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State-resolved measurements of the energy distributions of no scattered at Ge surfaces
Surface
STATE-RESOLVED MEASU~~ENTS DISTRIBUTIONS OF NO SCATTERED
Received
17 March
1986: accepted
for publication
Science 17X (1986) 798405 North-Hohand, Amsterdam
OF THE ENERGY AT Ge SURFACES
12 June 19%
Velocity distributions for NO( 1,” 3 0. I”) molecules scattered from an oxidized Ge surface have been measured for various rotational states as a function of incident energy, incident angle and substrate temperature. Resonant two”.pboton ionization by a tunable ultraviolet laser and time-of-flight spectrascopy in combination with supersonic molecutar beam-surface scattering were used for these measurements. Detailed experimental arrangements, data analyses and a brier discussion of experimental results are presented in this paper.
1. Introduction The dynamics of molecule/surface interaction is most directly studied by molecular beam experiments and is usualIy divided into two channels trapping/desorption and direct inelastic scattering - which can in favourable cases be distinguished by recording angular and velocity distributions of the particles coming off the surface [I]_ The introduction of iaser-induced fluorescence (LIF) [2] and resonantly enhanced muIt~photo~ ionization (REMPI) [3-61, enabled, in addition, the determination of the imernal state (rotation and vibration) populations. A fully state-resolved description requires. however, the determination of the translational energy distributions in individual internal states, apart from the respective fluxes. Experiments of this type have been first performed by Hager et al. [4] by the combined use of REMPI and time-of-flight (TOF) techniques. and an experimental system based on quite simple principles will be described in the present paper together with a Few representative results obtained for NO scattered at an oxidized Ge surface. Rotational state populations for the NO/Ge-Ox system have been investigated previously by means of LIF [7]. * Alexander von Humboldt Awardee. Permanent Harry Road, San Jose, CA 951204099. USA.
address:
IBM Almaden
~3~-~~~/~6/~~3.5~ 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
Research
Center,
650
F. Budde et al. / Energy distributions of NO scattered at Ge surfaces
799
2. Experimental
The experimental arrangement is shown schematically in fig. 1. It is the same as that used in our previous LIF study just mentioned [7], however modified for combined REMPI TOF measurements. A supersonic, continuous molecular beam of NO is generated in a three-stage differentially pumped source after expansion through a 0.07 mm diameter nozzle and passing through a skimmer with 0.7 mm orifice placed 10 mm downstream. The translational energy of the beam molecules is varied by heating the nozzle up
(a)
I
PhotodIode
’
2w
Dye laser
Excimer laser
Computer
T---
J
-----------7
I L_________.______
1
MultIplier
I ________.
Fig. 1. Experimental arrangement for REMPI TOF measurements of NO scattered from a GeO surface; (a) overall setup and (b) detailed sketch of the sample and the cylindrical cage used for TOF detection.
to 900 K and/or by seeding with helium. The angle of incidence with respect to the surface normal, 8], can be varied by rotating the manipulator axis onto which the sample is mounted. The Ge(ll1) surface is cleaned [7] by oxidizing with NO, and flashing off the formed GeO. After several flashing-oxidizing cycles the surface is oxidized once again and the experiments are carried out with the Ge-Ox surface. The base pressure in the scattering chamber is about 2 x fWXO Torr, but may rise up to 1 X lWR Torr with a 1: 10 NO/He beam mixture due to the large amount of helium. For determining velocity distributions of molecules scattered at the surface, a cylindrical grid (6 mm height, 17 mm diameter) made of wire mesh is placed in front of the sample and held at ground potential. NO molecules passing through the center of this grid are ionized by a pulsed laser beam (pulse duration 8 ns) which is weakly focussed (f= 880 mm) along the axis. After leaving the cage the ions are accelerated by an electric field of ~~~~-~~~~ V towards a secondary electron multiplier at a distance of about 5 cm from the ionization region and detected. Since the translational energy of the molecules is not affected by the photoionization process the recorded time-of-flight distribution (corrected by the calculated 0.75 ps flight time from the grid to the detector) corresponds to the passage of the neutral particles across a distance of 8.5 mm. By shifting the sample with respect to the axis formed by the center of the cage and the multiplier entrance (as sketched in fig. lb), particles from varying scattering angies @rcan be collected. To obtain the TOF distribution of the incident molecules, the cage is moved into the center of the primary beam and the ions are detected in line-of-sight with a second multiplier. Formation of ions is achieved by the frequency-doubled light of a pulsed tunable dye laser (h around 226 nm) through the following resonantly enhanced two-photon ionization process:
2 NU+(X'Z+,
/I,
J) t- e-(Ekin).
By tuning the laser frequency, the ionization of molecules takes place out of individual rotationa states (J “), yielding TOF distributions for molecules with the respective J”. The current signal of the multiplier is converted into voltage and after amplification fed into a transient retarder which is triggered by the ionizing laser pulse. The TOF spectra were recorded through 1024 channels, each of a 62.5 ns width. In order to achieve a satisfactory signal-to-noise ratio typically 1500 spectra were accumulated which takes about 7 min. A computer is used for further data processing.
F. Budde et al. / Energy distributions of NO scattered at Ge surfaces 3.
801
Results and analysis
The TOF spectra are transformed into the flux velocity which are related to the measured TOF density distributions I(u)
=n(t)
distributions n(t) by
]dt/du)u.
I(u)
(I)
A set of typical TOF spectra for three different scattering angles and for a fixed rotational state (J” = 5/2) is reproduced in fig. 2a. Fig. 2b shows the resulting flux velocity distributions. They consist of two parts which are attributed to the two different scattering channels [8]: The low velocity component is ascribed to trapping/desorption, while the high velocity component is due to direct inelastic scattering. For quantitative analysis the low velocity component of the measured velocity distributions is fitted with a non-linear least-squares fitting routine [9], using a flux velocity distribution given by [lO,ll] Z(u)
=Au3 exp[
-B(u-
(2)
uO)‘].
A is a normalization factor, u0 a flow velocity, and B a width parameter. This functional form is capable of representing the velocity distribution of the scattered particles or of a supersonic incident beam as well as a pure Maxwell-Boltzmann velocity distribution with u, = 0. B = m/2kT is related to the temperature in a moving frame of reference. In a supersonic beam u,, is about the same as (u) (defined below). The (flux) mean kinetic energy (E), the mean velocity (u), and the spread of the velocity distribution ((I ‘) can be derived from the velocity moments M, (i = 0, 1, 2) defined as [12] M,=
u’I(u) /m
du,
(3)
0
NO-He/GeO
NO-He/GeO Ts : 450
K
Bi = 60’ oens1ty
‘\\ -q=
0’
,x
k’, 0
‘~*” ,
,
,
;‘3+-_I
20 40 60 Time of Flight [ps 1
0
1000 Velocity
2000
[m/s1
Fig. 2. (a) TOF signals (density) of scattered NO at J” = 5/2 with Ei = 820 meV, Bi = 60°, tit = O”, 30° and 60” as indicated, and T, = 450 K; (b) converted into flux versus velocity.
802
F. Buddeet id. / Enqv
where I(v) is the flux velocity
~j.~~~j~U~j~~S of NO scaftgred
distribution,
06
Ge sut&x%
The mean velocity
is then given by (4)
(lJ> = MI/W, and the mean translational (E)
energy by
= $rz(u”) = ~nzM2/M,
(5)
fm is the mass of the NO molecule).
characterized
The spread of the veIoeity by its mean square deviation
distribution
is
(6) To quantitatively
separate
the two scattering
channels,
we first calculate
M,,,
Fig. 3. Flux velocity distributions of incident and scattered NO beams at J”= 5/2: (a) incident beam with E, = 180 meV: (b) incident beam with E, = 820 meV; (c) scattered NO, with E, = 1X0 meV, 6, = 60°, Bf = 0’ and < = 450 K; and (d) scattered NO with E, = 820 meV, 0, = 60”. ff, = 60° and r, = 450 K. Results of least-squares fitting of the incident beams and of the trapping/desorption components of the scattered NO are indicated in dashed curves.
F. Budde et of. / Energy d~~tr~b~t~~n~of NO scattered at Ge surfaces
803
A4i and M. for the trapping/desorption part from the best-fit curve. We then substract the fitted curve from the experimentally observed data to obtain the corresponding quantities for the direct inelastic scattering components. Fig. 3 shows some examples for fitting the experimental data by the least-squares procedure. The characteristics of the incident beams are also displayed in this figure. The results of these fittings show that for a NO beam with Ei= 180 meV, di = 60*, 8, = O* (fig. 3c), the calculated values are (u} = 675 m/s, (E,) = 78 meV, (e2) = 0.106. Under different conditions with Ei = 820 meV, 8; = 8, = 60“ (fig. 3d), we obtain (u) = 760 m/s, ( EE) = 94 meV, (u’) = 0.047 for the trapping/desorption component and (u) = 1800 m/s, (E,) = 486 meV for the direct inelastic component. One should mention, however, that the low L+component has a TOF line shape somewhat different from a pure Maxwell-Boltzmann distribution. For He-seeded beams (as in fig_ 3d) this deviation is more pronounced and (E,) for the trapping/deso~tion part is slightly larger than 2kT, (T, is the surface temperature). It should be noted that M, is proportional to the flux into the detector and thereby to the population density NJ,, of the respective rotational level. The relative populations of different rotational states can be related with respect to each other by normalization with the square of the laser intensity, I:, and by taking into account the Honl-London factors S,,,,,, [13]: NJ”
29” + 1
c&5LI,‘&,,,
(7)
*
If we now return to the data of fig. 2, we see that the number of particles of
Ei =
i\
L----r
0
820 meV
7
10
20 Ttme
--------
o:‘Flqh+
LO
50
[ ps]
Fig. 4. TOF signals (density versus time) of scattered NO at J” = 5/2 with Bi = 60° and T, = 450 K for three different incident kinetic energies: (a) Ei = 820 meV, (b) Ei = 360 meV, (c) E, = 180 meV.
804
F. Budde et ul. / Enerm distrihumns
of NO sccrttered ut Gr surJues
NO-He/GeO Ts = 320 K
J” q69/2
0
1000
Veioclty
2000 lmisl
3( IO
Fig. 5. Flux velocity distributions of scattered NO with E, = 730 meV. 8, = Br = 45O and T, “320 K at (a) J” = 5/2. (b) .I” = 45/2 and (c) J” = 69/2.
the high velocity component decreases markedly by moving away from the specular detection angle (8, = 60”) and is nearly not detectable at normal direction (0, = O”), which is quite in contrast to the behavior of the low velocity component. This result supports the assignment of the former to direct-inelastic scattering (whose flux should be peaked near the specular angle) while the latter is due to trapping/desorption exhibiting an isotropic angular distribution. Fig. 4 shows a set of TOF data for which only the incident kinetic energy E, was varied: While the position of the peak maximum of the trapping/desorption part remains unchanged on the time scale, that of the direct inelastic scattering part shifts to shorter times with increasing Ei. This result confirms further the separation into the two scattering channels as indicated. Fig. 5 shows the velocity distributions for a high and a low J” state of scattered NO with Ei = 730 meV and oi = 0, = 45”. A full set of TOF spectra for different rotational levels is presented elsewhere [8]. These data allow the separate determination of the population NJ,, of the trapping/desorption channel (yielding a rotational temperature T,) and of the direct inelastic scattering part (exhibiting the well-known “rainbow” features), as well as of the corresponding translational energies ( Ef,,,, ). State-resolved experiments of
i? Budde et al. / Energy d~stri~~tio~ of NO scattered at Ge surfaces
805
the kind described here provide therefore the most detailed insights into the dynamics of molecule-surface interactions which are at present possible.
Acknowkdgements
The authors thank Dr. J. Segner and Dr. W. Vielhaber for technical assistance. TJC is grateful to the Alexander von Humboldt-Stiftung for a Senior US Scientists Award. FB would like to thank the Studienstiftung des Deutschen Volkes for a scholarship. Financial support was obtained from the Deutsche Forschungsgemeinschaft (SFB 128).
References [l] J.A. Barker and D.J. Auerbach, Surface Sci. Rept. 4 (1985) 1. [2] F. Frenkel, J. HLlger, W. Krieger, H. Walther, CT. Campbell, G. Ertl, H. Kuipers and J. Segner, Phys. Rev. Letters 46 (1981) 152; G.M. McClelland, G.D. Kubiak, H.G. Rennagel and R.N. Zare, Phys. Rev. Letters 46 (1981) 831; A.W. Kleyn, AC. Luntz and D.J. Auerbach, Phys. Rev. Letters 47 (1981) 1169; J.W. Hepburn, F.J. Northrup, G.L. Ogram, J.C. Polanyi and J.M. Williamson, Chem. Phys. Letters 85 (1982) 127. [3] M. Asscher, W.L. Guthrie, T.-H. Lin and G.A. Somorjai, Phys. Rev. Letters 49 (1982) 76. [4] J. Hager, Y.R. Shen and H. Walther, Phys. Rev. A31 (1985) 1962. [5] R.J. Hamers, P.L. Houston and R.P. Merrill, J. Chem. Phys. 83 (1985) 6045. [6] C.T. Rettner, F. Fabre, J. Kimman and D.J. Auerbach, Phys. Rev. Letters 55 (1985) 1904, [7] A. Modl, H. Robota, J. Segner, W. Vielhaber, M.C. Lin and G. Ertl, J. Chem. Phys 83 (1985) 4800. [8] A. MadI, T. Gritsch, F. Budde, T.J. Chuang and G. Ertl, Phys. Rev. Letters 57 (1986) 384. [9] See for example: W. Mtiller and T. Kick, Basic Programme fur die angewandte Statistik (Olden~~g, Mtinchen, 1983). [lo] K.C. Janda, J.E. Hurst, C.A. Becker, J.P. Cowin, L. Wharton and D.J. Auerbach, Surface Sci. 93 (1980) 270. [ll] G. Comsa and R. David, Surface Sci. Rept. 5 (1985) 145. [12] J. Lapujoulade and Y. Lejay, J. Chem. Phys. 63 (1975) 1389. [13] M.S. Chou, A.M. Dean and D. Stem, J. Chem. Phys. 78 (1983) 5962.
STATE-RESOLVED MEASU~~ENTS DISTRIBUTIONS OF NO SCATTERED
Received
17 March
1986: accepted
for publication
Science 17X (1986) 798405 North-Hohand, Amsterdam
OF THE ENERGY AT Ge SURFACES
12 June 19%
Velocity distributions for NO( 1,” 3 0. I”) molecules scattered from an oxidized Ge surface have been measured for various rotational states as a function of incident energy, incident angle and substrate temperature. Resonant two”.pboton ionization by a tunable ultraviolet laser and time-of-flight spectrascopy in combination with supersonic molecutar beam-surface scattering were used for these measurements. Detailed experimental arrangements, data analyses and a brier discussion of experimental results are presented in this paper.
1. Introduction The dynamics of molecule/surface interaction is most directly studied by molecular beam experiments and is usualIy divided into two channels trapping/desorption and direct inelastic scattering - which can in favourable cases be distinguished by recording angular and velocity distributions of the particles coming off the surface [I]_ The introduction of iaser-induced fluorescence (LIF) [2] and resonantly enhanced muIt~photo~ ionization (REMPI) [3-61, enabled, in addition, the determination of the imernal state (rotation and vibration) populations. A fully state-resolved description requires. however, the determination of the translational energy distributions in individual internal states, apart from the respective fluxes. Experiments of this type have been first performed by Hager et al. [4] by the combined use of REMPI and time-of-flight (TOF) techniques. and an experimental system based on quite simple principles will be described in the present paper together with a Few representative results obtained for NO scattered at an oxidized Ge surface. Rotational state populations for the NO/Ge-Ox system have been investigated previously by means of LIF [7]. * Alexander von Humboldt Awardee. Permanent Harry Road, San Jose, CA 951204099. USA.
address:
IBM Almaden
~3~-~~~/~6/~~3.5~ 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
Research
Center,
650
F. Budde et al. / Energy distributions of NO scattered at Ge surfaces
799
2. Experimental
The experimental arrangement is shown schematically in fig. 1. It is the same as that used in our previous LIF study just mentioned [7], however modified for combined REMPI TOF measurements. A supersonic, continuous molecular beam of NO is generated in a three-stage differentially pumped source after expansion through a 0.07 mm diameter nozzle and passing through a skimmer with 0.7 mm orifice placed 10 mm downstream. The translational energy of the beam molecules is varied by heating the nozzle up
(a)
I
PhotodIode
’
2w
Dye laser
Excimer laser
Computer
T---
J
-----------7
I L_________.______
1
MultIplier
I ________.
Fig. 1. Experimental arrangement for REMPI TOF measurements of NO scattered from a GeO surface; (a) overall setup and (b) detailed sketch of the sample and the cylindrical cage used for TOF detection.
to 900 K and/or by seeding with helium. The angle of incidence with respect to the surface normal, 8], can be varied by rotating the manipulator axis onto which the sample is mounted. The Ge(ll1) surface is cleaned [7] by oxidizing with NO, and flashing off the formed GeO. After several flashing-oxidizing cycles the surface is oxidized once again and the experiments are carried out with the Ge-Ox surface. The base pressure in the scattering chamber is about 2 x fWXO Torr, but may rise up to 1 X lWR Torr with a 1: 10 NO/He beam mixture due to the large amount of helium. For determining velocity distributions of molecules scattered at the surface, a cylindrical grid (6 mm height, 17 mm diameter) made of wire mesh is placed in front of the sample and held at ground potential. NO molecules passing through the center of this grid are ionized by a pulsed laser beam (pulse duration 8 ns) which is weakly focussed (f= 880 mm) along the axis. After leaving the cage the ions are accelerated by an electric field of ~~~~-~~~~ V towards a secondary electron multiplier at a distance of about 5 cm from the ionization region and detected. Since the translational energy of the molecules is not affected by the photoionization process the recorded time-of-flight distribution (corrected by the calculated 0.75 ps flight time from the grid to the detector) corresponds to the passage of the neutral particles across a distance of 8.5 mm. By shifting the sample with respect to the axis formed by the center of the cage and the multiplier entrance (as sketched in fig. lb), particles from varying scattering angies @rcan be collected. To obtain the TOF distribution of the incident molecules, the cage is moved into the center of the primary beam and the ions are detected in line-of-sight with a second multiplier. Formation of ions is achieved by the frequency-doubled light of a pulsed tunable dye laser (h around 226 nm) through the following resonantly enhanced two-photon ionization process:
2 NU+(X'Z+,
/I,
J) t- e-(Ekin).
By tuning the laser frequency, the ionization of molecules takes place out of individual rotationa states (J “), yielding TOF distributions for molecules with the respective J”. The current signal of the multiplier is converted into voltage and after amplification fed into a transient retarder which is triggered by the ionizing laser pulse. The TOF spectra were recorded through 1024 channels, each of a 62.5 ns width. In order to achieve a satisfactory signal-to-noise ratio typically 1500 spectra were accumulated which takes about 7 min. A computer is used for further data processing.
F. Budde et al. / Energy distributions of NO scattered at Ge surfaces 3.
801
Results and analysis
The TOF spectra are transformed into the flux velocity which are related to the measured TOF density distributions I(u)
=n(t)
distributions n(t) by
]dt/du)u.
I(u)
(I)
A set of typical TOF spectra for three different scattering angles and for a fixed rotational state (J” = 5/2) is reproduced in fig. 2a. Fig. 2b shows the resulting flux velocity distributions. They consist of two parts which are attributed to the two different scattering channels [8]: The low velocity component is ascribed to trapping/desorption, while the high velocity component is due to direct inelastic scattering. For quantitative analysis the low velocity component of the measured velocity distributions is fitted with a non-linear least-squares fitting routine [9], using a flux velocity distribution given by [lO,ll] Z(u)
=Au3 exp[
-B(u-
(2)
uO)‘].
A is a normalization factor, u0 a flow velocity, and B a width parameter. This functional form is capable of representing the velocity distribution of the scattered particles or of a supersonic incident beam as well as a pure Maxwell-Boltzmann velocity distribution with u, = 0. B = m/2kT is related to the temperature in a moving frame of reference. In a supersonic beam u,, is about the same as (u) (defined below). The (flux) mean kinetic energy (E), the mean velocity (u), and the spread of the velocity distribution ((I ‘) can be derived from the velocity moments M, (i = 0, 1, 2) defined as [12] M,=
u’I(u) /m
du,
(3)
0
NO-He/GeO
NO-He/GeO Ts : 450
K
Bi = 60’ oens1ty
‘\\ -q=
0’
,x
k’, 0
‘~*” ,
,
,
;‘3+-_I
20 40 60 Time of Flight [ps 1
0
1000 Velocity
2000
[m/s1
Fig. 2. (a) TOF signals (density) of scattered NO at J” = 5/2 with Ei = 820 meV, Bi = 60°, tit = O”, 30° and 60” as indicated, and T, = 450 K; (b) converted into flux versus velocity.
802
F. Buddeet id. / Enqv
where I(v) is the flux velocity
~j.~~~j~U~j~~S of NO scaftgred
distribution,
06
Ge sut&x%
The mean velocity
is then given by (4)
(lJ> = MI/W, and the mean translational (E)
energy by
= $rz(u”) = ~nzM2/M,
(5)
fm is the mass of the NO molecule).
characterized
The spread of the veIoeity by its mean square deviation
distribution
is
(6) To quantitatively
separate
the two scattering
channels,
we first calculate
M,,,
Fig. 3. Flux velocity distributions of incident and scattered NO beams at J”= 5/2: (a) incident beam with E, = 180 meV: (b) incident beam with E, = 820 meV; (c) scattered NO, with E, = 1X0 meV, 6, = 60°, Bf = 0’ and < = 450 K; and (d) scattered NO with E, = 820 meV, 0, = 60”. ff, = 60° and r, = 450 K. Results of least-squares fitting of the incident beams and of the trapping/desorption components of the scattered NO are indicated in dashed curves.
F. Budde et of. / Energy d~~tr~b~t~~n~of NO scattered at Ge surfaces
803
A4i and M. for the trapping/desorption part from the best-fit curve. We then substract the fitted curve from the experimentally observed data to obtain the corresponding quantities for the direct inelastic scattering components. Fig. 3 shows some examples for fitting the experimental data by the least-squares procedure. The characteristics of the incident beams are also displayed in this figure. The results of these fittings show that for a NO beam with Ei= 180 meV, di = 60*, 8, = O* (fig. 3c), the calculated values are (u} = 675 m/s, (E,) = 78 meV, (e2) = 0.106. Under different conditions with Ei = 820 meV, 8; = 8, = 60“ (fig. 3d), we obtain (u) = 760 m/s, ( EE) = 94 meV, (u’) = 0.047 for the trapping/desorption component and (u) = 1800 m/s, (E,) = 486 meV for the direct inelastic component. One should mention, however, that the low L+component has a TOF line shape somewhat different from a pure Maxwell-Boltzmann distribution. For He-seeded beams (as in fig_ 3d) this deviation is more pronounced and (E,) for the trapping/deso~tion part is slightly larger than 2kT, (T, is the surface temperature). It should be noted that M, is proportional to the flux into the detector and thereby to the population density NJ,, of the respective rotational level. The relative populations of different rotational states can be related with respect to each other by normalization with the square of the laser intensity, I:, and by taking into account the Honl-London factors S,,,,,, [13]: NJ”
29” + 1
c&5LI,‘&,,,
(7)
*
If we now return to the data of fig. 2, we see that the number of particles of
Ei =
i\
L----r
0
820 meV
7
10
20 Ttme
--------
o:‘Flqh+
LO
50
[ ps]
Fig. 4. TOF signals (density versus time) of scattered NO at J” = 5/2 with Bi = 60° and T, = 450 K for three different incident kinetic energies: (a) Ei = 820 meV, (b) Ei = 360 meV, (c) E, = 180 meV.
804
F. Budde et ul. / Enerm distrihumns
of NO sccrttered ut Gr surJues
NO-He/GeO Ts = 320 K
J” q69/2
0
1000
Veioclty
2000 lmisl
3( IO
Fig. 5. Flux velocity distributions of scattered NO with E, = 730 meV. 8, = Br = 45O and T, “320 K at (a) J” = 5/2. (b) .I” = 45/2 and (c) J” = 69/2.
the high velocity component decreases markedly by moving away from the specular detection angle (8, = 60”) and is nearly not detectable at normal direction (0, = O”), which is quite in contrast to the behavior of the low velocity component. This result supports the assignment of the former to direct-inelastic scattering (whose flux should be peaked near the specular angle) while the latter is due to trapping/desorption exhibiting an isotropic angular distribution. Fig. 4 shows a set of TOF data for which only the incident kinetic energy E, was varied: While the position of the peak maximum of the trapping/desorption part remains unchanged on the time scale, that of the direct inelastic scattering part shifts to shorter times with increasing Ei. This result confirms further the separation into the two scattering channels as indicated. Fig. 5 shows the velocity distributions for a high and a low J” state of scattered NO with Ei = 730 meV and oi = 0, = 45”. A full set of TOF spectra for different rotational levels is presented elsewhere [8]. These data allow the separate determination of the population NJ,, of the trapping/desorption channel (yielding a rotational temperature T,) and of the direct inelastic scattering part (exhibiting the well-known “rainbow” features), as well as of the corresponding translational energies ( Ef,,,, ). State-resolved experiments of
i? Budde et al. / Energy d~stri~~tio~ of NO scattered at Ge surfaces
805
the kind described here provide therefore the most detailed insights into the dynamics of molecule-surface interactions which are at present possible.
Acknowkdgements
The authors thank Dr. J. Segner and Dr. W. Vielhaber for technical assistance. TJC is grateful to the Alexander von Humboldt-Stiftung for a Senior US Scientists Award. FB would like to thank the Studienstiftung des Deutschen Volkes for a scholarship. Financial support was obtained from the Deutsche Forschungsgemeinschaft (SFB 128).
References [l] J.A. Barker and D.J. Auerbach, Surface Sci. Rept. 4 (1985) 1. [2] F. Frenkel, J. HLlger, W. Krieger, H. Walther, CT. Campbell, G. Ertl, H. Kuipers and J. Segner, Phys. Rev. Letters 46 (1981) 152; G.M. McClelland, G.D. Kubiak, H.G. Rennagel and R.N. Zare, Phys. Rev. Letters 46 (1981) 831; A.W. Kleyn, AC. Luntz and D.J. Auerbach, Phys. Rev. Letters 47 (1981) 1169; J.W. Hepburn, F.J. Northrup, G.L. Ogram, J.C. Polanyi and J.M. Williamson, Chem. Phys. Letters 85 (1982) 127. [3] M. Asscher, W.L. Guthrie, T.-H. Lin and G.A. Somorjai, Phys. Rev. Letters 49 (1982) 76. [4] J. Hager, Y.R. Shen and H. Walther, Phys. Rev. A31 (1985) 1962. [5] R.J. Hamers, P.L. Houston and R.P. Merrill, J. Chem. Phys. 83 (1985) 6045. [6] C.T. Rettner, F. Fabre, J. Kimman and D.J. Auerbach, Phys. Rev. Letters 55 (1985) 1904, [7] A. Modl, H. Robota, J. Segner, W. Vielhaber, M.C. Lin and G. Ertl, J. Chem. Phys 83 (1985) 4800. [8] A. MadI, T. Gritsch, F. Budde, T.J. Chuang and G. Ertl, Phys. Rev. Letters 57 (1986) 384. [9] See for example: W. Mtiller and T. Kick, Basic Programme fur die angewandte Statistik (Olden~~g, Mtinchen, 1983). [lo] K.C. Janda, J.E. Hurst, C.A. Becker, J.P. Cowin, L. Wharton and D.J. Auerbach, Surface Sci. 93 (1980) 270. [ll] G. Comsa and R. David, Surface Sci. Rept. 5 (1985) 145. [12] J. Lapujoulade and Y. Lejay, J. Chem. Phys. 63 (1975) 1389. [13] M.S. Chou, A.M. Dean and D. Stem, J. Chem. Phys. 78 (1983) 5962.