Lifetime of an adsorbate-substrate vibration measured by sum frequency generation : H on Si(111)

Journal of Electron Spectroscopy and Related Phenomena, 54155 ( 1990 ) 27-38 Elsevier Science Publishers B.V., Amsterdam

27

Lifetimeofan~r~~~~evibrationmeasuredbySum Frequency Generation : H on Si(ll1). P. Guyot-Sionnesta,

P. Dumasb, and Y. J. Chabalc.

a : Laboratoire pour 1’Utilisation du Rayonnement Electromagnetique, Centre Universitaire Paris-Sud, Orsay, F91405, France. b : Laboratoire de Spectroscopic Infrarouge et Raman, 2 rue Henri Dunant, Thiais, F94320, France. C : AT&T Bell Laboratories, Murray Hill, New Jersey 07974, USA. ABSTRACT The lifetime of the stretching vibration of Hydrogen on Silicon (111) surface is measured by time-resolved Sum Frequency Generation. It varies from 1.4 + 0.2 ns at 95 K to 0.55 f 0.1 ns at 460 K. We suggest that the relaxation occurs via 4-phonons processes. 1. INTRODUCTION The study of relaxation dynamics of adsorbates vibrations down to the picosecond timescale is a new emerging field. Such studies are only now becoming possible because of improvements in the laser technology, the invention of new surface optical probes and an excellent control of the surfaces studied. They will allow a better understanding of the nature and pathways of energy transfer at surfaces. In particular, vibrational relaxation should affect the reactivity of adsorbates, their diffusion and desorption rates. In general, the infrared linewidth of an adsorbate vibration is related to both dephasing time T2 and lifetime Tl. The FWHM of an homogeneously broadened line is explicitely given by Ao= 2/T2 = 2Lt’2* + lfl’l where T2* is the pure dephasing time (e.g. 1 cm-l linewidth corresponds to 10 ps dephasing time or 5 ps lifetime). Until recently, it was thought that the linewidths of the adsorbate vibrations were often dominated by their lifetime.1 Later, however, measurements of the temperature-dependence of vibrational linewidths showed that pure dephasing2*3*4 could be the dominant contribution. In general, the knowledge of the linewidth is not sufficient to separate the contributions from dephasing or lifetime.2,5,6 Direct time-resolved measurements are therefore required to determine Tl. As with the earlier relaxation studies for molecules in gas , liquids and condensed phases, we can expect that the number of decay channels for a particular excitation increases strongly with the molecular complexity. Therefore, as a first insight into this opening field, one should look at the most simple and the best characterized systems.

0368-2048/90/$03.50

0 1990 -

Elsevier Science Publishers B.V.

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The first studies on the relaxation of adsorbate vibrations used conventional linear absorption and transient bleaching. To compensate for the weak surface optical density, poorly characterized high surface area materials had to be used.7-9 On the other hand, to study single crystal surfaces, the potential of the nonlinear optical techniques of Sum-Frequency Generation (SFG) was recognized early lo-13 and it has been demonstrated recently.14 Since, data on the relaxation of adsorbates on single crystal meta115p16, semiconductor17 and insulator surfaces 18 have been available using SFG ,transient reflectivity or fluorescence techniques. We report here our work on the lifetime of the Si-H stretching vibration for the Si(lll):H surface. This is a highly ideal s stem for which detailed spectroscopic measurements have been performed199 H0. The Si-H stretch vibration is at 2083.7 cm-l at room temperature with a 0.9 cm-l natural linewidthzo. The lineposition and linewidth vary significantly with temperature, in accord with a dephasing mechanism via scattering from a 200 cm-l silicon phonon2o. In already published work we have presented the first Sum Frequency timeresolved measurements on this system 17. With our time resolution of 200 ps, we had found a lifetime of 0.8kO.l ns at room temperature. In this present work, we investigate the possibility of shorter components of the population decay. The sample temperature can also be varied from 95 K to 460 K and the temperature dependence of the lifetime allows to rule out some otherwise energetically allowed decay mechanisms. 2. GENERALITIES ON THE SUM FREQUENCY TECHNIQUE In the past few years the nonlinear optical techniques of Second Harmonic Generation and Sum-Frequency Generation (SFG) have emerged as useful surface probe@. Both techniques rely on second order nonlinear optical processes. As an intense electromagnetic field irradiates a material the polarisability that varies linearly for weak fields becomes nonlinear. This leads, from a spectral viewpoint, to various frequency mixing processes22. Of particular interest here, Second Harmonic, Sum Frequency and Difference In the dipole Frequency processes arise from the second order polarisability. approximation, the polarisability P comes from the second order susceptibility $2) . x(2’ is a third rank tensor such that

P(-l-twz) = Xt2’: E(wl) : E(w

)

(I)

For xc2) to be nonzero, it is clear that the material must have no center of inversion. Given this, there exists a variety of non centrosymetric crystals that can withstand large laser powers. They are widely used for generating powerful coherent light at wavelengths that are not directly accessible by lasers. Among these are the KDP (Potassium Dihydrogen Phosphate) and AgGaS2 ( Silver Gallium Sulfide) used in our laser system. On the other hand, centrosymetric materials like silicon have a vanishing ~(2) and they do not allow second order processes. However, the surface of a centrosymetric material is intrinsically noncentrosymetric and it often

29

remains the major source of nonlinear radiation. This is the basis for the surface sensitivity of SFG. Although the number of emitted photons is small, typically 103 for 101s incident photons. They are easily detected because of their monochromaticity and directionality. A complete expression of the nonlinear susceptibility of a molecule involves a semiclassical perturbative treatment of its interaction with the electromagnetic field. For SFG, this expression can be found in several publicationslo-1392. In a more intuitive approach, we consider here the resonant second order nonlinearity as a perturbation of the molecular polarisability by a normal mode excitation such that ao,$) P(t)=(cY$+----rr -dq q(t) + . ..) &ii,(t)

where the normal notations,

mode

is driven

by the IR field,

with the conventional

(3) Ap is the population difference between the ground state and the excited state. The induced polarisability at the sum frequency is then

(4) It is therefore clear that the mode is active for SFG only and IR active. The total surface susceptibility is expressed as

if it is raman active

(5) The first term is the resonant contribution of the excited mode. It depends on the molecular coverage N and on the average molecular orientation. The second term incorporates all the other slowly varying contributions from the adsorbates or the substrate and is called nonresonant. For an optically smooth surface, the generated field can be calculated from the optical constants of the surrounding media and the lasers characteristics. The number of photons detected, S, is proportional to 17

(6) A is the average beam cross section and T is the pulse duration. First, we observe that the spectrum is affected by the nonresonant susceptibility. If it is negligible as in our case, the spectrum of an isolated resonance is essentially Second, one remarks that the damage similar to the absorbtion spectrum. threshold usually limits the visible beam energy density U&/A. The signal is then proportional to the IR peak power U&i?. As a consequence, it is advantageous to perform SFG experiment with short pulse laser sources SFG as a surface tool for vibrational spectroscopy has been explored for some years. The first attemptlo, using a nanosecond Nd-doped yttrium-aluminiumgarnet (Nd:YAlG) laser pumping an optical parametric amplifier in the 3pm range, showed a promising Sum Frequency signal from silica samples but without a succesful identification of its origin. Later, two approaches showed One of themll, synchronising a clearly the surface sensitivity of SFG. discretely tunable CO2 laser and the doubled output of a nanosecond Yag laser, showed that resonant SFG could be obtained from dyes deposited on a silica surface. This approach was not continued because of its difficulty but it has produced, up to now, the only work covering the 10pm range. The other approach12 used a picosecond Nd:YAlG laser pumping a parametric amplifier for the 3 lmi range. With SFG it has been ossible to detect and identify vibrations of adsorbed molecules on insulators B1~12,liquids23*2*, metals and semiconductors13~25, and liquid-solid interface@. At the same time, the specific selection rules of SFG have been verified and the technique has also been used to determine the orientation of adsorbates on low refractive indices materials24. For transparent material, total internal reflection can very much enhance the signa125. For materials with a large refractive index, the signals are in general easier to obtain because of the larger perpendicular surface field. On the other hand, the weaker parallel field makes the measurement of the orientation more dificult. With short laser pulses, fast surface dynamics could be followed. The first time resolved SFG experiments looked at the vibrational relaxation of adsorbatesl4815.17. Lifetime measurements are performed by a simple combination of SFG and transient bleaching. In this scheme, the surface is first excited by an intense infrared beam. This leads to a new population difference Ap for the adsorbate vibration. The SFG from a delayed pair of a weak infrared beam and a visible beam is then detected. Since the SFG signal is proportional to (ApI (Eq. 3 to 5) it gives directly the ground state recovery time. 3. OPTICAL SYSTEM In our set-up, we start from an active-passive mode-locked Nd:YAlG generating 30 ps pulses of 40 mJ at 1.064 pm at 10 Hz. 15 mJ pump a travelling-wave dye laser that uses Kodac Q-switch dyes no5 or no1 dissolved

31

in 1.2. dichloroethane. The very short fluorescence lifetime of those dyes and their low quantum yield require transverse pumping geometry and accurate synchronizationz’. The spontaneous emission from a first cell is spectrally selected by a 1200 grooves/mm grating placed at 50 cm from 100 urn slits. This sets the dye laser resolution to about a wavenumber. A second cell amplifies the beam on a transverse line focus to about 50 uJ. It is then focused by cylindrical lenses on a third tranversaly pumped cell. This last stage allows a high energy output of 500 uJ tunable fom 1.4 um to 1.2 urn using the two dyes. With only 2 cc of solution per cell and a microstirring device, the efficiency is stable for weeks thus making the dye laser a cheap and user-friendly system. Its only drawback is the poor beam quality due to the transverse pumping geometry and some thermal effects due to insutXcient stirring. This dye laser pulse is then mixed collinearly with 4 mJ of 1.064 um radiation in a AgGaS2 crystal (1 cm length). The output infrared is generated by Difference Frequency. It is tunable from 1350 cm-l to 2300 cm-l with energies ranging from 15 uJ to 70 rJ. Energies up to 300 uJ have also been obtained with 12 mJ 1.064 radiation, but the crystal shows then signs of surface damage after less than a thousand shots. The linewidth is about 2.5 cm-l limited by the Nd:YAlG linewidth, the divergence is small ( < 1 mrd) and the pulse width is around 20 ps following the variations of the pump laser. With a correctly aligned system, the power fluctuations are in the 20% range. The long term stability is limited by the pump laser. Overall this system is very satisfactory and has been running smoothly for months. The infrared is then separated into a pump and probe beam. The pump goes through a variable delay and is incident on the surface at 60” with a 400 urn beam diameter (l/2 power). The probe beam is at 50” in a 270 e diameter beam. Their energies at the sample are respectively 35 and 3 ClJ. Both beams are superimposed on a helium neon beam for alignment purposes. The visible pulse at 532 nm is obtained by doubling the 1.064 w radiation in a 1 cm KDP incident surface at 55’. crystal. the It * From the FTIRRAS ‘Measurement, the’ teak surface absorption in total internal reflection is 2.5 10-S. In our geometry, it should be 1.2 10-S. From our laser resolution and the pump energy density, we estimate that 25% of the Si:H are excited within the probe spot. This should lead to a 75% decrease in the probe SFG signal at saturation. 4. SAMPLE PREPARATION Polished silicon (111) wafers are treated to present a thin oxide layer and can be kept in distilled water for months. The last step before studying the sample is the dissolution of this thin oxide in 40% NH4F solution for 6 mn2o. This The sample is then rinsed with makes very reliably a Si(lll):H surface. distilled water and quickly introduced in a well baked UHV chamber, under Argon flow. A saphire window in a flange is used as entry and exit of the beams. The reflection losses are minimized since all beams are p-polarised and the angle of incidence is close to the Brewster angle. The chamber is slowly pumped down to 10-Z mbar with a sorption pump before opening the Slow pumping and clean conditions are valve to a turbomolecular pump. essential to the preservation of the sample. After opening the valve, the pressure in the chamber goes down to 10-a mbar in 2 hours and reaches 1 10sg

32

mbar after 16 hours. The sample is held tight, by screws and washers, in direct contact with a stainless steel reservoir . A chrome1 alumel thermocouple is set between one of the washers and the sample. For cooling, liquid nitrogen is pumped into the reservoir yielding a sample temperature of 95 K. For heating, a filament is turned on inside the reservoir and brings slowly the sample temperature to 460K. 5. RESULTS AND DISCUSSION In Fig. 1 we show the SFG spectra obtained at the three temperatures. At room temperature a calibration with a CO gas cell gives a line center of 2083.5M.35 cm-l close to the FTIRRAS value of 2083.7 cm-1 . The linewidth is 3.5M.35 cm-l . For 95 K, the linecenter shifts by 2.4M.2 cm-l while at 460K the shift is -2.9rt0.3 cm-1 . These are in agreement with the value measured by FTIRRAS of 2.6M.l cm-l and -2.7zLO.lcm-l respectively2o.

2090

2085

Frequency (cm

2080

2075

- I)

Fig. 1: SFG spectra of Si:H at 95K (dark squares), 300K (open losanges, x2.5) and 460K (dark losanges, x 8). The dashed lines are lorentsian fits used as guide for the eye. It confirms that the measured temperatures are close to the true surface temperatures even under laser illumination. Indeed, with 20 mJ/cm2 as the maximum energy density of the green beam, one can calculate that the maximum temperature rise after a laser shot is about 30K at room temperature. However the carriers lifetime is long for this passivated surface, therefore the temperature rise of the lattice should take place well after the sum-frequency process is over and it should not affect the measurement. The average green power being about 1 mW deposited over 0.5 mm2, the average heating should be completely negligible. The total linewidths are changing from 2.4f0.2 cm-l at 95K to 5.4f0.5 cm-l at 460K. The laser width is estimated at 2.5 cm-l. The main effect of this

33

linewidth variation is a large drop of the signal from 95 K to 460K since the SFG signal varies as the square of the linewidth. Lifetime: Our new results agree with our earlier data. We measure a lifetime of 9OOk80 ps at room temperature, within the error of our earlier measurement. Experimentally, we observe a signal decrease from 60 to 80% upon saturation. !I’his agrees with the estimate above. The temperature dependence of the Si-H stretch lifetime is shown in Fig.2 and Fig.3. At 95K a lifetime of 145of200 ps is measured. At 460K, the lifetime is definitely shorter, being 0.55kO.l ns.

I

-2

I

-1

0

-2

I

-1 0 Pump Delay (ns)

d

-2

-1

I

0

Fig. 2: Recovery of the SFG signal after saturation as a function of pump delay. We plot the logarithm of l-& where r is the ratio of the SFG signal with the pump off and on. It is equivalent to log( 2p(v=l) ).

2

0 0

100

200

300

Temperature

400

500

600

( K )

Fig. 3: Plot of the lifetime as a function of temperature. The dashed dotted line is for the emission of 3-bending modes at 690 cm-l. The dashed line is for a process with emission of three bending modes at 630 cm-l and a phonon at 200 cm-l.

34

The errors bars in Fig. 3 reflect several measurements. We estimate that systematic errors due to variations in the surface energy density of the pump over the 2 ns delay could artificially reduce the measured lifetime by less than 20% but leave the relative values unchanged. From the temperature dependence we can learn what mechanisms are responsible for the decay of the vibration. Because the vibrational quantum is smaller than the bandgap, electronic mechanisms are not possible. The decay must then occur via multiphonon emission. As a rule, the process with the least amount of phonons should be favored 28. The Si-H bending mode is at 637 cm-1 (q=O)299o. It is predicted to have a rather large dispersion with energies in the 600 to 700 cm-l range31ss2. Three bending modes could therefore just The temperature dependence of this make up for the 2083 cm-l needed. process will simply be 1/T1 = (l+nlXl+n2Xl+n$-nln2,n3

(7)

where n are the thermal population of the phonon of energy w n= (exp ho&T -1)-l Clearly, as shown in fig.3, the temperature dependence of this process is too weak, and it can be discarded. The next step is to introduce a Silicon phonon. Three bending plus a phonon of energy less than 250 cm-l would satisfy the energy conservation. With this restriction the temperature dependence can be accomodated only for phonons between 150 and 250 cm-l. Given the high density of surface phonons around 200 cm-l, our result is reasonable. A phonon at 200 cm-1 is also responsible for the dephasing of the stretching vibration indicating some anharmonic coupling2o. We suggest therefore that one decay mechanism for the stretching vibration could be the spontaneous emission of three bending modes around 630 cm-1 and one silicon phonon aroud 200 cm- 1. Other restrictions not considered here are symetry requirements and momentum conservation. Since the surface presents surface modes (the Lucas mode) around 500 cm-1 31*32, it is also possible that the decay occurs through 4 phonons of 520 cm-l. The temperature dependence of that process would also fit the data very well. We realize that these are only a few of the 4-phonons combinations that could explain the data and theoretical justifications will be needed. On the other hand, higher order processes would have a stronger temperature dependence and they can be ruled out. In our previous work we had evoked a few of the possible problems associated with our measurement. Indeed, theoretical calculations predicted a 20 ns lifetime 4. We should therefore look for effects that could lead to the shorter measured lifetime. One of them could be fast Treanor pumping to higher vihrationnal levels due to the high excitation density33. Subsequent relaxation would then occur through a band gap excitation leading to an artificially short lifetime. The first step in this V-V transfer would the exchange

35

(Si:H v=l) + (Si:H v=l)

--->

@i-H v=O) + @i-H v=2) + AE

Because of the bond anharmonicity, this is energetically favored (AE = -6Ocm-1 s4 1. It could be a rapid process induced by dipole-dipole coupling or phonon scattering. Its characteristic feature should be an initial decay rate inversely proportional to the excitation density, followed by a nonexponential behaviour. We have therefore performed the measurements at lower exitation density and, as shown in Fig.4, a variation of more than a factor of 2 in the excitation density does not affect the lifetime within our error bars. The data in Fig.2 and Fig.4 indicate also a single exponential decay within our accuracy. For those reasons, we feel confident that Treanor effects are not very important here. This implies that the transfer rate is slower than the relaxation rate. Theoretical estimates are however needed.

-60

Pump delay ( ns ) Fig. 4: Logarithm of Cl-&) as a function of pump delay. The pump energies are 35 p,J (open squares) and 15 CJ (filled losanges)

-40

-20

0

20

to

Pump Delay (ps) Fig. 5: Saturation at short times. The data are taken at 95K. The squares are the experimental data, the line is a fit with a 22 ps pulse and a 1.4 ns lifetime.

With our shorter pulsewidth, we can also investigate the existence of shorter For ordered systems, phonons dispersion could components of the lifetime. play an important role. Indeed, over the time scale of the dephasing T2 (> 30 ps at 95 K), we should expect that the optically induced high population of the Si-H phonon at q=O will scatter over the whole phonon branch. Because the vibrational quantum number is conserved, this will not affect our saturation measurement directly. However, phonon dispersion might then allow optical transitions between v=l and the v=2 phonons at our laser frequency. In the experiment this would show up as a fast component of the relaxation. For the Si:H stretching vibration, the theoretical dispersion of the v=l branch (~40 cm1)31,32 is less than the expected anharmonicity (= 60 cm-1P. Optical transitions

36

between the two phonons branches are therefore unlikely at our frequency This could explain why we do not observe any fast transient. Indeed, at 95 K, the linewidth is less than 0.3 cm-1 so that any decay process must be slower than 15 ps. This would be readily detectable but it is not observed as shown in Fig. 5. Dephasing: Information about dephasing times can also be obtained from transient measurements. In the SFG process, the infrared beam first excites all the SiH in a coherent manner. After some time, this coherence is lost. This can happen by dephasing (T2) and the coherence decays as exp -t/I’2 . It can also happen because of slightly different frequencies due to inhomogeneous broadening. When the green beam is incident on the surface, it samples the remaining coherence. Therefore, introducing a delay between the visible and infrared beams allows the measurement of the dephasing. The Coherent Antistokes Raman Scattering (CARS) techniques that has been widely used in the past for T2 measurements in the gas and condensed phase@@ is very similar. We have therefore performed this simple measurement at 95 K and 300K. The pump is blocked and the SFG signal from the infrared probe and the green is recorded as a function of green delay. As shown in Fig.6, the signal has a sharp rise and a slower decay given by exp-2tfT2. The time resolution is determined by the rising edge and is around 10 ps. As a consequence, the decay of the coherence is not resolved at 300 K since we know that the linewidth implies a T2 of the order of 11 ps. At 95 K, the effect of the coherence is clearly seen, indicating a decay time of 30 ps or a linewidth of 0.3 cm-l. This linewidth is larger than the extrapolated value from FTIRRAS measurement 2. and it could be due to inhomogeneity specific to our sample.

Fig. 6: SFG signal as a function infrared probe beam.

of delay between

the visible

beam and the

These simple transient measurements can be useful in some cases. For example, when the coherence can be followed over many lifetimes, they help to

37

determine the mechanism for line broadening. For narrow linewidths, they can also compete with high resolution spectroscopy. Intrinsically, however, they do not provide more information than well conceived spectroscopic measurements since they do not separate dephasing and inhomogeneity. As a remedy, for inhomogeneous lineshapes, a photon echo experiment could give access to Tz. Our system will be a good candidate for such an experiment. 6. CONCLUSION: In this work, we have measured the temperature dependence of the lifetime of the Si-H stretch vibration for the Si(lll):H surface. The lifetime varies from 1.4 ns at 95K to 0.55 ns at 460K. We suggest that the deexcitation could occur via i) emission of three bending modes and one silicon phonon around 200 cm1 or ii) four silicon surface modes around 520 cm-l. No shorter lifetime components have been observed. We have also shown that linewidths can be otained from the time-resolved dephasing of the vibration. We still can learn a lot from the study of the vibrational relaxation dynamics on this model surface. In particular, we will study the deuterated surface. Since less phonons will be required to dump the energy of the Si:D stretching vibration (-1520 cm-l), the lifetime should be much shorter. We will also probe the effects of high surface charge carrier density on the vibrational properties of Si:H for this surface. In the future, two independantly tunable lasers will allow us to investigate thoroughly the dynamics of the vibrational transfers. With improved signals, the study of the lifetime at defects could also be carried out. REFERENCES [ll B. N. J. Persson and R. Ryberg, Phys. Rev. Lett, 48 (1982) 549. [21 J. W. Gadzuk and A. C. Luntz, Surf. Science 144 (1984) 429. 133 B. N. J. Persson, F. M. Hoffman and R. Ryberg, Phys. Rev. B 34,2266 (1986). 141 J. C. Tully, Y. J. Chabal. K. Raghavachari, J. M. Bowman and R. R. Lucchese, Phys. Rev. B 31(1985) 1184. [53 R. G. Tobin, Surf. Sci. 183 (1987) 226. [63 Y. J. Chabal Surf. Sci. Reports 8 (1988) 211. 171 E. J. Heilweil, M. P. Casassa, R. R. Cavanagh and J. C. Stephenson, J. Chem. Phys. 810984) 2856. 183 E. J. Heilweil, M. P. Casassa, R. R. Cavanagh and J. C. Stephenson, J. Chem. Phys. 82 (1985) 5216. 191 E. J. Heilweil, J. C. Stephenson and R. R. Cavanagh, J. Chem. Phys. 92 (1988) 6099. [lo] H. W. K. Tom, R. H. Page and Y. R. Shen. Reported in H. W. K. Tom, Ph. D thesis, University of California, Berkeley, 1984 (unpublished). [ill X. D. Zhu, H. Suhr and Y. R. Shen, Phys. Rev. B 35 (1987) 3047. [123 J. H. Hunt, P. Guyot-Sionnest and Y. R. Shen, Chem. Phys. Lett. 133 (1987) 189. [131 A. L. Harris, C. E. Chidsey, N. J. Levinos, N. D. Loiacono, Chem. Phys. Lett. 1410987) 350. [141 A. L. Harris and N. J. Levinos, J. Chem. Phys. 90 (1989) 3878.

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