2820
J. Phys. Chem. 1992, 96, 2820-2826
(iv) This kind of heterogeneous system can be useful for some applications. Its use as a chemical sensor for the detection of gaseous oxidant has been d e v e l o ~ d ? ~Besides. in nonlinear oetics. ;mall metallic clusters of A eiectrons can give rise to a ihird harmonic generation and a nonlinear refractive index.30 (29) Henrion, L.; Derost, G.; Barraud, A.; Ruaudel-Teixier, A. Sens. Acfuators 1989, 17, 493.
Acknowledgment. This work has been partly supported by the Ministery of Research under the program on Molecular Engineering- (MRES-19881. . Registry No. [EDTTTF(SC,,),], 117701-65-2; 12, 7553-56-2; behenic acid, 112-85-6. (30) Prasad, P. N. Thin Solid Films 1987, 152, 275.
Ultrafast Charge-Transfer Dynamics at SnS2 Surfaces Joseph M. Lanzafame,**t’LR. J. Dwayne MiUer,+J Annabel A. Muenter,t.l and Bruce A. Parkinsons Department of Chemistry and Institute of Optics, University of Rochester, River Station, Rochester, New York 14627; Photographic Research Laboratories, Eastman Kodak Company, Rochester, New York 14652-2308; and Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523 (Received: September 16, 1991; In Final Form: November 22, 1991)
The carrier dynamics at dye-sensitized SnSz surfaces were studied using a variety of picosecond techniques. Fluorescence quenching studies of the rate of electron injection from adsorbed oxazine into the conduction band have determined the rate to be 3 X lo” s-I, corresponding to an electron-transfer time of 40 f 20 fs. The corresponding localization of the free carrier in the conduction band of the semiconductor is observed to occur in 1-10 ps. Picosecond pumpprobe studies of the ground-state recovery of the oxazine determine the back-electron-transferprocess to occur on the 10-ps time scale. Theoreticaljustification for the initial electron injection time scale is offered using the complete molecular Liouville equation within the Mori-Zwanzig projection operator formalism.
Introduction In recent years, there has been great interest in ultrafast electron dynamics at interfaces. Heterogeneous interfaces are of fundamental importance in the fields of solar energy and photography, and there is great interest in the mechanism of electron transfer across these interfaces. Laser technology has pushed open the time window so that carrier dynamics can be investigated at ever shorter times. With the time barrier removed, one can begin to answer fundamental questions about electron-transfer reactions: How fast can the dynamics be? What factors limit the dynamics at short times? Many researchers have developed theories to explain ultrafast electron dynamics and determine charge-transfer rates.I4 In the normal Marcus-Levich picture of electron a nuclear continuum is necessary to stabilize the charge transfer. That is, the electron tunnels resonantly from the reactant channel to the product channel followed by the resonance being broken by relaxation in the nuclear continuum of either species. This nuclear reorganization process plays a crucial role in the Marcus-Levich theory, providing the upper limit for the electron-transfer rate. For electron-transfer reactions between molecular species in solution, this treatment has been quite successful. Molecular species have a relatively simple, well-defined electronic structure with a very large continuum of nuclear degrees of freedom supplied by the reacting species and the bath. The situation is significantly different for dye-sensitized carrier injection at semiconductor surfaces. In this case, the dye is a molecular species with a discrete electronic spectrum and a continuum of nuclear degrees of freedom. The semiconductor has a quasi-continuum of electronic states, with considerable corresponding delocalization of the wave function over many electronic states. The time scale of this delocalization is that of the electronic dephasing in the conduction band, and the charge-transfer event may be stabilized not by nuclear relaxation University of Rochester.
* Eastman Kcdak Co.
Colorado State University. NSF Science and Technology Center for Photo-induced Charge Transfer
but by electronic delocalization. In the theoretical section below, a model is developed and discussed to verify this hypothesis. In recent years much work has been done in the study of ultrafast carrier dynamics at interfaces. This work includes various studies of electron injection a t dye-sensitized semiconductor surfaces using a variety of semiconductors.’22 In most instances, the surfaces studied were not atomically smooth and contained a large surface-state density so that the actual electron injection
(1) Kobayashi, T.; Takagi, Y.; Kandori, J.; Kemnitz, K.; Yoshihara, K. Chem. Phys. Lett. 1991, 180, 416. (2) Sakata, T.; Hashimoto, K.; Hiramoto, M. J. Phys. Chem. 1990, 94, 3040. (3) Charle, K. P.; Willig, F. Chem. Phys. Lett. 1978, 57, 253. (4) Suzuki, M.; Nasu, K. J . Chem. Phys. 1990, 92, 4576. (5) Hush, N. S. J . Chem. Phys. 1958, 28, 962. (6) Marcus, R. Faraday Discuss. Chem. SOC.1982, 74, 7. (7) Marcus, R.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265. (8) Marcus, R. J . Phys. Chem. 1990, 94, 1050. (9) Hashimoto, K.; Hiramoto, M.; Kajiwara, T.; Sakata, T. J . Phys. Chem. 1988, 92, 4636. (10) Kemnitz, K.; Nakahima, N.; Yoshihara, K.; Matsunami, H. J . Phys. Chem. 1989, 93, 6704. (1 1) Hashimoto, K.; Hiramoto, M.; Sakata, T. J . Phys. Chem. 1988, 92, 4272. (12) Hashimoto, K.; Hiramoto, M.; Lever, A. B. P.; Sakata, T. J . Phys. Chem. 1988, 92, 1016. (13) Itoh, K.; Chiyokawa, Y.; Nakao, M.; Honda, K. J. Am. Chem. SOC. 1984, 106, 1620. (14) Nakashima, N.; Yoshihara, K.; Willig, F. J . Chem. Phys. 1980, 73, 3553. (15) Liang, Y.; Ponte Goncalves, A. M.; Negus, D. K. J . Phys. Chem. 1983, 87, 1. (16) Liang, Y.; Ponte Goncalves, A. M. J . Phys. Chem. 1985, 89, 3290. (17) Crackel, R. L.; Struve, W. S. Chem. Phys. Lett. 1985, 120, 473. (18) Kamat, P. V.;Chauvet, J. P.; Fessenden, R. W. J . Phys. Chem. 1986, 90, 1389. (19) Spitler, M.; Parkinson, B. A. Longmuir 1986, 2, 549. (20) Willig. F.; Eichberger, R.; Sundrasen, N. S.; Parkinson, B. A. J . Am. Chem. SOC.1990, 112, 2702. (21) Eichberger, R.; Willig, F. Chem. Phys. 1990, 141, 1S9. (22) Lanzafame, J. M.; Min, L.; Miller, R. J. D.; Muenter, A. A,; Parkinson, B. Mol. Crysf. Liq. Cryst. 1991, 194, 287.
0022-365419212096-2820%03.00/0 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 2821
Ultrafast Charge-Transfer Dynamics at SnS, Surfaces
"i
6i
I
NUMBER OFSTATES
5
w
E c i
-1
0
Nanometers Figure 1. STM image of SnS,. The raw image has been low-pass filtered to remove frequency components corresponding to distances below the instrument resolution. Notice the near perfect surface construction, STM images have found the surfaces to be atomically flat over regions as large as 10000 A2.
could not be completely isolated from the problems of surface nonuniformity and the influence of surface states. In an attempt to answer the fundamental questions about electron-transfer mechanisms, a search was made for an ideal system with very fast dynamics with as few chemical complications as possible. The system chosen for these studies was dye-sensitized SnS2 Various researchers have that SnS2 has excellent surface properties. SnS, is a flat, atomically smooth (over greater than 10OOO A2) semiconductor whose surface contains few surface states (see Figure 1) and terminates with a plane of nonbonding orbitals. This surface quality allows for strong coupling between the sensitizing agent and the semiconductor without the complication of surface-state processes interfering with the direct electron injection. SnS2 exhibits a strong proclivity to adsorbdyes onto its surface, observable as a significant red shift in the Asorption, photocurrent, and emission spectra. The bandgap of SnS2 is sufficiently large, 2.2 eV, so that dyes can be easily found that have a first excited singlet state transition that is lower in energy than the band transition of the semiconductor and whose first excited state is above the conduction band edge. These properties allow exclusive excitation of the dyesensitizing agent whose singlet state is isoenergetic with the electronic states of the conduction band. The dye chosen as the sensitizing agent for the studies presented here was oxazine 1. Oxazine 1 has negligible dimer formation even at fairly high concentration^.^^ Minimization of dimer formation is important for the near-monolayer coverages to be studied here, since energy transfer to dimers complicates the analysis of the kinetics. Furthermore, the oxazine ground state is midgap in energy, and its first singlet state is approximately 0.35 eV above the conduction band edge (based on the first reduction potential of oxazine in solution;23see Figure 2B). The adsorbed oxazine is only partially solvated, and hence the system energetics may have shifted somewhat; however, one would expect no more than a 0.1-eV shift relative to vacuum and, therefore, the electron transfer should still be occurring under barrierless conditions. Theory A theoretical model was developed using the complete molecular Liouville equation and the Mori-Zwanzig projection operator (23) Parkinson, B. A. Langmuir 1988, 4, 967. (24) Seilmeier, A.; Scherer, P. 0. J.; Kaiser, W. Chem. Phys. Lett. 1984, 105, 140.
VB
I
to derive the rate equation for the electron transfer. The system is modeled as a single electronic level in the dye half space (the states denoted by k in space /3) and a dense quasicontinuum of states in the semiconductor half-space (denoted by j in space a). We can then write the combined Hamiltonian (within the rotating wave approximation) in the time-independent form
H = cpa)EjauaI + Ik/3)EkB(k@I+ c(ia)Tf(k@I(1) ia
ia
are the energies of the dye states and the where Eja and conduction band states and v*& is the coupling between the dye state k@ and the conduction Land electronic states ja. The state of the system at any time t is given by the complete molecular density matrix p(t). This density matrix satisfies the Liouville equation, given by dp/dt = -i[H,p] = -iLp
(2)
where L (L = + L') is the Liouville operator which corresponds to the commutation operation of H with the operand. The density matrix contains the complete information regarding the state of the system at any time. Not all of this information is necessary, much of it is redundant or superfluous. In this case, the only pertinent information is the relative population of the dye and conduction band electronic states. Therefore, to derive the reduced equations of motion for these populations, we construct (25) Zwanzig, R. Physica (Cltrecht) 1964, 30, 1109. (26) Tokuyama, M.; Mori, H. Prog. Theor. Phys. 1976,55,411. (27) Mukamel, S. J . Chem. Phys. 1979, 71, 2012.
2822 The Journal of Physical Chemistry, Vol. 96, No. 7, 1992
the following set of orthonormal molecular operators: (3)
where d, is the number of states in the space 4, and the summation over i goes from 1 to N , N being the total number of electronic levels considered in the spaces a and 0 ( N for a, 1 for 0). The choice of semiconductor states considered is important since it will be reflected in the resulting equation of motion. Only states physically relevant should be considered as will be shown below. The density matrix can now be expanded as
+ P'
At) = Cu,(f)A,, 4
4J = a,P
Lanzafame et al. realistic and give a qualitative understanding of the real physics of the system. We now construct the second order terms of (R(t - 7 ) ) , which are given by
where cc refers to the complex conjugate, and
(5)
where u,(t) are complex numbers corresponding to the Tr [A*,,p(t)] and where p' is constructed orthogonal to A?,. The density matrix is now effectively partitioned into diagonal ( X , U , ( ( ) A , ~ )and off-diagonal (p') elements. At this point, we have effectively reduced the total information to only the relevant information, the populations of the various levels given by P,, where
This can also be written 1
(Rhf,,,p,(t - 7 ) ) = --
Vo2exp[iwkj(t - T)] -t cc (19)
(RL2Jf - 7 ) ) = (l/da) C Vo2exp[iwkj(t - 7)] j,k=l
The Zwanzig-Mori projection operator technique can now be employed to derive the reduced equations of motion for the populations. The vector u whose components are ua, up is now introduced along with the Mori projection operator, P, whose action on operator X is given by:
px E CA//(A,/JX)
We now assume that the semiconductor quasi-continuum is dense enough to be considered a real continuum (a fair approximation at room temperature) and replace the summation over levels with an integration with respect to energy. That is
p(Ej) = da/26
and its complement, Q, given by Q = 1 - P. We now have
wkj
P d t ) = C%$(t)A,,
(8)
4
The Mori-Zwanzig formalism gives exactly the closed reduced equation of motion for our population vector u (for any choice of P):
$ofd7 ( R ( t - 7))u(7)
(9)
The operator R(t - 7) is a tetradic operator (as is L ) given by R(t - 7) = L exp[-iQL(t - 7 ) ] Q L (10) (L)aa,fis
(20)
(7)
/
du/dt = -i(L)u -
+ cc
= Tr (A*aaLA,&
( R ( t - 7))aa,bp = Tr [A*aaR(t- 7)AppI
/h
= (Ek -
(22) (23)
With the equations in this form, integration is trivial. The integral is simply 2rhp(Ej)G(t - 7), the 6 function indicating that the transfer is fast relative to the shift in population. The rate expression, exact to second order in the coupling, can now be calculated by putting eq 21 into eq 13 and using eq 6 to relate the vector u to the actual population. This gives the following expression: dPa/dt = (Vo2rhda/6)l'6(t - 7) Pp(7) d7 0
(24)
(11)
The complex conjugate contributes equally, and the result can then be reformulated as
(12)
dPa/dt = 8V02rhp(a)Pp(t)
(25)
For our particular projection P, PLP = 0, indicating that there is no net change in the total population of the system. R(t - 7) can be expanded in power series in QL'(see ref 27) and only the even powers in QL' are nonzero, and we thus write
This can be considered as a simple rate equation where the rate of oing from space 0to space a to second order in the coupling, kif, is given by
du/dt = -surd' ( R ( t - 7))u(7)
The higher order terms (Rc4),R@),...) can also be constructed. However, within the random phase approximati0n,2~>*~ they cancel and so the above expression is exact to second order. The random phase approximation is a generally good approximation for systems with a high number of states and in this particular instance is an excellent assumption once we consider the quasi-continuum of the semiconductor sufficiently dense to be approximated by a true continuum. When the electron resonantly tunnels across the interface into the very large electronic phase space of the semiconductor, it samples the whole quasi-continuum of the conduction band on the time scale of the electronic dephasing time (10-50 fs for
( R ( t - 7 ) ) = (Rc2)(t- 7 ) )
+ ( R ( 4 ) (-t
(13)
+ ...
(14) At this point, it becomes necessary to introduce a model for the electronic states and the coupling. For illustrative purposes only, we choose a very simple model for the system. The coupling between the dye state and all relevant semiconductor states is assumed to be constant, Vo. This is not a bad assumption as long as we limit the energy spread of the semiconductor electronic states considered. Setting the SI state of the dye as the origin, we consider only the semiconductor states between -6 and 6 (see Figure 2A), and we consider the density of these states to be isotropic over this range. If one considers this range as corresponding to the full width at half-maximum of the Gerischer curve of the dye and takes this range to lie well above the conduction band edge of the semiconductor, these assumptions are not un7))
kLy = 8rh Vo2p(a)
(26)
(28) Mayer, J . E.; Mayer, M . G. Sfatistical Mechanics, 2nd ed.; Wiley: New York, 1977; Chapter 13. (29) Feynman, R. P. Statistical Mechanics; W. A. Benjamin: Reading, M A , 1972; Chapter 9.
Ultrafast Charge-Transfer Dynamics at SnS, Surfaces semiconductors) and breaks the resonance with the electronic state of the dye. At this point the electron is localized in the semiconductor half-space and, because of the very large density of states mismatch between the semiconductor and the dye half space, the electron has no recurrence time with the transferring level of the dye. Examining the result more carefully, it can be noted that the solution is directly analogous to Fermi's Golden Rule. The transfer rate depends only on the electronic density of states and the electronic coupling. These conditions are sufficient for the propagation of the electron into the semiconductor and separation from the initial molecular site. Further, it is not necessary to invoke the nuclear degrees of freedom of the system to stabilize the charge-transfer event since the transfer results in delocalization of the electronic wavefunction over the conduction band on the sub-50-fs time scale of the electronic dephasing. In a normal Marcus approach, the relaxation of the nuclear degrees of freedom, both intramolecular and intermolecular, is the rate-limiting step in an electron-transfer event-on the order of 100 fs for most molecular The electron dephasing described above is significantly faster than typical nuclear relaxation processes and the limit for the electron transfer is now the electron dephasing time of the semiconductor (as fast as 10 fs). We believe the assumptions made in the derivation of this expression (random phase approximation, rotating wave approximation, constant coupling assumption, continuum approximation) are reasonable for the system of interest and justify the final expression.
Experimental Procedures Sample preparation was accomplished as described previously.22 The SnS, samples were freshly cleaved by placing cellophane tape on the surface and slowly pulling it back to remove the top layer. The freshly exposed surface was then sensitized by placing one drop of the oxazine solution onto it, allowing it to sit for 60 s, and then blotting the solution with lens paper. The oxazine solutions used were of three different concentrations: 3.6 X lo4, 1.8 X and 4.95 X lo-' M. After sensitization, the absorption spectrum of the dye on the surface was taken to determine the concentration of the dye on the surface and check for the presence of dimers using a Perkin-Elmer Lambda 9 spectrometer with an integrating sphere to collect any scattered light. The concentrations of dye on the surface were reproducible for the different solutions and were qualitatively, though not quantitatively, related to the concentration of the solution. The SnS, samples were grown using the procedure discussed p r e v i o ~ s l y .The ~ ~ SnS, samples were of two varieties: an unintentionally doped sample with a low donor concentration (less than lOI5 ~ m - and ~ ) a low As-doped sample (donor concentration of 1OI7~ m - ~ ) . The fluorescence quenching of the dye on the semiconductor surface was determined using two methods. First the quenching was estimated by taking the fluorescence spectrum using a Spex Fluorolog I1 spectrofluorimeter, equipped with double monochromators in both excitation and emission channels, and comparing the fluorescence of the dye sensitized semiconductor to that of a reference. The reference used was oxazine adsorbed on 3M Magic tape. The oxazine on the tape had an absorptivity similar to that of the oxazine on the semiconductor. The quenching rate was determined more accurately by using time-correlated single-photon counting to take advantage of its greater sensitivity and lower background noise. The excitation laser was a Coherent 7200 series cavity-dumped dye laser with pyridine 1 as the gain medium. The dye laser was synchronously pumped by 750 mW of doubled Nd:YAG (532 nm). The tape samples were excited with 5-nJ, 668-nm pulses at 1.9 MHz with a 1-mm spot size. The SnS, samples were excited using IO-nJ, 685-nm pulses at 1.9 MHz with a 1-mm spot size as well. The
The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 2823
CW Modelocked Nd:YLF Laser
I
I
I-l-Z-fl I
t
I
I
Hybridly Modelocked Cavity-dumped dye laser
I
A t 4
Figure 3. One-color pump-probe setup. The beam splitters (BSI, BS2) are both 70% transmissive. The setup allows for differential data collection in both transmission (trans) and reflection (ref). The dye laser puts out I-ps pulses with 30 nJ of energy at repetition rates from 1 MHz down to 1 kHz. The A 0 stabilizer is a Liconix Model 50SA power stabilizer which keeps the amplitude fluctuations of the laser to less than 1%. Galva represent the rapid scanning galvanometer delay line, PD represents the Si photodiodes, and the Diff Amp is a Tektronix A M 502 differential amplifier.
fluorescence from these samples was collected using a 0.25-m monochromator with 0.3-mm slits and a Hamamatsu 6-pm microchannel plate R2809-1 l photocathode. For the semiconductor samples a Hoya Optics R-72 infrared passing filter was placed over the collection lens to filter out the 685-nm pump. The instrument response time was 40 ps. Fluorescence decay curves were taken both before and after adsorbing dye, the background decay curves subtracted, and the curves fit using a multivariable exponential fitting routine. These results will be discussed further below. To better determine the actual carrier dynamics, however, a direct time-domain measurement was performed. This was initiated using one-color pump-probe spectroscopy to follow the dye ground-state recovery and free camer dynamics. The experimental setup is shown in Figure 3. The laser used was a hybridly mode-locked, cavity-dumped, synchronously pumped dye laser using pyridine 1 as the gain medium and DTDCI (Exciton) as the saturable absorber. The dye laser was pumped by the KTP doubled pulses from a continuous-wave, mode-locked Nd:YLF laser equipped with a Liconix Model 50SA power stabilizer which keeps the amplitude fluctuations of the IR to less than 0.5%. The dye laser provided 1-ps pulses at repetition rates from 1 MHz down to 10 kHz with an energy of 30 nJ/pulse. These pulses were focused to 75 km using an 8-cm focal length lens with a 1' angle between pump and probe pulses. Since the wavelength of the laser is below the bandgap, the probe can be detected in transmission as well as reflection. While the time resolution should not be sufficient to resolve the electron injection itself, other important dynamical considerations exist. This study was conducted to i'ollow the carrier relaxation and recombination of the electrons in the semiconductor and the ground-state recovery of the oxazine. To achieve the highest possible signal-to-noise ratio, a rapid scanning g a l ~ a n o m e t e was r ~ ~ employed as the optical delay line
2824 The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 for the probe. The galvanometer provided a 100-ps delay at 20 Hz; data were collected in only one direction of the delay. Splitting the probe pulse into a probe and reference pulse pair allowed for the use of differential detection using a Tektronix Model AM502 differential amplifier and a DT-2821 data translation board interfaced to an IBM PC. This allowed for data collection at up to 150 kHz. This data collection scheme provided for high signal-to-noise ratio detection of fairly small modulations of the probe (1 part in IO6). Studies of free carriers generated directly in the semiconductor were undertaken using the transient grating t e c h n i q ~ e . ~The ~-~~ laser used was a 500-H~Q-switched, mode-locked Nd:YAG laser with a Pockel's cell to select a single pulse from the Q-switch pulse train. The YAG fundamental (1.064 pm) was doubled using CD*A as the nonlinear crystal, and the 532-nm pulses were used as the excitation arms of the grating (loo angle between the two excitation pulses) and the fundamental served as the probe. The pulse width was 100 ps, and the pulse energies were attenuated to 10 nJ in the green and 2 pJ at the fundamental. The pump and probe pulses were both focused to 200 pm, corresponding to an excitation of 5 X i0l2 photocarriers/cm2. The probe was brought in to the sample at the Bragg angle, and the diffracted pulse from the probe detected using silicon photodiodes. The excitation was modulated using a mechanical chopper at 250 Hz, and detection achieved using a lock-in amplifier with a 300-ms time constant at this frequency. The signal from the lock-in was sent to an X-Y recorder and a DT-2801-A A/D board in an Everex 286/16 computer.
Results and Discussion Previously, it has been shown that oxazine-sensitized SnS2 exhibits an unusually large quantum yield for dye-sensitized photocurrent. Typically, quantum yields for photocurrent for dye-sensitized single-crystal oxide semiconductors are on the order of 3%/absorbed photon. The low quantum yields have been attributed to weak electronic coupling or rapid back-electrontransfer processes which limit the injection efficiency. In contrast, the quantum yield for electron transfer and collected current is greater than 80 percent at SnS2surfaces.23 This high efficiency has been attributed to the surface quality as discussed above. The lack of an insulating layer on the surface and the preferential adsorption suggest that the observed high quantum efficiency for electron transfer arises from strong electronic coupling between the dye and the surface leading to fast electron transfer (faster than the back reaction). However, one would like to measure both the forward and backward electron-transfer rate constants to fully understand the reasons behind the high quantum yield. To study the forward transfer rate, the excited-state lifetime of oxazine was studied using fluorescence quenching. The fluorescence spectra of oxazine on SnS2show strong quenching when compared to the oxazine on tape reference, as shown in Figure 4A. When excited at 640 nm, the sensitized SnS2showed very weak fluorescence with a spectrum similar to the oxazine on tape. This indicates that this fluorescence originates from molecules not strongly coupled to the surface, since the red shift in the emission spectrum associated with surface adsorption is not present. However, when the oxazine is excited near the absorption maximum for the adsorbed dye (680 nm), no fluorescence above the scattered light background was observed. This observation leads to the determination of a lower limit to the fluorescence quenching of at least lo3. Time-correlated single-photon-counting experiments were performed in order to better determine the fluorescence quenching ratio, by reducing the background scatter. The fluorescence decay (32) Edelstein, D. C.; Romney, R. B.; Scheuermann, M. Rev. Sci. Instrum.
-. 62. --. -519.
-1991.
(33) Eichler, H. J. Loser-induced Dynamic Gratings; Springer-Verlag:
Germanv. - ~ ~ ,, ~ 1986. ~-. -~ -
. . ~
(34) Kasinski, J . J.; Gomez-Jahn, L. A.; Faran, K. J.; Gracewski, S . M.; Miller, R. J. D. J . Chem. Phys. 1989, 90, 1253. (35) Gomez-Jahn, L. A,; Miller, R. J. D., submitted to J . Chem. Phys.
Lanzafame et al. 106
q 3
A
x
0
I
100
2 TIME (ns)
4
Figure 4. Fluorescence quenching data. (A) Emission spectra of the adsorbed oxazine. The long dashed spectrum is oxazine on tape, the solid line is the spectrum of sensitized SnS2 when excited at 640 nm, and the short dashed spectrum is sensitized SnSzexcited at 680 nm. On the basis of these data, the quenching ratio was determined to be greater than lo3. (B)Single-photon-counting studies of the oxazine emission. The upper decay curve is for oxazine on tape, the lower decay curve is oxazine on SnS, (multiplied by 125). This demonstrates the quenching to be (9 i 5 ) X lo4 corresponding to an excited-state lifetime of 40 i 20 fs.
curve is shown in Figure 4B. The decays of the oxazine on tape samples were fit to a single-exponential decay with a 2.6 f 0.1 ns lifetime. The decay curves for the dye sensitized semiconductor are more complex and were fit to two exponentials: an instrument response limited decay of 40 ps, and a longer decay of 900 f 100 PS. The longer decay shows a concentration dependent intensity and virtually disappears at low coverages. In the decay curve shown here it is only 1% of the integrated intensity of the entire curve. This component is ascribed to the dye molecules which are either weakly adsorbed or not strongly coupled electronically to the surface, corresponding to those observed in the fluorescence spectrum of the dye-sensitized SnS, excited at 640 nm as noted above. These dye molecules are most likely isolated from the surface by intervening dye molecules due to the formation of aggregates or microcrystals of dye, uncoupled surface sites, or because they are simply poorly coupled due to orientational effects. The instrument response limited decay is attributed to the fluorescence from adsorbed molecules strongly coupled to the surface, indicating that the electron injection rate is faster than 40 ps. To better determine the exact electron injection rate, the integrated intensity of the fluorescence was studied. The integrated intensities of the fast components of the sensitized semiconductor decay curves were compared to the intensities of the oxazine on tape reference samples. The intensity was then corrected for the absorbance of the dye at the excitation wavelength, the transmission of the filters used, multichannel plate sensitivity, and laser pulse energy. This calculation yielded a quenching factor of (9 f 5 ) X lo4. These values are constant for the three concentrations studied. Assuming electron injection is the only new nonradiative channel in the semiconductor samples, the value for the quenching yields an electron injection rate of 3 X corresponding to an electron-transfer time of 40 f 20 fs. Having hypothesized that the coupling between dye and semiconductor is very strong and having measured such strong fluorescence quenching, we need to consider whether or not we are exciting the S, state of the dye directly. It would seem possible
Ultrafast Charge-Transfer Dynamics at SnS2 Surfaces
The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 2825 1.2,
‘OI
I
-1.4 -10
-2
0
’
10
20
TIME
Figure 5. Representative reflective pumpprobe studies of sensitized intrinsically doped SnS2. The data were taken at 667 nm using a 5.5-nJ pump and 250-pJ probe at 250 kHz. The decay has been ascribed to the
ground-state recovery of the adsorbed oxazine. The decay is nonexponential with a fast (approximately 10 ps) decay and a longer decay of several hundred picoseconds. The relative magnitude of the longer decay varies with the position of the surface being probed. that we were directly exciting a continuum analogue of a charge-transfer complex. However, since the absorption spectrum of the dye on the semiconductor retains its vibronic structure, a state localized in the dye is indicated. Furthermore, no new charge-transfer band appears in the absorption spectrum. The fluorescence quenching studies were carried out on the unintentionally doped SnS2samples exclusively. Doped samples are prone to the formation of intense surface space charge fields. These surface fields assist electron separation from the parent cation. While this serves to aid in the quantum yield of electron injection, it also creates a barrier to ground-state recovery leading to an effective bleaching of the ground state absorption and therefore a reduction in observed emission. Consequently, knowledge of the time scale of the ground-state recovery is important for verifying that the fluorescence quenching results are not distorted by bleaching of the ground state. Further, the ground-state recovery reflects the back electron transfer which is important for determining the overall photocurrent yield. To prevent bulk dynamics from interfering with the detection of the surface dynamics, the ground-state recovery was studied in reflection (see Figure 3) using one-color pumpprobe spectroscopy. This eliminates the effective integration of bulk phenomenon by the entire crystal length by probing only the surface region. Representative results are shown in Figure 5 for an unintentionally doped sample. This signal appears only when the SnSzis sensitized. In situ cleaving of the surface layer eliminates the signal completely, and subsequent resensitizing restores it. Consequently, it is reasonable to assign the signal to the bleaching of the ground-state absorption of the dye by the pump and the decay to the ground-state recovery. The observed signal has two features of note. The dominant feature of the signal is a very fast, approximately 10 ps, decay which appears to be the dominant recovery time. However, there is also a longer decay of several hundred picoseconds whose magnitude relative to the fast decay is generally small and varies, disappearing completely in many cases, as different positions on the surface are studied. The most logical explanation for this observation is that the fast decay is due to the ground-state recovery of the strongly coupled dye molecules and that the longer component is due to the ground-state recovery of less strongly coupled dye molecules. These less strongly coupled molecules may be correlated to the long 900-ps decay observed in the fluorescence quenching studies as well as the fluorescence spectra for the oxazine on SnS2 pumped at 640 nm. This result demonstrates conclusively that ground-state bleaching is not a problem in the fluorescence quenching experiments discussed above. If the unidirectional charge transfer is so strongly favored by the density of states mismatch as discussed in the theory section above, how does the electron tunnel from the conduction band
40 (ps)
60
80
Figure 6. Transmission pump-probe studies of doped and intrinsic SnS,.
The single line corresponds to the intrinsic semiconductor (left axis), the double line is the low As doped SnS, (right axis). Notice the two components of opposite sign, the initial increase in absorption of the probe convolved with the longer lived decrease in absorption. The intrinsic scan was achieved at 690 nm using IO-nJ pump with a 3-nJ probe. The As doped sample was studied at 690 nm using a 3.2-nJ pump with a 1-nJ probe. The pulse repetition rate for both samples was 250 kHz. Notice the order of magnitude difference in signal intensity between the intrinsic and As doped samples. back to the parent cation of the dye molecule on the surface? The most likely answer lies in the rapid relocalization of the electronic wave function after the initial forward transfer and delocalization. If the wave function is delocalized over all the available electronic states of the conduction band, an acceptor on the surface would look l i e the eye of a needle to a camel: there would not be enough driving force to localize the electronic wave function on the molecular acceptor. This difficulty is likely overcome by the various fields present both in the bulk and especially at the surface. The fields in the crystal and the scattering they cause reduce the “camel’s” size by localizing the electronic wave function. Further, the surface fields give rise to space charge quantization of the conduction band quasi-continuum which would reduce the density of states mismatch. Evidence of rapid localization phenomenon has been observed, as discussed below. Studies of the SnS, bulk carrier dynamics were undertaken, in the absence of dye, using one color pump-probe spectroscopy in the transmission configuration. Representative results for an unintentionally doped sample are shown in Figure 6. These samples show a signal composed of two component modulations opposite in sign. There is an initial decrease in transmission of the probe (approximately 1 part in lo5modulation of the probe) followed by an increase in transmission. These signals are ascribed to bulk processes since the same samples studied in reflection showed no equivalent signal. The states being probed are most likely generated by impurity absorption. To test the impurity absorption assignment of the signal, a low As doped sample was studied (Figure 6). The doping process is expected to lead to a higher concentration of bulk defects due to strain or dislocation defects in the lattice as well as defects associated with the As itself. In fact, the signal was over an order of magnitude larger (approximately 1 part in lo4 modulation) for the doped versus the unintentionally doped semiconductor for crystals of approximately the same thickness. A power dependence of the signal demonstrated that the signal was linear in power, ruling out two-photon processes. The signal level itself relative to the intrinsically doped sample supports the assignment of the signal to impurity absorption. As was the case with the intrinsically doped samples, the observed signal from the As-doped sample appears to be the convolution of two processes. There is an initial pulse width limited (1 ps) increase in absorption following the optical ionization of the impurities which decays within the pulse width. This increased absorption should be assigned to new absorption bands originating from the initially prepared states, i.e., the ionized impurity level and the free carriers. This signal is convolved with a modulation
Lanzafame et al.
2826 The Journal of Physical Chemistry, Vol. 96, No. 7, 1992
in the intrinsically doped SnS,, accounting for the short lifetime of the free carriers. In the dye-sensitized SnS,, this fast localization allows for the rapid recovery of the ground state of the dye by back transfer of the injected electrons to the parent cation of the oxazine. Conclusions
$ 1
li
‘t I \ 0
1
2
TIME (ns)
Figure 7. Transient grating data. This shows that the carrier lifetime at the surface is less than 30 ps, after deconvolution of the pulse width. The excitation intensity (532 nm) corresponded to 5 X 10l2generated photocarriers/cm*with a fringe spacing of 3 pm.
of the probe opposite in sign (decreased absorption) that is postulated to arise from the bleaching of the impurity absorption. The impurity absorption is seen to recover in approximately 200 ps. The free carrier signal has a much shorter carrier lifetime than might normally be expected and suggests that the generated carrier’s wave function is quickly localized. These rapid localization processes suggest that there are more bulk defects than initially presumed. Normally, SnSzis considered to be essentially defect free. The two-dimensional structure of the semiconductor along with the fact that it is macroscopically constructed in thin sheets leaves open the possibility of strain defects in the layers and the possibility of two-dimensional confiiement of the electronic wave function. In addition, the ionic nature of the semiconductor may serve as a localizing potential. To further investigate the carrier relaxation dynamics, surface grating studies were conducted. In these experiments, the excitation pulses were deliberately chosen to be above bandgap in order to directly generate electron-hole pairs in the surface region of the unintentionally doped SnSz sample. The 532-nm excitation pulses were crossed forming a grating image on the surface corresponding to the interference pattern of the light. A below bandgap probe pulse was diffracted off the grating which monitors the time evolution of the grating image. The results are shown in Figure 7. A pulse width limited decay of the grating is observed corresponding to a carrier recombination time of less than 30 ps after deconvolution. This decay is too fast to be attributed to surface state recombination which requires spatial diffusion of the carriers to the surface. This result supports the assignment of the free carrier signal in the pump-probe experiment and demonstrates that there exist very fast carrier localization dynamics
The fluorescence quenching studies allow us to conclude that the electron injection from the oxazine 1 SI level into the conduction band of the SnS, occurs in 40 f 20 fs, corresponding to an injection rate of approximately 3 x Using one-color reflective pump-probe spectroscopy, we have observed the ground-state recovery of the oxazine 1 to be quite fast, approximately 10 ps (although there appears to be a distribution of recovery times), demonstrating that there are some very fast electron localization processes occurring in the semiconductor. The fact that the ground state recovers rapidly offers further support to the assignment of the fluorescence quenching to electron injection exclusively, eliminating bleaching of the ground state as an explanation for the low fluorescence yield of the oxazine sensitized SnS,. Using one-color pump-probe spectroscopy in transmission, we have observed subpicosecond bulk carrier dynamics in SnS,, suggesting strongly wave function localizing fields in the SnS,. The overall dynamical picture obtained from these studies is one of a 40-fs electron transfer followed by rapid localization which assists the back electron-transfer process. The back transfer rate is slower than the forward rate but still quite fast with a distribution of recovery times ranging from 10 to several hundred picoseconds with most of the oxazine molecules recovering in 10 ps. A forward electron-transfer rate of this magnitude can be justified theoretically, using a simple constant coupling model in the complete molecular Liouville equation within the MoriZwanzig projection operator formalism. This model, while simplistic in its treatment of the coupling, is physically reasonable and yields an injection rate depending only on the coupling and the density of states of the semiconductor. There is no need to invoke nuclear relaxation to stabilize charge transfer and the fundamental limit on interfacial charge transfer at semiconductor surfaces is the dephasing time of the electronic wave function in the conduction band. It should be noted that while the forward transfer reaction requires only dephasing of the electron wave function and no energy relaxation, the back electron transfer requires relaxation to localize the wave function and break the resonance with the conduction band electronic states.
Acknowledgment. We acknowledge Shaul Mukamel for many insightful discussions with respect to the theory. R.J.D.M. acknowledges support through an A. P. Sloan Fellowship, a Camille and Henry Dreyfus Teacher-Scholar Award, and a NSF Presidential Young Investigator Award. J.M.L. acknowledges a Laboratory for Laser Energetics Fellowship for partial support. This work was supported by the NSF Science and Technology Center for Photo-induced Charge Transfer, Grant CHE-88 10024. Registry No. S2Sn, 1315-01-1; oxazine, 11084-05-2.
