Line shape of photodesorption yield

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Surface Science 165 (1986) L12-L20 North-Holland, Amsterdam

SURFACE SCIENCE LETTERS LINE S H A P E OF P H O T O D E S O R P T I O N YIELD

Z.W. GORTEL, P. PIERCY and R. TESHIMA Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2J1

and H.J. K R E U Z E R Department of Physics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5

Received 29 July 1985; accepted for publication 26 September 1985

For photodesorption of physisorbed molecules by resonant laser-molecular vibrational coupling, we calculate the frequency dependence of the photodesorption yield due to homogeneous and inhomogeneous line broadening.

In photodesorption of physisorbed molecules by resonant laser-molecular vibrational coupling, an infrared laser beam impinging onto an adsorbatecovered surface of a solid is resonantly coupled into some internal vibrational mode of the adsorbed molecule. The feasibility of this process has been demonstrated by Heidberg et al. [1] for CH3F adsorbed on NaC1, and by Chuang and Seki [2] for pyridine on KCI and Ag, and by Hussla et al. [3] for N H 3 on Cu and Ag. A recent review has been compiled by Chuang [4]. In a previous paper [5] we have calculated the photodesorption rate as a function of the laser intensity I 0. For short laser pulses the experimentally measured yield is proportional to the rate. We ~ssumed that all adsorbed molecules have the same vibrational frequency ~2 of the infrared active mode and that the frequency of the laser light, distributed with some width F~ around f2~, is perfectly tunes to the molecular vibration frequency, i.e., ~2~ = ~2. Experimentally it is possible to vary $2~ within certain limits and study the spectral dependence of the photodesorption rate [1]. By comparing these spectra with infrared absorption bands due to molecular vibrations of adsorbed molecules, one hopes to identify the internal vibrational mode participating in the resonant photodesorption process [1,2]. However, both spectra can differ in some significant details and these differences, if interpreted correctly, can provide information on details of the photodesorption process 0039-6028/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

Z. W. Gortel et al. / Line shape of photodesorption yield

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itself and on details of the surface potential. The spectral dependence of the photodesorption rate comes about through at least three different mechanisms: (i) homogeneous line broadening, (ii) inhomogeneous line broadening, and (iiB higher order, such as one-photon-one-phonon processes where the absorption of a photon by the internal vibrational mode of the adsorbed molecule is accompanied by the simultaneous absorption or emission of a phonon through the coupling via the surface potential. Homogeneous line broadening of the internal vibrational level of adsorbed molecules is first of all caused by decay mechanisms whereby the vibrational energy of the molecule is dissipated into either the electronic [6] or other vibrational/translational (phonon) [6] degrees of freedom of the adsorbate and solid. Theoretical estimates lead to level widths of 1-3 cm-~. Dephasing, due to the interaction of the vibrational mode with lower frequency frustrated translational and rotational modes of the molecule, has also been suggested [8,9] to account for temperature dependent level widths of = 10 cm-1. Inhomogeneous line broadening is caused by heterogeneity due to different adsorption sites, and due to imperfections in the underlying substrate. Also, random partial coverage leads to a statistical distribution of vibrational frequencies due to varying molecular environments. Resulting line widths in the order of 10 cm-~ are possible [10]. In this letter we will study the influence of inhomogeneous broadening of the IR absorption line on the photodesorption spectrum. The homogeneous case was recently studied by Fain and Lin [11] and also by us elsewhere [12]. A full microscopic theory of vibrational line widths, including both lifetime and dephasing effects, will be reported later [7] along with a more detailed analysis of the resulting homogeneously broadened photodes0rption signal. The calculation of the photodesorption rates is based on a master equation for the occupation function n~(t) of a molecule in a state (i, o) d

t~ z

Vm ,~x '

N

E E [(L;,;:+ e,7)

v'=0

+ e,,:',)

(,)]

i~'t,

i'=0

- E (PcJ "''+

Qc;v) n','(t).

(1)

Here i labels the states of energy E i of the molecule as a whole in the surface potential via which it is interacting with the solid. E, is negative and discrete for the bound states; all molecules trapped into such states form the adsorbate. E, is positive and equal to h2k2/2m for the continuum; particles in the continuum form the free gas phase. The label v above counts the quanta of the internal molecular vibration into which the laser couples. It is assumed to be harmonic up to Vmax where the oscillator is truncated. The energy of the molecule in the(/, v) state is E l = E~ + hl2(v + ½) where I2 is the frequency of

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Z. 14/. Gortel et al. / Line shape of photodesorption yield

its internal vibration. LI'.',"is the rate with which the coupling of the molecular dipole moment to the electromagnetic field of the laser causes transitions up and down the vibrational ladder. The minimal coupling method in the dipole approximation employed here allows only for transitions from (i, v) to ( i ' = i, v' = v + 1). In the present approach, within lowest order perturbation theory, this is the only rate containing information about homogeneous broadening (width Fv) of the vibrational levels of the molecules [5,7,13]. Once in state (i, v) the molecule can emit or absorb a phonon ending in some other state (i', v'), changing in general both its state of motion in the surface potential and that of its internal vibration. The appropriate transition probability per unit time is P,,,,. v',, The coupling between the internal vibrational degree of freedom of the molecule and its center-of-mass motion with respect to the surface leads to the elastic tunneling probability Q~Iv for a transition (i, o) ~ (continuum, v'). This probability is nonzero only if the total energy of the molecule in the initial state (i, v) is positive, i.e. if

El'= E,+ hg2(v + ½) > 0.

(2)

For elastic tunneling this energy is equal to the total energy of a molecule in a final continuum state p2/2m + h~2(v' + ½). The transitions Q~','" lead to desorption along with the inelastic tunneling transitions Pc",'" in which a phonon is either emitted or (less likely at low temperatures) adsorbed. Obviously P~'s'" is nonzero even if condition (2) is not satisfied. All transition probabilities in (1) were calculated in ref. [5] according to Fermi's golden rule from a microscopic Hamiltonian. The surface potential used is a one-dimensional Morse potential. In ref. [5], eq. (1) was then solved by matrix diagonalization and the photodesorption rate constant for the homogeneous case RoH was identified with the lowest eigenvalue X0(I2, I21; I 0) of the rate matrix. ?~0 as a function of laser frequency 12~ is peaked around I2 and its width is related, although not equal, to F = F~ + F v, F, being the width of the laser line and F v the homogeneous width of the vibrational level. Turning now to the case of inhomogeneous line broadening, we assume that the vibrational frequencies of the adsorbed molecules are statistically distributed around some mean frequency ~. Denoting by f(I2 - ~ ) dO the probability of having a molecule with vibrational frequency in the interval d$2 around I2, we get the inhomogeneous photodesorption rate constant as [12] R ~ " ( ~ , ~ ; I0) = f 0 ~ x 0 ( ~ , ~,; I0) f ( ~ -

~ ) d~.

(3)

For our subsequent analysis we choose f to be a Gaussian with width F~ << ~. As a model system we consider CH3F adsorbed on NaCI for which both experimental data [1] and a theoretical analysis [5] exist. The solid, treated in the Debye model has a unit cell of mass Ms = 58.5 amu; its Debye temperature

Z. W. Gortel et al. / Line shape of photodesorption yieM Table 1 Parameters of the model systems for C H 3 F / N a C I :

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oo = 2 ( m A + rnB)Vo/(h't) 2, r = 2 ( m A +

ma)kaTD/(hy) 2 System

V0 (kJ/mol)

y- 1 (,~)

Oo

r

F (cm 1)

I II 1II IV

22.14 22.53 23.05 23.05

0.369 0.369 0.364 0.364

22.6 22.8 22.8 22.8

53.9 53.9 52.7 52.7

1 1 1 10

Fig. Fig. Fig. Fig.

2 3 4 5

is T D = 281 K; the refractive index is n r = 1.5, and the incident laser beam strikes the surface at an angle of 60 ° with the surface normal. The infrared active m o d e of the molecule is its v3 vibration, i.e. F - stretching against CH~-. With F closer to the surface and the molecule adsorbed upright on the surface, the infrared absorption centers around ~ = 970 c m - 1 (i.e., h l 2 / k a T n = 4.98) [1] and has a full width F ~ = 2 0 cm -1 [14]; we take Vmax = 2 . TO fix the parameters of the surface Morse potential we set its depth V0 equal to the heat of adsorption measured [1] to be between 22 and 28 k J / m o l , although a value twice as large also seems possible [15]. N o t h i n g is k n o w n about the range ~,-1 of the surface potential except that it is certainly less than 1 ,~. We therefore consider four different model systems with the parameters listed in table 1. In fig. 1 we present the photodesorption rate R~H as a function of the laser intensity I 0 for T = 50 K, for system I and for the laser tuned to the mean molecular vibrational frequency, i.e., I21 = 9. For comparison the lowest eigenvalue 7~0(12 = 9 , /2j = 9 ; I 0 = RdH of the rate matrix is also plotted as a dotted line. The corresponding plots for systems II and IIIare almost identical - the photodesorption rate is not sensitive to such small changes of parameters of the surface potential. We note that for moderate intensities both rates increase like I~, with a = 1.9 in the present case. For higher intensities saturation is reached. This happens, in the case of inhomogeneous line broadening, i.e. for R~H, over a much larger range of intensities because the molecules which are out of resonance with the laser light saturate at higher intensities than those in resonance. F o r the calculation of )~0, or R~, on the other hand, we assume that all adsorbed molecules are in resonance. While the values of R~" and of )% at saturation are the same, R~H is much smaller below saturation because laser light resonantly desorbs only a fraction = F / F s < 1 of the adsorbed molecules. At the higher temperature of, say, T--- 100 K the results are qualitatively the same but here we have a = 1 below saturation. Whereas the intensity dependence of the resonant rate (i.e., for I2~ = 9 ) is not a very sensitive function of the surface potential parameters, it is so for the spectral dependence of the rate. This is illustrated in figs. 2 - 4 , in which the rates at T = 50 K and for a laser intensity I 0 = 5 × 1 0 3 W / / c m 2, i.e. below the

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Z. ~ Gortel et al. / Line shape of photodesorption yield

T

=

50K

10 4

... ....""" f

10 3

RH / I

102

101

i0~01

L

102

103

104

105

106

107

Io (Wlcm 2) Fig. 1. Resonant, inhomogeneous photodesorption rate constant R~H(~, f21 = ~2; 1o) as a function of laser intensity foi" model system 1. The dotted line represents the lowest eigenvalue of the rate matrix ~ 0 ( ~ = I2, ~21 = 9 ; 10).

saturation threshold, are plotted as a function of the laser frequency ~2~ for systems I, II and III, respectively. In the most common situation, presented in fig. 2, the photodesorption spectrum has the same shape as the IR absorption band (dotted line) except that its maximum is slightly shifted towards lower frequencies. Note that this result is valid only for F < F ~ - i.e. provided homogeneous broadening is insignificant compared to the inhomogeneous line width. When the depth of the surface potential is slightly increased, as in system II, the photodesorption spectrum changes dramatically, as seen in fig. 3. It now deviates markedly from the IR absorption line shape by experiencing sudden drops below certain laser frequencies. The explanation of this behaviour is simple. The most effective last step leading to desorption is the elastic tunneling transition QSI'' from the state (i, v) with lowest possible total energy satisfying condition (2). For all systems considered here it is the state ( i = 6, o = 1). Lowering the laser frequency I2I, the molecules with lower

Z.W. Gortel et aL / Line shape of photodesorption yield

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f--7

,

•

J

,

-Ib

-12

-8

-4

Ne-,~ (cm -1) Fig. 2. Photodesorption rate constant as a function of the laser frequency for model system I. The dotted line represents a Gaussian with width F~ and the maximum adjusted to that of R~N. v i b r a t i o n a l f r e q u e n c y [2 = ~2~ d e s o r b m o s t e f f e c t i v e l y u n t i l the m o l e c u l e s are r e a c h e d for w h i c h c o n d i t i o n (2) is n o l o n g e r v a l i d for t h e p a r t i c u l a r s t a t e (i, v). T h e elastic t u n n e l i n g f r o m this state, so far t h e m o s t e f f e c t i v e d e s o r p t i o n

I

T = 50K

Io 0 == 5 X× 1 0 3 W / c m /

/

-16

-12

I

I

-8

-4

0

I

I

I

I

4

8

12

16

l'),e-- N (cm -1 ) Fig. 3. As fig. 2 but for system II.

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Z. W. Gortel et al. / Line shape of photodesorption yield

! T = 50K

IO = 5 X

/

103W/cm 2

t

i

-16

-12

I

I

-8

-4

ae-fi

i

J

4

8

I

112

16

cm -1)

Fig. 4. As fig. 2 but for system llI.

channel, becomes inoperative. The inelastic tunneling from this state also becomes much smaller because now it is possible only via absorption of a phonon from the solid - a very ineffective process at low temperatures. As a result, the contribution to the desorption of molecules most strongly coupled to the laser light decreases dramatically, resulting in the sudden, almost step-like drop, observed in fig. 3. There are two factors which determine the interval of laser frequencies over which that drop takes place. First, at higher temperatures, inelastic tunneling does not drop so dramatically when the (i, v) level sinks below the continuum threshold. Secondly, if the intensity dependence of ~0 is weaker, molecules from a wider range of vibrational frequencies around 121 are desorbed, resulting in a less dramatic drop in the dependence of R~H on (21. Both effects can be seen by increasing the temperature from T = 50 to 100 K. At intensities above the saturation threshold only a small asymmetry of the photodesorption line remains. A sudden decrease of the photodesorption yield can also happen for I2~ > ~, as seen in fig. 4 for system III. The photodesorption spectrum now has two peaks, whereas the IR band has only one at ~2~= ~. Such a double peak structure is much more difficult to wash out by raising the temperature or increasing the intensity above the saturation threshold. One might argue that the line shapes seen in figs. 3 and 4 are the result of setting the homogeneous part of the vibrational line width at a rather small value of F = 1 cm-1. Setting F = 10 c m - ] in fig. 5 we see, however, that the main effects are not qualitatively altered.

Z. W. Gortel et aL / Line shape of photodesorption yield

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T = 50K I0 = 5 X 103W/cm

2

7= 0.05

I -16

~2 -I

I -8

L -4

f~e-~

i 4

0

(cm-1)

Fig. 5. As fig. 2 but for system IV. In this p a p e r we have shown that the i n h o m o g e n e o u s l y b r o a d e n e d p h o t o d e s o r p t i o n rate as a function of laser frequency should, in m o s t cases, r e s e m b l e the infrared a b s o r p t i o n s p e c t r u m of the relevant internal m o l e c u l a r v i b r a t i o n of the a d s o r b e d molecule. However, striking differences can show up, such as a s t r o n g a s y m m e t r y of the p h o t o d e s o r p t i o n s p e c t r u m or a d o u b l e p e a k structure. These effects can be traced to the s u d d e n switching off of the m o s t effective d e s o r p t i o n channel, n a m e l y elastic tunneling. A careful analysis of the differences b e t w e e n the p h o t o d e s o r p t i o n a n d I R a b s o r p t i o n s p e c t r a should p r o v i d e quite u n i q u e i n f o r m a t i o n a b o u t excited states of the surface p o t e n t i a l a n d a b o u t the p h o t o d e s o r p t i o n process in general. This w o r k was s u p p o r t e d in p a r t b y grants f r o m the N a t u r a l Sciences a n d Engineering R e s e a r c h Council o f C a n a d a ( N S E R C ) .

References [1] J. Heidberg, H. Stein, A. Nestmann, E. Hoefs and I. Hussla, in: Proc. MRS Symp. on Laser-Solid Interactions and Laser Processing, 1978, Boston, Eds. S.D. Ferris, H.J. Leamy and J.M. Poate (AIP, New York, 1979) p. 49; J. Heidberg, H. Stein, E. Riehl and A. Nestmann, Z. Physik. Chem. NF 121 (1980) 145; J. Heidberg, H. Stein and E. Riehl, Phys. Rev. Letters 49 (1982) 666,

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Z. IV. Gortel et al. / Line shape of photodesorption yieM

[2] T.J. Chuang, J. Chem. Phys. 76 (1982) 3828; T.J. Chuang and H. Seki, Phys. Rev. Letters 49 (1982) 382. [3] I. Hussla, H. Seki, T.J. Chuang, Z.W. Gortel,. H.J. Kreuzer and P. Piercy, Phys. Rev. B, to be published. [4] T.J. Chuang, Surface Sci. Rept. 3 (1983) 1. [5] Z.W. Gortel, H.J. Kreuzer, P. Piercy and R. Teshima, Phys. Rev. B27 (1983) 5066. [6] B.N.J. Persson and M. Persson, Solid State Commun. 36 (1980) 175; B.N.J. Persson and M. Persson, Surface Sci. 97 (1980) 609. [7] Z.W. Gortel, H.J. Kreuzer, P. Piercy and R. Teshima, in preparation. [8] J.W. Gadzuk and A.C. Luntz, Surface Sci. 144 (1984) 429. [9] B.N.J. Persson and R. Ryberg, Phys. Rev. Letters 54 (1985) 2119. [10] F.M. Hoffmann, Surface Sci. Rept. 3 (1983) 107; B.N.J. Persson and R. Ryberg, Phys. Rev. B24 (1981) 6954. [11] B. Fain and S.H. Lin, Chem. Phys. Letters 144 (1985) 497. [12] Z.W. Gortel, H.J. Kreuzer, P. Piercy and Teshima, to be published. [13] C. Jedrezejek, J. Vacuum Sci. Technol. to be published. [14] J. Heidberg I. Hussla and Z. Szilagyi, J. Electron Spectrosc. Related Phenomena 30 (1983) 53. [15] J. Heidberg, private communication.