J. Phys. Chem. B 2008, 112, 11601–11604
11601
Temperature Dependence of Exciton Diffusion in Conjugated Polymers O. V. Mikhnenko,*,†,‡ F. Cordella,† A. B. Sieval,§ J. C. Hummelen,†,| P. W. M. Blom,† and M. A. Loi† Zernike Institute for AdVanced Materials, UniVersity of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands, Dutch Polymer Institute, P.O. Box 902, 5600 AX, EindhoVen, The Netherlands, Solenne BV, Zernikepark 12, 9747 AN, Groningen, The Netherlands, and Stratingh Institute for Chemistry, UniVersity of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands ReceiVed: May 13, 2008; ReVised Manuscript ReceiVed: June 27, 2008
The temperature dependence of the exciton dynamics in a conjugated polymer is studied using time-resolved spectroscopy. Photoluminescence decays were measured in heterostructured samples containing a sharp polymer-fullerene interface, which acts as an exciton quenching wall. Using a 1D diffusion model, the exciton diffusion length and diffusion coefficient were extracted in the temperature range of 4-293 K. The exciton dynamics reveal two temperature regimes: in the range of 4-150 K, the exciton diffusion length (coefficient) of ∼3 nm (∼1.5 × 10-4 cm2/s) is nearly temperature independent. Increasing the temperature up to 293 K leads to a gradual growth up to 4.5 nm (∼3.2 × 10-4 cm2/s). This demonstrates that exciton diffusion in conjugated polymers is governed by two processes: an initial downhill migration toward lower energy states in the inhomogenously broadened density of states, followed by temperature activated hopping. The latter process is switched off below 150 K. I. Introduction Optical excitations in conjugated polymers are strongly bound electron-hole pairs, which are called Frenkel excitons and usually are localized on a single conjugated segment. Once created, excitons tend to migrate toward the lower energy sites, i.e. longer conjugated segments, by means of energy transfer. Due to the disorder of the polymer chains in thin films such a migration is a random walk, which can be regarded as a diffusion process. Exciton diffusion is one of the physical phenomena that governs the performance of polymer optoelectronic devices. For instance, in solar cells, the average distance that excitons diffuse during their lifetime, the exciton diffusion length, determines the number of excitons that reach the dissociation interface where they can be cleaved into unbound electrons and holes and contribute to the photocurrent.1 In light emitting diodes, the exciton diffusion length is a measure for the amount of parasitic quenching by the metallic electrodes.2 Understanding the exciton diffusion process is of crucial importance to design new materials to improve device performance. Recently, great effort has been made to determine the exciton diffusion parameters in conjugated polymers at room temperature.1-9 For various derivatives of the conjugated polymer poly(p-phenylene vinylene) (PPV) a typical LD of 5-6 nm has been reported at room temperature. A direct way to measure the exciton diffusion length LD is to monitor photoluminescence (PL) quenching in polymer/fullerene bilayer heterostructures as a function of polymer thickness (Figure 1). The exciton diffusion coefficient D can be extracted from the PL time-resolved * Corresponding author. E-mail:
[email protected]. † Zernike Institute for Advanced Materials, University of Groningen. ‡ Dutch Polymer Institute. § Solenne BV. | Stratingh Institute for Chemistry, University of Groningen.
Figure 1. PL decays of 240 nm thick reference MDMO-PPV film (solid line) and heterostructured samples of two polymer thicknesses, 32 nm (dashed line) and 13 nm (dotted line), measured at room temperature. The PL decays are normalized to their maximum value. The inset illustrates the composition of heterostructures.
measurements (Figure 2) in these heterostructures, leading to a room temperature value6 of D ) 3 × 10-4 cm2/s. However, knowledge of the room temperature characteristics alone does not provide insight into the mechanisms that govern the exciton diffusion process in conjugated polymers. In order to elucidate these mechanisms, we have investigated the temperature dependence of the exciton diffusion in the range of 4-293 K. Measurements of LD and D as a function of temperature reveal that the diffusion of excitons is governed by two subsequent steps: upon exciton creation, a downhill migration toward lower energy sites takes place, which is followed by thermally activated hopping. Below 150 K, the latter process is switched off, leading to temperature independent exciton dynamics. II. Experimental Methods Our model material is MDMO-PPV (poly[2-methyl-5-(3′,7′dimethyloctyloxy)-p-phenylenevinylene]), which is of particular
10.1021/jp8042363 CCC: $40.75 2008 American Chemical Society Published on Web 08/26/2008
11602 J. Phys. Chem. B, Vol. 112, No. 37, 2008
Mikhnenko et al. that considers the evolution of the exciton concentration n in time and space:7
∂n(x, t) n(x, t) ∂ 2n(x, t) - S(x)n(x, t) + G(x, t) )+D ∂t τ ∂x2 (1)
Figure 2. Fitting of the PL decays of the 13 nm thick sample at 4 and 293 K by using the diffusion model. The PL decays are normalized to their maximum value. Open circles denote experimental data; the black solid lines are the best fits with eq 2; the dashed line is the modeled PL decay at 4 K with the high temperature exciton diffusion coefficient. The PL decay at 293 K is up-right shifted for clarity. The fitting of the relative quenching efficiency with eq 4 at 4 K is presented as an inset.
interest because it has been widely used in solar cell applications.10 MDMO-PPV was spun from chlorobenzene under dry nitrogen atmosphere on top of a less than 30 nm thick insoluble cross-linked fullerene layer, called poly(F2D) (see inset in Figure 1), which plays the role of the exciton quenching wall.1,3,7 The synthesis and basic chemical characterization of this diacetylene fullerene derivative F2D can be found elsewhere.7 Thickness variation of the polymer layer in the range of 5-40 nm was achieved by changing the solution concentration, keeping the same spin conditions. As a reference sample, we used a more than 200 nm thick MDMO-PPV film spin coated on a clean quartz substrate. Since interface-related exciton quenching effects can be neglected in such a thick sample, it can be considered as a quencher free reference. Root mean square roughness measured with atomic force microscopy (AFM) on an area of 100 µm2 was found to be less than 1 nm for the surfaces of the quartz substrates and the spin coated layers. Thicknesses were measured with atomic force microscopy (AFM) and nulling zone ellipsometry. To measure PL decays, the samples were excited by a 100 fs pulsed Kerr mode locked Ti-sapphire laser, frequency doubled at about 400 nm. The initial exciton density was estimated to be ∼1014 cm-3, being several orders of magnitude less than needed for exciton-exciton annihilation.9 The PL decays were recorded by a Hamamatsu streak camera; the data were wavelength integrated in the overall emission spectral region and normalized to the zero time value in order to be used in the modeling. During the experiments, the samples were kept under vacuum (10-6-10-5 mbar at room temperature), and no degradation was observed. Temperature dependence measurements where performed in a constant flow helium cooled cryostat. III. Results Figure 1 shows measured wavelength integrated PL decays of the reference and of two heterostructured samples at room temperature. The heterostructures with MDMO-PPV films of smaller thicknesses show shorter PL decay times due to the diffusion limited exciton quenching at the polymer-fullerene interface.1,3 The amount of the quenched excitons for every sample is determined by the exciton diffusion coefficient, which we extract by fitting the experimental PL decays with a model
Because of the sample symmetry, n depends only on one spatial coordinate x, which is normal to the film and denotes the distance from the free interface; τ represents the exciton lifetime in a quencher free polymer film and D is the exciton diffusion coefficient. Since the samples were excited with a short pulse, the generation term G(x, t) can be replaced by the initial distribution, which we assume to be uniform due to the low value of the absorption coefficient at the excitation wavelength (4 × 10-3 nm-1). The term S(x) is responsible for the interface quenching and is governed by boundary conditions. The fullerene-polymer interface can be safely assumed to be a perfect quencher;1,3 hence, the first boundary condition is n(L, t) ) 0, with L as the polymer thickness. In contrast to the earlier assumption7 that there is no quenching at the free interface, we found experimental evidence that surface quenching occurs at the MDMOPPV-vacuum interface as well due to a change in the spincoated film morphology close to the interface (see the Supporting Information). This can be taken into account by setting n(0, t) ) 0. Under these conditions, eq 1 can be simplified to a Cauchy problem that can be solved analytically (see the Supporting Information). Since we estimated that self-absorption is negligible in the studied thickness range, the PL intensity is proportional to the exciton concentration and the PL decay was obtained by integration of n(x, t) over the film thickness L: ∞
e-Dtπ (2k - 1) ⁄L 8 n(t) ) 2 R(t) π (2k - 1)2 k)1
∑
2
2 2
(2)
where R(t) is the normalized PL decay of the quencher free reference sample. This expression was used to fit the experimental PL decays as shown in Figure 2 to extract the exciton diffusion coefficient D, which is the only fit parameter. In order to obtain the exciton diffusion length LD ) τD, the relative quenching efficiency Q was measured as:
Q)1-
total PL of heterostructured sample total PL of reference sample
(3)
where the total PL is the time integral of the normalized decay. Integration of eq 2 leads to an analytical expression for Q, which is used in the modeling:
Q(L) )
2LD L tanh L 2LD
(4)
Here the exciton diffusion length LD is the only fit parameter. The measured dependence of the relative quenching efficiency on polymer thickness Q(L) at 4 K and its fitting with eq 4 are reported in the inset of Figure 2 as an example. Figure 3a summarizes the measured temperature dependence of the exciton diffusion length and the coefficient. The data in the range of 150-293 K show a relatively strong dependence on T, while in the low temperature regime between 4 and 150 K the dependence is weak. It is important to note that these two regimes are also present in the temperature dependence of the maximum position of the steady state PL spectrum, which corresponds to the pure electronic (0-0) transition (Figure 3b).
Exciton Diffusion in Conjugated Polymers
Figure 3. (a) Temperature dependence of the exciton diffusion length LD (circles) and the diffusion coefficient D (squares). The two temperature regimes with different trends are highlighted. (b) Temperature dependence of the steady state PL spectrum peak position, which was determined by the Gaussian fit in the vicinity of the (0-0) maximum.
Figure 4. Illustration of the exciton diffusion process under different temperatures. The Gaussian density of states is represented by the distribution of the energies of excitonic states. The T-dependent shift of the PL spectrum maximum is originated by the exciton-phonon coupling, which determines the position of the energy level of the most populated states. (a) The downhill migration fully determines the exciton diffusion process at low temperatures. (b) At high temperatures, the thermally activated hopping also contributes to the exciton diffusion length.
IV. Discussion A blue shift of the steady state PL spectrum with increasing temperature has been previously observed in disordered materials, including conjugated polymers.11-19 Due to disorder in these materials the density of excitonic states (DOS) is inhomogeneously broadened. Such a broadened distribution can be represented by a Gaussian (excitonic) DOS, as schematically depicted in Figure 4. The half-width σ of the Gaussian is a measure for the disorder present in the material. The creation of excitons in the high energy tail of the DOS by absorption of UV light is followed by their downhill migration toward lower energy sites. Such a process is sometimes regarded as thermalization in the literature. The relaxation ends when excitons reach the energy level of the most populated states. This energy level is proportional to -σ2/KT under conditions of thermodynamic quasi-equilibrium and, more generally, is responsible for the
J. Phys. Chem. B, Vol. 112, No. 37, 2008 11603 (0-0) peak position of the steady state PL spectrum. At low temperatures (Figure 4a), such a level is situated deep in the tail of the Gaussian DOS, whereas at high temperatures excitons are thermally disturbed and distributed closer to the middle of the DOS (Figure 4b). The energy increase of the level of the most populated states with temperature causes the blue shift of the PL spectrum. As Figure 3b shows, the T-dependence of the steady state PL spectrum is weak in the low temperature regime. At such temperatures the energy separation between the most populated states and their nearest neighbors is large (Figure 4a). Phonons of high energy are needed to promote excitons to higher energy states in order to blue shift the level of the most populated states. Since such phonons are only present if temperature is high enough, the T-dependence of the peak position of PL spectrum is weak at low temperatures. The two temperature regimes of D and LD, shown in Figure 3a, can also be qualitatively explained in the same physical framework. The downhill migration brings excitons to the level of the most populated states (Figure 4a and b). Further hopping requires absorption/emission of a phonon, consequently the sample temperature starts to play a role. At low temperatures the exciton-phonon coupling is weak and excitons cannot hop any more. Thus, in this case, the exciton diffusion is limited by the downhill migration process. Since such a process is temperature-independent, the exciton diffusion is also expected to be only weakly temperature-dependent. As temperature increases, the probability of phonon absorption by excitons increases. The level of the most populated energy sites climbs uphill on the DOS leading to the decrease of the energy difference between the occupied and neighboring sites (Figure 4a and b). If the temperature is high enough, the thermally actiVated hopping becomes favorable (Figure 4b), which does not lead to a significant change of the exciton energy but contributes to the exciton diffusion. Indeed, the temperature dependence of the exciton diffusion length appears to be strong above 150 K (Figure 3a). Thus in the high temperature regime, the exciton diffusion consists of two steps, namely the downhill migration and the thermally activated hopping, while at lower temperatures the downhill migration fully determines the exciton diffusion process. In order to extract the exciton diffusion coefficient D, we fit the experimental data in Figure 2 on the time scale of the exciton lifetime (solid lines). For T ) 293 K, the fit with D ) 3.2 × 10-4 cm2/s gives a satisfactory description of the PL decay. On the other hand, for T ) 4 K, the fit using D ) 1.4 × 10-4 cm2/s is of poorer quality. The experimental PL decay at short times (
