arXiv:1207.1036v1 [cond-mat.mtrl-sci] 4 Jul 2012 ehdas ffr nih ntedmnt excitonic PL- dependent dominate temperature the by in mechanisms insight transport offers This also studies. thick- method (PL) by Photoluminescence properties dependent transport ness excitonic to the effects, effects, determine interference boundary optical and as penetration quencher aspects morphological including cec,ogncti l htvlacclspv their pave applications cells first photovoltaic towards way film thin organic ficiency, nldn l atr bv 0%adpwrconversion % power 4 and to % up of 70 efficiencies above factors fill including C acceptor electron the (DIP). 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A. 1 21 3 2 uisMxmlin nvriy mHbad 77 W¨urzb 97074 Hubland, Am University, Julius-Maximillians nvriyo usug nvri¨tsre1 65 Augsb 86159 Universit¨atsstrae 1, Augsburg, of University nvriyo ttgr,Paewlrn 7 06 Stuttgar 70569 57, Pfaffenwaldring Stuttgart, of University . 4 4 nogncblyrpho- bilayer organic In . A aen mHbad 77 W¨urzburg Germany 97074 Hubland, Am Bayern, ZAE 1 .Roller, T. Dtd aur 5 2021) 15, January (Dated: 8 ? 2 To . .Engels, B. lesae ra ntergtisto g b,telat- the film 1b), organic within fig. the inhomogeneities of structural by inset influenced right light being the ter vs. in the (dark areas employed intensity shaded we diffuse blue quality versus To specular film of the 1b). ratio the for fig. along measure of a inset i.e. define (right normal, direction surface of transport the tilting exciton along mosaic- crystallite deg film averaged 0.04 DIP an Furthermore, only by charaterized 1b). peak is ity Bragg fig. (100) of the inset (left at oscillations by indicated Laue is planes pronounced lattice the of coherence long-range ino I rsalt egt fi.1c). (fig. heights crystallite DIP distribu- of Gaussian tion integrated has the error structure complementary representing a film by function underlying described is the and deduced of been model a crys- data on the Based this with Laue-oscillations. agreement by in determined nm height, tallite 70 about of thickness a al vprtdo n afo h I tpe wedge stepped DIP the of half one on evaporated ther- mally (CuPc) Phthalocyanine Copper with prepared were nams pih retto ftemolecules the to of corresponding orientation upright nm 1.66 almost an about of spacing lattice reported (001) ana- previously the was geometries. confirmed various samples scans at Bragg-Brentano diffraction the X-ray by of detail in structure lyzed slides. film glass resulting cleaned on The epitaxy by beam prepared molecular were samples organic DIP purpose, this For studies. o h htlmnsec P)suisDPti films thin DIP studies (PL) Photoluminescence the For 1 .Br¨utting,W. ewe h xio iuinlnt of length diffusion exciton the between n ce eerto swl snon-perfect as well as penetration ncher taoe8 tatvto nrisof energies activation at K 80 above rt igaditrrtdb nadvanced an by interpreted and hing co iIdn-eyee(I)has (DIP) Di-Indeno-Perylene uctor rcina roei temperatures. cryogenic at eraction tndniy eo 0Kacoherent a K 80 Below density. iton r.Tmeauedpnetstudies dependent Temperature ers. 13 3 scnb en hsrtopasat peaks ratio this seen, be can As . r,Germany urg, .Pflaum J. r Germany urg ,Germany t, so h organic the of ms eanalyses ce 1 , 4a 1 n the and 2

of the excitons will reach the quenching interface within their radiative lifetime, thus strongly reducing the PL

signal. On the other hand for films thicker than LD the PL signal is expected to dependent only on the absorp- tion and therefore should be identical for the free and the

quencher-covered areas. As a result, LD in the molecu- lar layer can be determined by thickness dependent PL measurements. It is important to stress at this point that 18 according to the layer thicknesses and LD under study as well as by the small spectral overlap for DIP, contri- butions to quenching by Fluorescence Resonance Energy Transfer (FRET) can be neglected9. However, the situation becomes more complex for real samples, especially if the absorption layer thickness ap- proaches the excitation wavelength within the organic material. For thicknesses equal or larger than nλ/4 in- terference effects have to be taken into account20, requir- ing detailed information on the indicatrix of the organic material. Therefore, to quantify exciton quenching one has to calculate at first the intensity profile of incident light across the sample yielding the initial exciton density. Accounting for light reflection at the organic interfaces yields the depth dependent intensity profile19,20

FIG. 1. (a) Structural model of DIP. (b) X-ray structural I(z) − − − analyses and Laue-oscillations (upper left inset) indicating = e αz + ρ2e α(2d z) the high crystallinity of the DIP films. The ratio between I0 −αd specular intensity (dark blue area) and the diffuse scattering +2ρe cos( 2k(d z) δ) (1) − − − intenity (light blue area) has been considered as a measure for the structural quality of the DIP layers (upper right in- Here z describes the position in the film (z = 0 refers set). (c) Model of the DIP film texture together with possible to the glass/organic-interface), α is the absorption coef- exciton recombination processes. Integration of the Gaussian ficient, ρ is the reflection coefficient at the organic in- distribution of the DIP crystallite heights (black curve) yields terface, d is the sample thickness, k is the wave vector the complementary error function (red curve). and δ is the phase shift occurring upon reflection at the backside of the organic layer. With n(z,t) being the local exciton density at time t, the continuity equation reads (inset of fig. 2), acting as exciton quencher due to its HOMO and LUMO positions of 5.1 eV and 3.2 eV with 2 7,21 dn(z, t) ∂ n(z,t) n(z,t) respect to those of DIP, 5.4 eV and 2.9 eV . The PL = D + G(z,t) (2) dt ∂z2 − τ intensity of the DIP films, illuminated through the sub- strate by a NdYag-Laser at 532nm, was measured by a For given exciton lifetime τ, the exciton generation sensitive CCD detector after passing a 590 nm long pass term G(z,t) under constant illumination, i.e. at steady filter to block background intensity of the excitation. For state conditions ( dn(z, t)/ dt = 0), is expected to be a given DIP layer thickness, the comparison of the rela- proportional to the light intensity profile. Appropri- tive PL intensity ratio Q=PLQ/PLnQ, recorded on the ate boundary conditions can be achieved by neglecting ∂n(z,t) nQ Q bare (PL ) and the CuPc-covered (PL ) area reveals quenching at the glass/organic-interface, ∂z =0 z=0 contributions from non-radiative decay channels and dis- and assuming either complete quenching, n(z,t)=0, or ∂n(z,t) 17 sociation of excitons . In films thinner than L most no quenching, ∂z = 0, at the organic/quencher- D z=d

3 or organic/air-interface, respectively. Real samples will thicknesses of 300 nm Q is still below 0.6, indicating the always operate between these two extremes, i.e. par- existence of a significant, almost thickness independent tial quenching might occur at the organic/air-interface quenching contribution. e.g. due to surface states as well as non-ideal quenching at the organic/quencher-interface. For perfect quenching the absolute value of the slope and accordingly the ex- citon concentration gradient will be at maximum Smax at the quencher interface. This provides a measure for the quenching quality V = S/Smax, where S is the slope at the organic/quencher-interface assuming incom- plete quenching. Obviously, V assumes values between 0 and 1. As for more complex intensity profiles eq.(2) can no longer be solved analytically, we employed an ansatz based on superposition of Dirac delta functions G(z) = δ(z z )/τ as generation term. The low ex- − 0 citon densities in our PL studies render the diffusion to be concentration independent and therefore nδ(z,z0) can FIG. 2. Thickness dependent quenching ratio be used in the generation profile. A convolution of the Q nQ Q=P L /P L . The fit (blue line) corresponds to the light intensity profile, including interference effects and model discussed in text accounting for interference effects nδ(z,z0) results in and interdiffusion at the DIP/quencher interface. The inset displays the sample structure.

d

n(z)= Φ I(z0) nδ(z,z0) dz0 (3) To relate these results to the underlying film morphol- Z · · 0 ogy, complementary studies on the temperature depen- The factor Φ describes the quantum efficiency of exci- dent PL have been carried out on DIP layers of vari- ton generation upon photon absorption. Assuming non- ous thicknesses. Fig. 3a shows the PL intensity as a radiative decay processes in the absorption layer to be of function of the inverse thermal energy recorded on thin minor importance, the detected PL intensity corresponds (30 nm) and thick (290 nm) DIP layers with an with- −1 to the number of excitons not quenched within their ra- out quenching layer. Below 0.145 (keV ) , i.e. above nQ diative lifetime 80 K, the fluorescence of the free (PL ) and of the CuPc covered (PLQ) DIP volume is thermally activated, with PLnQ showing a distinct increase with thickness d cosh(z0/LD) from 12 meV to about 21 meV. This tendency can be PL = k I(z0) 1 V dz0 (4) · Z  − cosh(d/LD)  related to different exciton density gradients as a func- 0 tion of layer thickness. A steeper concentration gradi- Here we used the common definition of the exciton dif- ent, occurring for thinner films, reduces the effective en- 14 fusion length LD = √Dτ. For V = 0 each exciton con- ergy required for transport . In addition, this is con- tributes to photoluminescence thereby yielding the inte- firmed by the quencher covered 30 nm thick DIP film grated intensity profile. Using eq.(4) the PL signal can whose PLQ activation energy is about four times smaller be calculated for any given I(z0). The thickness depen- than that of the uncovered film. Finally, the value of 21 dent Q measured at room temperature (RT) is displayed meV for the thickest DIP film is in good agreement with in fig. 2. Three distinct features can be clearly identified: the PL activation energy of covered DIP irrespective of

First, Q does not approach zero even for dDIP 0, sug- layer thickness and, therefore, refers to exciton transport → gesting imperfect quenching at the DIP/CuPc interface. within the DIP crystallites. In analogy to charge car- Second, the oscillatory thickness behavior of Q refers to rier transport studies on long-range ordered molecular the presence of interference effects. Third, even for film stacks5 we attribute the temperature dependent fluores- 4 cence behavior to exciton-phonon-interaction constitut- (d > 100nm) show an almost constant Q over the en- ing a non-radiative decay channel which is suppressed tire temperature range. This points directly at the mor- towards lower temperatures, i.e. upon freezing-out non- phological origin of this phenomenon which can be in- local phonon modes11. This assumption is corroborated terpreted by the previously discussed spatial extension by the observed activation energy range which coincides of DIP crystallites along the exciton transport direction, with that of non-local phonon modes in polyaromatic sin- i.e. normal to the (001) plane (fig 1). For thick films gle crystals5,16. Furthermore, data for all thicknesses in (d > 100nm) non-radiative as well as radiative recom- fig. 3 reveals the PL intensity to become temperature bination processes take place during exciton transport independent below 80 K. Caused by an almost coherent within a single crystalline domain, due to a substan- transport of the (free) excitonic species within the crys- tial energy barrier at the grain boundaries. However, talline DIP fraction12 without dissipative effects by static for thin films (d < 100nm), where most of the crystal- inhomogenities. lites will stretch across the entire film, exciton transport and recombination are substantially determined by the respective quenching interface. Consequently, the vari- ation with temperature is mainly governed by the PLQ contribution to Q. Furthermore this model is supported by the fact that the temperature independent Q below 80 K is significantly smaller for thin than for thick DIP films as quenching is still present in case of the former whereas in thick films excitons are not being capable of reaching the quenching DIP/CuPc interface and there- fore relax to the ground state by the same mechanisms as for the uncovered DIP section. Finally, this model also explains the non-vanishing quenching contribution for very thick films (fig. 2). In this case, the intrinsic crystallite size, which agrees very well with the optimized thickness deduced from the

Ispec/Idiff ratio measured by X-ray (fig. 1b), initiates a pronounced 3D island growth (Volmer-Weber growth) together with an enhanced surface roughening as con- firmed by detailed x-ray analyses and atomic force mi- croscopy (AFM)2. As indicated in fig. 1c this topography promotes the penetration of the top-deposited molecular quenching material into the grain boundaries, leading to a significant contribution by lateral exciton diffusion and FIG. 3. (a) Comparison of the PL(T) behavior with and with- dissociation to the PL quenching of about 50 % even for out quenching layer for the thickest and thinnest film of this thicknesses larger than 250 nm. In addition, this trend is study. (b) Temperature dependent Q for five representative supported by the better overlap of the electronic wave- DIP layer thicknesses normalized to the room temperature function and the molecular transition dipoles within the value. Thinner layer show the signature of a thermally ac- (001) plane, presumably entailing the lateral components tivated Q above 80 K whereas below this temperature, the ratio remains constant. of the tensorial diffusion constant to be larger than the out-of-plane component6,9. A lower limit for the lateral As it becomes obvious from fig. 3b, the thickness de- LD of several tens of nanometres has been reported which 22 pendent Q is characterized by a temperature dependent overall matches our observation . However care has to decrease for thin DIP films followed by an temperature be taken as those values have been determined in the independent regime below 80K. In contrast, thick films presence of metallic nanostructures which might influ- 5 ence the exciton dynamics e.g. by plasmon mediated consideration of eq.(1) and amounts to 1.4. Though influ- non-radiative recombination. enced by the respective interface morphology, this result Summarizing these results, we suggest a relation to ac- as well as the relative phase shift δ almost matches π/2 count for the morphological impact of real quencher in- which is theoretically expected for a standing-wave with terfaces, thereby resembling the aforementioned comple- open end (organic/air interface) versus that with fixed mentary error function end (organic/quencher interface). Finally, the discussed transport model also renders the thickness dependent in- terface roughness which according to the rapid roughen- β 2 ′ d d ing model observed for DIP scales as σ=d with β=0.75 . Q = Q R + (1 R) erfc − 0 (5)  − ·  σ   In summary, we have investigated the exciton transport in long-range ordered molecular thin films by PL quench- The average crystallite height and surface roughness ing, explicitly accounting for interference effects as well as are described by d0 and σ whereas R qualitatively con- structural properties at the respective quencher interface. tains all effects which limit the relative quenching in case Based on a diffusion model in combination with comple- of thick layers. Modelling the thickness dependent Q by mentary morphological analysis we were able to describe our extended exciton diffusion model, comprising effects the thickness and temperature dependent PL quenching by optical interference and quencher interface morphol- behavior of DIP. The resulting thermal transport behav- ogy, reveals the fit shown in fig. 2 and an LD of 90 nm ior indicated coherent exciton transport in a tempera- for DIP. This value is in good agreement with previous ture regime below 80 K. The diffusion length of 90 nm reports using spectral photocurrent measurements inter- is in striking agreement with the average DIP crystallite preted by a model of Feng and Ghosh3,8. Comparing the height and, with prospect on implementation in organic estimated average crystallite height of d0 = 85 nm with photovoltaics, indicates the decisive role of structural or-

LD renders the correlation between these properties to be der on the exciton transport in molecular semiconduc- evident. Furthermore, the adjusted reflection coefficient tors. ratio between the free and the CuPc-covered DIP volume Financial support by Deutsche Forschungsgemeinschaft can be deduced by fitting the measured data points under (project No. PF385/4) and BASF is acknowleged.

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