(C1-) + r(s) from its nearest-neighbor substrate atom (whose radius is r(s)). Suppose that as a consequence of an Auger decay the C1- is converted to a C1÷. The orbitals which one now uses to calculate hopping integrals have the radius of a C1°. Thus one expects a reduction of the Cl-substrate hopping integrals by a factor on the order of f = exp [ 1 - r(Cl-)/r(Cl°)] ,
(1)
assuming the neighboring ion to be small (i.e. r(s),~ r(Cl-)). The argument that leads to (1) is that if r(s) is negligible the hopping matrix element is proportional to exp(-d/r(C1-)) in the unperturbed state and exp(---d/r(Cl°)) after the double ionization event. In both cases, since r(s) is small, d ~ r(C1-) and eq. (1) follows directly. Using the covalent radius (0.99)~) of C1 as an approximation to r(Cl °) and r(Cl-) = 1.81 N, the factor f i s seen to be ~0.4. Since the two-hole hopping rate scales as the square of the hopping integral one can therefore anticipate a reduction of about an order of magnitude in this rate because of the orbital shrinkage that results from reduced intra-atomic screening in a doubly-ionized surface atom. Combining the effects of two-hole localization and orbital shrinkage one finds that the elastic reneutralization rate is perhaps 50 times slower than one would estimate on the basis of a typical inverse band width. It remains to consider inelastic modes of reneutralization, of which the most important is interatomic Auger decay. Here an electron from the substrate hops on to the doubly ionized surface species, while a second electron carries off the energy released in the process. From angle resolved photoemission data for chemisorbed overlayers we know that the Auger width of a single valence hole in a surface atom is <-1 eV [171. (Results from ion neutralization spectroscopy are harder to interpret because, in that experiment, the ions are impinging on a surface with ~ 1 0 eV of kinetic energy [18].) Again in this case, however, the reneutralization rate is
P.J. Feibelman / Reneutralization bottleneck in Auger initiated desorption
L53
reduced due to orbital shrinkage in the two-hole state. The Auger matrix element is governed by the overlap of the doubly-ionized-desorbate orbitals with those of the neighboring surface atoms and therefore the transition probability is reduced by the square of a factor such as (1), i.e. by an order of magnitude or so. The arguments presented here indicate that because of the localization and orbital shrinkage effects associated with creating two holes on a single atom there exists a reneutralization bottleneck. The rate of reneutralization of a doubly ionized surface atom can accordingly be in the range of 10 -13 to 10 -14 s,making the escape of such an ion into the vacuum a reasonably likely possibility. Since the isotope effect [19] in ESD and PSD comes from the velocity dependence of the probability of reneutralization, this effect should be considerably diminished in Auger induced desorption as compared to single-hole initiated desorption. Since the two-hole hopping time scales as the square of the coordination number, reneutralization bottleneck effects should be stronger for desorbate species which are coordinated to fewer surface atoms. This work was supported by the US Department of Energy, DOE, under Contract DE-AC04-76-DP00789.
References [ 1] M.L. Knotek and P.J. Feibelman, Phys. Rev. Letters 40 (1978) 964. [2] P.J. Feibelman and M.L. Knotek, Phys. Rev. B18 (1978) 6531. [3] M.L. Knotek and P.J. Feibelman, Surface Sci. 90 (1979) 78. [4] M.L. Knotek, V.O. Jones and V. Rehn, Phys. Rev, Letters 43 (1979) 300. [5] B. Bell, M.H. Cohen, R. Gomer and A. Madhukar, Surface Sci. 61 (1976) 656. [6] W. Brenig, Surface Sci. 61 (1976) 659; Z. Physik B23 (1976) 361. [7] P.A. Redhead, Can. J. Phys. 42 (1964) 886. [8] D. Menzel and R. Gomer, J. Chem. Phys. 41 (1964) 3311. [9] ¥. lsikawa, Rev. Phys. Chem. Japan 16 (1942) 83,117. [10] M.L. Yu, Phys. Rev. 19 (1979) 5995; A.Kh. Ayukhanov and E. Turmashev, Soviet Phys.-Tech. Phys. 22 (1977) 1289; J.L. Hock and D. Lichtman, Surface Sci. 77 (1978) L184. [11] G.A. Sawatzky, Phys. Rev. Letters 39 (1977) 504. [12] M. Cini, Solid State Commun. 24 (1977) 681; 20 (1976)605. [13] P.J. Feibelman and E.J. McGuire, Phys. Rev. B15 (1977) 3575. [14] The binding follows from the fact that a hole cannot gain more than Nt in kinetic energy. Thus to separate two holes whose repulsion-energy on the same site is U it must be true that U < 2Nt. 115] See ref. [13], footnote 19. [16] E. Antonides, E.C. Janse and G.A. Sawatzky, Phys. Rev. BI5 (1977) !669. [17] A typical case is shown for an overlayer of H on Ti(0001) in fig. la of P.J. Feibelman, D.R. Hamann and F.J. Himpsel, Phys. Rev. B, in press. The H ls level is below the Ti s-d bands and thus a hole in this level cannot diffuse into the bulk solid. Accordingly its width, ~ 1 eV, must be attributed to Auger decay. [18] H.D. Hagstrum, Phys. Rev. 139 (1965) A526. [19] T.E. Madey, J.T. Yates, D.A. King and C.J. Uhlaner, J. Chem. Phys. 52 (1970) 5215; C. Leung, Ch. Steinbrgicheland R. Gomer, J. Appl. Phys. 14 (1977) 79.
SURFACE SCIENCE LETTERS RENEUTRALIZATION BOTTLENECK IN AUGER INITIATED DESORPTION Peter J. FEIBELMAN Sandia Laboratories *, Albuquerque, New Mexico 87185, USA
Received 11 August 1980; accepted for publication 16 September 1980
The rate of reneutralization of a doubly ionized surface species is shown to be 10-100 times slower than that of a singly ionized one, due to localization and orbital shrinkage effects associated with intra-atomic hole-hole interaction. Thus reneutralization is much less probable in Auger induced desorption than in single-hold initiated desorption.
The recognition [1-4] that electron and photon stimulated desorption (ESD and PSD respectively) are core-hole initiated phenomena, for many interesting surface systems, has led to widespread interest in using these experiments to analyze surface bonding. On the other hand it has long been evident that the phenomena following the initial excitation event, in stimulated desorption, are potentially as complicated as in any dissociation reaction, involving complex ion motions and possible electron-transfer. These phenomena can have a profound influence on ESD and PSD partial and total cross-sections and accordingly much of the theoretical attention that has been given to desorption has focussed on them [ 5 - 9 ] . The dominant theme in considering the escape of an initially excited positive surface ion (neutrals have not been detected directly and negatives have only been of interest recently [ 10]) has been that the probability of its leaving a surface without being reneutralized is low, since the time scale for electron motion is of the order of 1 0 - I s - 1 0 -16 s, corresponding to a typical band width of a few eV, whereas that for ions is ~10 -14 s corresponding to phonon energies of a few tens of meV. In this note I would like to draw attention to the fact that this comparison of time scales can be drastically altered in the case of Auger initiated desorption in which the first step in the desorption process is the creation of two or three holes on the desorbate species [1]. The argument stems from two key concepts, twohole localization due to hole-hole repulsion and orbital shrinkage due to reduced screening in a multi-hole state. One proceeds from the recognition that reneutralization and hole-motion off an ion are simply two different descriptions of the same phenomenon. The motion * A US DOE facility. L51
L5 2
P.J. Feibehnan / Reneutralization bottleneck in Auger initiated desorption
therefore becomes relevant to reneutralization phenomena that two valence holes on the same site are bound to one another if their Coulomb repulsion U is large compared to an appropriate single particle band width Art [ 1 1 - 1 4 ] , where t is a hopping matrix element and N a coordination number. Because of this binding, elastic reneutralization will occur only via two-hole hopping, which proceeds at a rate which is a factor ~ N t / U slower than the one-hole hopping rate which is of O(Nt) [15]. This agreement has been shown to explain the atomic-like Auger spectra of Idled band materials like Cu [16], and can account for an increase of a factor >~5 in reneutralization times, assuming N to be small, t < 1 eV as in typical band structure and U = 1 0 - 2 0 eV. In desorption from single coordination site (i.e. N = 1) this effect is particularly important. However, let us now consider whether it is correct to use a value of t which is characteristic of usual band structures. Here the important concept is that due to the substantial reduction in intra-site screening when two electrons are removed from a single atom, the lowest unfilled orbitals have a considerably reduced spatial extent. As a consequence their overlap with wave-functions on neighboring sites is exponentially diminished and the hopping time is correspondingly increased. Consider for example the desorption of an adsorbed C1. In the initial state the C1 is adsorbed as a C1- and is at a distance d = r(C1-) + r(s) from its nearest-neighbor substrate atom (whose radius is r(s)). Suppose that as a consequence of an Auger decay the C1- is converted to a C1÷. The orbitals which one now uses to calculate hopping integrals have the radius of a C1°. Thus one expects a reduction of the Cl-substrate hopping integrals by a factor on the order of f = exp [ 1 - r(Cl-)/r(Cl°)] ,
(1)
assuming the neighboring ion to be small (i.e. r(s),~ r(Cl-)). The argument that leads to (1) is that if r(s) is negligible the hopping matrix element is proportional to exp(-d/r(C1-)) in the unperturbed state and exp(---d/r(Cl°)) after the double ionization event. In both cases, since r(s) is small, d ~ r(C1-) and eq. (1) follows directly. Using the covalent radius (0.99)~) of C1 as an approximation to r(Cl °) and r(Cl-) = 1.81 N, the factor f i s seen to be ~0.4. Since the two-hole hopping rate scales as the square of the hopping integral one can therefore anticipate a reduction of about an order of magnitude in this rate because of the orbital shrinkage that results from reduced intra-atomic screening in a doubly-ionized surface atom. Combining the effects of two-hole localization and orbital shrinkage one finds that the elastic reneutralization rate is perhaps 50 times slower than one would estimate on the basis of a typical inverse band width. It remains to consider inelastic modes of reneutralization, of which the most important is interatomic Auger decay. Here an electron from the substrate hops on to the doubly ionized surface species, while a second electron carries off the energy released in the process. From angle resolved photoemission data for chemisorbed overlayers we know that the Auger width of a single valence hole in a surface atom is <-1 eV [171. (Results from ion neutralization spectroscopy are harder to interpret because, in that experiment, the ions are impinging on a surface with ~ 1 0 eV of kinetic energy [18].) Again in this case, however, the reneutralization rate is
P.J. Feibelman / Reneutralization bottleneck in Auger initiated desorption
L53
reduced due to orbital shrinkage in the two-hole state. The Auger matrix element is governed by the overlap of the doubly-ionized-desorbate orbitals with those of the neighboring surface atoms and therefore the transition probability is reduced by the square of a factor such as (1), i.e. by an order of magnitude or so. The arguments presented here indicate that because of the localization and orbital shrinkage effects associated with creating two holes on a single atom there exists a reneutralization bottleneck. The rate of reneutralization of a doubly ionized surface atom can accordingly be in the range of 10 -13 to 10 -14 s,making the escape of such an ion into the vacuum a reasonably likely possibility. Since the isotope effect [19] in ESD and PSD comes from the velocity dependence of the probability of reneutralization, this effect should be considerably diminished in Auger induced desorption as compared to single-hole initiated desorption. Since the two-hole hopping time scales as the square of the coordination number, reneutralization bottleneck effects should be stronger for desorbate species which are coordinated to fewer surface atoms. This work was supported by the US Department of Energy, DOE, under Contract DE-AC04-76-DP00789.
References [ 1] M.L. Knotek and P.J. Feibelman, Phys. Rev. Letters 40 (1978) 964. [2] P.J. Feibelman and M.L. Knotek, Phys. Rev. B18 (1978) 6531. [3] M.L. Knotek and P.J. Feibelman, Surface Sci. 90 (1979) 78. [4] M.L. Knotek, V.O. Jones and V. Rehn, Phys. Rev, Letters 43 (1979) 300. [5] B. Bell, M.H. Cohen, R. Gomer and A. Madhukar, Surface Sci. 61 (1976) 656. [6] W. Brenig, Surface Sci. 61 (1976) 659; Z. Physik B23 (1976) 361. [7] P.A. Redhead, Can. J. Phys. 42 (1964) 886. [8] D. Menzel and R. Gomer, J. Chem. Phys. 41 (1964) 3311. [9] ¥. lsikawa, Rev. Phys. Chem. Japan 16 (1942) 83,117. [10] M.L. Yu, Phys. Rev. 19 (1979) 5995; A.Kh. Ayukhanov and E. Turmashev, Soviet Phys.-Tech. Phys. 22 (1977) 1289; J.L. Hock and D. Lichtman, Surface Sci. 77 (1978) L184. [11] G.A. Sawatzky, Phys. Rev. Letters 39 (1977) 504. [12] M. Cini, Solid State Commun. 24 (1977) 681; 20 (1976)605. [13] P.J. Feibelman and E.J. McGuire, Phys. Rev. B15 (1977) 3575. [14] The binding follows from the fact that a hole cannot gain more than Nt in kinetic energy. Thus to separate two holes whose repulsion-energy on the same site is U it must be true that U < 2Nt. 115] See ref. [13], footnote 19. [16] E. Antonides, E.C. Janse and G.A. Sawatzky, Phys. Rev. BI5 (1977) !669. [17] A typical case is shown for an overlayer of H on Ti(0001) in fig. la of P.J. Feibelman, D.R. Hamann and F.J. Himpsel, Phys. Rev. B, in press. The H ls level is below the Ti s-d bands and thus a hole in this level cannot diffuse into the bulk solid. Accordingly its width, ~ 1 eV, must be attributed to Auger decay. [18] H.D. Hagstrum, Phys. Rev. 139 (1965) A526. [19] T.E. Madey, J.T. Yates, D.A. King and C.J. Uhlaner, J. Chem. Phys. 52 (1970) 5215; C. Leung, Ch. Steinbrgicheland R. Gomer, J. Appl. Phys. 14 (1977) 79.