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Desorption kinetics of Li atoms from LiF under electron bombardment
490
Nuclear
Instruments
and Methods
in Physics
Research
B58 (1991) 490-495 North-Holland
Desorption kinetics of Li atoms from LiF under electron bombardment 0. Kreitschitz, Ch. Polster, W. Husinsky and G. Betz Institut
ftir Allgemeine Physik, Technische Universitiit Wien, Wiedner HauptstraBe 8-10, A-1040 Wien, Austria
Measurements on electron stimulated desorption (ESD) of Li atoms in the electronical ground state (Li’) from air-cleaved LiF(lOO) surfaces have been performed. The electron energy was varied between 50 and 450 eV. After electron bombardment was stopped, a prompt decrease of the Lie signal followed by a delayed emission of Lie was observed. In the temperature range from 620 to 720 K the delayed emission of Lie shows a behavior, which could not be explained by diffusion of F centers to the surface only. Delayed emission of Lie up to minutes was observed and we therefore suggest, that energy must be stored in the bulk through the formation of F center aggregates in order to explain the experimentally observed behavior of the delayed emission. A system of rate equations has been developed, which describes the kinetics of formation and decay of F center aggregates.
1. Introduction Alkali
halides
are
very
appropriate
materials
for
(ESD) because of their well known and simple crystal structure. The basic features for the desorption mechanism of neutral alkali as well as halogen atoms are generally accepted [l-4], even recent experiments on nonthermal halogen emission indicate that the desorption mechanism is not fully understood yet [5]. If an electron impinges on the lattice it predominantly transfers energy to the halogen sublattice causing valence electronic excitation. The electronic excitation leads via intermediate steps to the formation of F-H center pairs [6]. With increasing temperature creation of spatially well separated F-H pairs becomes effective [7]. While H centers are mobile even at temperatures as low as 30 K [8], the F center diffusion is limited to temperatures above a few hundred kelvin [9]. H centers having diffused to the surface cause the emission of neutral halogen atoms, while diffusion of F centers to the surface leads to the formation of neutral alkali atoms [lo], which will evaporate if the alkali vapor pressure is high enough, i.e., at sufficiently high target temperatures. At low temperatures, where the evaporation rate is the limiting process of neutral alkali desorption, alkali islands or even a metallic alkali overlayer can form on the surface [11,12]. The formation of alkali islands [13-171 on the surface influences the ESD characteristics and might even inhibit desorption. In addition fast diffusion to the surface followed by self trapping of ‘hot holes’, which are a precursor of F and H centers, might occur [5]. Such a process would add another contribution to desorption not requiring F or H center diffusion to the surface and is not included in the model developed below. At temperatures above 500 K at typical current studying
electron
0168-583X/91/$03.50
stimulated
desorption
0 1991 - Elsevier Science Publishers
densities of 10 pA/mn? evaporation is no longer the rate limiting process. In this case measurements of desorption, produced by short pulsed electron and photon beams, are suitable experimental methods to obtain information about the diffusion process of F centers [18,19]. After a given irradiation time the beam is turned off and the delayed emission of alkali atoms reflects the diffusion time of the F centers to the surface. Green et al. [19] have developed a diffusion model of F centers with respect to the desorption process of ground-state Li atoms from LiF under short pulsed electron irradiation. An additional effect, which might influence the desorption behavior, is the aggregation of F centers [9] in the bulk region near the surface. F center aggregates can be identified as alkali metal colloids imbedded in the crystal. Optical absorption measurements, small angle X-ray scattering and Raman scattering techniques on alkali halides revealed [9], that under ionizing radiation a part of the F centers produced are converted into alkali metal aggregates in a certain temperature range. In the work by Green et al. [19] it was pointed out, that no agglomeration of F centers has been taken into consideration. Formation of Li islands or of an Li overlayer can be neglected due to the sufficiently high target temperatures. In this paper we want to report about results of the desorption behavior of ground state Li atoms after the electron beam is stopped (delayed desorption or emission). Especially, attention is drawn to the delayed emission of Li atoms in connection with the formation and the decay of F center aggregates in the bulk region near the surface. During electron irradiation F centers will agglomerate forming aggregates (colloids). After the irradiation is stopped, the decay of the colloids into F centers will strongly influence the delayed emission of Li atoms. A system of rate equations has been devel-
B.V. (North-Holland)
0. Kreitschitz
oped to describe the delayed emission the basis of F center aggregation.
et al. / Li atoms
of Li atoms
fromLIF under electron bombardment
on ‘;: 3105 4 :
2. Experimental
setup
Air-cleaved (100) single crystal surfaces of LiF have been irradiated with electrons (50-450 ev). Space charge effects of the electron beam on the one hand and detection efficiency on the other hand restricted us to a small useable current regime, where we could measure the current density dependence (7-11 l.tA/rnrn’) of the delayed desorption yield. The angle of incidence of the electron beam was 30° with respect to the target normal. Two plates of stainless steel have been mounted in front of the electron gun. During the measurement the two plates were connected to ground. The geometry of the plates was chosen in such a way, that all electrons leaving the gun would strike the plate if a voltage of 300 V would be applied on one plate. This provided a method to measure the total electron beam current without need for further correction for secondary electrons. In addition, the profile of the electron beam was measured by moving a wire with a diameter of 0.2 mm stepwise through the electron beam. Thus we could measure the absolute electron beam current density. The UHV chamber was maintained at a base pressure The LiF of 5 x lo-lo mbar during the measurements. targets were cleaned in the vacuum chamber by prolonged heating at 700 K. Thermocoax heating controlled by a temperature control unit performed uniform heating and cooling of the target between room temperature and 750 K. The target temperature was measured with a thermocouple, which was in good thermal contact with the target surface. The desorbed Li atoms were detected by a quadrupol mass analyzer viewing the LiF surface perpendicularly. The pulses from the electron multiplier were processed digitally in a pulse counting mode. The dwell time was restricted to 20 ms.
3. Experimental
491
results
Fig. 1 shows the delayed desorption of neutral Li atoms at 720 K for a current density of 10 ltAA/mm* for four different bombardment times (1, 2, 4 and 6 s). The Li signal during bombardment (area Al in fig. 1) shows a prompt decrease by about one order of magnitude after the electron beam is stopped. This is followed by a delayed emission (area A2 in fig. 1). The prompt signal decrease (time constant i 20 ms) can be easily distinguished from the delayed emission (order of seconds) as is shown in fig. 2. It is also evident from fig. 2 that different processes must be responsible for prompt and delayed emission of Li atoms.
I IO5
2 0 3.104 5; 0’.z l.104 4
3.103
TIME [set] Fig. 1. The emission
of ground-state Li atoms from LiF under pulsed electron irradiation is shown in a logarithmic plot. After the electron bombardment is stopped, the Li signal exhibits a prompt decrease in less than 20 ms followed by a delayed emission in the order of seconds. Al represents the yield of desorbed Li under electron irradiation and A2 the yield of the delayed signal, respectively.
In this paper we will mainly concentrate on this delayed emission. At temperatures above 700 K an obvious maximum in the delayed emission appears for bombardment times of a few seconds (fig. 1). For bombardment times of more than 20 s the maximum becomes less pronounced. However, for lower temperatures (650 K) the bombardment time has to be increased to more than 50 s in order to observe a maximum in the delayed emission at all. The prompt and delayed contributions can still be clearly separated. At even lower temperatures (< 500 K) Li evaporation from the surface becomes the rate limiting process and no influence of aggregate formation on the desorption yield can be observed. No longer two contributions to the
-prompt
de0ease
-delayed
&XI-ease
~_-_.~.c..
_._l
L’
I I
Fig. 2. The existence of two different contributions to the delayed emission of Li’ are shown in detail. The bold line represents the fast decrease ( i 20 ms) due to diffusion and the plain line represents the (slow) delayed emission caused by agglomeration in the bulk. IV. DESORPTION
492
0. Kreitschitz ”
I
2OOeVe-
/
/
+
680K
r?
I ”
LiF
I
et al. / Li atoms from LiF under electron bombardment
”
”
.
t 0
, ,,,,,,,,,,,,,,,,I,,,,,,,;
20
40
60
IRRADIATION
80
100
TIME
120
140
[set]
Fig. 3. Experimental data of the delayed emission yield of Li atoms as a function of irradiation time are presented for a constant current density of 8 PA/mm2 at 680 K. Saturation is reached at a fluence of approximately 1.5 X 10”e/cm2.
delayed emission as shown in fig. 2 can be distinguished. The F center production rate depends on the energy of the impinging electrons. At a temperature of 710 K the electron energy was varied from 50 up to 400 eV for two different irradiation times (8 and 10 s, respectively) and the same current density (3 10 uA/mm*). The ratio Al/A2 (as defined in fig. 1) was found to be a function of the electron energy. It exhibits a minimum at an electron energy of 100 eV. Furthermore, a dependence of the delayed emission on the current density could be observed. The delayed emission of Lie increases with higher current densities. In fig. 3 the yield of the delayed emission of Li atoms (area A2) was measured as a function of irradiation time. Saturation was reached at an irradiation time of 35 s which corresponds to a fluence of 1.8 X 10” e/cm2 (3 1 Grad). This is the fluence range for which F center agglomeration has been observed spectroscopically [8] in bulk irradiation experiments using X-rays.
the number of F centers trapped by the agglomerate. An increasing F center production will result in an enhanced trapping and thus causes an increase in agglomerate size and number until equilibrium is reached again. Vice versa, a reduction in F center production (decreasing or stopping electron bombardment) will cause shrinking of the colloid size and number. This dynamical behavior can be described by a system of rate equations. Some simplifications on the model according to our special experimental conditions have been made. For low-energy electrons the penetration depth is below 100 A [20]. Most of the F centers are created at a depth of less then 30 A, which corresponds to the maximum of deposited energy for 200 eV electrons. The diffusion time of the F centers is in the order of microseconds in the temperature range from 620 to 720 K [lo]. Under these circumstances no depth dependence of the F-center concentration has to be taken into account and their diffusion time to the surface was neglected. Furthermore, the loss of F centers by trapping at impurity sites or dislocation lines has not been taken into account, either. It is assumed, that every F center reaching the surface causes an evaporation event (desorption efficiency is 100%). Under the conditions mentioned above the rate equations can be expressed for a system, where F center agglomerates up to size n, i.e. F(l), F(‘). . . , F(“) are considered: dF”’ ~ = p _ aF’l) + 5 dt
i=3
h=2
+ 21,FC2’ - ~/Q(F”‘)~, _dF’*’ = dt
dF’“’ 7=’ 4. Model A review of various investigations made on the agglomeration of F centers into colloids in irradiated or additively colored solids is given by Hughes 191. High dose X- and y-ray irradiation of alkali halide crystals reveals the tendency of F centers to form colloids in the bulk. A thermodynamical model of the colloid state has been developed and is discussed in ref. [9]. The system of F centers and their aggregates form a one component-two-phase system in equilibrium with the crystal. The F centers behave like the vapour phase in contact with the colloids which behave like the solute or solid phase. In thermodynamical equilibrium the number of F centers ‘evaporating’ from an agglomerate is equal to
n-1 [;F(‘) _ c /c,F”‘F’~
l,F’3’
_
m+1
k2F(1)F(2)
_
[,ld2’
-I
+
,&(F(‘))‘,
(2)
F(m+‘) _ k F(i)F(m) _ 1 F’“’ m
+ ,k,_iF(‘)F(“-‘),
dF’“) -= dt
(1)
m
(3)
F’“, + kn_iFo)F(n--l) n
t represents the time, n the number of equations, F”’ the concentration of agglomerates, consisting of i F(l) centers (F(l) + F center, F(*) -+ M center, FC3’+ R centers etc.). P describes the effectively produced F centers per unit time, which are not lost due to recombination with H centers and k;, Ii are the rate constants. The quantity k, is responsible for the growth of the F(‘+‘) center and Ii (for i > 1) for the decay of the F”’ center. a is the loss parameter for F centers due to diffusion to the surface followed by desorption. Thus
0. Kreitsehitz
et al. / Li atoms from LiF under electron bombardment
nF(‘) is the number of F centers lost per unit time due to evaporation and was measured in our experiment. For the temperature range of our measurements (620 -+ 720 K) the evaporation rate [l7] is high enough that we can neglect any residence time of Li atoms at the surface before evaporation [19]. For the nonequilibrium state the rate equations were solved numerically by a Runge-Kutta algorithm, while the equilib~um conditions can be obtained an~yti~ly from
~
6
Growth and decay of F center aggregation is assumed to be only due to ‘absorption’ or ‘evaporation’ of a F center from an agglomerate, i.e. by the reaction F”’ + F(r) +.+E(‘+‘).
493
8
10
Simulation
I
12
14 16 18 20 22 TIME [set] Fig. 5. Experimental data fitted by a simulation taking F center aggregatesinto account consisting of up to six F centers (n = 6). The parameters chosen in the rate equations are: P = 5800, a = 700, I, = 17, 1, = 8, I4 = 7, I, = 5, I, = 2.5, k, = 2, k, = 2.5, k, = 2.5, k, = 2.7. k, = 5.5.
Growth or decay processes of aggregates of the form F(r) + F(l) + I?(‘) cf
F’3’
have not been taken into account, because of the low probabi~ty of such a process and also reactions of the type F(‘) + F(J) c, F(‘+J),
____3 +4 --t5 -6
!_,L_r
.r~ 4.5
,--_A..-i.,
were opti-
5. Discussion
i, j > l,
were neglected because of the low mobility of aggregates compared to F centers. Fig. 4 shows the results for the calculated delayed emission of Li atoms after an electron bombarding time of 4 s for different numbers n of rate equations. Here n represents the largest aggregate F(“) which is assumed to be formed. The bold line represents the calculation with six equations. Compared to calculations with smaller n, it turns out that with increasing n the maximum first appears and becomes more and more pronounced and shifts on the time scale. We get strong evidence that this behavior continues with greater n. The production term P and the loss parameter were
3.7
held constant while the other parameters mized in each calculation.
Equations Equations Equations Equations
\__,
5.4 TIME [see]
6.2
7
Fig. 4. The difference in behavior of the Li emission (area A2 of fig. 1) for different numbers of rate equations (n) reveal, that with increasing n the structure of the delayed emission approaches continuously the experimental observed behavior.
During irradiation an excess of F centers over II centers exists due to preferential trapping of H centers [21] and in addition due to their much higher velocity they will diffuse into the bulk or to the surface. These excess F centers can form F center aggregates. The most complex phase in colloid formation is the nucleation stage. Dislocation lines as well as impurity sites act as sinks for F centers. So it is very probable, that in general formation of small F center aggregates starts from such special sites. Jain and Lidiard [21] presented a model of colloid growth in alkali halides including the influence of preferential nucleation sites. However, they confined their discussion to high irradiation doses (order of Grad), where it can be assumed that the nucleation stage is past. The model developed here describes the build-up process of F center aggregates including the nucleation stage during irradiation and their consequent decay after electron irradiation is stopped. The small penetration depth of electrons and the high temperatures we are dealing with leads to the basic assumptions of the model: (i) the diffusion time of F centers is in the order of microseconds at temperatures of 700 K. Compared with the time of formation and decay of colloids (order of seconds) diffusion processes can be neglected; (ii) no spatial dependence of the F(‘) center concentration is assumed. The formation of H center clusters has been neglected too. At the high temperatures we are dealing with, H center cluster are not stable [22]. In fig. 5 a comparison of simulations with experimental data is shown. At an irradiation time of 2 s good agreement has been achieved. But with increasing IV. DESORFTION
0. Kreitschitz
et al. / LI atoms from LiF under electron bombardment
Fig. 6. Simulation of the growth and decay of F”’ centers (i=l, 2, . ..( 6) in a logarithmic plot. These aggregate concentrations correspond to the simulation in fig. 5 (irradiation time: 2 s).
bombarding time the calculated peak in the delayed emission shifts less in time than observed in the experiment. The reason for this deviation is, that the largest aggregate size chosen in the calculations (n = 6) is too small to match the real size of aggregates formed. Indeed, in fig. 4 it was shown, that with increasing n the rn~rn~ of the delayed emission shifts to later times. The position of the maximum on the time axis can be controlled by the largest aggregate size. The rate constants for production of F”) centers were chosen in such a way, that M centers were created with less probability than R centers, etc. and the rate constants for the decay were chosen vice versa. In the calculations, formation of agglomerates occurs as long as the F center production term P is not equal zero (irradiation). At a given time t, P is set equal zero and delayed emission and the decay of agglomerates will occur. As can be seen from fig. 5 the prompt onset of emission with irradiation is in agreement with the calculations. For a certain temperat~e and irradiation dose a definite aggregate size distribution exists [21]. In fig. 6 the calculated concentrations of all aggregates (n = 6) corresponding to the fit of fig. 5 (irradiation time is 2 s) are shown. The most probably formed aggregate is assumed to be the aggregate consisting of six F centers. The largest aggregate formed influences predominantly the position of the delayed maximum. If larger aggregates are taken into account, the result will be a shift of the delayed maximum to larger times. Generally, the greater the aggregate size is, the larger is the decay time of these aggregates (Thomson effect [9]). The dependence of the delayed desorption behavior of Li atoms on the current density is complex. We found an increasing delayed desorption yield with increasing current density for constant bombarding time and temperature. Increasing current density means an
increasing concentration of F centers in the interaction volume. This enhancement in concentration enables the formation of larger aggregates with the result of an increasing delayed desorption yield of Li atoms. But not only the growth of colloids may be influenced by a change in current density. One may expect, that primary electrons may excite or ionize agglomerated F centers. Increasing F-H center recombination with fluence can also limit the extend of agglomeration. These processes slow down the growth of colloids or even inhibit further growth. Such saturation effects have been observed experimentally 191. Hughes and Lidiard [21,23] calculated, that the concentration of agglomerated F centers should follow tX (1 < n < 2) in NaCl under ionizing radiation, where t is representing the irradiation time. In our experiment at small irradiation times x takes the value of 1.2, at larger irradiation times (> 15 s) the delayed yield increases more slowly until it reaches saturation (35 s) as can be seen in fig. 3. 6. Conclusions The delayed desorption of ground-state Li atoms is strongly influenced by the aggregate size formed in the bulk region near the surface during high dose electron irradiation. This influence is evident in the temperature range where aggregates are formed and evaporation is not the rate limiting process. The model developed, describes the delayed desorption behavior and the deviations from the experimental data can be explained by a too small aggregate size considered in the calculations. The problem of giving physical relevance to the rate constants used cannot be solved without including other experimental methods (optical spectroscopy, etc.) to measure the size distribution of the aggregates during irradiation and decay. Extension of the model to take F-H recombination and diffusion into account are in progress. The interesting speculation, whether inhibition or even decay of colloids by primary electrons or by recombination of clustered F centers with H centers may occur and to what extend it is important, needs further investigations.
Acknowledgement The authors gratefully acknowledge financial support by the &terreichischer Fonds zur Fiirderung der wissenschaftlichen Forschung (project No.: 6797).
References [l] A good collection of recent relevant articles can be found in: Desorption Induced by Electronic Transitions, DIET IV, eds., G. Betz and P. Varga (Springer, Berlin, 1990).
[2] Z. Postawa. J. Rutkowski. A. Poradzisz and M. Szymonski. Nucl. Instr. and Mirth. 818 (1987) 574. [3] N. Itoh. Nucl. Insrr. and Meth. 132 (1976) 201. [4] M. Szymonski. Radial. Eff. 52 (19RO) 9. [5] M. Szymonki. J. Kolodziej. P. C~uba. P. Piatkowski. A. PoradT.iw and N.II. Talk. these Proceedings (8th Int. Workshop on Inelastic Ion-Surface Collisions, Wr. Neu,tadt. 1YYO)Nucl. Instr. and Mcth. 858 (1991) 485. [6] R.T. Williams, KS. Song. W.I.. Faust and G.H. Leung. Phys. Rev. 1~33 (1986) 7232. [7] R.T. Willams. Semicond. Insul. 5 (1983) 457. (X] I’. Durand. Y. Farge and X4. Lambert. J. Phys. Chcm. Solids 30 (1969) 1353. [9] A.E. ~lughcs and SC. Jain. Adv. Phys. 28 (1979) 717. [IO] G.M. I.ouhriel. T.A. Green. and P.M. Richards. R.G. Alhridge D.W. Cherry. R.K. Cole. R.F. Haglund. Jr.. L.T. Hudson. M.H. Mendenhall. D.M. Newns, P.M. SavundararaJ. K.F. Snowdon and N.H. Talk. Phys. Rev. Let:. 57 (1986) 1781. [ll] P. Wurz and C.H. Becker, Surf. Sci. 224 (1989) 559. [ 121 X4. Sqmonski. J. Ruthowski. A. Poradzisz. Z. Postawa
1131 1141 [15] [Ih] [17] [lg] [19] [ZO] [21] [22] 1231
and B. Jorgensen. DIET II. eds.. W. Brenig and P. Menzel (Springer. Berlin. 1985). D.G. Lord and T.E. Gallon. Surf. Sci. 36 (1973) 606. D.S. Cota Arab and B.D. Powell. Surf. Sci. 51 (1975) 504. G. Singh and T.E. Gallon, Solid State Commun. 51 (1984) 2x1. G. Roy. G. Singh and T.E. Gallon. Surf. Sci. 152/153 (1985) 1042. J. Sarnthein, P. Wun. W. Ilusinsky and G. Betr. Surf. SCI. 241 (1991) 6. R.F. Haglund Jr.. N.11. Talk. G.M. Louhriel and R.A. Rosenberg. Nucl. Insrr. and Meth. B18 (1987) 549. T.A. Green. C;.M. I.ouhriel. P.M. Richards. X.H. Talk and R.F. Haglund Jr.. Phys. Rev. 835 (1987) 781. I.M. Bronsthteyn and A.N. Protscnko. Radio F.ng. Elwtron Phys. 15 (1970) 677. Uma Jain and A.B. Iidiard. Philos. Mag. 35 (1977) 245. A.E. Highes. Comments Solid State Phys. (1978) 8. 83. A.E. llughcs and A.B. Lidiard. AERE Harwell Kep. (1977) R1331Y.
IV. DESOKITION
Nuclear
Instruments
and Methods
in Physics
Research
B58 (1991) 490-495 North-Holland
Desorption kinetics of Li atoms from LiF under electron bombardment 0. Kreitschitz, Ch. Polster, W. Husinsky and G. Betz Institut
ftir Allgemeine Physik, Technische Universitiit Wien, Wiedner HauptstraBe 8-10, A-1040 Wien, Austria
Measurements on electron stimulated desorption (ESD) of Li atoms in the electronical ground state (Li’) from air-cleaved LiF(lOO) surfaces have been performed. The electron energy was varied between 50 and 450 eV. After electron bombardment was stopped, a prompt decrease of the Lie signal followed by a delayed emission of Lie was observed. In the temperature range from 620 to 720 K the delayed emission of Lie shows a behavior, which could not be explained by diffusion of F centers to the surface only. Delayed emission of Lie up to minutes was observed and we therefore suggest, that energy must be stored in the bulk through the formation of F center aggregates in order to explain the experimentally observed behavior of the delayed emission. A system of rate equations has been developed, which describes the kinetics of formation and decay of F center aggregates.
1. Introduction Alkali
halides
are
very
appropriate
materials
for
(ESD) because of their well known and simple crystal structure. The basic features for the desorption mechanism of neutral alkali as well as halogen atoms are generally accepted [l-4], even recent experiments on nonthermal halogen emission indicate that the desorption mechanism is not fully understood yet [5]. If an electron impinges on the lattice it predominantly transfers energy to the halogen sublattice causing valence electronic excitation. The electronic excitation leads via intermediate steps to the formation of F-H center pairs [6]. With increasing temperature creation of spatially well separated F-H pairs becomes effective [7]. While H centers are mobile even at temperatures as low as 30 K [8], the F center diffusion is limited to temperatures above a few hundred kelvin [9]. H centers having diffused to the surface cause the emission of neutral halogen atoms, while diffusion of F centers to the surface leads to the formation of neutral alkali atoms [lo], which will evaporate if the alkali vapor pressure is high enough, i.e., at sufficiently high target temperatures. At low temperatures, where the evaporation rate is the limiting process of neutral alkali desorption, alkali islands or even a metallic alkali overlayer can form on the surface [11,12]. The formation of alkali islands [13-171 on the surface influences the ESD characteristics and might even inhibit desorption. In addition fast diffusion to the surface followed by self trapping of ‘hot holes’, which are a precursor of F and H centers, might occur [5]. Such a process would add another contribution to desorption not requiring F or H center diffusion to the surface and is not included in the model developed below. At temperatures above 500 K at typical current studying
electron
0168-583X/91/$03.50
stimulated
desorption
0 1991 - Elsevier Science Publishers
densities of 10 pA/mn? evaporation is no longer the rate limiting process. In this case measurements of desorption, produced by short pulsed electron and photon beams, are suitable experimental methods to obtain information about the diffusion process of F centers [18,19]. After a given irradiation time the beam is turned off and the delayed emission of alkali atoms reflects the diffusion time of the F centers to the surface. Green et al. [19] have developed a diffusion model of F centers with respect to the desorption process of ground-state Li atoms from LiF under short pulsed electron irradiation. An additional effect, which might influence the desorption behavior, is the aggregation of F centers [9] in the bulk region near the surface. F center aggregates can be identified as alkali metal colloids imbedded in the crystal. Optical absorption measurements, small angle X-ray scattering and Raman scattering techniques on alkali halides revealed [9], that under ionizing radiation a part of the F centers produced are converted into alkali metal aggregates in a certain temperature range. In the work by Green et al. [19] it was pointed out, that no agglomeration of F centers has been taken into consideration. Formation of Li islands or of an Li overlayer can be neglected due to the sufficiently high target temperatures. In this paper we want to report about results of the desorption behavior of ground state Li atoms after the electron beam is stopped (delayed desorption or emission). Especially, attention is drawn to the delayed emission of Li atoms in connection with the formation and the decay of F center aggregates in the bulk region near the surface. During electron irradiation F centers will agglomerate forming aggregates (colloids). After the irradiation is stopped, the decay of the colloids into F centers will strongly influence the delayed emission of Li atoms. A system of rate equations has been devel-
B.V. (North-Holland)
0. Kreitschitz
oped to describe the delayed emission the basis of F center aggregation.
et al. / Li atoms
of Li atoms
fromLIF under electron bombardment
on ‘;: 3105 4 :
2. Experimental
setup
Air-cleaved (100) single crystal surfaces of LiF have been irradiated with electrons (50-450 ev). Space charge effects of the electron beam on the one hand and detection efficiency on the other hand restricted us to a small useable current regime, where we could measure the current density dependence (7-11 l.tA/rnrn’) of the delayed desorption yield. The angle of incidence of the electron beam was 30° with respect to the target normal. Two plates of stainless steel have been mounted in front of the electron gun. During the measurement the two plates were connected to ground. The geometry of the plates was chosen in such a way, that all electrons leaving the gun would strike the plate if a voltage of 300 V would be applied on one plate. This provided a method to measure the total electron beam current without need for further correction for secondary electrons. In addition, the profile of the electron beam was measured by moving a wire with a diameter of 0.2 mm stepwise through the electron beam. Thus we could measure the absolute electron beam current density. The UHV chamber was maintained at a base pressure The LiF of 5 x lo-lo mbar during the measurements. targets were cleaned in the vacuum chamber by prolonged heating at 700 K. Thermocoax heating controlled by a temperature control unit performed uniform heating and cooling of the target between room temperature and 750 K. The target temperature was measured with a thermocouple, which was in good thermal contact with the target surface. The desorbed Li atoms were detected by a quadrupol mass analyzer viewing the LiF surface perpendicularly. The pulses from the electron multiplier were processed digitally in a pulse counting mode. The dwell time was restricted to 20 ms.
3. Experimental
491
results
Fig. 1 shows the delayed desorption of neutral Li atoms at 720 K for a current density of 10 ltAA/mm* for four different bombardment times (1, 2, 4 and 6 s). The Li signal during bombardment (area Al in fig. 1) shows a prompt decrease by about one order of magnitude after the electron beam is stopped. This is followed by a delayed emission (area A2 in fig. 1). The prompt signal decrease (time constant i 20 ms) can be easily distinguished from the delayed emission (order of seconds) as is shown in fig. 2. It is also evident from fig. 2 that different processes must be responsible for prompt and delayed emission of Li atoms.
I IO5
2 0 3.104 5; 0’.z l.104 4
3.103
TIME [set] Fig. 1. The emission
of ground-state Li atoms from LiF under pulsed electron irradiation is shown in a logarithmic plot. After the electron bombardment is stopped, the Li signal exhibits a prompt decrease in less than 20 ms followed by a delayed emission in the order of seconds. Al represents the yield of desorbed Li under electron irradiation and A2 the yield of the delayed signal, respectively.
In this paper we will mainly concentrate on this delayed emission. At temperatures above 700 K an obvious maximum in the delayed emission appears for bombardment times of a few seconds (fig. 1). For bombardment times of more than 20 s the maximum becomes less pronounced. However, for lower temperatures (650 K) the bombardment time has to be increased to more than 50 s in order to observe a maximum in the delayed emission at all. The prompt and delayed contributions can still be clearly separated. At even lower temperatures (< 500 K) Li evaporation from the surface becomes the rate limiting process and no influence of aggregate formation on the desorption yield can be observed. No longer two contributions to the
-prompt
de0ease
-delayed
&XI-ease
~_-_.~.c..
_._l
L’
I I
Fig. 2. The existence of two different contributions to the delayed emission of Li’ are shown in detail. The bold line represents the fast decrease ( i 20 ms) due to diffusion and the plain line represents the (slow) delayed emission caused by agglomeration in the bulk. IV. DESORPTION
492
0. Kreitschitz ”
I
2OOeVe-
/
/
+
680K
r?
I ”
LiF
I
et al. / Li atoms from LiF under electron bombardment
”
”
.
t 0
, ,,,,,,,,,,,,,,,,I,,,,,,,;
20
40
60
IRRADIATION
80
100
TIME
120
140
[set]
Fig. 3. Experimental data of the delayed emission yield of Li atoms as a function of irradiation time are presented for a constant current density of 8 PA/mm2 at 680 K. Saturation is reached at a fluence of approximately 1.5 X 10”e/cm2.
delayed emission as shown in fig. 2 can be distinguished. The F center production rate depends on the energy of the impinging electrons. At a temperature of 710 K the electron energy was varied from 50 up to 400 eV for two different irradiation times (8 and 10 s, respectively) and the same current density (3 10 uA/mm*). The ratio Al/A2 (as defined in fig. 1) was found to be a function of the electron energy. It exhibits a minimum at an electron energy of 100 eV. Furthermore, a dependence of the delayed emission on the current density could be observed. The delayed emission of Lie increases with higher current densities. In fig. 3 the yield of the delayed emission of Li atoms (area A2) was measured as a function of irradiation time. Saturation was reached at an irradiation time of 35 s which corresponds to a fluence of 1.8 X 10” e/cm2 (3 1 Grad). This is the fluence range for which F center agglomeration has been observed spectroscopically [8] in bulk irradiation experiments using X-rays.
the number of F centers trapped by the agglomerate. An increasing F center production will result in an enhanced trapping and thus causes an increase in agglomerate size and number until equilibrium is reached again. Vice versa, a reduction in F center production (decreasing or stopping electron bombardment) will cause shrinking of the colloid size and number. This dynamical behavior can be described by a system of rate equations. Some simplifications on the model according to our special experimental conditions have been made. For low-energy electrons the penetration depth is below 100 A [20]. Most of the F centers are created at a depth of less then 30 A, which corresponds to the maximum of deposited energy for 200 eV electrons. The diffusion time of the F centers is in the order of microseconds in the temperature range from 620 to 720 K [lo]. Under these circumstances no depth dependence of the F-center concentration has to be taken into account and their diffusion time to the surface was neglected. Furthermore, the loss of F centers by trapping at impurity sites or dislocation lines has not been taken into account, either. It is assumed, that every F center reaching the surface causes an evaporation event (desorption efficiency is 100%). Under the conditions mentioned above the rate equations can be expressed for a system, where F center agglomerates up to size n, i.e. F(l), F(‘). . . , F(“) are considered: dF”’ ~ = p _ aF’l) + 5 dt
i=3
h=2
+ 21,FC2’ - ~/Q(F”‘)~, _dF’*’ = dt
dF’“’ 7=’ 4. Model A review of various investigations made on the agglomeration of F centers into colloids in irradiated or additively colored solids is given by Hughes 191. High dose X- and y-ray irradiation of alkali halide crystals reveals the tendency of F centers to form colloids in the bulk. A thermodynamical model of the colloid state has been developed and is discussed in ref. [9]. The system of F centers and their aggregates form a one component-two-phase system in equilibrium with the crystal. The F centers behave like the vapour phase in contact with the colloids which behave like the solute or solid phase. In thermodynamical equilibrium the number of F centers ‘evaporating’ from an agglomerate is equal to
n-1 [;F(‘) _ c /c,F”‘F’~
l,F’3’
_
m+1
k2F(1)F(2)
_
[,ld2’
-I
+
,&(F(‘))‘,
(2)
F(m+‘) _ k F(i)F(m) _ 1 F’“’ m
+ ,k,_iF(‘)F(“-‘),
dF’“) -= dt
(1)
m
(3)
F’“, + kn_iFo)F(n--l) n
t represents the time, n the number of equations, F”’ the concentration of agglomerates, consisting of i F(l) centers (F(l) + F center, F(*) -+ M center, FC3’+ R centers etc.). P describes the effectively produced F centers per unit time, which are not lost due to recombination with H centers and k;, Ii are the rate constants. The quantity k, is responsible for the growth of the F(‘+‘) center and Ii (for i > 1) for the decay of the F”’ center. a is the loss parameter for F centers due to diffusion to the surface followed by desorption. Thus
0. Kreitsehitz
et al. / Li atoms from LiF under electron bombardment
nF(‘) is the number of F centers lost per unit time due to evaporation and was measured in our experiment. For the temperature range of our measurements (620 -+ 720 K) the evaporation rate [l7] is high enough that we can neglect any residence time of Li atoms at the surface before evaporation [19]. For the nonequilibrium state the rate equations were solved numerically by a Runge-Kutta algorithm, while the equilib~um conditions can be obtained an~yti~ly from
~
6
Growth and decay of F center aggregation is assumed to be only due to ‘absorption’ or ‘evaporation’ of a F center from an agglomerate, i.e. by the reaction F”’ + F(r) +.+E(‘+‘).
493
8
10
Simulation
I
12
14 16 18 20 22 TIME [set] Fig. 5. Experimental data fitted by a simulation taking F center aggregatesinto account consisting of up to six F centers (n = 6). The parameters chosen in the rate equations are: P = 5800, a = 700, I, = 17, 1, = 8, I4 = 7, I, = 5, I, = 2.5, k, = 2, k, = 2.5, k, = 2.5, k, = 2.7. k, = 5.5.
Growth or decay processes of aggregates of the form F(r) + F(l) + I?(‘) cf
F’3’
have not been taken into account, because of the low probabi~ty of such a process and also reactions of the type F(‘) + F(J) c, F(‘+J),
____3 +4 --t5 -6
!_,L_r
.r~ 4.5
,--_A..-i.,
were opti-
5. Discussion
i, j > l,
were neglected because of the low mobility of aggregates compared to F centers. Fig. 4 shows the results for the calculated delayed emission of Li atoms after an electron bombarding time of 4 s for different numbers n of rate equations. Here n represents the largest aggregate F(“) which is assumed to be formed. The bold line represents the calculation with six equations. Compared to calculations with smaller n, it turns out that with increasing n the maximum first appears and becomes more and more pronounced and shifts on the time scale. We get strong evidence that this behavior continues with greater n. The production term P and the loss parameter were
3.7
held constant while the other parameters mized in each calculation.
Equations Equations Equations Equations
\__,
5.4 TIME [see]
6.2
7
Fig. 4. The difference in behavior of the Li emission (area A2 of fig. 1) for different numbers of rate equations (n) reveal, that with increasing n the structure of the delayed emission approaches continuously the experimental observed behavior.
During irradiation an excess of F centers over II centers exists due to preferential trapping of H centers [21] and in addition due to their much higher velocity they will diffuse into the bulk or to the surface. These excess F centers can form F center aggregates. The most complex phase in colloid formation is the nucleation stage. Dislocation lines as well as impurity sites act as sinks for F centers. So it is very probable, that in general formation of small F center aggregates starts from such special sites. Jain and Lidiard [21] presented a model of colloid growth in alkali halides including the influence of preferential nucleation sites. However, they confined their discussion to high irradiation doses (order of Grad), where it can be assumed that the nucleation stage is past. The model developed here describes the build-up process of F center aggregates including the nucleation stage during irradiation and their consequent decay after electron irradiation is stopped. The small penetration depth of electrons and the high temperatures we are dealing with leads to the basic assumptions of the model: (i) the diffusion time of F centers is in the order of microseconds at temperatures of 700 K. Compared with the time of formation and decay of colloids (order of seconds) diffusion processes can be neglected; (ii) no spatial dependence of the F(‘) center concentration is assumed. The formation of H center clusters has been neglected too. At the high temperatures we are dealing with, H center cluster are not stable [22]. In fig. 5 a comparison of simulations with experimental data is shown. At an irradiation time of 2 s good agreement has been achieved. But with increasing IV. DESORFTION
0. Kreitschitz
et al. / LI atoms from LiF under electron bombardment
Fig. 6. Simulation of the growth and decay of F”’ centers (i=l, 2, . ..( 6) in a logarithmic plot. These aggregate concentrations correspond to the simulation in fig. 5 (irradiation time: 2 s).
bombarding time the calculated peak in the delayed emission shifts less in time than observed in the experiment. The reason for this deviation is, that the largest aggregate size chosen in the calculations (n = 6) is too small to match the real size of aggregates formed. Indeed, in fig. 4 it was shown, that with increasing n the rn~rn~ of the delayed emission shifts to later times. The position of the maximum on the time axis can be controlled by the largest aggregate size. The rate constants for production of F”) centers were chosen in such a way, that M centers were created with less probability than R centers, etc. and the rate constants for the decay were chosen vice versa. In the calculations, formation of agglomerates occurs as long as the F center production term P is not equal zero (irradiation). At a given time t, P is set equal zero and delayed emission and the decay of agglomerates will occur. As can be seen from fig. 5 the prompt onset of emission with irradiation is in agreement with the calculations. For a certain temperat~e and irradiation dose a definite aggregate size distribution exists [21]. In fig. 6 the calculated concentrations of all aggregates (n = 6) corresponding to the fit of fig. 5 (irradiation time is 2 s) are shown. The most probably formed aggregate is assumed to be the aggregate consisting of six F centers. The largest aggregate formed influences predominantly the position of the delayed maximum. If larger aggregates are taken into account, the result will be a shift of the delayed maximum to larger times. Generally, the greater the aggregate size is, the larger is the decay time of these aggregates (Thomson effect [9]). The dependence of the delayed desorption behavior of Li atoms on the current density is complex. We found an increasing delayed desorption yield with increasing current density for constant bombarding time and temperature. Increasing current density means an
increasing concentration of F centers in the interaction volume. This enhancement in concentration enables the formation of larger aggregates with the result of an increasing delayed desorption yield of Li atoms. But not only the growth of colloids may be influenced by a change in current density. One may expect, that primary electrons may excite or ionize agglomerated F centers. Increasing F-H center recombination with fluence can also limit the extend of agglomeration. These processes slow down the growth of colloids or even inhibit further growth. Such saturation effects have been observed experimentally 191. Hughes and Lidiard [21,23] calculated, that the concentration of agglomerated F centers should follow tX (1 < n < 2) in NaCl under ionizing radiation, where t is representing the irradiation time. In our experiment at small irradiation times x takes the value of 1.2, at larger irradiation times (> 15 s) the delayed yield increases more slowly until it reaches saturation (35 s) as can be seen in fig. 3. 6. Conclusions The delayed desorption of ground-state Li atoms is strongly influenced by the aggregate size formed in the bulk region near the surface during high dose electron irradiation. This influence is evident in the temperature range where aggregates are formed and evaporation is not the rate limiting process. The model developed, describes the delayed desorption behavior and the deviations from the experimental data can be explained by a too small aggregate size considered in the calculations. The problem of giving physical relevance to the rate constants used cannot be solved without including other experimental methods (optical spectroscopy, etc.) to measure the size distribution of the aggregates during irradiation and decay. Extension of the model to take F-H recombination and diffusion into account are in progress. The interesting speculation, whether inhibition or even decay of colloids by primary electrons or by recombination of clustered F centers with H centers may occur and to what extend it is important, needs further investigations.
Acknowledgement The authors gratefully acknowledge financial support by the &terreichischer Fonds zur Fiirderung der wissenschaftlichen Forschung (project No.: 6797).
References [l] A good collection of recent relevant articles can be found in: Desorption Induced by Electronic Transitions, DIET IV, eds., G. Betz and P. Varga (Springer, Berlin, 1990).
[2] Z. Postawa. J. Rutkowski. A. Poradzisz and M. Szymonski. Nucl. Instr. and Mirth. 818 (1987) 574. [3] N. Itoh. Nucl. Insrr. and Meth. 132 (1976) 201. [4] M. Szymonski. Radial. Eff. 52 (19RO) 9. [5] M. Szymonki. J. Kolodziej. P. C~uba. P. Piatkowski. A. PoradT.iw and N.II. Talk. these Proceedings (8th Int. Workshop on Inelastic Ion-Surface Collisions, Wr. Neu,tadt. 1YYO)Nucl. Instr. and Mcth. 858 (1991) 485. [6] R.T. Williams, KS. Song. W.I.. Faust and G.H. Leung. Phys. Rev. 1~33 (1986) 7232. [7] R.T. Willams. Semicond. Insul. 5 (1983) 457. (X] I’. Durand. Y. Farge and X4. Lambert. J. Phys. Chcm. Solids 30 (1969) 1353. [9] A.E. ~lughcs and SC. Jain. Adv. Phys. 28 (1979) 717. [IO] G.M. I.ouhriel. T.A. Green. and P.M. Richards. R.G. Alhridge D.W. Cherry. R.K. Cole. R.F. Haglund. Jr.. L.T. Hudson. M.H. Mendenhall. D.M. Newns, P.M. SavundararaJ. K.F. Snowdon and N.H. Talk. Phys. Rev. Let:. 57 (1986) 1781. [ll] P. Wurz and C.H. Becker, Surf. Sci. 224 (1989) 559. [ 121 X4. Sqmonski. J. Ruthowski. A. Poradzisz. Z. Postawa
1131 1141 [15] [Ih] [17] [lg] [19] [ZO] [21] [22] 1231
and B. Jorgensen. DIET II. eds.. W. Brenig and P. Menzel (Springer. Berlin. 1985). D.G. Lord and T.E. Gallon. Surf. Sci. 36 (1973) 606. D.S. Cota Arab and B.D. Powell. Surf. Sci. 51 (1975) 504. G. Singh and T.E. Gallon, Solid State Commun. 51 (1984) 2x1. G. Roy. G. Singh and T.E. Gallon. Surf. Sci. 152/153 (1985) 1042. J. Sarnthein, P. Wun. W. Ilusinsky and G. Betr. Surf. SCI. 241 (1991) 6. R.F. Haglund Jr.. N.11. Talk. G.M. Louhriel and R.A. Rosenberg. Nucl. Insrr. and Meth. B18 (1987) 549. T.A. Green. C;.M. I.ouhriel. P.M. Richards. X.H. Talk and R.F. Haglund Jr.. Phys. Rev. 835 (1987) 781. I.M. Bronsthteyn and A.N. Protscnko. Radio F.ng. Elwtron Phys. 15 (1970) 677. Uma Jain and A.B. Iidiard. Philos. Mag. 35 (1977) 245. A.E. Highes. Comments Solid State Phys. (1978) 8. 83. A.E. llughcs and A.B. Lidiard. AERE Harwell Kep. (1977) R1331Y.
IV. DESOKITION