Journal ArticleWe show that one-electron band theory fails to describe optical absorption in PPV and the absorption spectrum can be described only within a Coulomb-correlated model. The lowest optical state is an exciton, whose binding energy is estimated theoretically to be 0.90 ± 0 . 1 5 e V Measurements of the photoconductivity quantum efficiency in poly[2-methoxy,5-(2'-ethyl-hexyloxy)-l,4 phenylenevinylene] reveal a binding energy in good agreement with the theoretical value

Chandross, M.

Vardeny, Zeev Valentine

English

The University of Utah: J. Willard Marriott Digital Library

PHYSICAL REVIEW B VOLUME 50, NUMBER 19 15 NOVEMBER 1994-1 Excitons in poly(para-phenylenevinylene) M. Chandross Department of Physics, University of Arizona, Tucson, Arizona 85721 S. Mazumdar Department of Physics and The Optical Sciences Center, University of Arizona, Tucson, Arizona 85721 S. Jeglinski, X. Wei, and Z. Y. Vardeny Department of Physics, University of Utah, Salt Lake City, Utah 84112 E. W. Kwock and T. M. Miller AT&T Bell Laboratories, Murray Hill, New Jersey 07974 (Received 25 August 1994) We show that one-electron band theory fails to describe optical absorption in PPV and the absorption spectrum can be described only within a Coulomb-correlated model. The lowest optical state is an exciton, whose binding energy is estimated theoretically to be 0.90::': 0.15 eV. Measurements of the photoconductivity quantum efficiency in poly[2-methoxy,5-(2' -ethyl-hexyloxy)-1,4 phenylenevinylene] reveal a binding energy in good agreement with the theoretical value. The role of electron correlations in 7T-conjugated poly-mers has been a topic of continuing debate for more than a decade. l ,2 Current interest in 7T-conjugated polymers stems from the recent demonstration of electroluminescence in poly(p-phenylenevinylene) (Ref. 3) (PPV) (see Fig. 1) and poly[2-methoxy,5-(2' -ethyl-hexyloxy)-I,4 phenylene-vinylene] (Ref. 4) (MEH-PPV). The nature of the primary photoexcitations in PPV derivatives is presently highly controversial.5 Indirect evidence for the excitonic nature of the lowest photoexcitation, implying moderate to strong Coulomb interactions,2 is found in a number of experiments,6-9 but estimates of the exciton binding energy Eb vary widely, from 0.4 (Ref. 10) to 1.1 eV.8 In contrast, the observation of photoconductivity (PC) at the absorption threshold has been interpreted as an indication of delocalized electrons and holes in the lowest excitation,l1 and therefore of weak Coulomb interaction. 1 We present here direct theoretical and experimental dem-onstrations of the excitonic nature of the lowest excitations of PPY. Theoretically, we give a convincing proof that the optical absorption in PPV and its derivatives cannot be ex-plained within one-electron theories, and estimate E b in PPV as 0.90±0.15 eY. From measurements of the PC quantum efficiency in MEH-PPV we then determine experimentally E b =0.95±0.15 eY. Our theoretical model is similar to the Pariser-Parr-Pople (PPP) model for 7T-conjugated systems, H= U2, ni,rni,L + ~2, Vij(ni-1)(nj-l) i,j - 2, t i,.[ c 1 uC,' u + c,t uC i u]. (ij),u " " (1) Here cl,u creates a 7T electron of spin 0' on carbon atom i, ni,U=cl,uCi,u, ni='Luni,u, and tij is the one-electron hop-0163-1829/94/50(19)/14 702(4)/$06.00 50 ping integral «) implies nearest neighbors). We consider standard tij =t=2.4 eV for the phenyl bonds. In order to have the lowest optical state at comparable energies, we choose t ij = tl (t2) = 1.9 (2.9) eV for the single (double) bonds of the vinylene units for noninteracting electrons, and 2.2 (2.6) eV for interacting electrons. Our conclusions are independent of the magnitudes of t ij . U and Vij are the on-site and long-range Coulomb interactions, respectively. V ij are assumed to have the Ohno12 form, (2) where R ij is the distance, in A, between carbon atoms i and j. We have verified that the results obtained with other forms of Vij are identical. Unlike the standard PPP model, we con-sider the entire range of interactions from the Huckel model (U=O) to the full PPP potential (U=4.64t). E(k) -----jf------ d 3 " d , ' ----------- ----------- 0 ~-_r_ _ _.::d, -----t----- d3 ----------+---------7k FIG. 1. Band structure of PPV with the unit cell shown as an inset. 14702 © 1994 The American Physical Society RAPID CO\I\1l -';ICA no-.;s EXCITONS IN POLY(para-PHENYLENEVINYLENE) 14703 0.8 "..... (a) ~ c ~ 0.6 .0 ... 0 '-' Q) () C ~ ~ .0 « .0 ~ o c o ... c. o '" .0 « 0.4 0.2 0.0 ':-1 --'-~--!c3--'---5':---.J'--~ Photon Energy (eV) (b) U=O (Huckel) 2 3 4 Energy It FIG. 2. (a) Experimental absorption spectrum of a thin film of MEH-PPY. (b) Calculated linear absorption for a 12-unit PPV oli-gomer with a linewidth parameter f=O.3 eY. (c)-(f) calculated linear absorption for an 8-unit oligomer for U = 2.4, 4.8, 8, and 11.13 eV, respectively, with f = 0.4 eV. The solid and dashed ar-rows on the x axes in (e) and (f) indicate the HF band threshold and the nB u' respectively. For U = 0 the band description is valid. The band struc-ture of PPV is shown in Fig. 1. Electrons in the d i and d7 bands are delocalized over all carbon atoms, while the local-ized I and 1* bands have electron densities only on carbon atoms 2, 3, 4, and 5 (Fig. 1, inset). The experimental absorption spectrum of a MEH-PPV thin film [see Fig. 2(a)] has a low-energy band that peaks at 2.4 eV (peak I), two additional small peaks at 3.7 and 4.7 eV (peaks II and III, respectively), and a strong broad band cen-tered at 5.9 eV (peak IV). Very similar absorptions are ob-served in other PPV derivatives,B while in PPV itself the 3.7-eV peak appears as a distinct shoulder14 on a broad peak I. We therefore consider the spectrum of Fig. 2(a) as charac-teristic of the 7T-conjugation network of PPV, with the side-groups affecting the absorption spectrum weakly. Conse-quently, our theoretical work is for PPV only. The calculated U = 0 absorption spectrum for a 12-unit capped PPV oligomer finds a single central peak in between two strong transitions [see Fig. 2(b)]. The strong absorption at low energy corresponds to d1---+dt transitions. The high density of states of the I and 1* bands lead to the second strong absorption at high energy, while the weak central peak is predominantly due to the degenerate d 1 ---+ I * and 1---+ d t transitions. All optical transitions involving the d 2 , d3 , d~, and d; bands are weak. The occurrence of a single central peak is associated with the accidental degeneracies peculiar to the Huckel model. 15 The origin of four, instead of three, peaks in the absorp-tion spectrum must be attributed to electron correlations. For U>O, we include configuration interaction (CI) with all single excitations (hereafter SCI).14,16 The limitations of the SCI approximation are understood from comparisons of re-cent SCI (Ref. 16) and exact finite-chain calculations17 of the third-order optical nonlinearity of the polydiacetylenes. SCI misses the covalent even-parity A g states,18 but both SCI and finite-chain calculations find that optical nonlinearity is de-termined almost entirely by the optically allowed odd-parity 1Bu exciton, a dominant Ag exciton (the mAg) above the IB u' and the threshold of the conduction band (the nB u)' Thus SCI captures the essential qualitative physics of the energy region of interest here. Our estimates for the exciton binding energy are based on such qualitative considerations and not quantitative comparisons, as SCI is known to over-estimate the band gap. In Figs. 2(c)-2(f) we show the calculated absorption spectra for an eight-unit capped PPV oligomer for Ult= 1.0, 2.0, 3.33, and 4.64, respectively. At U/t= 1, the central peak of the U = 0 spectrum has weakened, while the intense high-energy peak has split into two peaks of compa-rable intensities. With further increase in Ult to 2.0 a distinct absorption appears in the region of peak III, but the overall absorption is still different form the experimental spectrum. Only for U It = 3.33 and 4.64 do the calculated spectra re-semble the experimental spectrum. The evolution of the spectra in Figs. 2(c)-2(f) can be understood from analysis of the CI wave functions. 19 At the smallest U, the CI and Hartree-Fock (HF) results are nearly the same. HF induces mixing of Huckel ground-state and excited configurations, thus reducing the intensities of all absorptions. The central peak, weak to begin with, thus dis-RAPID CO'\I,\1l "Ie <\ f10"S 14704 CHAND ROSS, MAZUMDAR, JEGLINSKI, WEI, VARDENY, KWOCK, AND MILLER "0 ;7 ~8 !5 > [;!. 0 10 20 30 Q) ~ No. Unit.:. >. U=O U=3.33t U=4.64t QIJ 1-0 10 -Q) ~ HF I II I'Ll ~ f-.~ • ...., • -<1l 6f- !!!!!!!!! HF ...., _inBu '() x -nB}~ =~mAg I'Ll f--!!!!!!!! rnAJ) = g -- ~~1Bu 2f- -- 1Bu~ FIG. 3. Excitation energy spectra of a 12-unit PPV oligomer for U = 0 and an 8-unit PPV oligomer for U = 3.33t and 4.64t, respec-tively. The 1Bu, mAg, nBu, and the HF band threshold are indi-cated. The inset shows the HF band threshold for U= 3.33t against the number of PPV units. appears. CI between the 1--> I * and the d I --> I * and 1--> d ~ leads to the splitting of the high-energy peak in Fig. 2(c). At still larger U, CI is stronger, and peaks II, III, and IV in Figs. 2(e) and 2(f) arise from transitions to states that are strong admixtures of configurations involving the I and I * levels. The appearance of a larger number of absorptions, upon in-cluding CI, is well known in molecular quantum chemistry. IS In Fig. 3 we show the excitation energies for U / t = 0, 3.33, and 4.64. The conduction-band edge for U>O in SCI is the HF gap,16 above which the states are seen to be continu-umlike and more closely spaced than the U = 0 band levels. The band edge was also calculated separately according to the prescription of Ref. 17, viz., the mA g state is first iden-tified as the unique A g state with exceptionally large dipole coupling with the 1B u; the band threshold nB u state is then identified from its large dipole coupling with the mA g' As seen in Fig. 3, the two estimates of the conduction-band threshold are close. The nBu is weakly dipole coupled to the ground state and is not visible in absorption.17 As shown in the inset of Fig. 3, the HF band threshold does not change significantly beyond eight units. Thus the only difference in a long chain would be the appearance of a true continuum above the band threshold. Peak I in Figs. 2(e) and 2(f) is due to transition to the 1B u' The discrete nature of the energy spectrum in this region for nonzero U indicates that the 1B u' and several other low-lying states, are excitons. The dense levels immediately below the continuum edge for U/t=4.64 are linear combinations of the dl-->l*, l-->d~, and 1--> I * configurations. These levels occur above the band threshold for U = 3.33t. Transitions to these levels give rise to peak II in Figs. 2(e) and 2(f). Our measurement of the PC quantum efficiency (see below) shows that the conduction-band threshold is below peak II, indicating that the full PPP potential is too large. We therefore do not discuss U = 4.64t any further. The experimental peak at 3.7 eV [Fig. 2(a)] corresponds 0.8 0.4 ~ ~ ~ 0.6 'c :J 'c .ci :J 0.3 .ci § § 1J Qi Q) 0.4 >= u c 0.2 E 0 ::J .0 C (5 0 Il ::J <{ 0.2 0.1 G U a.. 0.0 0.0 1 Photon Energy (eV) FIG. 4. PC quantum efficiency of an ITO/MEH-PPV/Al photo-diode, with the ITO being biased at + 5 and - 5 V, respectively. The absorption spectrum of a thin film of MEH-PPV is also shown. to peak II in Fig. 2(e). Although the energies of peak II and the band threshold are too high within SCI, the remarkable similarity between the experimental and the calculated spec-tra allows us to correctly estimate the continuum threshold in PPY. We use two independent approaches to estimate this threshold. The first approach is based on the comparison of calculated and experimental linear absorption. The second is based on a similar comparison involving nonlinear spectroscopy.8.20 The arrows on the x axis of Fig. 2(e) give the locations of the nB u and the HF band threshold. Scaling the calculated energy levels above the 1B u such that the calculated peak II will occur at 3.7 eV, we find the continuum threshold at - 3.4 e Y. Since the exciton in PPV is at - 2.4 e V, an upper limit of E b - 1.0 e V is thus obtained. An independent estimate of the lower limit for E b is ob-tained from the relative location of the mA g , which has been found to occur 0.5-0.6 eV above the 1Bu exciton in both two-photon absorption20 and electroabsorption.8 From com-parison of grevious SCI (Ref. 16) and exact finite-chain calculations 7 for the polydiacetylenes, it is known that SCI predicts an upper limit for !l.E m / E b, where !l.E m is the en-ergy difference between the mA g exciton and the 1B u exci-ton. This is expected, as higher-order CI lowers the energies of the A g states more than the B u states. From our calculated !l.E m / E b = 0.68 for U = 3.33t and the experimental !l.E m of 0.5 eV, we predict a lower limit of 0.75 eV for E b . Note that our approaches involving comparisons to experiments by-pass the problems associated with "gas-phase" calculations. Our theoretical estimate of Eb in PPV is thus 0.90::+:::0.15 eY. We have determined Eb in MEH-PPV experimentally by measuring the PC quantum efficiency TJ( w), as a function of the photon excitation energy from 1.5 to 4 eV (see Fig. 4). PC was measured in a MEH-PPV photodiode,21 constructed in a sandwich configuration of a semitransparent indium-tin-oxide (ITO) bottom electrode, an -lOoo-A MEH-PPV layer, and an aluminum (AI) top electrode. The measure-ments were at room temperature in vacuum, and the modu-lated illumination was provided from a premonochromatized 300-W xenon lamp through the ITO electrode, biased at + 5 and - 5 V, respectively. The PC spectrum was then divided RAPID CO'\1\1l "OleA rIo,,"s 50 EXCITONS IN POLY(para-PHENYLENEVINYLENE) 14705 by the spectral response of the system and the number den-sity of the absorbed photons to give the spectrum of 1]( w) . As seen in Fig. 4, both 1] curves have two onsets: one at the exciton energy near 2.2 eV and the other at ~3.1 eV, where 1] starts to show a much steeper increase, even though there is no corresponding features in the absorption spectrum (note that the absorbance of MEH-PPV varies only slightly at ~ 3.1 e V and the increase in 1] cannot be caused by changes of the photon penetration depth around this energy22). Our PC quantum yield in MEH-PPV is in agree-ment with the photocurrent measurements in PPV (Ref. 22) up to 2.9 eV for biases from -2 to +2 Y. The bias voltages of :!:: 5 V, much larger than those used previously,22 and 10 times larger than the built-in potential of 0.5 V caused by the work-function difference between the two electrodes,23 apply an external field of ~:!:: 5 X 105 V/cm, thus compensating for the inhomogeneity of the internal electric field. The PC spec-tra from the first onset to below the second onset probably result from exciton dissociation or ionization.13 Their relative magnitudes at 2.54 eV are in agreement with the photoin-duced I-V characteristics of MEH-PPV light-emitting diodes?3 The more important second onset clearly shows a different process being turned on at ~3.1 eV and the most natural explanation is that it arises from the continuum threshold, since at this high electric field direct-carrier pho-togeneration gives a much higher signal than carriers pro-duced by exciton dissociation. The photogenerated carriers might also aid the dissociation of localized excitons by im-pact ionization. Linear extrapolation24 of 1]( w) gives the lo-cation of the continuum threshold at 3.1:!::0.1 eY. Since the 1Bu exciton in MEH-PPV is located at 2.15:!::0.05 eV, our 1 A. 1. Heeger, S. Kivelson, 1. R. Schrieffer, and W. P. Su, Rev. Mod. Phys. 60, 781 (1988). 2D. Baeriswyl, D. K. Campbell, and S. Mazumdar, in Conjugated Conducting Polymers, edited by H. Kiess (Springer-Verlag, Ber-lin, 1992). 3 J. H. Burroughes et ai., Nature 347, 539 (1990). 4G. Gustafsson et ai., Nature 357, 477 (1992). 5 Proceedings of Optical Properties of Conjugated Polymers and Fullerenes, Salt Lake City, Utah, 1994, edited by L. Rothberg and Z. V. Vardeny [Mol. Cryst. Liq. Cryst. (to be published)]. 6R. Kersting et al., Phys. Rev. Lett. 70, 3820 (1993). 7U. Rauscher, H. Bassler, D. D. C. Bradley, and M. Hennecke, Phys. Rev. B 42, 9830 (1990). 8J. M. Leng et al., Phys. Rev. Lett. 72, 156 (1994). 9J. w. P. Hsu et ai., Phys. Rev. B 49, 712 (1994). lOp. Gomes da Costa and E. M. Conwell, Phys. Rev. B 48, 1993 (1993). 11 C. H. Lee, G. Yu, and A. J. Heeger, Phys. Rev. B 47, 15543 (1993). 12K. Ohno, Theor. Chim. Acta 2,219 (1964). 13K. Pichler et ai., J. Phys. Condens. Matter 5, 7155 (1993). 14J. Comil, D. Beljonne, R. H. Friend, and J. L. BfI!das, Chern. Phys. Lett. 223, 82 (1994), discusses the 3.7-eV peak in PPV. experimental estimate of Eb is 0.95:!::0.15 eY. Nearly the same binding energy is obtained from our measurements of PC quantum efficiencies in other PPV derivatives, as well as with calcium as the top electrode. These results will be re-ported elsewhere. In photoluminescence-detected magnetic-resonance (PLDMR) measurements, visible excitation yields a PL-enhancing polaron resonance in PPV's as well as in other 1T-conjugated polymers,z5 Recent measurements with UV excitation has found PL-quenching polaron PLDMR in MEH-PPV above a threshold energy that is very close to the continuum threshold found in this paper?6 If the PL-quenching resonance is due to itinerant-band polarons, it would be entirely consistent with our estimate of E b . In conclusion, explicit inclusion of electron correlation is essential for a theoretical description of PPV and its deriva-tives. Comparisons of theoretical calculations and experi-mental linear and nonlinear optical spectra predict an exciton binding energy of 0.95:!:: 0.15 e V, in excellent agreement with the binding energy extracted from measurements of PC quantum efficiency. Our conclusion has important implica-tions for the entire class of 1T-conjugated polymers. We are grateful to J. L. Bredas for sending us a copy of Ref. 14 prior to publication, and S. Abe and J. Shinar for valuable discussions. Work at Arizona was supported by grants from the NSF (Grant No. ECS-940881O), AFOSR (Grant No. F496209310199), and ONR (Grant No. N000149410322). Work at Utah was supported by grants from the DOE (Grant No. DE-FG 03 93 ER45490) and NSF (Grant No. DMR-9222047). This paper also reports calculations of absorptions in short PPV oligomers (up to five units) within a limited SCI that retains some of the single excitations. The issue of excitons versus bands was not discussed. 15L. Salem, Molecular Orbital Theory of Conjugated Systems (Ben-jamin, New York, 1966). 16S. Abe, M. Schreiber, W. P. Su, and 1. Yu, Phys. Rev. B 45, 9432 (1992). 17D. Guo et ai., Phys. Rev. B 48, 1433 (1993). 18B. S. Hudson, B. E. Kohler, and K. Schulten, in Excited States, edited by E. C. Lim (Academic, New York, 1982), Vol. 6. 19M. Chandross et al. (unpublished). 20C. J. Baker, O. M. GeIsen, and D. D. C. Bradley, Chern. Phys. Lett. 201, 127 (1993). 21 G. Yu, C. Zhang, and A. J. Heeger, Appl. Phys. Lett. 64, 1540 (1994). 22R. N. Marks et al., J. Phys. Condens. Matter 6, 1379 (1994). 23X. Wei et al., Phys. Rev. B 49, 17480 (1994). 24R. G. Kepler and Z. G. Soos, Phys. Rev. B 47, 9253 (1993). 25L. Swanson et al., Phys. Rev. B 46, 15072 (1992), and references therein. 26 J. Shinar (private communication). 

Excitons in poly(para-phenylenevinylene)

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Excitons in poly(para-phenylenevinylene)

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