The Effect of Oxygen Induced Degradation on Charge Carrier Dynamics in

Transcription

1 Electronic Sulementary Material (ESI) for Journal of Materials Chemistry A. This journal is The Royal Society of Chemistry 2014 The Effect of Oxygen Induced Degradation on Charge Carrier Dynamics in P3HT:PCBM and Si-PCPDTBT:PCBMThin Films and Solar Cells Safakath Karuthedath, Tobias Sauermann, Hans-Joachim Egelhaaf, Reinhold Wannemacher, C.J. Brabec, Larry L. Lüer * Otical Sectroscoy and Microscoy of Nanostructured Materials, IMDEA Nanociencia, C/ Faraday, 9, Cantoblanco (Madrid), Sain. Belectric OPV GmbH, Landgrabenstr. 94, Nürnberg, Germany. Bavarian Center for Alied Energy Research, Fürther Str. 250, Nürnberg, Germany 4i-MEET, Friedrich-Alexander University, Martensstr. 5, Erlangen, Germany SUPPORTING INFORMATION: Table of contents: A B C D E F Derivation of the fitting function for charge decay in degraded samles A closer look at the generation factor Femtosecond transient absortion in Si-PCPDTBT films Femtosecond transient absortion in P3HT:PCBM films Absortion sectra Pulsed TA measurements A Derivation of the fitting function for charge decay in degraded samles Degradation can cause a background of sace charges that ersist even in the absence of irradiation, by introducing dee tras for one carrier tye. These background carriers do not give rise to a transient absortion (TA) signal (because they are not hotoinduced), but they do influence the decay kinetics of the hotoinduced olarons, because they contribute to recombination. 1

2 We assume degradation-induced defects in the donor (P3HT or Si-PCPDTBT) hase that act as accetors for electrons. 1 The autodissociation equilibrium, given by the dissociation and recombination coefficients k d and k a, resectively, cause an excess density of ositive olarons that, uon hotoexcitation of negative and ositive olarons, causes a deviation of olaron recombination kinetics from simle bimolecular behavior. The kinetic scheme is given by [ g(l) 0 k + n L ] A k d ka A +, (S1) where 0 signifies a neutral olymer strand, and n are negative olarons in the donor and accetor hase, resectively, A and A - are neutral and negatively charged defects in the donor hase. The generation term g(l) in our exerimental setu is a boxcar function that deends on light intensity L. Since the density of negative olarons in the donor hase can be neglected, an interaction between these latter secies and A can be neglected. Electroneutrality then requires that at all times, A + n = (S2) Assuming comlete ionization of defect sites, we get A = const = A tot (A tot being the total density of degradation-induced defect sites) and therefore (t) = n(t) + A tot (S3) For eq. S3 to hold during the exerimentally accessible time range, we also require the autoionization equilibrium to be faster than the tyical recombination times, i.e. in S1, k d + k a k n(t) L. This assumtion is different from the one by Seemann et.al [1]., who assume that k a is very slow and thermally activated, which is justified in their system by the observation of a hoto-induced build-u of ersistent background carriers. Here, we do not 1 The assumtion of electron donors would lead to the same concentration-time law for P3HT olarons, under the given assumtions. 2

3 observe such a henomenon, and we are concerned with an unknown electrochemistry (i.e. we do not know the redox otentials of the irreversible hotoinduced defects while Seemann et al, studying reversible oxygen effects, can rely on the known redox otential of the O 2 /O - 2 system). The rate equation for negative olarons is thus given by dn dt = G(L) k L (t) (n(t) + A tot) n(t) (S4) In order to account for disersive effects, we choose a olynomial ansatz for the recombination coefficient: k L (t) = k 0 γ L t (S5) The exerimentally obtained differential absortion ΔA(t), is related to the olaron concentration via the Beer-Lambert law, A(t) = A(t) umon A(t) um off = σ (t) d, (S6) Where σ is the ositive olaron absortion cross-section at the robe wavelength of 970 nm, d is the film thickness, and Δ(t) is given by (t) = (t) umon (t) um off (S7) When the um ulse is off, n(t) = 0; from S3 we then obtain (t) umoff = A tot (S8) Inserting S3 and S8 into S7, we obtain (t) = n(t), (S9) And inserting S9 into S6 and rearranging gives n(t) = A(t)/(σ d) (S10) 3

4 We insert S10 into S4 and obtain after rearranging d A(t) dt = σ d g(l) (σ k L (t) d) [ A(t) + σ k r ' (t) = k r (t) We define a sectroscoic recombination rate constant (σ generation term G ' (L) = σ d) d A tot ] A(t) (S11) and a sectroscoic d g(l). From S6 and S8 we learn that the absortion caused by the background olarons is P = σ d A tot. Inserting these relations into S11, we obtain finally A background d A(t) dt = G ' (L) k r ' (t) [ A(t) + A background ] A(t) (S12) Equation S12 is solved numerically by standard ODE (ordinary differential equation) solvers. By variation of G ' (L), k r ' (t), and Abackground, we fit the calculated transient absortion rofile to the exerimental one. For each samle and degradation level, we fit all measured dynamics at different light intensities globally. Minimizing the global error squared with standard nonlinear otimization techniques, checking that no systematic deviations are resent, and using σ cm 2 for P3HT and σ cm 2 for Si-PCPDTBT, and d=250 nm, we obtain the device arameters k r (t) and A tot quantitatively at each degradation level. In eq. S12, the fitting arameters A background and γ (inside k L (t)) both act on the long term asymtotic form of the concentration-time deendence. This raises the question how strong the cross talk between these arameters is exected to be in the fits. Below, we give some simulations that show quite distinct long-time behaviors for variation of γ and A background P, resectively. In Fig. S1a, both γ=0 and A background = 0. In this case, eq. S12 has the following solution: A(t) = [ 1 A(0) + k L t ] 1, (S13) 4

5 which has an intensity indeendent long-time asymtote of A(t) = [k L t] 1, which is the same for all starting concentrations and has a sloe of -1 in a double logarithmic reresentation. In Fig. S1b, we leave A background = 0 but set γ = 0.3. As can easily be shown, the long-time asymtote is still linear in a double logarithmic reresentation and indeendent of the starting concentration, but the sloe is now 1 - γ = 0.7. Finally, in Fig.S1c, we set γ = 0 and A background = In this case, an entirely different long-time solution is obtained: At a time when A background becomes comarable to the remaining olaron absortion ΔA(t), the decay trace deviates from bimolecular recombination. After very long times, A background >> ΔA(t), so the bracket in S12 becomes a constant, and the solution is a stretched exonential. As can be seen in Fig. S1c, such a stretched exonential does not have a linear long-time asymtote, instead it bends towards infinite sloe in a double logarithmic reresentation, nor is the long-term behavior intensity indeendent: for long times, all curves in Fig. S1c are y-shifted relicas of each other meaning that they deviate by a constant factor. In Fig. S1d finally, A background = The condition A background >>ΔA(t) is now obtained at a much later time than in Fig. S1c. For this reason, the two regimes (linear sloe and final stretched exonential) can both be observed searately, at least at high intensities. When the stretched exonential art sets in after the intensity indeendent asymtote of the bimolecular decay has already been reached, it follows that also all stretched exonentials are indeendent of the initial concentration. The amount of intensity deendence still resent in the stretched exonential art is therefore a robe for the background carrier concentration. Therefore, a global fitting of various curves at different starting concentrations, as erformed here, is mandatory to disentangle γ from A background. Summarizing this curve discussion, a variation of γ causes a change in the sloe of the linear asymtote, while a change in A background changes the time at which A background and ΔA(t) become comarable, which results in a deviation from the straight line behavior and in turn 5

6 controls how much of the initial intensity variation is still visible in the long time exonential decay hase. These henomena are well distinguished and therefore both A background and γ can be fitted at the same time with low cross talk, but only if several curves of different starting concentration are fitted at the same time. This justifies the rocedure we adoted for the analysis of the charge dynamics in Fig. 3, main manuscrit. Figure S1.a 6

7 Figure S1.b Figure S1.c 7

8 Figure S1.d B A CLOSER LOOK AT THE GENERATION FACTOR G G in S12 and S1 (and in eq. 1 and 5 in the main text) is the rate of generation of free charges. It is roortional to the incident hoton flux er area and film thickness, the roortionality constant being the yield for hoton absortion, exciton dissociation and charge searation: G = J h /d φ abs φ diss φ se, (S14) It is convenient to summarize the yields for absortion, exciton dissociation and charge searation into the generation term, because these rocesses and also their counter layers hoton scattering, exciton deactivation, and geminate recombination, resectively - all occur on the femto to icosecond time scale and therefore do not contribute to the microsecond kinetics. In S14, J h is the hoton flux in cm -2, d (in cm) is the film thickness, φ abs is the absortion robability in the film (φ abs = 0.93 in P3HT as the enetration deth at the 8

9 uming wavelength of 532 nm is much smaller than the film thickness, while in Si- PCPDTBT:PCBM, it is only about 10%) and φ se is the charge searation robability after a hoton has been absorbed. We do not need to consider the inhomogeneity of olaron generation along the deth axis due to the finite light enetration deth for wavelengths of strong absortion, because charge carrier diffusion through the film thickness occurs on a time scale faster than our exeriment. Effects such as exciton annihilation or icosecond charge recombination can be safely excluded by using weak continuous wave lasers as in the resent case. Since the external quantum efficiency, EQE, is given by: EQE = φ abs φ diss φ se φ extr, (S15) we can insert S15 into S14 yielding: EQE/φ extr = Gd/J h (S16) We can call the term recombination relative to absorbed hotons). EQE/φ extr the free olaron yield (i.e. olarons that survived geminate We used S14 to fit the on curves under illumination In Fig. 2, and then S16 to calculate the free olaron yield (see Fig. 4a, black symbols) from the fitting arameter G and the um intensity. In the fitting, we noted a strong interdeendence between k r, γ and c b, both γ and cb tending towards zero. This can be understood by the fact that in Fig.2, continuous illumination has been used. Most of the data oints are within 50% from the maximum, so that µ does not vary much and hence γ is close to zero. For the same reason, c b cannot be fitted accurately because the effect of background carriers is only seen at low carrier concentrations, of which 9

10 we have only 2 reasonable data oints in Fig.2. For this reason, we fixed both γ and c b to zero in the fitting of G. The results are dislayed in Fig. 4a for P3HT:PCBM at various degradation levels, showing no significant change of G under increased degradation. C Femtosecond transient absortion in Si-PCPDTBT Femtosecond transient absortion (TA) sectroscoy is used to trace hotohysics that occur on a time scale of femto to icoseconds. In organic hotovoltaics, exciton dissociation and geminate recombination, rominent loss rocesses that reduce the generation yield, have been shown to occur on this time scale. In contrast to microsecond TA, where essentially only one tye of hotoexctation (ositive olarons in the donor hase) is visible, in femtosecond TA we additionally observe neutral singlet excitons. The TA sectra of singlets and olarons generally overla, so matrix decomosition techniques need to be used to obtain the timeresolved oulation of singlet excitons and olarons searately. We follow a rocedure called target analysis described by van Stokkum et al[2]. In short, we aly Beer-Lambert s Law, A(t,w) = i c i (t)σ i (w) (S17) to reroduce the measured transient absortion sectrum A(t,w), which deends on time t and robe energy w, by a suerosition of states I with characteristic time-resolved concentration c i (t) and energy-resolved absortion cross-section σ(w). Eq. S17 can be written in matrix form: A = c σ (S18) 10

11 In eq. S18, each column of the c matrix reresents one comlete concentration-time deendence of a state i, while each row of the σ matrix reresents the full (time-invariant) sectrum of that state i. Of course, any linear combination E of the sectra in the σ matrix E = s σ, (S19) S being the sectral weight matrix, can also solve eq. S18, as can be seen by introducing S19 into S18: A = c s 1 E (S20) and substituting c s 1 c ' : A = c ' E (S21) The concentration-time matrix c SEQ of a strictly sequential reaction 0 S 1 S 2 S 3 0 (no back reactions, no arallel reactions, no arallel generation of the excited states S i from the ground state 0) is analytically known [2]. Hence, assuming a strictly sequential reaction, we can find the E matrix by simly multilying the inverted c SEQ with the measured TA sectrum: E = (c SEQ ) 1 A (S22) In case the assumtion of a strictly sequential reaction ath haens to be right, then c = c SEQ from which immediately follows E = σ. In this simle case, evaluation of S22 directly yields the sectra of the hotohysical states σ i (w). Generally, however, hotohysical reaction aths are not strictly sequential. In organic hotovoltaics, it has been shown that art of the olaron generation occurs on a time scale < 100fs, and thus in arallel with singlet generation. Singlets can sequentially convert into olarons, but in arallel they can directly decay to the ground state by some ultrafast mechanisms (exciton annihilation, ultrafast deactivation of 11

12 short-lived charge transfer state between donor and accetor). If we aly S22 in this general case, then the resulting matrix E will not directly reresent the sectra of the hotohysical states, but suerositions of these, according to S19.The rows in E are therefore called evolution-associated differential sectra (EADS), while the rows in the σ matrix are called secies-associated differential sectra (SADS). In order to solve S19, the sectral weight matrix s must be found using additional hotohysical knowledge. This is done by designing a test matrix σ test, consisting of a sectral model for all contributing excited states, satisfying existing hotohysical knowledge but roviding some adjustable arameters. Using the standard Levenberg-Marquardt otimization technique, we minimize the error between the E matrix obtained from S19 and the one obtained from S22, by varying the free arameters in σ test. In doing so, we obtain also the sectral weight matrix s, which we can use to go from the sequential concentration matrix to the actual one. In the last ste, the concentration matrix is fitted to a target model containing all ossible reaction aths and associated rate constants. In our case, this last ste is not necessary. Since we are interested in the olaron yield er absorbed hoton, we can get this information directly from the sectral weight matrix. To illustrate the above rocedure, we resent below the single stes for obtaining the olaron yield in ristine Si-PCPDTBT. First we aly eq. S22 to find the E matrix that best reroduces our measured TA sectrum, which is given on the left in fig. S2. We do this by non-linear otimization of the exonential lifetimes in the sequential concentration matrix c SEQ, by minimizing the error between the calculated A (using eq.21) and the measured one. The quality of the fit is shown in Fig. S2, right: all dynamic features are nicely reroduced, namely (i) a fast decay of hotoinduced absortion (PA) around 0.9 ev, (ii) a fast build-u of PA around 1.4 ev, and (iii) a fairly constant hotobleach (PB) around 1.6 ev. 12

13 Fig. S3 shows the EADS (rows of the E matrix), that can be used in eq. S21 to calculate the reroduced TA sectrum (Fig. S3 right) after building the c matrix with the lifetimes of the EADS, given in the inset. The second ste is to aly S19 to fit the EADS by a suerosition (with relative weights in matrix s) of the sectra of the hotoexcitations in matrix σ. We assume only 2 hotoexcitations: singlet excitons and olarons. Since both these hotoexcitations involve the electronic system of Si-PCPDTBT, they share the same hotobleach (PB). Irresective whether a olaron or a singlet exciton is formed on a conjugated segment of Si-PCPDTBT, the bleach it creates is always the same. The sectral weights that we obtain, are therefore directly roortional to the concentration of the secies. As shown in Fig. S4, the sectrum of the singlet exciton involves, aart from the PB features at 1.7 and 1.9 ev, a PA band at 0.87 ev with vibronic relicas at 1.04 and 1.2 ev, a stimulated emission band at 1.34 ev, and a higher energetic PA band at 2.55 ev. The olaron sectrum contains, aart from PB, a PA at 1.03 ev followed by vibronic relicas at 1.18 and 1.34 ev, and a broad PA at 2.3 ev. Multilying these sectra with the sectral weights that are given in the inset of Fig.S4, yields the thick lines in Fig. S3, showing near erfect agreement with the EADS sectra (thin lines). The sectral weights can therefore be considered reliable. Finally, the olaron yield at 100 s is obtained by using the inset of Fig. S4 to divide the olaron sectral weight in EADS2 by the sum of the singlet and olaron sectral weights in EADS0. This rocedure yields the first blue symbol in Figure 4a, main manuscrit, for 0% JSC loss. Then the whole rocedure is reeated with analogous TA sectra of the degraded samles. 13

14 Figure. S2: (left) TA sectrum of ristine Si-PCPDTBT after uming at 390 nm with 150 fs, 10 nj ulses of 300 µm sot size; (right) global fit using eq. S22. Figure. S3: EADS (rows of E matrix) and associated lifetimes(thin lines). Thick lines: EADS reroduced using eq. S19 with the SADS (σ matrix) and sectral weights as shown below. 14

15 Figure. S4: SADS (rows of the σ matrix) and corresonding sectral weights to reroduce the EADS in Fig. S3 D FEMTOSECOND SPECTROSCOPY IN P3HT:PCBM FILMS EADS sectra for P3HT:PCBM films were obtained in the same way as described above for Si-PCPDTBT. An analogous treatment to obtain secific sectral weights for olarons and singlets is however comlicated by the resence of two donor hases (amorhous and ordered), each with distinct otical robes for singlets, olarons and the corresonding bleach. A target analysis of P3HT:PCBM films will be the focus of a forthcoming ublication. Here, we follow the simlified treatment of Guo et al [3] who obtained secific kinetics for singlet and charged states by subtracting the singlet contribution to the charge transient at 1.24 ev, which they found to be about one third of the maximum of the singlet absortion band at 1.0 ev, which is ure because there is no oscillator strength for the charge absortion band at that robe energy. Alying this rocedure to our EADS yields sectral weights of the singlet and olaron bands, however with unknown relative cross-sections because the otical robes for 15

16 P3HT olarons and singlets are not locked via the common PB signal as in our treatment of the Si-PCPDTBT data. Therefore, alying Guo s treatment cannot yield the absolute olaron yield, as our target analysis can, but only a quantity which is roortional to it. In order to trace degradation effects, a quantity which is roortional to the known ristine IQE is however sufficient. In Fig. 4a of the main manuscrit, we therefore scaled the olaron yields from the EADS (red symbols) to match the black symbol for the ristine samle. It is found that the olaron yields for the degraded samle do not show a significant deendence on degradation, in agreement with the microsecond data which are absolute. 16

17 E Absortion sectra 17

18 F Pulsed TA measurements Pulsed transient absortion measurements were erformed with a 532nm laser with 300 icosecond ulses. LITERATURE: [ 1] A. Seemann, T. Sauermann, C. Lungenschmied, O. Armbruster, S. Bauer, H.-J. Egelhaaf, J. Hauch, Solar Energy,2010, 85, [2] Ivo H.M. van Stokkum *, Delmar S. Larsen, Rienk van Grondelle, Biochimica et Biohysica Acta, 2004, 1657, [3] J. Guo, H. Ohkita, H. Benten, S. Ito, J. Am. Chem. Soc. 2010,132,

19 19