J . Phys. Chem. 1993, 97, 2-4
2
LETTERS Picosecond Spectroscopy of Excited States Based on Nonlinear Electron Photoemission A. Durandin,+T.-M. Liu, M. Pope,' S.-C. Sheu, and N. E. Geacintov Chemistry Department and Radiation and Solid State University, New York University, 29 Washington Place, New York,New York 10003 Received: June 9, 1992; In Final Form: November 12, 1992
A new general method was developed suitable for measuring the lifetime of excited states in the condensed phase. This method is based on a multistep photoemission process in which the decay of an excited state generated by one pulse is measured by the use of a delayed probe pulse. The effective lifetime of a chargetransfer exciton state in tetracene was measured to be -20 ps.
Photoemission of electrons from a condensed phase can occur even when the absorbed photon energy is lower than the ionization potential of that phase. In such cases, the mechanisms of photoionization may involve interactions between excited states or excited state-photon absorption phenomena, giving rise to superlinear intensity dependences of photoelectron yields. In general, it is difficult to identify the excited states which serve as intermediates in second or higher order photoionization processes, particularly if their lifetimes are in the subnanosecond range. We have developed a new general method for measuring picosecond lifetimes of transient electronically excited states in the condensed phase, and the same method can be used to measure subpicosecond lifetimes. This method is based on a multistep photoemission process in which the rate of decay of an excited state generated by a first pulse is measured by the use of a second (probe) pulse. We have used crystalline tetracene as a model system, and our provisional conclusion is that we have observed a charge-transfer state with an energy of 2.9 eV and an effective lifetime of -20 ps in the surface region ( N 15 A) of the crystal. Photoemission occurs via a single-photon ionization of this CT state. Photoemission in organic molecular crystals is competitive in rate with that of decay from higher excited states to lower excited states within'a molecular manifold. These rates can be in the subpicosecond range.' Tetracene is of interest because it has been well-studied, can be obtained in pure form, has a low fluorescence efficiency* (which makes it a good candidate for a nonfluorescence technique), and has a charge-transfer (CT) state3 whose lifetime has never been measured. In this paper, we show that using a multistep process for producing photoemission, it is possible to measure lifetimes. The experimental technique involves the use of our modified Millikan ~ h a m b e rin, ~which a small crystal ( 4 0 - p m diameter) of tetracene is suspended in nitrogen at 1 atm of pressure. The suspended crystal is negatively charged initially, and the loss of that chargeas a result of photoemission is the measured quantity. By measuring the rate of the loss of charge, the emission photocurrent is deduced. We measure the loss of charge by recording the field strength that is required to balance the crystallite against the force of gravity.4 In a typical experiment, a suspended crystallite is excited by the first light pulse beam consisting of the 15 pulses/s, 355-nm
' Visiting from Instituteof Physical Energetics, Latvian AcademyofScience, Riga, Latvia.
harmonic of a YAG laser (20-ps fwhm as measured using a pentacene crystal as a detector, to be described more fully in another paper), and subsequently by a suitably delayed probe pulse derived from the same beam. In the present case, the wavelengths of the primary and probe beams were the same. The rate of decay of the population of excited states created by the first beam is probed by the delayed second beam, which interacts with the surviving excited states to produce photoemission. In the present case, the primary beam itself produces photoemission by a multistep process so it is necessary to sort out the contributions from each beam. The mechanism of the photoemission process is deduced by measuring the maximum kinetic energy (KEmax)of the escaping electrons and by measuring the light intensity (I)dependence of the photoemission current (Y). As an example, if the photoemission process depended on the cube of the light intensity, i.e., Y LZ P, then at coincidence of the primary and probe beams of equal intensity, the light intensity would be doubled, and the yield would be 4 times greater than that produced by the sum of the yields when the primary and secondary beams do not produce overlapping excited-state populations. In general, if beams of equal intensity and energy are used, then the ratio YmJYmin = 2"-', where YmaX, Ymin, and n are respectively the maximum and minimum photoemission yields and the calculated intensity dependence of the photoemission. This relationship holds only when each beam produces photoemission. The ionization energy of crystalline tetracene is 5.3 eV,s the singlet and triplet states lie a t 2.3 and 1.65 eV, respectively: the vertical bandgap has been put a t 3.5 eV,' and a C T state at 2.9 eV has been identified.* The first excited singlet-state lifetime (excluding bimolecular processes) is about 200 ps.9 In the present experiment, the maximum kineticenergy of the emitted electrons was found to be 1.1 eV, implying that in the multistep photoemission process, the combined energy (to be referred to as the equivalent single photon energy, Ep)of the interacting states was 6.4 eV. Thus, if a photon at 3.5 eV were to photoionize a free electron in the conduction band at 3.5 eV, the value of E, would be 7.0 eV; since the measured E, was 6.4 eV, the photonfree electron mechanism is eliminated. The light intensity dependence of the photoemission was greater than quadratic; it was 2.3 f 0.1. This eliminates the direct two-photon ionization mechanism, for which Y a: P and E, = 7.0 eV. The photoemission yield as a function of the delay time between the primary and probe pulse is shown in Figure 1. The point of coincidence is determined by using photoemission from the particle as the indicator; when maximum photoemission is measured,
0022-3654/58/2097-0002%04.00/0 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 1 , 1993 3
Letters
The rate equations would be
d[Slldt =
a t ) - k,[Sl - r,,[SI2
(7)
where k is the absorption coefficient (cm-I), IO is the maximum light intensity (cm-2 SI), time t is measured in picoseconds, At is the delay time between first and the delayed second pulse, and 7.1 ps is the standard deviation of the half-width of the lightpulse.
0.3
-200
-150
0
-50
-100
50
100
150
200
dT (Delay Time : ps.) Figure 1. Time-resolved multistep photoemission yield from tetracene single crystal as a function of the delay time between the prompt and delayed light pulse. The prompt and delayed light pulses are interchangeable. Excitation is by the 355 nm harmonic of the laser, the pulse width of which is 20-ps fwhm. The calculated lifetime of the chargetransfer state is 20 ps. See text for additional details.
coincidence is achieved. The maximum photoemission yield can be measured in advance by sending in an undivided (full intensity) beam. The yield at this intensity is assumed to be the same (factoring in reflection losses) as that obtained when the primary and probe beams are coincident. The intensities of the primary and probe pulses were approximately equal, with a mean deviation of less than 30%. The light intensity dependence of the photoemission process was 2.3 f 0.1. Possible mechanisms for photoemission would include photonphoton, photon-singlet exciton, photon-CTd (CTd is a C T state generated directly by a photon), singlet-singlet, photon-free or trapped electron, CTd CTd, photon-CT, (CT, is a C T state generated indirectly by singlet-singlet annihilation), CT, + CT,, electron CT,, and singlet singlet + singlet. Of the above, only the (photon + CT,) and the (electron CT,) could satisfy the observed light intensity dependence of Y a P 3 * 0 1 and the measured value of E , = 6.4 eV. The photon energy is 3.5 eV and the CT energy is 2.9 eV (regardless of whether it is CT, or CTd), adding up to 6.4 eV. The free electron energy is coincidentally also about 3.5 eV so the (e - CT,,or d) mechanism would satisfy the energy requirement and it also happens to satisfy the light intensity dependence requirement. For reasons to be mentioned later, the (e- CT,, or d) mechanism is not favored, so in the analysis to follow, the photon-CT, mechanism will be used. The relevant processes are the following:
+
+
+
+
hv + So
-
SI
(1) excitation to the first singlet state with absorption coefficient k; k N lo3 cm-I at 355 nm;Io
SI + S I -s*
(2)
singlet-singlet fusion with rate constantt1 yss= lo-’ cm3 s-l;
S*
-
CT,
-+ -
C T state is formed with efficiency12 7
hu
+ CT,
(3) = 0.01-1 at 4.6 eV;
h+ e-* (4) CT, is photoionized with a cross-section u producing the photoemitted electron e-*, and the hole, or cation radical h+;
-
SI so (5) unimolecular singlet decay with rate constant9 k, = 5 X lo4 SKI;
-
CT, S, decay of C T state with an effective rate constant k ’ c ~ .
(6)
The photoemission yield as a function of the delay time At is given by
Y(A7‘)= J-IG(r,At)[CT](t,At)
dt
(10)
from (7); p 5< [SI< Z,depending on exciton concentration (1 1)
from (9); [CT,] a [SI2;therefore Z < [CT,] < Z2 (12) The (e - CTJ mechanism cannot be ruled out; it is not favored because the photon concentration is many orders of magnitude greater than that of the free electron concentration. In addition, the (e - CTi) process would give a light intensity dependence varying between 1.5 and 2.5, with the 2.5 value appearing when the yssS2contribution is relatively small compared with the k,S contribution in eq 7. This however, is not the case; the y s s S contribution is major.ItJ3 This leaves the photon CTi mechanism. Using eq 4, which shows that the photoemission process depends on the product of the photon and CTi concentrations, and eq 12, it follows that
+
Z2 < [hu][CTi] < Z3
(13) The observed dependence of P i 0 . l is due to a greater role of the singlet-singlet annihilation (see eq 7). Taking S,,, GZ lOI9/cm3as calculated from the light intensity, absorption coefficient, and pulse shape, and the values for k,,yss, and 7 taken from eqs 2, 3, and 5, and only variable is k’c~.The range of values for tl and the value of u are not important for determining the shape of the curve that is shown in Figure 1. Equations 7 and 9 were solved numerically, excluding diffusion, and the fit between the calculated curve and the data is shown in Figure 1. The deduced effective value for k ’ c ~was 5 X 1 O 1 O s-1. However, electron emission takes place from a layer 10-15 A deep, so at the present stage, we cannot attribute our measured lifetime to that of the charge-transfer (CT) state in the bulk, which must be longer, because in our mathematical analysis, we omitted the possible role of surface quenching of excited states. In addition, we have omitted the effect of singlet excitons on the concentration of nearest-neighbor C T excitons (which we will refer to as reactive C T excitons), which presumably are the ones involved in the photoemission process. This interaction leads to quenching of the singlet exciton and to a dissociation of the C T exciton into a free hole and electron, which subsequently recombine. The total energy of this (S-CT) reaction is less than the ionization energy of the crystal, so no photoemission takes place. The net result of this (S-CT,) reaction is paradoxical in the sense that while the CT state is reconstituted after dissociation, the total time that the CT state is in the reactive form during the 20-ps period that the light pulse is in existence, is decreased, while the overall lifetime of the C T excition can even increase. In any event, since the singlet excitons do not quench the C T exciton, the net effect of the singlet-CT concentration is to decrease the effective k ? ~in an as yet undetermined manner. The combined effects of surface quenching and singlet exciton dissociation leads to a k ? ~or -20 ps.
4
The Journal of Physical Chemistry, Vol. 97, No. 1, 1993
In previous papers, the lifetime of the CT exciton was estimated to range from 10-9to 1O-' s,I4and the mechanism of photoemission was attributed to the electron-CT process. These experiments were carried out under steady state conditions a t a much lower light intensity. A direct comparison of results is therefore not possible, but will be discussed in a future publication. The data in the time region -50 to -200 ps are not accounted for by the theoretical basis provided herein. We cannot explain this slight deviation at present. However, we have a conjecture. The lack of symmetry in Figure 1 can be caused by the inequality in the intensities of the first and the delayed second light pulse, coupled with a small upsurge in the C T exciton population that trails after the cessation of the symmetrical Gaussian light pulse. The upsurge in the C T exciton population can be caused by the interaction of singlet excitons with C T excitons. The singlet excitons would dissociate the C T excitons, which would reconstitute themselves after a recombination time interval. This will be discussed more fully in a subsequent publication. The use of the standard high-vacuum photoemission apparatus should reveal more detailed information about the excited states involved in photoemission. One interesting observation that must be made is that the light intensity dependence seems to rule out an important role for direct generation of C T states by the 3.5-eV photon. This would imply that the efficiency of carrier generation at 3.5 eV (laser energy) is so small that the bimolecular process in eq 8, coupled with the high ionization efficiency at 4.6 eV (due to singlet-singlet fusion) is the dominant ionization mechanism. Note Added in hoof. We have stated that eqs 7 and 9 were solved numerically excluding diffusion. This is incorrect. Diffusion of singlet excitons (only) was included. Equation 7 must therefore be modified to include the diffusion term D d2[S]/dx2. The complete equation, including the diffusion, was solved using
Letters as a basis the solution in Carslaw and Jaeger.16 If diffusion is omitted, then the C T lifetime would be 16 ps.
Acknowledgment. This work was supported by the DOE Grant No. DEFG0286-ER60405. Acknowledgement is made of valuable discussions with Olof B. Widlund, Howard Fink, and Charles E. Swenberg. References and Notes (1) Voltz, R. In Inrernational Discussion of Progress and Problems in Contemporary Radiation Chemistry;Santar, I., Ed.; Academia: Prague, 197I ; p 160. (2) Bowen, E.J.; Mikiewicz, E.;Smith, F . W. Proc. Phys.Soc. (London) 1949, A62, 26. (3) Pope, M.; Burgos, J.; Giachino, J. J . Chem. Phys. 1965, 43, 3367. Sebastian, L.; Weiser, G.; Bissler, H. 1985, 61, 125. (4) Altwegg, L.;Pope, M.; Arnold, S.;Fowlkes, W. Y.; Hamamsy, M. A. Rev. Sci. Instrum. 1982, 53, 332. (5) Hirooka, T.; Tanaka, K.;Kuchitsu, K.; Fujihara, M.; Inokuchi, H.; Harada, Y.Chem. Phys. Lett. 1973, 18, 390. (6) Mfiller, H.; Bissler, H. J . Lumin. 1976, 12/13, 259. (7) Tomkiewicz, Y.; Groff, R.P.; Avakian, P. J . Chem. Phys. 1971,54, 4504. (8) Sebastian, L.; Weiser, G.; Bissler, H. Chem. Phys. 1981, 61, 125. (9) Alfano, R.R.; Shapiro, S.L.; Pope, M. Opt. Commun. 1973,9,391. (IO) Mizuno, K.; Matsui, A.; Sloan, G. J. J . Phys. SOC.(Jpn.) 1984, 53, 2799. Brce, A.; Lyons, L. E. J. Chem. Soc. 1960, 5206. (1 1) Campillo, A. J.; Hyer, R. C.; Shapiro, S.L.; Swenberg, C. E. Chem. Phys. Lerr. 1977, 48, 495. (12) Silinsh, E. A. Organic Molecular Crystals; Springer-Verlag: Berlin, 1980; p 132. (13)Heisel, F.; Miehe, J. A.; Schott, M.; Sepp, B. Chem. Phys. Len. 1976, 43, 534. (14) Pope, M.; Burgos, J. Mol. Cryst. 1966, I , 395. (15) Arnold, S.; Pope, M.; Hsieh, T. K. T. Phys. Sratus Solidii B 1979, 94, 263. (16)Carslaw, H. S.;Jaeger, J. C. Conducrion of Heat in Solids, 2nd 4.; Oxford University Press: London, 1959;p 71,q 2. The values used were" D = 40 A* ps-' and h 1.24X lo-' A-1 (corresponding to a 10% quenching at the surface).
