- Email: [email protected]
Si(100)
Surface Science 528 (2003) 35–41 www.elsevier.com/locate/susc
Tunneling effect in electron-stimulated desorption of Liþ from LiF/Sið1 0 0Þ L. Markowski
*
Institute of Experimental Physics, University of Wrocław, pl. Maxa Borna 9, 50-204 Wrocław, Poland
Abstract It is shown that the kinetic-energy distributions of 6 Liþ and 7 Liþ ions desorbed during electron irradiation from the system LiF/Si(1 0 0) exhibit fine structures. Their character suggests that they correspond to Liþ ions emitted according to the wave packet squeezing desorption model. This observation enables us to determine the final repulsion potential active in the Liþ desorption process. The oscillatory-structure onsets show that these potentials have the potentialenergy barrier of a height of about 1.4 eV for the virgin LiF samples and of about 2.8 eV for LiF preirradiated with a dose of 50 lC/mm2 . For preirradiated samples the oscillatory structures are less pronounced, but for such samples relatively strong and very narrow peaks located at 2.12 eV for 6 Liþ and at 2.03 eV for 7 Liþ , respectively, can be detected. These peaks are interpreted as ions trapped in the temporary bound-states located above the vacuum level of the sample. Due to a relatively high transmission coefficient the ions can tunnel trough the temporary existing potential barrier. The lifetime of the potential barrier estimated from the peak energy width and the Heisenberg uncertainty principle is about 7 fs. Some other aspects of the dynamic lattice distortion are also discussed. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Alkali halides; Desorption induced by electronic transitions (DIET); Ion–solid interactions
1. Introduction Among a variety of systems for which atom/ion desorption induced by electronic transitions can be observed the alkali halides seem to be particularly interesting. First of all, these materials form crystals with a simple cubic lattice of the NaCl-type. Secondly, analysis of experimental data appears to be much less complicated if we take into account that for ionic systems the interaction which causes positive ion desorption can be very well approximated by an almost pure Coulomb potential.
*
Tel.: +48-71201307; fax: +48-71-328-7365. E-mail address: [email protected] (L. Markowski).
During electron irradiation, alkali halide crystals predominantly emit alkali and halogen atoms, and the processes evoking their desorption are rather well understood [1,2]. On the other hand, the mechanism of positive ion emission is much more controversial. The observed correlation between the alkali ion ionization threshold and the positive-ion emission yield [3] suggests that the ion ejection is initiated by an inter-atomic Auger process, and it is running in similar way as in the Knotek and Feibelman model [4]. Theoretical calculations [5,6] give us, however, not so unique answer, leaving still open the question whether the repulsive configuration exists sufficiently long for ion desorption to occur. Moreover, some experimental results indicate that positive ions can be produced by
0039-6028/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0039-6028(02)02607-9
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L. Markowski / Surface Science 528 (2003) 35–41
gas-phase collisions between desorbed atoms and secondary electrons [7]. Nevertheless, further precise measurements of the positive ion energy and mass distributions performed by Kołodziej et al. [8] showed that alkali ions are really emitted due to Coulomb instability of the crystal lattice. Very recent investigations of Liþ emission from the LiF/ Si(1 0 0) system confirm that lithium ions are mainly emitted from the adatom sites, when the charge reversal takes place on a fluorine ion located just below it [9]. Moreover, the observations of small oscillations on the Liþ kinetic-energy distributions (KEDs) curves allowed us to suggest that lithium ion ejection from its normal surface site is followed by the wave packet squeezing desorption (WPS) mechanism [10,11]. In this work we would like to reinforce this hypothesis by presenting new experimental results.
2. Experimental Our experimental and sample preparation procedures have been discussed previously [9,12], and here they will be only briefly mentioned. Thin layers of LiF vapour 1–12 monolayers (ML) thick were deposited on a clean Si(1 0 0) single crystal (Si substrate was flash annealed up to 900 K in situ and then its structure and cleanliness were checked by LEED and AES) in ultrahigh vacuum (base pressure, 2 1010 mbar). Depositions were performed at 100, 300 and 500 K. An 300 eV electron beam, pulsed by deflector plates with a frequency of 10 kHz and of 20 ns pulse width, and average current density of 4 nA/mm2 , was incident on the LiF/Si(1 0 0) sample at 45° relative to the surface normal. KEDs of desorbed positive ions were measured with a calibrated time-of-flight (TOF) spectrometer. The ion acceptance angle detection, measured with respect to the surface normal, was lower than 1°3000 .
ever, desorption of Hþ , 6 Liþ , 7 Liþ and Fþ dominates significantly other species observed. The 6 Liþ and 7 Liþ peaks can be well represented by smooth bell-shaped curves and only small oscillations at high-energy side could be detected (i.e. for their shorter flight times). No noticeable changes in these peaks were observed for several successive TOF mass spectra collected. Nevertheless, when accumulated electron dose was further increased, the main peak for both lithium isotopes appears to be accompanied by another small peak. In Fig. 1 typical spectrum obtained for 50 lC/mm2 electron dose is presented and these additional peaks are marked by arrows. Due to very short electron pulses of small current density, chopped with a relatively low frequency, to obtain high irradiation dose the sample was exposed to the continuous electron beam for several minutes. Then for such samples the TOF spectra measurements were undertaken. To extract character of these fine structures the experimental 6 Liþ and 7 Liþ peaks were described by smooth, slightly asymmetric bellshaped functions and then the simple subtraction procedure was applied. The final results obtained for 10 ML LiF deposited and measured at 300 K, for TOF spectra collected from newly prepared samples and for samples exposed to 50 lC/mm2 electron beam are presented in Fig. 2 (dashed and solid line, respectively) in the ion kinetic-energy domain. In this figure the intensity of 6 Liþ is cor-
3. Results and discussion The mass spectra of positive ions emitted from LiF/Si(1 0 0) samples during electron bombardment reveal a relatively rich structure [12]. How-
Fig. 1. TOF spectrum for electron-stimulated desorption of 6 Liþ and 7 Liþ ions from the 10 ML LiF/Si(1 0 0) system obtained for the sample exposed to 50 lC/mm2 electron dose. Stimulation electron energy is 300 eV. LiF deposited and measured at 300 K.
L. Markowski / Surface Science 528 (2003) 35–41
Fig. 2. Comparison of oscillatory components of KEDs of 6 Liþ and 7 Liþ desorbed from 10 ML LiF/Si(1 0 0) after the subtraction procedure (see text), for virgin (dashed line) and for damaged samples (electron dose 50 lC/mm2 , solid line).
rected according to the natural abundance of 6 Li/ 7 Li. For virgin samples the fine structures exhibit rather regular oscillations that have their onset at an ion energy of about 1.4 eV. The origin of these oscillations has been already discussed in Ref. [9], and recently, more detailed calculations clearly indicate that they are related to the contribution of lithium ions emitted from LiF by the WPS mechanism [13]. In the WPS model the excitation and deexcitation sequences take place in similar way as in the well-known Antoniewicz desorption model [14]. However, because the equilibrium positions of the excited- and ground-state potentials nearly coincide, no or little classical kinetic energy is achieved. Nevertheless, the excited-state potential is much deeper and narrower than the ground-state one, and the energy necessary for desorption is achieved owing to the increasing momentum uncertainty of a squeezed wave packet. In the theoretical calculations and analysis of experimental data two main simplifying approximations are typically made: (i)
37
in the time-dependent Schr€ odinger equation describing a particle being in the excited-state a deexcitation rate is assumed to be position independent; (ii) the final repulsion potential Uþ ðrÞ and excited-state potential U2þ ðrÞ can be split into the z-dependent and lateral-dependent potentials [11]. The KEDs can be even obtained in an analytical form if z- and lateral-dependent potentials are represented by the Morse and harmonic potentials, respectively [11]. A more general formula for the KED of neutral particles desorbing in the direction normal to the surface was given by Gortel in Ref. [15, Eq. (3)]. Particularly for the case of coinciding equilibrium positions of the ground state and excited state potentials no classical momentum is gained. Consequently, the time integrand present in this equation (Ref. [15], Eq. (3)) becomes effectively proportional to a relatively slowly varying energy-dependent factor and to the oscillating term ( ) Z ffi p 1 z2þ 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 0 sin dz 2m½E Uþ ðz Þ ; þ ð1Þ 4 h z1 ðEÞ where m is the mass of desorbing particle, z2þ is the equilibrium position of the excited-state potential U2þ ðzÞ measured with respect to the ground-state potential equilibrium position zo (in our case we put zo ¼ 0), and z1 ðEÞ represents the classical turning point on the final repulsion potential Uþ ðzÞ for the particle with a kinetic energy E. From experimental point of view, this means that if WPS desorption dominates, the distinct maxima should occur on the KED curves approximately at energies El for which the following equation is fulfilled Z ffi 1 z2þ 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 0 dz 2m½El Uþ ðz Þ ¼ l þ j p: h z1 ðEl Þ 4 ð2Þ In this equation the parameter l ¼ 0; 1; 2; . . . numbers successive maxima observed on the ions KED. The j value is the number of the antinodes between z1 ðEÞ and z2þ of the continuum wave function corresponding to the ion kinetic energy Eo , for which the first maximum on the ions KED is registered. Returning to the experimental data, we see (Fig. 2) that for LiF exposed to prolonged irradiation the oscillatory structure is not so regular
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L. Markowski / Surface Science 528 (2003) 35–41
as for virgin samples. Simultaneously, for such samples a relatively strong, narrow-energy peak, located at about 2 eV and accompanied by a few satellite peaks, appears. For intermediate dosages a mixture of virgin and damaged oscillatory structures makes their analysis rather difficult. For damaged samples the 7 Liþ oscillatory structure disappears almost completely, and the onset of that registered for 6 Liþ seems to be shifted towards the energy about 2.8 eV. The presence of the oscillatory structure onset indicates that both for the virgin and for the damaged LiF samples the final repulsion potential Uþ ðzÞ must have a characteristic potential barrier. These potential barrier heights should be 1.4 V for the virgin sample and 2.8 V for samples exposed to 50 lC/mm2 electron dose, respectively. We have to point out here that when we considered pure repulsive Uþ ðzÞ potential (in our test the Born–Mayer analytical form was used) the experimental data could not be adequately reproduced. Especially, the maximum observed for lower ion energies remained unexplained. Eq. (2) allows us to determine the shape of the final repulsion potential to the left of its equilibrium position without detailed knowledge of the ground-state and excited-state potentials (here only the z2þ position is important). Nevertheless, in further calculations the ground-state potential was assumed to be harmonic with a characteristic vibrational frequency corresponding to hx equal to 71 meV for 7 Liþ [16], and the final Uþ ðzÞ and excited-state U2þ ðzÞ potentials were approximated by the Morse potential. The results of our calculations for 6 Liþ and j ¼ 5 for virgin samples and j ¼ 4 for samples exposed to 50 lC/mm2 electron dose are presented in Fig. 3(a). We can notice that for the obtained Uþ ðzÞ potential there is a considerable probability that Li2þ will undergo transitions, not to the continuumstate, but to a one of the bound-state En belonging to Uþ ðzÞ potential. Let us suppose that the very narrow peak and its smaller satellite peaks observed for damaged LiF samples are connected with the transitions to the bound-states. We have tested this hypothesis by extending the fitting procedure using Uþ ðzÞ potential composed of two parts (both having the Morse form). For such a potential additionally to Eq. (2) we require that,
Fig. 3. The Morse potentials Uþ ðzÞ (top panel) calculated for virgin (dashed line) and for damaged samples (electron dose 50 lC/mm2 , solid line) (top panel) using Eq. (2) only. The wave functions corresponding to the first energy-maximum in the observed oscillatory structures are also shown. The Uþ ðzÞ potentials determined for damaged samples using Eqs. (2) and (3) (bottom panel). Two wave functions corresponding to the third and fifth bound-state of 6 Liþ in the Uþ ðzÞ potential, with energies 2.12 and 2.57 eV are also shown.
within WKB approximation used here, the allowed bound-state energy En for n ¼ 0; 1; 2; . . . must fulfill the following equation (well known as the Bohr–Sommerfeld rule in the old quantum theory) Z 1 z2 ðEn Þ 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 0 dz 2m½En Uþ ðz Þ ¼ n þ p; ð3Þ h z1 ðEn Þ 2 where z1 ðEn Þ and z2 ðEn Þ is the classical turning point to the left and to the right of the z2þ position, respectively. Moreover, we claim that at z2þ position both parts of the Uþ ðzÞ potential and their first derivative are continuous. The best fit for Uþ ðzÞ potential prepared in this way is obtain when in Eq. (2) we chose j ¼ 4. The final result of our calculations is presented in Fig. 3(b). In this figure two wave functions corresponding to the third and fifth bound-state of 6 Liþ in the Uþ ðzÞ potential, with energies 2.12 and 2.57 eV are also
L. Markowski / Surface Science 528 (2003) 35–41
shown. Knowing the Uþ ðzÞ potential we are able to calculate KED of ions desorbed by WPS mechanism RðEÞ and the population Rn ðEn Þ of the bound-states. The results are presented in Fig. 4. In these calculations Li2þ potential depth was chosen to be U2þ ¼ 20 eV. This potential range parameter and the inter-atomic Auger transition 1 and rate were taken rather arbitrarily to be 2 A 14 1 5 10 s , respectively. Obviously, one has to keep in mind that at some time disintegration of the two-hole state created by the inter-atomic Auger process can occur, preventing positive-ion desorption. In consequence the obtained theoretical KEDs can be further deformed. The obtained results indicate that if the peaks observed experimentally are really connected with the ions coming from the bound-states, the width of Uþ ðzÞ potential barrier formed must be very thin (it depends on the potential shape beyond the barrier which in Fig. 3(b) was chosen arbitrary and marked by dashed line). Otherwise, the transmission coefficient will be very small and, in consequence, these ions would not be detected experimentally. On the other hand, we can state that for higher bound-states the expected transmission coefficient will be much higher than those for lower ones. Thus, to explain the reasons for which the pronounced peak is located just at about 2 eV we have to discuss the dynamical aspects of
Fig. 4. The KEDs RðEÞ and the population probabilities Rn ðEn Þ of the bound-states (vertical lines) calculated for 6 Liþ (solid line) and 7 Liþ (dashed line) and j ¼ 4. The Uþ ðzÞ potential used was determined from Eqs. (2) and (3) and based on the experimental data obtained for 10 ML LiF/Si(1 0 0) exposed to 50 lC/mm2 electron dose. The other parameters are also shown.
39
the problem. At the time t ¼ 0, due to surface rumpling effect, the Liþ ion lies slightly below the plane determined by the surface fluorine ions [17,18]. Our data analysis shows that when this ion is additionally ionized, its position almost does not change. Nevertheless, the radius of the Li2þ ion is expected to be smaller than that of Liþ . The strong Coulomb interaction of Li2þ with neighbouring fluorine ions causes that their orbitals become deformed considerably very quickly. A similar evolution of the electronic polarization will occur after the inter-atomic Auger transition, but now the electron clouds of fluorine ions tend to be oriented towards the two holes located under the desorbing Liþ ion. The process of charge redistribution within neighbouring fluorine ions, due to low masses of electrons, finishes very quickly, within a time below 1015 s. This causes that a repulsive interaction between the Liþ and F ions of interest, and related to the overlap of their electron clouds (well known as the Pauli repulsion), rapidly decreases. As a consequence, the high Uþ ðzÞ potential barrier lowers and the lifetimes of the higher bound-states are very short, and due to the Heisenberg uncertainty principle the ions related to these states will be spread out in energy. The Pauli repulsion term decrease connected with the electronic polarization can be estimated to be about 0.8 V. This is the main reason for so weak intensity of the peaks observed between 2 and 2.8 eV. After the time about 1015 s the lattice rearrangement takes place. Now, the Liþ ions which have not been desorbed before and still occupy the bound-states are released to the continuum spectrum of states. From the energy width of the most pronounced peak (2.12 eV for 6 Liþ and 2.03 eV for 7 Liþ , respectively) we can estimate that the potential barrier disappears in this stage with a characteristic time of about 7 fs. This value can be correlated with the frequency corresponding to the longitudinal optical mode which for bulk LiF is 1:27 1014 s1 . This gives us the characteristic relaxation time 7.9 fs. As it is predicted the energy level corresponding to n ¼ 0 is always the most populated bound-state (see Fig. 4). Simultaneously, the ions trapped in this state have a negligible probability to tunnel through the potential barrier. Therefore, all the ions belonging
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L. Markowski / Surface Science 528 (2003) 35–41
to this state should experimentally form the continuous energy distribution. Indeed, in our KEDs we observe such a relatively broad maximum (see Fig. 2). Its position is about 0.8 eV, and it is almost the same for 6 Liþ and 7 Liþ , and for virgin and damaged samples. In this case, however, to calculate the proper energy distribution, the kinetic of Uþ ðzÞ potential changes has to be known and the time-dependent perturbation theory has to be involved. Inspecting the results presented in Fig. 3(a) we notice that the Uþ ðzÞ potential determined for the samples exposed to 50 lC/mm2 electron dose is almost the same as the one obtained for virgin samples, and it seems that it is only shifted up by about 1.4 V. Prolonged electron irradiation certainly creates several different kinds of defect in the LiF layer. This will cause that the discreteness of the WPS effect is smoothed out. Nevertheless, the 1.4 V shift suggests that for damaged samples the Liþ desorption component discussed in this paper occurs mainly from sites for which a Vk -center is located in the fifth sublayer below the site of emitted ion (for LiF the lattice constant is 4.028 ). This, however, does not imply that a similar A shift will be produced in the full KED of desorbed ions, which was already mentioned as determined by ions emitted from the adatom sites. In fact, in our measurements the overall shift typically does not exceed 0.2 eV. This can be explained by a strong temperature increase in the close neighbourhood of the defect just created. The local temperature may be as high as several thousand Kelvin and it will induce the adion hopping process. Finally, the ion can be transferred far away from the defect, to the site for which its binding energy is much higher.
4. Conclusions We have shown that, during electron bombardment, the bound-states located above the vacuum level of the LiF crystal can give a detectable contribution to the Liþ desorption flux. For LiF there is a direct possibility to compare the results obtained for 6 Liþ and 7 Liþ which confirm justness of the hypothesis that these ions can be emitted by a quasi-tunneling effect. In particu-
lar, prolonged electron irradiation causes a shift of bound-state energy levels enhancing the tunneling effect significantly. We hope that these observations give us a further progress in our understanding of the electron-stimulated desorption phenomenon of positive ions from alkali halides crystals. Careful inspection of the experimental data obtained for NaCl and presented in Ref. [8], indicates that they are rather general and valid not only for LiF, but for other ionic materials as well. The most promising is the fact that with applications of the WPS model, apart from the effects discussed in this paper, we can properly describe the total shape of the KEDs of desorbing alkali and halogen positive ions (these results will be published in a separate paper). This model explains as well why in alkali halides the desorption yield of positive ions strongly increases for the stimulating electron energy corresponding to the alkali ion ionization threshold rather than to the ionization threshold of halogen ions. As it was presented, small oscillation can be observed on the Liþ KEDs as the result of the WPS desorption scenario. This is a purely quantum-mechanical effect, and as such is strongly correlated to the mass of ions. Thus, although it depends on the particular potentials involved during the desorption process, one can expect that the higher ion masses the harder this effect will be to detect. Nevertheless, it seems that the effects discussed in this paper can be strongly enhanced in the twophoton excitation experiments (using synchrotron and infrared radiation).
Acknowledgements This work was financially supported by the University of Wrocław, Grant no. 2016/W/IFD/ 2002.
References [1] M. Szymo nski, J. Kołodziej, Z. Postawa, P. Czuba, P. Piaßtkowski, Prog. Surf. Sci. 48 (1995) 83. [2] M. Szymo nski, J. Kołodziej, P. Czuba, P. Piaßtkowski, A. Poradzisz, N.H. Tolk, J. Fine, Phys. Rev. Lett. 67 (1991) 1906.
L. Markowski / Surface Science 528 (2003) 35–41 [3] T.R. Pian, M.M. Traum, J.S. Kraus, N.H. Tolk, N. Staffel, G. Margaritondo, Surf. Sci. 128 (1983) 13. [4] M.L. Knotek, P.J. Feibelman, Phys. Rev. Lett. 40 (1978) 964. [5] R.E. Walkup, Ph. Avouris, Phys. Rev. Lett. 56 (1986) 524. [6] N. Itoh, A.M. Stoneham, A.M. Harker, Surf. Sci. 217 (1989) 573. [7] R.E. Walkup, Ph. Avouris, A.P. Ghosh, Phys. Rev. Lett. 57 (1986) 2227. [8] J. Kołodziej, P. Czuba, P. Piaßtkowski, Z. Postawa, M. Szymo nski, Nucl. Instr. Meth. B 116 (1996) 113. [9] L. Markowski, Surf. Sci. 501 (2002) 235.
[10] [11] [12] [13] [14] [15] [16] [17] [18]
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Z.W. Gortel, A. Wierzbicki, Surf. Sci. 239 (1990) L565. Z.W. Gortel, A. Wierzbicki, Phys. Rev. B 43 (1991) 7487. L. Markowski, F. Gołek, Surf. Sci. 425 (1999) 287. L. Markowski, Acta Physica Polonica A, submitted for publication. P.R. Antoniewicz, Phys. Rev. B 21 (1981) 3811. Z.W. Gortel, Phys. Lett. A 167 (1992) 421. J. Pireaux, P.A. Thiry, R. Caudano, Surf. Sci. 162 (1985) 132. G.E. Laramore, A.C. Switendick, Phys. Rev. B 7 (1973) 3615. J. Vogt, H. Weiss, Surf. Sci. 501 (2002) 203.
Tunneling effect in electron-stimulated desorption of Liþ from LiF/Sið1 0 0Þ L. Markowski
*
Institute of Experimental Physics, University of Wrocław, pl. Maxa Borna 9, 50-204 Wrocław, Poland
Abstract It is shown that the kinetic-energy distributions of 6 Liþ and 7 Liþ ions desorbed during electron irradiation from the system LiF/Si(1 0 0) exhibit fine structures. Their character suggests that they correspond to Liþ ions emitted according to the wave packet squeezing desorption model. This observation enables us to determine the final repulsion potential active in the Liþ desorption process. The oscillatory-structure onsets show that these potentials have the potentialenergy barrier of a height of about 1.4 eV for the virgin LiF samples and of about 2.8 eV for LiF preirradiated with a dose of 50 lC/mm2 . For preirradiated samples the oscillatory structures are less pronounced, but for such samples relatively strong and very narrow peaks located at 2.12 eV for 6 Liþ and at 2.03 eV for 7 Liþ , respectively, can be detected. These peaks are interpreted as ions trapped in the temporary bound-states located above the vacuum level of the sample. Due to a relatively high transmission coefficient the ions can tunnel trough the temporary existing potential barrier. The lifetime of the potential barrier estimated from the peak energy width and the Heisenberg uncertainty principle is about 7 fs. Some other aspects of the dynamic lattice distortion are also discussed. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Alkali halides; Desorption induced by electronic transitions (DIET); Ion–solid interactions
1. Introduction Among a variety of systems for which atom/ion desorption induced by electronic transitions can be observed the alkali halides seem to be particularly interesting. First of all, these materials form crystals with a simple cubic lattice of the NaCl-type. Secondly, analysis of experimental data appears to be much less complicated if we take into account that for ionic systems the interaction which causes positive ion desorption can be very well approximated by an almost pure Coulomb potential.
*
Tel.: +48-71201307; fax: +48-71-328-7365. E-mail address: [email protected] (L. Markowski).
During electron irradiation, alkali halide crystals predominantly emit alkali and halogen atoms, and the processes evoking their desorption are rather well understood [1,2]. On the other hand, the mechanism of positive ion emission is much more controversial. The observed correlation between the alkali ion ionization threshold and the positive-ion emission yield [3] suggests that the ion ejection is initiated by an inter-atomic Auger process, and it is running in similar way as in the Knotek and Feibelman model [4]. Theoretical calculations [5,6] give us, however, not so unique answer, leaving still open the question whether the repulsive configuration exists sufficiently long for ion desorption to occur. Moreover, some experimental results indicate that positive ions can be produced by
0039-6028/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0039-6028(02)02607-9
36
L. Markowski / Surface Science 528 (2003) 35–41
gas-phase collisions between desorbed atoms and secondary electrons [7]. Nevertheless, further precise measurements of the positive ion energy and mass distributions performed by Kołodziej et al. [8] showed that alkali ions are really emitted due to Coulomb instability of the crystal lattice. Very recent investigations of Liþ emission from the LiF/ Si(1 0 0) system confirm that lithium ions are mainly emitted from the adatom sites, when the charge reversal takes place on a fluorine ion located just below it [9]. Moreover, the observations of small oscillations on the Liþ kinetic-energy distributions (KEDs) curves allowed us to suggest that lithium ion ejection from its normal surface site is followed by the wave packet squeezing desorption (WPS) mechanism [10,11]. In this work we would like to reinforce this hypothesis by presenting new experimental results.
2. Experimental Our experimental and sample preparation procedures have been discussed previously [9,12], and here they will be only briefly mentioned. Thin layers of LiF vapour 1–12 monolayers (ML) thick were deposited on a clean Si(1 0 0) single crystal (Si substrate was flash annealed up to 900 K in situ and then its structure and cleanliness were checked by LEED and AES) in ultrahigh vacuum (base pressure, 2 1010 mbar). Depositions were performed at 100, 300 and 500 K. An 300 eV electron beam, pulsed by deflector plates with a frequency of 10 kHz and of 20 ns pulse width, and average current density of 4 nA/mm2 , was incident on the LiF/Si(1 0 0) sample at 45° relative to the surface normal. KEDs of desorbed positive ions were measured with a calibrated time-of-flight (TOF) spectrometer. The ion acceptance angle detection, measured with respect to the surface normal, was lower than 1°3000 .
ever, desorption of Hþ , 6 Liþ , 7 Liþ and Fþ dominates significantly other species observed. The 6 Liþ and 7 Liþ peaks can be well represented by smooth bell-shaped curves and only small oscillations at high-energy side could be detected (i.e. for their shorter flight times). No noticeable changes in these peaks were observed for several successive TOF mass spectra collected. Nevertheless, when accumulated electron dose was further increased, the main peak for both lithium isotopes appears to be accompanied by another small peak. In Fig. 1 typical spectrum obtained for 50 lC/mm2 electron dose is presented and these additional peaks are marked by arrows. Due to very short electron pulses of small current density, chopped with a relatively low frequency, to obtain high irradiation dose the sample was exposed to the continuous electron beam for several minutes. Then for such samples the TOF spectra measurements were undertaken. To extract character of these fine structures the experimental 6 Liþ and 7 Liþ peaks were described by smooth, slightly asymmetric bellshaped functions and then the simple subtraction procedure was applied. The final results obtained for 10 ML LiF deposited and measured at 300 K, for TOF spectra collected from newly prepared samples and for samples exposed to 50 lC/mm2 electron beam are presented in Fig. 2 (dashed and solid line, respectively) in the ion kinetic-energy domain. In this figure the intensity of 6 Liþ is cor-
3. Results and discussion The mass spectra of positive ions emitted from LiF/Si(1 0 0) samples during electron bombardment reveal a relatively rich structure [12]. How-
Fig. 1. TOF spectrum for electron-stimulated desorption of 6 Liþ and 7 Liþ ions from the 10 ML LiF/Si(1 0 0) system obtained for the sample exposed to 50 lC/mm2 electron dose. Stimulation electron energy is 300 eV. LiF deposited and measured at 300 K.
L. Markowski / Surface Science 528 (2003) 35–41
Fig. 2. Comparison of oscillatory components of KEDs of 6 Liþ and 7 Liþ desorbed from 10 ML LiF/Si(1 0 0) after the subtraction procedure (see text), for virgin (dashed line) and for damaged samples (electron dose 50 lC/mm2 , solid line).
rected according to the natural abundance of 6 Li/ 7 Li. For virgin samples the fine structures exhibit rather regular oscillations that have their onset at an ion energy of about 1.4 eV. The origin of these oscillations has been already discussed in Ref. [9], and recently, more detailed calculations clearly indicate that they are related to the contribution of lithium ions emitted from LiF by the WPS mechanism [13]. In the WPS model the excitation and deexcitation sequences take place in similar way as in the well-known Antoniewicz desorption model [14]. However, because the equilibrium positions of the excited- and ground-state potentials nearly coincide, no or little classical kinetic energy is achieved. Nevertheless, the excited-state potential is much deeper and narrower than the ground-state one, and the energy necessary for desorption is achieved owing to the increasing momentum uncertainty of a squeezed wave packet. In the theoretical calculations and analysis of experimental data two main simplifying approximations are typically made: (i)
37
in the time-dependent Schr€ odinger equation describing a particle being in the excited-state a deexcitation rate is assumed to be position independent; (ii) the final repulsion potential Uþ ðrÞ and excited-state potential U2þ ðrÞ can be split into the z-dependent and lateral-dependent potentials [11]. The KEDs can be even obtained in an analytical form if z- and lateral-dependent potentials are represented by the Morse and harmonic potentials, respectively [11]. A more general formula for the KED of neutral particles desorbing in the direction normal to the surface was given by Gortel in Ref. [15, Eq. (3)]. Particularly for the case of coinciding equilibrium positions of the ground state and excited state potentials no classical momentum is gained. Consequently, the time integrand present in this equation (Ref. [15], Eq. (3)) becomes effectively proportional to a relatively slowly varying energy-dependent factor and to the oscillating term ( ) Z ffi p 1 z2þ 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 0 sin dz 2m½E Uþ ðz Þ ; þ ð1Þ 4 h z1 ðEÞ where m is the mass of desorbing particle, z2þ is the equilibrium position of the excited-state potential U2þ ðzÞ measured with respect to the ground-state potential equilibrium position zo (in our case we put zo ¼ 0), and z1 ðEÞ represents the classical turning point on the final repulsion potential Uþ ðzÞ for the particle with a kinetic energy E. From experimental point of view, this means that if WPS desorption dominates, the distinct maxima should occur on the KED curves approximately at energies El for which the following equation is fulfilled Z ffi 1 z2þ 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 0 dz 2m½El Uþ ðz Þ ¼ l þ j p: h z1 ðEl Þ 4 ð2Þ In this equation the parameter l ¼ 0; 1; 2; . . . numbers successive maxima observed on the ions KED. The j value is the number of the antinodes between z1 ðEÞ and z2þ of the continuum wave function corresponding to the ion kinetic energy Eo , for which the first maximum on the ions KED is registered. Returning to the experimental data, we see (Fig. 2) that for LiF exposed to prolonged irradiation the oscillatory structure is not so regular
38
L. Markowski / Surface Science 528 (2003) 35–41
as for virgin samples. Simultaneously, for such samples a relatively strong, narrow-energy peak, located at about 2 eV and accompanied by a few satellite peaks, appears. For intermediate dosages a mixture of virgin and damaged oscillatory structures makes their analysis rather difficult. For damaged samples the 7 Liþ oscillatory structure disappears almost completely, and the onset of that registered for 6 Liþ seems to be shifted towards the energy about 2.8 eV. The presence of the oscillatory structure onset indicates that both for the virgin and for the damaged LiF samples the final repulsion potential Uþ ðzÞ must have a characteristic potential barrier. These potential barrier heights should be 1.4 V for the virgin sample and 2.8 V for samples exposed to 50 lC/mm2 electron dose, respectively. We have to point out here that when we considered pure repulsive Uþ ðzÞ potential (in our test the Born–Mayer analytical form was used) the experimental data could not be adequately reproduced. Especially, the maximum observed for lower ion energies remained unexplained. Eq. (2) allows us to determine the shape of the final repulsion potential to the left of its equilibrium position without detailed knowledge of the ground-state and excited-state potentials (here only the z2þ position is important). Nevertheless, in further calculations the ground-state potential was assumed to be harmonic with a characteristic vibrational frequency corresponding to hx equal to 71 meV for 7 Liþ [16], and the final Uþ ðzÞ and excited-state U2þ ðzÞ potentials were approximated by the Morse potential. The results of our calculations for 6 Liþ and j ¼ 5 for virgin samples and j ¼ 4 for samples exposed to 50 lC/mm2 electron dose are presented in Fig. 3(a). We can notice that for the obtained Uþ ðzÞ potential there is a considerable probability that Li2þ will undergo transitions, not to the continuumstate, but to a one of the bound-state En belonging to Uþ ðzÞ potential. Let us suppose that the very narrow peak and its smaller satellite peaks observed for damaged LiF samples are connected with the transitions to the bound-states. We have tested this hypothesis by extending the fitting procedure using Uþ ðzÞ potential composed of two parts (both having the Morse form). For such a potential additionally to Eq. (2) we require that,
Fig. 3. The Morse potentials Uþ ðzÞ (top panel) calculated for virgin (dashed line) and for damaged samples (electron dose 50 lC/mm2 , solid line) (top panel) using Eq. (2) only. The wave functions corresponding to the first energy-maximum in the observed oscillatory structures are also shown. The Uþ ðzÞ potentials determined for damaged samples using Eqs. (2) and (3) (bottom panel). Two wave functions corresponding to the third and fifth bound-state of 6 Liþ in the Uþ ðzÞ potential, with energies 2.12 and 2.57 eV are also shown.
within WKB approximation used here, the allowed bound-state energy En for n ¼ 0; 1; 2; . . . must fulfill the following equation (well known as the Bohr–Sommerfeld rule in the old quantum theory) Z 1 z2 ðEn Þ 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 0 dz 2m½En Uþ ðz Þ ¼ n þ p; ð3Þ h z1 ðEn Þ 2 where z1 ðEn Þ and z2 ðEn Þ is the classical turning point to the left and to the right of the z2þ position, respectively. Moreover, we claim that at z2þ position both parts of the Uþ ðzÞ potential and their first derivative are continuous. The best fit for Uþ ðzÞ potential prepared in this way is obtain when in Eq. (2) we chose j ¼ 4. The final result of our calculations is presented in Fig. 3(b). In this figure two wave functions corresponding to the third and fifth bound-state of 6 Liþ in the Uþ ðzÞ potential, with energies 2.12 and 2.57 eV are also
L. Markowski / Surface Science 528 (2003) 35–41
shown. Knowing the Uþ ðzÞ potential we are able to calculate KED of ions desorbed by WPS mechanism RðEÞ and the population Rn ðEn Þ of the bound-states. The results are presented in Fig. 4. In these calculations Li2þ potential depth was chosen to be U2þ ¼ 20 eV. This potential range parameter and the inter-atomic Auger transition 1 and rate were taken rather arbitrarily to be 2 A 14 1 5 10 s , respectively. Obviously, one has to keep in mind that at some time disintegration of the two-hole state created by the inter-atomic Auger process can occur, preventing positive-ion desorption. In consequence the obtained theoretical KEDs can be further deformed. The obtained results indicate that if the peaks observed experimentally are really connected with the ions coming from the bound-states, the width of Uþ ðzÞ potential barrier formed must be very thin (it depends on the potential shape beyond the barrier which in Fig. 3(b) was chosen arbitrary and marked by dashed line). Otherwise, the transmission coefficient will be very small and, in consequence, these ions would not be detected experimentally. On the other hand, we can state that for higher bound-states the expected transmission coefficient will be much higher than those for lower ones. Thus, to explain the reasons for which the pronounced peak is located just at about 2 eV we have to discuss the dynamical aspects of
Fig. 4. The KEDs RðEÞ and the population probabilities Rn ðEn Þ of the bound-states (vertical lines) calculated for 6 Liþ (solid line) and 7 Liþ (dashed line) and j ¼ 4. The Uþ ðzÞ potential used was determined from Eqs. (2) and (3) and based on the experimental data obtained for 10 ML LiF/Si(1 0 0) exposed to 50 lC/mm2 electron dose. The other parameters are also shown.
39
the problem. At the time t ¼ 0, due to surface rumpling effect, the Liþ ion lies slightly below the plane determined by the surface fluorine ions [17,18]. Our data analysis shows that when this ion is additionally ionized, its position almost does not change. Nevertheless, the radius of the Li2þ ion is expected to be smaller than that of Liþ . The strong Coulomb interaction of Li2þ with neighbouring fluorine ions causes that their orbitals become deformed considerably very quickly. A similar evolution of the electronic polarization will occur after the inter-atomic Auger transition, but now the electron clouds of fluorine ions tend to be oriented towards the two holes located under the desorbing Liþ ion. The process of charge redistribution within neighbouring fluorine ions, due to low masses of electrons, finishes very quickly, within a time below 1015 s. This causes that a repulsive interaction between the Liþ and F ions of interest, and related to the overlap of their electron clouds (well known as the Pauli repulsion), rapidly decreases. As a consequence, the high Uþ ðzÞ potential barrier lowers and the lifetimes of the higher bound-states are very short, and due to the Heisenberg uncertainty principle the ions related to these states will be spread out in energy. The Pauli repulsion term decrease connected with the electronic polarization can be estimated to be about 0.8 V. This is the main reason for so weak intensity of the peaks observed between 2 and 2.8 eV. After the time about 1015 s the lattice rearrangement takes place. Now, the Liþ ions which have not been desorbed before and still occupy the bound-states are released to the continuum spectrum of states. From the energy width of the most pronounced peak (2.12 eV for 6 Liþ and 2.03 eV for 7 Liþ , respectively) we can estimate that the potential barrier disappears in this stage with a characteristic time of about 7 fs. This value can be correlated with the frequency corresponding to the longitudinal optical mode which for bulk LiF is 1:27 1014 s1 . This gives us the characteristic relaxation time 7.9 fs. As it is predicted the energy level corresponding to n ¼ 0 is always the most populated bound-state (see Fig. 4). Simultaneously, the ions trapped in this state have a negligible probability to tunnel through the potential barrier. Therefore, all the ions belonging
40
L. Markowski / Surface Science 528 (2003) 35–41
to this state should experimentally form the continuous energy distribution. Indeed, in our KEDs we observe such a relatively broad maximum (see Fig. 2). Its position is about 0.8 eV, and it is almost the same for 6 Liþ and 7 Liþ , and for virgin and damaged samples. In this case, however, to calculate the proper energy distribution, the kinetic of Uþ ðzÞ potential changes has to be known and the time-dependent perturbation theory has to be involved. Inspecting the results presented in Fig. 3(a) we notice that the Uþ ðzÞ potential determined for the samples exposed to 50 lC/mm2 electron dose is almost the same as the one obtained for virgin samples, and it seems that it is only shifted up by about 1.4 V. Prolonged electron irradiation certainly creates several different kinds of defect in the LiF layer. This will cause that the discreteness of the WPS effect is smoothed out. Nevertheless, the 1.4 V shift suggests that for damaged samples the Liþ desorption component discussed in this paper occurs mainly from sites for which a Vk -center is located in the fifth sublayer below the site of emitted ion (for LiF the lattice constant is 4.028 ). This, however, does not imply that a similar A shift will be produced in the full KED of desorbed ions, which was already mentioned as determined by ions emitted from the adatom sites. In fact, in our measurements the overall shift typically does not exceed 0.2 eV. This can be explained by a strong temperature increase in the close neighbourhood of the defect just created. The local temperature may be as high as several thousand Kelvin and it will induce the adion hopping process. Finally, the ion can be transferred far away from the defect, to the site for which its binding energy is much higher.
4. Conclusions We have shown that, during electron bombardment, the bound-states located above the vacuum level of the LiF crystal can give a detectable contribution to the Liþ desorption flux. For LiF there is a direct possibility to compare the results obtained for 6 Liþ and 7 Liþ which confirm justness of the hypothesis that these ions can be emitted by a quasi-tunneling effect. In particu-
lar, prolonged electron irradiation causes a shift of bound-state energy levels enhancing the tunneling effect significantly. We hope that these observations give us a further progress in our understanding of the electron-stimulated desorption phenomenon of positive ions from alkali halides crystals. Careful inspection of the experimental data obtained for NaCl and presented in Ref. [8], indicates that they are rather general and valid not only for LiF, but for other ionic materials as well. The most promising is the fact that with applications of the WPS model, apart from the effects discussed in this paper, we can properly describe the total shape of the KEDs of desorbing alkali and halogen positive ions (these results will be published in a separate paper). This model explains as well why in alkali halides the desorption yield of positive ions strongly increases for the stimulating electron energy corresponding to the alkali ion ionization threshold rather than to the ionization threshold of halogen ions. As it was presented, small oscillation can be observed on the Liþ KEDs as the result of the WPS desorption scenario. This is a purely quantum-mechanical effect, and as such is strongly correlated to the mass of ions. Thus, although it depends on the particular potentials involved during the desorption process, one can expect that the higher ion masses the harder this effect will be to detect. Nevertheless, it seems that the effects discussed in this paper can be strongly enhanced in the twophoton excitation experiments (using synchrotron and infrared radiation).
Acknowledgements This work was financially supported by the University of Wrocław, Grant no. 2016/W/IFD/ 2002.
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