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Laser excitation and desorption of adatoms
Volume 153, number 2,3
CHEMICAL
LASER EXCITATION Eric ALTENDORF Guelph- Waterloo Program
9 December
PHYSICS LETTERS
AND DESORPTION
1988
OF ADATOMS *
and Wing-Ki LIU I jiir
&hale
Work in Physics (GWP)2. Drparlmenf
of Physics, Univervily of Watrrloo,
Waterloo. Ontario. Canada N2L 3GI Received
17 August 1988; in final form 19 September
1988
The laser-induced vibrational excitation of an adatom bound to a harmonic lattice at T=O K is studied by integrating the classical generalized Langevin equation numerically. The anharmonicity of the adatom-surface bond plays an important role in inducing quasiperiodic and chaotic adatom motion.
1. Introduction Classical mechanics has been applied successfully to the study of the infrared multiphoton excitation and dissociation of polyatomic molecules in the gas phase [l-5]. Of particular interest is the observation that as the level of laser excitation increases, the molecular dynamics undergoes a “stochastic transition” from regular (or quasiperiodic) to chaotic motion, after which dissociation occurs. The corresponding problem of laser-stimulated desorption of adatoms has been studied classically by Murphy and George [ 6 1, Goodman [ 71, and Diestler and Riley [ 8 1. (For a review on the theory of laser-stimulated surface processes, see George et al. [ 91. ) In order to obtain analytical results, these authors assumed that the adatom is coupled by a harmonic force to the substrate which is modelled by a harmonic Iattice. In this case, however, the total system is harmonic and the classical motion is integrable. Furthermore, in the case of high-intensity laser excitation and desorption of adatoms, large amplitude motion of the adatoms occurs, and the harmonic model of the adatom-lattice bond is no longer adequate. It is the purpose of this paper to study the effects of an anharmonic adatom-lattice bond on the dynamics of laser-induced excitation and desorption of adatoms.
Recently we have employed the numerical scheme of Linz [lo] to solve the integro-differential generalized Langevin equation (GLE) governing the surface dynamics during the collision of a gas atom with a one-dimensional ( I-D) harmonic semi-infinite lattice at T= 0 K [ 11,12 1. Since the motion of an adsorbate is governed by the same equations, we have also used the Linz method to study the adatom vibrational dynamics and the existence of localized modes [ 11,131. We shall employ the same numerical procedure in our present investigation. In section 2, we summarize the equations of motion for our model system. The results and discussions of our investigation will be given in section 3.
2. Equations of motion Consider the system of an adatom of mass M interacting with a harmonic lattice of atoms of mass m. For simplicity we assume that the adatom is strongly coupled only to the surface atom, and we choose as our model of the lattice the semi-infinite 1-D harmonic chain with nearest neighbour interaction with force constant k. We assume a cold lattice so that all the lattice atoms are initially frozen in their equilibrium positions. The classical equation of motion of the system are then given by [7,8,1 I-141
* Research supported in part by NSERC of Canada. ’ NSERC University Research Fellow. 176
(1) 0 009-26 14/88/$ 03.50 0 Elsevier Science Publishers ( North-Holland Physics Publishing Division )
B.V.
Volume 153, number 2,3
CHEMICAL PHYSICS LETTERS
I
ii,+
9 December 1988
7‘
dt’~(t-t’)2i,(t’)=F,(t)/m,
I
(2)
X(o)=jr(t)exp(iwt)dt
(8)
0
where x and u1 are the adatom and surface atom coordinates, respectively, T/is the potential between the adatam and the surface atom, F, = -aI’/&, is the force acting on the surface atom by the adatom, and fexr is the external force applied to the adatom. For our 1-D model,
(3) where J, is the Bessel function of order n and oi =k/m. To describe the adatom-surface interaction, we use the Morse potential V(x)=D[exp(-r/b)-l]‘,
(4)
where T=X- U, - r. and r, is the equilibrium separation between the adatom and the surface atom. Assuming that the laser is coupled to the adatom only, the external forcef,,, is given by
and r(t)=x(t)-ul(t)-rr,.
The trajectory is started with the system in equilibrium and integrated up to a time T large compared to a typical period of oscillation of the system, and the power spectrum is obtained using the fast Fourier transform (FFT) algorithm. Since the time record of r(t) between 0 and T would not contain an integral number of cycles in general, a window function {f [ 1 -cos(2rrt/T)]} ‘I2 is applied to the data to force the assumed input data to be periodic before the FFT is taken, thus eliminating the spurious frequency components introduced by the sharp edge of the time recorded (a phenomenon known as leakage). We also calculate the average adatom bond energy over a given trajectory: T
[f,uUi*+V(r)]dt, “Cxr=&
cos((%r)
3
Cr, .
(6)
I,, is assumed to be fixed at 50 GW/cm* [ 151, but the amplification factor C is considered to be a variable parameter. Eqs. ( 1) and (2 ) are integrated numerically using the method of Linz [ lo- 13 1. We analyze the motion of the adsorbate by studying the power spectrum [ I 71 of the adatom-surface displacement: S(u)
= lim IX(o) T-CC
where
I2/T,
(10)
(5)
where q is the effective charge on the adatom, o,_ is the driving laser frequency, and E, is the local electric field strength at the adatom. The local field at an adsorbate depends on the polarizations of the substrate and the neighboring adsorbates, as well as on the surface roughness [ 15,161, and is very difficult to calculate. We thus follow the phenomenological approach of Jedrzejek et al. [ 161 by assuming that the local light intensity Z, is proportional to the incident laser intensity 10: I, = cE;/Slc=
(9)
(7)
where pu=mM/( m+M) is the reduced mass of the adatom-surface atom pair.
3. Results and discussions In the present study we choose the Morse parameters which correspond to the system of a sulphur atom on a nickel surface [IS]: 0=99.82 kcal/mol, b=0.91 A, and ro=1.24 8. The effective adatom charge is assumed to be q = 0.15 e [ 19 1. The lattice frequency is estimated from the Debye frequency of nickel by mo= $0~~29.45 pss’. The masses of this system are m=58.7 amu and M= 32.06 amu. The harmonic frequency o,= (2D/,u)‘/‘/b of the corresponding isolated Morse oscillator has a value of 69.8 ps-‘. For this system, we have shown [ 131 that for free adatom oscillations (i.e. fcxt =0)) a localized mode exists whose frequency o, decreases from 72.2 to 64.4 ps-’ as the initial energy in the adatom-surface bond increases from zero to the dissociation limit. Fig, 1 shows the average bond energy $ as a func177
0
d 4.0
4.5
5.0
5.5
log c
Fig. 1. Average adatom-surface bond energy Eb as a function of the local amplification factor C. The laser frequency is fixed at wL= - 56 ps~ ‘. All trajectories are integrated for a period of T= 4 PS.
tion of the amplification factor C as the laser frequency wL is fixed at 56 ps-‘. The behavior of the system can be divided into three different types: ( 1) For log C< 4.6 1, the average energy deposited into the adatom-surface bond is small. We plot in fig. 2 the power spectrum at low local intensity with C= 4 (log C= 0.6 ) , which roughly corresponds to the situation when the substrate behaves as a flat perfect conductor [ 151. The power spectrum contains two predominant sharp peaks (note the log scale) at the
Fig. 2. Power spectrum of the relative adatom-surface displacement for log C= 0.60 (I,= 200 GWjcm’) and frequency wL= 56 ps- I. The trajectory is integrated for a period of T= 8 ps and the data are windowed by {j [ 1- cos(at/ 2’)] } I” before the FFI is applied.
178
9 December 1988
CHEMICAL PHYSICS LETTERS
Volume 153, number 2,3
laser frequency o, and the low-energy localized mode frequency ma= 73 ps- ’ [ 13 1. This is similar to the behavior of a harmonic oscillator of natural frequency wp driven by a harmonic force of frequency wL. At higher local light intensities, harmonics of op and wL as well as their subharmonics and combination modes appear, as is illustrated in fig. 3 for the case of log Cc4.46. In this low absorption regime, the motion of the system is quasiperiodic. (2) As we increase the local light intensity so that 4.68~1og C< 5.06, the system enters a plateau region in which the average bond energy is about half the dissociation energy of the Morse potential. The motion of the system in this regime is chaotic, as illustrated by the broadband power spectrum given in fig. 4 for log C=4.90, corresponding to 1,=3.96x 10’ TW/cmZ. (3) Further increase in local light intensity (log C 3 5.09) leads to desorption immediately. Note that if the adatom-surface interaction is assumed to be harmonic, the system will only oscillate with the driving frequency oL and the harmonic localized mode frequency oP for any laser intensities, and the motion is periodic. Harmonics and subharmonics of ~0~ and up will not appear, and no chaotic motion will be observed. In fig. 5 we plot the average bond energy Eb as a function of the driving frequency wL for the cases of low and high local light intensities. For log C= 3.50 corresponding to the relative low local light intensity of Z, =0.16x lo3 TW/cm2, E,, has a maximum of
50.0
100.0
w
150.D
2
1.0
tps-'1
Fig. 3. Same as fig. 2 except that log C= 4.46 (1. = I .43 x IO3TW/ cm2).
CHEMICAL PHYSICS LETTERS
Volume 153, number 2,3
7’1 0.0
50.0
1no .I3 w
150.0
2n.u
@‘I
Fig. 4. Same as fig. 2 except that logCE4.90 (1,=3.96x lO’TW/ cm’).
24.9 kcal/mol at cur_=66 ps- ‘, which is very close to the localized mode frequency at this value of the bond energy [ 131. In this case, the motion at all WL is quasi-periodic, and no desorption is observed. For the case of high local amplification with log C= 5.06 (I,= 5.70x lo3 TW/cm*), &, exhibits a broad resonance for 50 G co,< 64 ps- ‘. In this resonance range, the trajectories at wL=52, 58 60, and 62 ps-’ are dissociating, while the remaining ones at oL= 50, 56 and 64 cm-’ are chaotic. Outside this resonance range, the trajectories are all quasi-periodic and nondissociating.
60.0
Ob.0
IW.0
wL(ps-‘l Fig. 5. Average adatom-surface bond energy I% as a function of laser frequency III,+.Labels C and II indicate chaotic and dissociating trajectories, respectively. Unlabelled points represent quasi-periodic trajectories. (- - - ) logC=3.50 ([*=0.16X 10’ TW/cm’); (---) logC~5.06 (1,=5.7x103 TW/cm*).
9 December 1988
The two curves in fig. 5 indicate that desorption may be induced by using two lasers of lower intensities. Indeed it is found that desorption occurs when the system is excited by a laser with local intensity I, = 0.63 x lo3 TW/cm* and frequency wL1= 64 ps-‘, and simultaneously pumped by a second laser with local intensity IZ=2.53x IO” TW/cmZ and frequency wLZ=60 ps-‘, even though no desorption is observed if the system is coupled to tither one of the lasers alone. This two-laser desorption is very sensitive to the laser frequencies: changing wL, and/or wL2by 2 ps-’ would not produce desorption. The above result suggests that the laser-stimulated excitation and desorption process proceeds in much the same way as the multiphoton dissociation of molecules [ 4 1. In the initial stage, the energy deposited in the adatom-surface bond is low, and the localized mode plays the role of the distinguishable vibrational states of the molecular case, allowing direct resonant laser pumping of this mode. As the adatom bond energy is raised, the system motion becomes quasiperiodic, in which the substrate modes become indirectly excited due to the anharmonic coupling with the adatom mode, although energy is still deposited into the system mainly through the adatom mode. This stage is illustrated by the low intensity regime of fig. 1. Then the quasicontinuum stage is reached in which the adatom mode is strongly coupled with the substrate modes, and the motion becomes chaotic. This is the plateau regime of fig. 1. Finally the system enters the dissociation regime in which there is no special pumped mode, and direct excitation of combination modes probably leads to rapid desorption. It should be remarked that the 1-D model is chosen for its simplicity. It has long been recognized that the three-dimensional (3-D) lattice is inherently more rigid than the 1-D lattice, yielding generally lower values for accommodation coefficients for the 3-D lattice [ 201. Thus it may be expected that employing a 3-D model substrate in our study would lower the threshold local intensities for desorption, since relaxation of the adatom-surface bond excitation into the substrate would be less efficient. However, the main reason for the high threshold intensity for desorption is due to the strong chemisorption bond (represented by the large value of D of the Morse potential), and the small effective 179
Volume 153, number 2,3
CHEMICAL
PHYSICS LETTERS
9 December
1988
charge q of the adatom, making the coupling to the laser field very weak. Hence we do not expect the direct laser pumping of the chemisorbed adatom-surface bond to be an efficient route to desorption. On the other hand, molecules with weaker admoleculesurface bond (DE 10 kcal/mol) and having large dipole moments would couple to the laser more strongly, and desorption of admolecules by laser excitation of the intramolecular bonds has been observed [ 2 11. The technique employed in the present study can be extended to treat such systems, and work in this direction is in progress.
191 T.F. George, J. Lin, A.C. Beri and WC. Murphy, Progr. Surface Sci. 16 ( 1984) 139. [IO] P. Linz, J. .4ssoc. Comp. Mach. 16 (1969) 295. [ I 1 ] E.Altendorf, M.Sc. Thesis, University of Waterloo ( 1988), unpublished. 112 E. Altendorf and W.-K. Liu, in: Proceedings of the Conference on the Dynamics of Chemically Reacting Systems, Swidno (WorldScientific. Singapore, 1988). to be published. 1’3 E. Altendorf and W.-K. Liu, in: Proceedings of the Third
References
[ IS ] C. Jedrzejek, K.F. Freed, S. Efrima and H. Metiu, Surface
Asia Pacific Physics Conference, Hong Kong (World Scientific, Singapore, 1988), to be puhhshed. [ 141 S.A. Adelmanand J.D. Doll, J. Chem. Phys. 61 (1974) 4242: M. Shugard, J.C. Tully and A. Nitzan, J. Chem. Phys. 66 (1977) 2534; S.A. Adelman, Advan. Chem. Phys. 44 (1980) 143, and references therein. Sci. 109 (1981)
[l] W.E. Lamb, in: Laser spectroscopy, Vol. 3, eds. J.L. Hall and J.L. Carlsten (Springer, Berlin, 1977) pp. 116-120; in: Laser spectroscopy, Vol. 4, eds. H. Walther and K.W. Rothe (Springer, Berlin, 1979) pp. 296-299. [2] SK. Gray, J.R. Stine and D.W. Noid, Laser Chem. 5 ( 1985) 209, and references therein. [ 31 D.L. Martin and R.E. Wyatt, Chem. Phys. 64 (1982) 203. [4] D.A. Jones and I.C. Percival, J. Phys. B 16 (1983) 2981. [5] W.-K. Liu, A.F. Turfa, W.H. Fletcher and D.W. Noid, J. Phys. Chem. 91 (1987) 834. [ 6 ] W.C. Murphy and T.F. George, Surface Sci. 102 ( 198 1) L46. [7]F.O.Goodman,SurfaceSci. 109 (1981) 341. [8] D.J. Die&r and M.E. Riley, Surface Sci. 150 ( 1985) L101; M.E. Riley and D.J. Diestler, Surface Sci. 165 (1986) 393.
180
191.
[ 161 T. Maniv and H. Mctiu, J. Chem. Phys. 76 (1982) 2697. [ 17 ] M.C. Wang and GE. Uhlenbeck, Rev. Mod. Phys. 17 ( 1945) 327.
[ 18 ] J.E. Black, P. Bopp, K. Liizenkirchen and M. Wolfsberg, J. Chem. Phys. 76 (1982) 6431; T.H. Upton and W.A. Goddard, Phys. Rev. Letters 46 (1981) 1635. [ 191 S. Andersson, Surface Sci. 79 ( 1979) 385. [20] F.O. Goodman, J. Phys. Chem. Solids 23 (1962) Surface Sci. 11 (1968) 283. [ 211 T.J. Chuang, Surface Sci. Rept. 3 (1983) 1;
1491;
T.J. Chuang, H. Seki and 1. Hussla, Surface Sci 158 (1985) 525; I. Hussla, J. Electron Spectry. 38 (1986) 65.
CHEMICAL
LASER EXCITATION Eric ALTENDORF Guelph- Waterloo Program
9 December
PHYSICS LETTERS
AND DESORPTION
1988
OF ADATOMS *
and Wing-Ki LIU I jiir
&hale
Work in Physics (GWP)2. Drparlmenf
of Physics, Univervily of Watrrloo,
Waterloo. Ontario. Canada N2L 3GI Received
17 August 1988; in final form 19 September
1988
The laser-induced vibrational excitation of an adatom bound to a harmonic lattice at T=O K is studied by integrating the classical generalized Langevin equation numerically. The anharmonicity of the adatom-surface bond plays an important role in inducing quasiperiodic and chaotic adatom motion.
1. Introduction Classical mechanics has been applied successfully to the study of the infrared multiphoton excitation and dissociation of polyatomic molecules in the gas phase [l-5]. Of particular interest is the observation that as the level of laser excitation increases, the molecular dynamics undergoes a “stochastic transition” from regular (or quasiperiodic) to chaotic motion, after which dissociation occurs. The corresponding problem of laser-stimulated desorption of adatoms has been studied classically by Murphy and George [ 6 1, Goodman [ 71, and Diestler and Riley [ 8 1. (For a review on the theory of laser-stimulated surface processes, see George et al. [ 91. ) In order to obtain analytical results, these authors assumed that the adatom is coupled by a harmonic force to the substrate which is modelled by a harmonic Iattice. In this case, however, the total system is harmonic and the classical motion is integrable. Furthermore, in the case of high-intensity laser excitation and desorption of adatoms, large amplitude motion of the adatoms occurs, and the harmonic model of the adatom-lattice bond is no longer adequate. It is the purpose of this paper to study the effects of an anharmonic adatom-lattice bond on the dynamics of laser-induced excitation and desorption of adatoms.
Recently we have employed the numerical scheme of Linz [lo] to solve the integro-differential generalized Langevin equation (GLE) governing the surface dynamics during the collision of a gas atom with a one-dimensional ( I-D) harmonic semi-infinite lattice at T= 0 K [ 11,12 1. Since the motion of an adsorbate is governed by the same equations, we have also used the Linz method to study the adatom vibrational dynamics and the existence of localized modes [ 11,131. We shall employ the same numerical procedure in our present investigation. In section 2, we summarize the equations of motion for our model system. The results and discussions of our investigation will be given in section 3.
2. Equations of motion Consider the system of an adatom of mass M interacting with a harmonic lattice of atoms of mass m. For simplicity we assume that the adatom is strongly coupled only to the surface atom, and we choose as our model of the lattice the semi-infinite 1-D harmonic chain with nearest neighbour interaction with force constant k. We assume a cold lattice so that all the lattice atoms are initially frozen in their equilibrium positions. The classical equation of motion of the system are then given by [7,8,1 I-141
* Research supported in part by NSERC of Canada. ’ NSERC University Research Fellow. 176
(1) 0 009-26 14/88/$ 03.50 0 Elsevier Science Publishers ( North-Holland Physics Publishing Division )
B.V.
Volume 153, number 2,3
CHEMICAL PHYSICS LETTERS
I
ii,+
9 December 1988
7‘
dt’~(t-t’)2i,(t’)=F,(t)/m,
I
(2)
X(o)=jr(t)exp(iwt)dt
(8)
0
where x and u1 are the adatom and surface atom coordinates, respectively, T/is the potential between the adatam and the surface atom, F, = -aI’/&, is the force acting on the surface atom by the adatom, and fexr is the external force applied to the adatom. For our 1-D model,
(3) where J, is the Bessel function of order n and oi =k/m. To describe the adatom-surface interaction, we use the Morse potential V(x)=D[exp(-r/b)-l]‘,
(4)
where T=X- U, - r. and r, is the equilibrium separation between the adatom and the surface atom. Assuming that the laser is coupled to the adatom only, the external forcef,,, is given by
and r(t)=x(t)-ul(t)-rr,.
The trajectory is started with the system in equilibrium and integrated up to a time T large compared to a typical period of oscillation of the system, and the power spectrum is obtained using the fast Fourier transform (FFT) algorithm. Since the time record of r(t) between 0 and T would not contain an integral number of cycles in general, a window function {f [ 1 -cos(2rrt/T)]} ‘I2 is applied to the data to force the assumed input data to be periodic before the FFT is taken, thus eliminating the spurious frequency components introduced by the sharp edge of the time recorded (a phenomenon known as leakage). We also calculate the average adatom bond energy over a given trajectory: T
[f,uUi*+V(r)]dt, “Cxr=&
cos((%r)
3
Cr, .
(6)
I,, is assumed to be fixed at 50 GW/cm* [ 151, but the amplification factor C is considered to be a variable parameter. Eqs. ( 1) and (2 ) are integrated numerically using the method of Linz [ lo- 13 1. We analyze the motion of the adsorbate by studying the power spectrum [ I 71 of the adatom-surface displacement: S(u)
= lim IX(o) T-CC
where
I2/T,
(10)
(5)
where q is the effective charge on the adatom, o,_ is the driving laser frequency, and E, is the local electric field strength at the adatom. The local field at an adsorbate depends on the polarizations of the substrate and the neighboring adsorbates, as well as on the surface roughness [ 15,161, and is very difficult to calculate. We thus follow the phenomenological approach of Jedrzejek et al. [ 161 by assuming that the local light intensity Z, is proportional to the incident laser intensity 10: I, = cE;/Slc=
(9)
(7)
where pu=mM/( m+M) is the reduced mass of the adatom-surface atom pair.
3. Results and discussions In the present study we choose the Morse parameters which correspond to the system of a sulphur atom on a nickel surface [IS]: 0=99.82 kcal/mol, b=0.91 A, and ro=1.24 8. The effective adatom charge is assumed to be q = 0.15 e [ 19 1. The lattice frequency is estimated from the Debye frequency of nickel by mo= $0~~29.45 pss’. The masses of this system are m=58.7 amu and M= 32.06 amu. The harmonic frequency o,= (2D/,u)‘/‘/b of the corresponding isolated Morse oscillator has a value of 69.8 ps-‘. For this system, we have shown [ 131 that for free adatom oscillations (i.e. fcxt =0)) a localized mode exists whose frequency o, decreases from 72.2 to 64.4 ps-’ as the initial energy in the adatom-surface bond increases from zero to the dissociation limit. Fig, 1 shows the average bond energy $ as a func177
0
d 4.0
4.5
5.0
5.5
log c
Fig. 1. Average adatom-surface bond energy Eb as a function of the local amplification factor C. The laser frequency is fixed at wL= - 56 ps~ ‘. All trajectories are integrated for a period of T= 4 PS.
tion of the amplification factor C as the laser frequency wL is fixed at 56 ps-‘. The behavior of the system can be divided into three different types: ( 1) For log C< 4.6 1, the average energy deposited into the adatom-surface bond is small. We plot in fig. 2 the power spectrum at low local intensity with C= 4 (log C= 0.6 ) , which roughly corresponds to the situation when the substrate behaves as a flat perfect conductor [ 151. The power spectrum contains two predominant sharp peaks (note the log scale) at the
Fig. 2. Power spectrum of the relative adatom-surface displacement for log C= 0.60 (I,= 200 GWjcm’) and frequency wL= 56 ps- I. The trajectory is integrated for a period of T= 8 ps and the data are windowed by {j [ 1- cos(at/ 2’)] } I” before the FFI is applied.
178
9 December 1988
CHEMICAL PHYSICS LETTERS
Volume 153, number 2,3
laser frequency o, and the low-energy localized mode frequency ma= 73 ps- ’ [ 13 1. This is similar to the behavior of a harmonic oscillator of natural frequency wp driven by a harmonic force of frequency wL. At higher local light intensities, harmonics of op and wL as well as their subharmonics and combination modes appear, as is illustrated in fig. 3 for the case of log Cc4.46. In this low absorption regime, the motion of the system is quasiperiodic. (2) As we increase the local light intensity so that 4.68~1og C< 5.06, the system enters a plateau region in which the average bond energy is about half the dissociation energy of the Morse potential. The motion of the system in this regime is chaotic, as illustrated by the broadband power spectrum given in fig. 4 for log C=4.90, corresponding to 1,=3.96x 10’ TW/cmZ. (3) Further increase in local light intensity (log C 3 5.09) leads to desorption immediately. Note that if the adatom-surface interaction is assumed to be harmonic, the system will only oscillate with the driving frequency oL and the harmonic localized mode frequency oP for any laser intensities, and the motion is periodic. Harmonics and subharmonics of ~0~ and up will not appear, and no chaotic motion will be observed. In fig. 5 we plot the average bond energy Eb as a function of the driving frequency wL for the cases of low and high local light intensities. For log C= 3.50 corresponding to the relative low local light intensity of Z, =0.16x lo3 TW/cm2, E,, has a maximum of
50.0
100.0
w
150.D
2
1.0
tps-'1
Fig. 3. Same as fig. 2 except that log C= 4.46 (1. = I .43 x IO3TW/ cm2).
CHEMICAL PHYSICS LETTERS
Volume 153, number 2,3
7’1 0.0
50.0
1no .I3 w
150.0
2n.u
@‘I
Fig. 4. Same as fig. 2 except that logCE4.90 (1,=3.96x lO’TW/ cm’).
24.9 kcal/mol at cur_=66 ps- ‘, which is very close to the localized mode frequency at this value of the bond energy [ 131. In this case, the motion at all WL is quasi-periodic, and no desorption is observed. For the case of high local amplification with log C= 5.06 (I,= 5.70x lo3 TW/cm*), &, exhibits a broad resonance for 50 G co,< 64 ps- ‘. In this resonance range, the trajectories at wL=52, 58 60, and 62 ps-’ are dissociating, while the remaining ones at oL= 50, 56 and 64 cm-’ are chaotic. Outside this resonance range, the trajectories are all quasi-periodic and nondissociating.
60.0
Ob.0
IW.0
wL(ps-‘l Fig. 5. Average adatom-surface bond energy I% as a function of laser frequency III,+.Labels C and II indicate chaotic and dissociating trajectories, respectively. Unlabelled points represent quasi-periodic trajectories. (- - - ) logC=3.50 ([*=0.16X 10’ TW/cm’); (---) logC~5.06 (1,=5.7x103 TW/cm*).
9 December 1988
The two curves in fig. 5 indicate that desorption may be induced by using two lasers of lower intensities. Indeed it is found that desorption occurs when the system is excited by a laser with local intensity I, = 0.63 x lo3 TW/cm* and frequency wL1= 64 ps-‘, and simultaneously pumped by a second laser with local intensity IZ=2.53x IO” TW/cmZ and frequency wLZ=60 ps-‘, even though no desorption is observed if the system is coupled to tither one of the lasers alone. This two-laser desorption is very sensitive to the laser frequencies: changing wL, and/or wL2by 2 ps-’ would not produce desorption. The above result suggests that the laser-stimulated excitation and desorption process proceeds in much the same way as the multiphoton dissociation of molecules [ 4 1. In the initial stage, the energy deposited in the adatom-surface bond is low, and the localized mode plays the role of the distinguishable vibrational states of the molecular case, allowing direct resonant laser pumping of this mode. As the adatom bond energy is raised, the system motion becomes quasiperiodic, in which the substrate modes become indirectly excited due to the anharmonic coupling with the adatom mode, although energy is still deposited into the system mainly through the adatom mode. This stage is illustrated by the low intensity regime of fig. 1. Then the quasicontinuum stage is reached in which the adatom mode is strongly coupled with the substrate modes, and the motion becomes chaotic. This is the plateau regime of fig. 1. Finally the system enters the dissociation regime in which there is no special pumped mode, and direct excitation of combination modes probably leads to rapid desorption. It should be remarked that the 1-D model is chosen for its simplicity. It has long been recognized that the three-dimensional (3-D) lattice is inherently more rigid than the 1-D lattice, yielding generally lower values for accommodation coefficients for the 3-D lattice [ 201. Thus it may be expected that employing a 3-D model substrate in our study would lower the threshold local intensities for desorption, since relaxation of the adatom-surface bond excitation into the substrate would be less efficient. However, the main reason for the high threshold intensity for desorption is due to the strong chemisorption bond (represented by the large value of D of the Morse potential), and the small effective 179
Volume 153, number 2,3
CHEMICAL
PHYSICS LETTERS
9 December
1988
charge q of the adatom, making the coupling to the laser field very weak. Hence we do not expect the direct laser pumping of the chemisorbed adatom-surface bond to be an efficient route to desorption. On the other hand, molecules with weaker admoleculesurface bond (DE 10 kcal/mol) and having large dipole moments would couple to the laser more strongly, and desorption of admolecules by laser excitation of the intramolecular bonds has been observed [ 2 11. The technique employed in the present study can be extended to treat such systems, and work in this direction is in progress.
191 T.F. George, J. Lin, A.C. Beri and WC. Murphy, Progr. Surface Sci. 16 ( 1984) 139. [IO] P. Linz, J. .4ssoc. Comp. Mach. 16 (1969) 295. [ I 1 ] E.Altendorf, M.Sc. Thesis, University of Waterloo ( 1988), unpublished. 112 E. Altendorf and W.-K. Liu, in: Proceedings of the Conference on the Dynamics of Chemically Reacting Systems, Swidno (WorldScientific. Singapore, 1988). to be published. 1’3 E. Altendorf and W.-K. Liu, in: Proceedings of the Third
References
[ IS ] C. Jedrzejek, K.F. Freed, S. Efrima and H. Metiu, Surface
Asia Pacific Physics Conference, Hong Kong (World Scientific, Singapore, 1988), to be puhhshed. [ 141 S.A. Adelmanand J.D. Doll, J. Chem. Phys. 61 (1974) 4242: M. Shugard, J.C. Tully and A. Nitzan, J. Chem. Phys. 66 (1977) 2534; S.A. Adelman, Advan. Chem. Phys. 44 (1980) 143, and references therein. Sci. 109 (1981)
[l] W.E. Lamb, in: Laser spectroscopy, Vol. 3, eds. J.L. Hall and J.L. Carlsten (Springer, Berlin, 1977) pp. 116-120; in: Laser spectroscopy, Vol. 4, eds. H. Walther and K.W. Rothe (Springer, Berlin, 1979) pp. 296-299. [2] SK. Gray, J.R. Stine and D.W. Noid, Laser Chem. 5 ( 1985) 209, and references therein. [ 31 D.L. Martin and R.E. Wyatt, Chem. Phys. 64 (1982) 203. [4] D.A. Jones and I.C. Percival, J. Phys. B 16 (1983) 2981. [5] W.-K. Liu, A.F. Turfa, W.H. Fletcher and D.W. Noid, J. Phys. Chem. 91 (1987) 834. [ 6 ] W.C. Murphy and T.F. George, Surface Sci. 102 ( 198 1) L46. [7]F.O.Goodman,SurfaceSci. 109 (1981) 341. [8] D.J. Die&r and M.E. Riley, Surface Sci. 150 ( 1985) L101; M.E. Riley and D.J. Diestler, Surface Sci. 165 (1986) 393.
180
191.
[ 161 T. Maniv and H. Mctiu, J. Chem. Phys. 76 (1982) 2697. [ 17 ] M.C. Wang and GE. Uhlenbeck, Rev. Mod. Phys. 17 ( 1945) 327.
[ 18 ] J.E. Black, P. Bopp, K. Liizenkirchen and M. Wolfsberg, J. Chem. Phys. 76 (1982) 6431; T.H. Upton and W.A. Goddard, Phys. Rev. Letters 46 (1981) 1635. [ 191 S. Andersson, Surface Sci. 79 ( 1979) 385. [20] F.O. Goodman, J. Phys. Chem. Solids 23 (1962) Surface Sci. 11 (1968) 283. [ 211 T.J. Chuang, Surface Sci. Rept. 3 (1983) 1;
1491;
T.J. Chuang, H. Seki and 1. Hussla, Surface Sci 158 (1985) 525; I. Hussla, J. Electron Spectry. 38 (1986) 65.