Semiconducting polymers: Fast response non-linear optical materials

Synthetic Metals, 15 (1986) 95 - 104

95

SEMICONDUCTING POLYMERS: FAST RESPONSE NON-LINEAR OPTICAL M A T E R I A L S A. J. HEEGER, D. MOSES and M. SINCLAIR

Institute for Polymers and Organic Solids, University of California, Santa Barabara, CA 93106 (U.S.A.)

Abstract Semiconductor polymers such as polyacetylene and polythiophene have experimentally demonstrated non-linear optical processes (photoinduced absorption, photoinduced bleaching and photoluminescence), with characteristic time scales in the picosecond range or faster. These phenomena are intrinsic and originate from the instability of these conjugated polymers toward structural distortion. The major shifts in oscillator strength due to photoexcitation of solitons, polarons and bipolarons lead to relatively large third-order non-linear optical processes (×(3)) on time scales of order 10 -13 s. These novel photoexcitations, largely overlooked in earlier analyses, are the key to understanding the non-linear optical properties of this growing class of semiconducting (conjugated) polymers.

1. Introduction: the origin of non-linear optical properties of semiconduct-

ing polymers In traditional three-dimensional semiconductors, the four-fold (or sixfold, etc.) coordination of each atom to its neighbor through covalent bonds leads to a rigid structure. In such systems, therefore, the electronic excitations can usually be considered in the c o n t e x t of this rigid structure, leading to the conventional concepts of electrons and holes as the dominant excitations. The non-linear optical properties of such materials arise either from electronic non-linearity within the framework of rigid band theory (i.e., redistribution of electrons among existing states) or from small deviations from rigid band theory (i.e., in the high electric field of an intense laser source the atomic displacements are significant, leading to non-linear coefficients in the polarizability tensor). The situation is semiconductor polymers is quite different; the two-fold coordination makes these systems generally more susceptible to structural distortion. As a result, the dominant 'electronic' excitations are inherently coupled to chain distortions. Thus, solitons, polarons and bipolarons are the excitations of major importance in this novel case of one-dimensional polymer semiconductors. These semiconducting polymers are therefore 0379-6779/86 / $3.50

© Elsevier Sequoia/Printed in The Netherlands

96 fundamentally and inherently non-linear. Moreover, the major structural rearrangements (to form the solitons, bipolarons, etc.) that lead to the nonlinear optical properties are known to occur on time scales of order 10 -13 s. Our point here is to emphasize the intrinsic non-linearity that arises from the e l e c t r o n - p h o n o n interaction in quasi-one-dimensional systems. This large and inherent non-linearity (largely overlooked by previous workers in the field) is, in our view, the key to understanding the non-linear optical properties of the growing class of semiconducting (conjugated)polymers. We focus on the origin of the non-linear response, which leads to a large thirdorder susceptibility, ×(3). The status of the field of non-linear optical properties (both second-order and third-order susceptibilities) of conjugated polymers was summarized in the proceedings of a recent ACS symposium [ 1 ]. Previous work focused on electronic non-linearity within the framework of a rigid structure; the polydiacetylene polymers (with a variety of sidegroups) have been the systems of principal interest. We illustrate these concepts through a brief summary of relevant experimental results on two systems: (1) Polyacetylene, (CH)x; the degenerate ground state leads to solitons as the important excitations and the dominant charge storage species. (2) Polythiophene; the ground state degeneracy is lifted so that polarons and bipolarons are the important excitations, with charge storage in bipolarons. As shown in Fig. 1, trans-(CH)x is a two-fold degenerate Peierls insulator, which allows for the possibility of non-linear excitations in the form of soliton-like bond-alternation domain walls, each with an associated electronic state at the center of the energy gap [2 - 6]. For polythiophene, on the other hand, the two structures sketched in Fig. 2 are not energetically equivalent. Polythiophene (PT) can be viewed as an sp2pz carbon chain in a structure somewhat analogous to that of cis-(CH)~, but stabilized in that H

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97

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structure by the sulfur, which covalently bonds to neighboring carbons to form the heterocycle. We briefly summarize the results of a series of experiments, which demonstrate that solitons are important excitations in trans-(CH)x and that the properties of these non-linear excitations can be directly studied through measurements on trans-(CH)x samples either during photoexcitation or after doping. The relevant concepts can be generalized to confined soliton pairs (bipolarons) and applied to a wide variety of conjugated polymers in which the ground state degeneracy is not present. Polythiophene (Fig. 2) is a protot y p e example of such systems. The importance of localized structural distortions around injected charges to form solitons, polarons and bipolarons in semiconducting polymers was discussed in an earlier paper [ 7a] and in published reviews [7b]. The soliton in (CH)~ is a topological kink in the electron-lattice system; a bond alternation domain wall connecting the two phases with opposite bond alternation. Since there is translational symmetry (the kink can be anywhere) and since the mass is small, the soliton should be mobile. The competition of elastic and condensation energies spreads the domain wall over a region of a b o u t 12 - 14a, where a is the C-C distance along the (CH)~ chain. Although single soliton defects can exist on imperfect chains (and have been studied extensively) [8a, b], intrinsic excitations, either photo-produced or doping induced, must occur in the form of soliton-antisoliton (S-S) pairs~ Associated with the structural kink is a localized electronic state with energy at the mid-gap (see Fig. 3(a)). This electronic state is a solution of the Schrodinger equation in the presence of the structural domain wall and can therefore a c c o m m o d a t e 0, 1 or 2 electrons [2 - 6]. The neutral soliton has one electron in the mid-gap state; the positive and negative charged solitons have zero or t w o electrons, respectively, in the mid-gap state. Consequently, the spin-charge relations of solitons are reversed; charged solitons are nonmagnetic, whereas a neutral soliton has spin 1/2. A charged soliton represents the lowest-energy configuration for an excess charge on a trans-(CH)x chain [ 3 - 6]; i.e., Es < A where Es is the energy for creation of a soliton and A is the energy for creation of an electron or hole, A = Eg/2. Both numerical calculations using a discrete lattice model [3], and analytical results for a continuum model [5, 6] indicate that (neglecting electron-electron Coulomb interaction):

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Charged solitons are therefore formed by electron transfer onto or off the polymer chains when doping with electron donors or acceptors or by injection o f an electron-hole pair through photoexcitation. An analogy can be constructed [9] between PT and (CH)x. As shown in Fig. 2, if one purposely leaves o u t the sulfur heteroatom, the resulting backbone structure is that of an sp:pz polyene chain consisting of four carbon alltrans segments linked through a cis-like unit. In such a structure the ground state is n o t degenerate (as sketched in Fig. 2). However, the energy difference per bond, AE/I, might be expected to be small; i.e., greater than zero (as in trans-(CH)x), b u t perhaps less than or comparable to that of cis-(CH)=. An obvious consequence of the lack of degeneracy is that the schematic PT structure of Fig. 4 cannot support stable soliton excitations [ 2 - 6, 1 0 - 12], since creating a soliton pair separated by a distance d would cost energy ~d(AE/l). This linear 'confinement' energy leads to bipolarons as the lowest energy charge transfer configurations in such a chain, with creation energy somewhat greater than (4/Tr)A (the creation energy for a bipolaron goes to eqn. (1) in the limit of zero confinement). The corresponding energy level diagram (for a positive bipolaron) is sketched in Fig. 3(b). The t w o gap states are e m p t y for a positive bipolaron (charge 2e) and filled for a negative bipolaron (charge --2e). Polaron excitations in such systems have an energy level diagram similar to that sketched in Fig. 3(b). In the polaron case, however, the gap states axe partially filled (e.g., one electron in the lower level, for a hole polaron), leading to additional sub-gap adsorption subsequent to polaron formation. C.B.

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99

The energy level diagrams sketched in Fig. 3 are o f principal importance to the non-linear optical properties o f this class o f polymers. Prior to charge injection by photoexcitation o f an electron-hole pair, all o f the oscillator strength is in the interband absorption, ricoI. After photoexcitation there is a major redistribution in oscillator strength to h¢~ s (or h¢Ol, fi¢o2, etc.) as shown in Fig. 4. These shifts in oscillator strength occur on a time scale ~ 1 0 -13 s. Thus these conjugated semiconductor polymers are intrinsically fast non-linear optical materials.

2. Photoexcitation: photoinduced absorption, photoinduced bleaching and photoluminescence Photoexcitation studies of conjugated semiconductor polymers were stimulated b y the calculations of Su and Schrieffer [13], which demonstrated that in trans-(CH)x an e - h pair should evolve into a pair of solitons within an optical phonon period, or a b o u t 10 -13 s. Thus the absorption spectrum was predicted to shift from ~¢~i to rico s (see Fig. 4) on a time scale of 10 ~3 s after photoexcitation. Photoinduced excitation have been observed and their dynamics have been studies. These experimental results on the photoinduced (PI) changes in absorption confirmed the predictions. Both photoinduced absorption and photoinduced bleaching have been observed, and the extremely fast time scale has been verified. The photogeneration of soliton-antisoliton pairs implies formation of states at the mid-gap. Time-resolved spectroscopy [14] has been used to observe the predicted absorption due to photogenerated intrinsic gap states in trans-(CH)x. Moreover, the time scale for photogeneration of these gap states has been investigated [ 15, 16 ]. Using sub-picosecond resolution, these studies demonstrated that the gap states and the associated interband bleaching are produced in less than 10 -13 s, consistent with the theoretical predictions. This time scale is observed directly in the photoinduced bleaching experiments, as shown in Fig. 5. Vardeny et al. [17] and Blanchet et al. [18] have observed the photoinduced absorption arising from both the mid-gap electronic transition (sketched in Fig. 3) and the associated infrared active modes introduced by the local lattice distortion. The results of Blancher et al. [18] are reproduced in Fig. 6. The 0.5 eV absorption is the mid-gap transition. The i.r. modes at 1370 cm -~ and 1260 cm -~ are consistent with the calculations of Mele and Rice [19] and Horowitz [20], which predict the appearance of i.r. active internal vibrational modes between each of the Raman modes of pure trans(CH)x. Infrared spectroscopy [ 2 1 - 2 3 ] of lightly d o p e d trans-(CH)x has demonstrated that the same spectroscopic features arise upon doping. Moreover, these doping-induced absorptions are independent of the dopant, and are therefore identified as intrinsic features of the d o p e d trans-(CH)x chain.

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These important results demonstrate that both the photoinduced spectroscopic features and those induced by doping are associated with the same charged state. Moreover, the observed frequencies and line shapes are consistent with those expected for charged soliton excitations [22, 23]. It has been argued [20] that these changes in infrared absorption are general fea-

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tures of charged localized states on the trans-(CH)x chain (solitons or polarons) and thus not definitive proof of the photogeneration of solitons. However, since these excitations have the reversed spin-charge relation of solitons, this ambiguity is settled [24]. Thus, for example, the PI modes can be used as a signature of soliton formation. There appear to be two relevant time scales for the photoexcitation and decay processes in trans-(CH)x: the picosecond regime, during which the photoexcitations are produced and undergo initial rapid decay; and the long time behavior (t > 10 -9 s), during which the residual excitations slowly decay. The picosecond regime has been studied by photoinduced bleaching [15, 16] and photoinduced dichroism [16]. Bleaching of the interband transition {with the implied redistribution of oscillator strength into the 0.5 eV and 1.4 eV peaks) was observed at sub-picosecond times. The magnitude of the bleaching at early times implies a high quantum efficiency for photoproduction of non-linear excitations; the optical anisotropy of trans-(CH)~ indicates that these are primarily intra-chain excitations. Pulsed photoconductivity measurements [25] show a large sub-nanosecond photocurrent, indicating that a significant fraction of the initial excitations are charged. These data are consistent with the Su-Schrieffer mechanism [13] for photoproduction of charged soliton-antisoliton pairs. The initial rapid decay (<10 -9 s) of the bleaching [15, 16], the photoinduced dichroism [16] and the fast photoconductivity [25] imply rapid non-radiative recombination of the oppositely charged solitons. After 10 -9 s, only a few percent of the initial photoexcitations remain. It is these long-lived residual excitations which were observed in the steady-state photoinduced absorption and light-induced e.s.r, measurements.

102 In addition to the intra-chain excitation processes, photoexcitation of electron-hole pairs on neighboring chains is expected to occur with finite probability because of the finite interchain bandwidth [26]. Such interchain pairs would form polarons and/or weakly b o u n d excitons. Although the magnetic properties expected for photogenerated polarons are n o t observed, such interchain excitations m a y play a transient role in the formation of the charged solitons that are observed at long times. As these polarons diffuse along and between chains t h e y will form solitons in two ways [24b] : (a) two polarons with the same charge on a single chain will lead to a pair of metastable charged solitons; (b) a polaron on a chain with a pre-existing neutral defect will convert the neutral soliton into a charged soliton [ 27 ]. The first process appears to be the dominant one; it involves no change in the net n u m b e r o f spins and therefore is consistent with the 1.e.s.r. data [24]. Although the second process can certainly occur (and is observed in highly disordered samples) [24], it is not important in higher quality samples. We note that a soliton-antisoliton pair with like charge on a chain is metastable; the pair can only be annihilated by an oppositely charged pair on the same chain. This may account for the long lifetime of the residual charged solitons observed in the steady-state photoinduced absorption. Photoexcitation spectroscopy has also been carried o u t for polythiophene [28 - 30]. From resonant Raman scattering, photoinduced absorption and photoluminescence, a fully consistent picture of the ground state and photoexcitations o f polythiophene was obtained. The non-degenerate ground state causes relatively strong confinement (indicated b y the Raman data), and fast radiative recombination (observed via luminescence with a maximum at 1.9 eV). As a result of the confinement (due to the non-degenerate ground state), the time scale for photoluminescence decay is in the picosecond regime [31]. Thus all aspects of the p h o t o processes occur on this short time scale. The photoinduced absorption results obtained from polythiophene imply a shift in oscillator strength from h¢o I into the gap state transitions (ha) 1 and h¢o2; see Fig. 3 (b)). Since polythiophene is the p r o t o t y p e of the non
3. Relationship o f the observed non-linear photoexcitation processes in semiconducting polymers to the phenomenology of non-linear optics. In bulk media, there is a non-linearity in the constitutive relationship between the induced polarization (Pi) proportional to the amplitude of the electric field of the incident light; the induced polarization may be expanded in a power series of the electric field components: Pi = Xi/1)Ey + Y~jh<2)EjEk + Xiy~z(3)EjEkEml In this expression, X(1) represents the linear optical properties; ×(2) and Xo) axe, respectively, the second- and third-order non-linear susceptibilities. Second harmonic generation, optical rectification and the linear electrooptic effect involve X(2), which occurs only in non-centrosymmetric media.

103 We focus here on ×¢3), which will be large whenever there is a major shift of oscillator strength in response to a pump photoexcitation leading to a saturable absorption (i.e., to photoinduced bleaching). The data obtained from polyacetylene and polythiophene demonstrate that such phenomena are observed in the class of semiconducting polymers that are the focus here. Moreover, the fundamental mechanisms sketched in Figs. 3 and 4 imply that these features are general and can be expected to occur in a wide (and growing!) class of such materials. The optical devices of interest involve non-linear optical signal processing in computers or in communications for functions such as switching, amplifying and multiplexing. These involve the manipulation of laser beams in thin transparent films. Such applications are based on a non-linear refractive index (n2); i.e., a refractive index n(w) that changes with light intensity I (proportional to E 2) : n ( w ) = no(W) + n2I

The non-linear coefficient n2 is related to X(3) by n2 = 167r2x(3) /ce l

The non-linear index n2 contributes to such well-known effects as selffocusing, self-trapping, phase conjugation, optical bistability, etc., all of which are fundamental to optical signal processing applications. The data summarized briefly above demonstrate that n2 should be inherently large in semiconducting polymers, and that the time response of n2 should be fast (picosecond or faster). Consequently, as a class of novel electronic materials, semiconducting polymers offer promise as fast-response non-linear optical materials for use in a variety of applications. 4. Conclusion In summary, semiconductor polymers such as polyacetylene and polythiophene exhibit non-linear optical processes (photoinduced absorption, photoinduced bleaching and photoluminescence) with characteristic time scales in the picosecond range or faster. These phenomena are intrinsic and originate from the instability o f these conjugated polymers toward structural distortion. The major shifts in oscillator strength due to photoexcitation of solitons, polarons and bipolarons lead to relatively large third-order nonlinear optical processes (×(3)) on time scales of the order of 10 -x3 s. We believe that these novel photoexcitations, largely overlooked in earlier analyses [32], are the key to understanding the non-linear optical properties of this growing class of semiconducting (conjugated) polymers.

Acknowledgements This work was supported by the Office of Naval Research. We thank Dr. M. Salour for stimulating discussions.

104 References 1 2 3 4 5 6 7a 7b 8a 8b 9 10 11 12 13 14 15 16 17 18 19 20 21a 21b 22 23 24a 24b 25a 25b 26a 26b 27 28 29 30 31 32

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