Photogeneration of Charge Carriers in (Phenyl-C61-butyric Acid

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Photogeneration of Charge Carriers in (Phenyl-C61-butyric Acid Methyl Ester) Mixed with Small Amount of Polymers Jaros#aw Jung, Anna Stefaniuk-Grams, and Jacek Ulanski J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06179 • Publication Date (Web): 06 Sep 2017 Downloaded from http://pubs.acs.org on September 7, 2017

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The Journal of Physical Chemistry

Photogeneration of Charge Carriers in (Phenyl-C61-butyric Acid Methyl Ester) Mixed with Small Amount of Polymers Jaroslaw Jung*, Anna Stefaniuk-Grams, Jacek Ulanski Lodz University of Technology, Department of Molecular Physics, Zeromskiego 116, 90-924 Lodz, Poland *[email protected]; tel. +48 42 631 32 05

ACS Paragon Plus Environment


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Abstract Photogeneration of charge carriers in closely packed phenyl-C61-butyric acid methyl ester (PCBM) was investigated by means of the xerographic discharge technique. It was found, that position of center of mass of the thermalized electron is positioned at distance which is integral multiplicity of the center-to-center distance between the adjacent PCBM molecules. For low electric field, 104 - 107 V/m, the most photogenerated electrons originate from the electrons thermalized at the molecule next but one to the geminate recombination center. For the threshold electric field (ca. 2x108 V/m) the expected value of the thermalization length, ca. 1.9 nm, is independent on the assumed distribution functions of thermalization distance of the electron-hole pairs. The Coulomb binding energy for this characteristic of PCBM electron-hole separation length is correlated with the threshold energy value separating the extrinsic and intrinsic photogeneration in fullerenes. The model predicts the observed experimentally threshold value of photon energy 2.25 eV, below which photogeneration yield in fullerene based materials decreases abruptly; then taking into account the average electronhole pair Coulomb binding energy 0.15 eV one can calculate the electric gap energy 2.4 eV, consistent with the literature data. It explains also how the presence of poly(3-hexylthiophene) influences the photogeneration process.


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1. Introduction For a number of years in many research and industrial laboratories an intensive research on application of organic semiconductors for construction of flexible, lightweight and cheap organic photovoltaic devices (OPVD) is carried out.1 The most popular active layers in OPVD are the so called bulk-heterojunction (BHJ) composites made of donor type polymeric organic semiconductors, such as e.g. regioregular poly(3-hexylthiophene) poly(3-hexylthiophene-2,5diyl) (P3HT), poly(benzodithiophene-co-thieno[3,4-b]thiophene)-based materials (PBDTTT) or poly(2,5-bis(3-hexadecyl-thiophen-2-yl)thieno[3,2-b]thiophene) (pBTTT)2,3,4 and acceptortype small-molecule semiconductors, mostly fullerene derivatives, like (phenyl-C61-butyric acid methyl ester) (PCBM)5 or others6. Such systems are still subject of intensive research, in spite of the fact that in last years the organic-inorganic hybrid materials called perovskites7 have attracted a lot of attention. Photovoltaic effect in OPVD with BHJ active layer originates from the specific morphology of the donor/acceptor mixture and the interface interactions. When thin BHJ films with a thickness ranging from tens to hundreds of nanometers, with appropriate donor to acceptor ratio are properly prepared, a dense interpenetrating network of donor and acceptor phases can be formed.8,9,10 The average distance between the photoexcitation zone and the p-n junctions should be very short and comparable to the average diffusion length of excitons (ranging from 5 nm to 10 nm for P3HT11,12,13,14 and around 5 nm for PCBM15). A simplified mechanism of the photovoltaic effect can be described as follows: excitons photogenerated in the semiconducting polymer and/or in the fullerene derivative diffuse into the p-n junction and occupy charge-transfer (CT) states. Energy of the CT states is equal to the energy difference between the highest occupied molecular orbital (HOMO) of a donor and the lowest unoccupied molecular orbital (LUMO) of an acceptor. In the



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P3HT/PCBM junction the CT states dissociate with very high efficiency, the electrons are transferred to PCBM molecules, and holes to the polymer molecules.16,17 Such photogeneration phenomenon can be described by the Onsager-Braun model.17,18,19 This model determines the probability of the excitons dissociation, and when applied to experimental data it allows to evaluate the distance between the donor and the acceptor molecules.20,21 The donor and acceptor phases constitute photogenerating and simultaneously transporting materials: the photogenerated holes and electrons are transported via polymer and via fullerene phases, respectively. In the OPVD prepared from the P3HT:PCBM 1:1 mixture, for a light from 410 nm to 650 nm range where the absorption of P3HT dominates, the internal power conversion (IPCE) and external quantum efficiency (EQE) take the highest values over the whole range of the absorbed light. For wavelengths below 410 nm, where light is absorbed mostly by PCBM, IPCE and EQE become smaller and they decrease further with decreasing light wavelength.22 Role of fullerene in OPVD is subject of intensive investigations since many years,17,23,24,25,26 nevertheless there are still several open questions, especially related to the role of the morphology of the polymer-fullerene composites. Recently Kästner et al.27 have shown that energy of the CT states at the PCBM-polymer interface depends on degree of ordering of the macromolecules and PCBM molecules in the interface region. Chow et al.28 have shown that formation of the excited states on PCBM limits performance of the OPVD due to internal conversion of the PCBM excited singlet states to PCBM triplet states and then to polymer triplet states where they recombine. Additionally the triplet states may deteriorate the material due to reaction with oxygen leading to formation of highly reactive superoxide radical anions. These findings are supported by investigations of femtosecond dynamics of charge separation in two PCBM-semiconducting polymer composites by means of Transient


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Absorption Spectroscopy.4 The authors have found, that ultrafast and highly efficient charge carriers separation occurs in the PCBM/polymer interface regions; by contrast in the composite regions where PCBM aggregates dominates, the photogeneration efficiency is marginal. Similarly Grancini et al.25,29 on a basis of theoretical calculations and analysis of two dimensional transient absorption maps came to the conclusion, that in the PCBM/polymer solar cells contribution of photogeneration in the PCBM phase to internal quantum efficiency (IQE) is negligible, even for light wavelength below 500 nm, where absorption by PCBM dominates. On the other hand in several published reports it was shown, that EQE, IPCE and IQE changes considerably in the short wavelength (high energy) light range, indicating, that role of PCBM as a medium where dissociation of excitons can occur, should not be neglected.1,21,24,25 Gélinas et al.30 have shown, that in the polymer/fullerene derivative systems crucial role in charge carriers dissociation play delocalized band-like states in the fullerene aggregates, where charge separation occurs at distances 4-5 nm, i.e. much larger then fullerene-fullerene distance. Moreover charge separation doesn’t require excess of energy above those needed to overcome Coulomb interaction, in contrast to predictions of Onsager theory based models, in which excess of energy in hot exciton states is needed.19 Different interpretation of the charge carrier photogeneration phenomenon in the PCBM was proposed by Hahn et al.31, where Onsager model was used to analyze IQE.32 This short review of few selected recent papers demonstrates that there is no commonly accepted mechanism of exciton dissociation in solar cells based on polymer/fullerene derivative systems and further studies are needed. Electronic structure of PCBM (and in general of fullerenes) are characterized by three specific energy parameters: optical band gap (Eopt), threshold energy (Eth) and electrical gap Eg. Above Eth = 2.25 eV the IQE rises sharply what can be associated with intrinsic photogeneration, while below Eth extrinsic photogeneration prevails. While the Eopt (1.84 ÷



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1.85 eV)33,34 and Eth values can be determined spectroscopically with good accuracy, determination of the Eg value for PCBM is controversial and it depends on the used experimental method. Photoemission and inverse photoemission methods yield Eg = 2.37 eV35; but from an analysis of IQE Hahn et al.31 calculated Eg = 2.45 eV, what is close to theoretical value Eg = 2.52 eV calculated for C60 by Shirley36; however cyclic voltammetry methods yield higher values, Eg = 2.65 ÷ 2.75 eV37; still higher values Eg = 2.98 eV was determined on a basis of UV-Visible absorption, electroabsorption and luminescence for C60 films, as reported by Kazaoui et al.33 In this paper we present the results of investigations of charge carrier photogeneration in layers of PCBM obtained by drop casting from solutions containing also small amount (5 wt % in relation to PCBM) of P3HT or of insulating polymers – poly(methyl methacrylate) (PMMA) or polystyrene (PS). The measurements were performed using the xerographic discharge method, and polymers were added in order to get good quality, homogeneous and pin-hole free films required for this method. Additionally it was possible to determine how the presence of the semiconducting polymer (P3HT) influences photogeneration of charge carriers in PCBM. Analysis was performed on a basis of the Onsager’s theory32 adopted for photogeneration process in disordered organic semiconductors.19,20,38 Such approach has allowed to determine distribution function of the thermalization length, value of electrical gap Eg and also an average distance of an electron at singled excited state S1 from geometrical center of the PCBM molecule. Finally we propose mechanism of photogeneration in PCBM and in PCBM/P3HT systems operating in the short wavelength range of the light, λ < 410 nm. 2. Experimental methods PC60BM (purity 99.5%) and P3HT (RR 95.5%, Mw=94,100) were purchased from Ossila; PMMA (Mw=350,000) and PS (Mw=350,000) were purchased from Sigma Aldrich. A few


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micrometers thick films for the surface potential decay (SPD) measurements were produced in air by the drop-casting method (3.5 µm - PCBM+5 wt % P3HT, 4.1 µm - PCBM+5 wt % PMMA and 5 µm - PCBM+5 wt % PS). Solution of PCBM with polymer in a chlorobenzene (with a concentration of PCBM equals to 20 mg/ml) was applied with a pipette on the metal substrate (steel with a thin layer of chromium) with a diameter of 2 cm. The samples were placed on a hot plate (at 40˚C) under a glass dome for 24 hour what ensured a slow evaporation of the solvent and formation of good quality, homogeneous and smooth films. For the absorption spectra measurements the samples with the same thicknesses were prepared in similar way from the same solutions on the quartz substrates. The UV-VIS absorption spectra were measured in air by a Varian Inc. Carry 5000 spectrophotometer in the range of 200 nm to 700 nm. The photoinduced decays of surface potential (Vp) were measured at room temperature by means of the xerographic discharge method.39,40,41 For this purpose originally designed and constructed measurement set-up was used which allows to determine photogeneration quantum yield for illumination with light in the spectral range 200–700 nm, with controlled photon flux in the range 1016-1019 photon/s/m2, under broad range of electric field 105–108 V/m, as described in details elsewhere.42 The xerographic discharge method consists in charging of the investigated photoconducting layer in dark by corona discharge and then in monitoring the decay of the surface potential caused by illumination. The layer of ions deposited on the free surface of the sample acts as a blocking electrode, so that the photoinjection of charge carriers can be neglected. This gives important advantage over the common photoconductivity measurements, where the photocurrent is usually affected by other effects such as photoinjection from electrodes and contact phenomena. The experimental data were used to calculate the photoinduced current Iph which is directly proportional to the surface potential decay rate according to the formula (1)43:



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I ph (t ) =

εε0 S dVp (t ) L dt

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(1)

where: ε - dielectric permittivity of the sample, ε0 - dielectric permittivity of the vacuum, S – area of the sample, L – thickness of the sample, dVp(t)/dt - the surface potential decay rate, and t is the time. The quantum efficiency of charge carriers photogeneration ϕ is proportional to the probability of electron-hole pairs photogeneration. The value of ϕ is manifested by a quotient of the photoinduced current Iph divided by the elementary charge e and the number of photons absorbed by the sample per unit time nf. From the SPD measurements one can determine values of ϕ for different electric field F = Vp0/L (where Vp0 is the initial surface potential) by the following formula41,44,45:

ϕ=

εε0 S eLn f

 dV p   dt

  dV    −  p   t0 +  dt t0 − 

(2)

where: e – is the elementary charge, (dVp(t)/dt)to- and (dVp(t)/dt)to+ - the surface potential decay rates just before and just after the light was on. In order to determine the nf value following parameters were taken into account: absorbance spectra of the sample, spectral sensitivity of the photodiode, irradiance spectra of the light source (mercury-xenon lamp), and transmittance spectra of the optical path (water, grey and interference filters). To describe phenomenon of the charge carriers photogeneration the 3-dimensional Onsager model32 of a geminate recombination of charge carriers was applied. According to this model the exciton which undergoes thermalization creates a pair of charges bounded by the Coulomb force. The holes and electrons are spaced at a thermalization length r0 with thermalization probability η0 called the charge carriers primary photogeneration quantum yield. It is assumed, that r0 and η0 are independent on the external electric field strength F.


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For analysis of the experimental results, we have used 5 radial distribution functions gR(r0) of r0 distance described by equations46,47: 1) Dirac delta:

gR (r0 ) = δ (r0 − r0M )

2) Gauss:

  r 4 2 −  0 g R ( r0 ) = r exp 0 3 π r0 M   r0 M

3) Exponential:

g R (r0 ) =

4) r2exponential:

g R (r0 ) =

5) Heaviside:

g R (r0 ) =

(3)

 r 1 exp − 0 r0M  r0M 4 3 0M

r

1 r0 M

  

2

  

(4)

  

 r 2 r0 exp − 2 0 r0 M 

(5)

  

(6)

[1(r0 ) − 1(r0 − r0M )]

(7)

where r0M is the distance between electron and hole for which gR(r0) takes the maximum (with an exception of the Exponential distribution function for which the maximum occurs for r0 = 0). Table 1 summarizes the formulas allowing determining the expected values of the thermalization lengths r0exp calculated according to equation: ∞

r0 exp = ∫ r0 g R (r0 )dr0

(8)

0

Table 1. Analytical formulas describing expected values of the thermalization lengths r0exp for radial distribution functions gR(r0) of thermalization length r0 defined by equations (3) - (7). gR(r0)

Dirac delta

Gauss

Exponential

r2exponential

Heaviside

r0exp

r0M

2π-1//2r0M

r0M

3r0M/2

r0M/2



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At constant ambient temperature (T = 2980 K) the bounded charge pairs existing at distance r0 may undergo a geminate recombination or dissociation into the free holes and electrons with probability dependent on the intensity of the external electric field F. The dissociation probability

Ω

was

described

by

the

equation

proposed

by

the

Mozumder48

as following:

Ω ( r0 , F ) = 1 −

kT ∞ e2  eFr0    Γ Γ   ∑ 1j 1j eEr0 j =0  kT   4πεε 0 kTr0

  

(9)

where k is the Boltzmann constant and Γ is the recurrence function :

Γ1 j ( x) = Γ1 j −1 ( x) −

exp(− x) x j j!

and Γ10 ( x) = 1 − exp(− x) .

(10)

The probability dissociation η of bounded electron-hole pairs spaced from each other at r0 distance for a fixed values of electric field F is given by:

η (r0 , F ) = η0 g S (r0 )Ω(r0 , F )

(11)

where gS(r0) is spatial distribution function given by gS(r0) = gR(r0)/4πro2. Now we can define the electric field dependent separation length rs which is the expected value of thermalization length: ∞

∫ r0η (r0 , F )dr0

rs (F ) =

0

ηT ( F )

(12)

where ηT(F) is the total probability of dissociation of excitons into free charge carriers described by equation38: ∞

ηT ( F ) = η0 ∫η (r0 , F )4πr02 dr0

(13)

0

We assume, that the probability ηT is equal to the quantum efficiency of photogenerated charge carriers ϕ and the theoretical curves ηT(F) were fitted to the experimental results obtained by means of the equation (2).


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3. Results As already explained in the Introduction, a small (5 wt %) amount of polymer was added to PCBM in order to produce homogeneous and continuous thin layers. To minimize possible influence of the polymer on the photogeneration measurements non-conducting polymers, PMMA or PS, were used. For comparison the photogeneration in PCBM doped with semiconducting polymer (P3HT) was also examined. Because the PCBM phase prevails in all investigated PCBM+5% polymer systems for the calculations of the photocurrent Iph (eq. 1) and photogeneration quantum yield ηΤ(λ) (eq. 13) the low frequency dielectric constants ε = 5 of C60 determined by Chern et al.49 was taken. The surface potential decay curves obtained for the PCBM+5%PMMA, PCBM+5%PS and PCBM+5%P3HT layers in the dark and under the illumination (λ = 410 nm) for positive and negative polarities of the sample, are shown in Fig. 1A. For each registered surface potential decay the photocurrent Iph was calculated using the equation (1), and then the relative photocurrent Iphrel was determined:

I phrel =

I ph I ph max

(14)

where Iphmax is the largest value among the photocurrents Iph measured for both polarizations for given sample. In the dark (t < 0 s) the surface potentials decline slowly for all the samples (Fig. 1A), and the flowing dark currents are very low (Figs 1B) due to poor conductivity of PCBM in the dark.



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When the light was on at t = 0 s, a significant rapid decay of the surface potential occurs due to flow of photogenerated charge carriers; the decay rate decreases with time. The kinetics of surface potential decay is correlated with magnitude of photocurrents and depends on polarization sign, as one can see on Fig. 1. For the PCBM+5%PMMA system the potential decay rate and photocurrent for positive polarization are much higher than for negative polarization, for which surface potential remains relatively high for very long time. This suggests that recombination and trapping of electrons affect the photoinduced surface potential decays rate for negative polarization. For the PCBM+5%PS and also for PCBM+5%P3HT systems the situation is reverse: the potential decay rate and the photocurrent for negative polarization are higher than for positive polarization and residual potential is higher for positive charged samples, however here the asymmetry is less pronounced than for the PCBM+5%PMMA layer. Basing on the surface potential decays rate determined for different wavelength from the range 240 nm – 680 nm and using the equation (2), the spectral dependences of photogeneration quantum yield ϕ(λ) were determined. The ϕ(λ) plots determined for the same electric field 8x106 V/cm for all samples are shown in Fig. 2. The symbatic correlation of ϕ(λ) with PCBM absorbance spectra (Fig. 2B)) indicates that the determined photogeneration quantum yield was not influenced by charge carriers photoinjection from the electrode.50,51 Moreover, one can conclude, that the photogeneration of nearly all charge carriers occurs in the dominant PCBM phase. It is in an accordance with the results reported by Mort et al.52 who observed similar relationship between the ϕ(λ) dependencies and the absorbance spectra of the C60 and C70 fullerenes. It is necessary to stress, that the amount of polymers was so low, that in the PCBM+5%PMMA and PCBM+5%PS systems the incident light was absorbed almost exclusively by PCBM (absorption spectra are shown in Fig. 2B). For the PCBM+5%P3HT


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system a higher absorption in the range 400 nm - 600 nm, which is specific to P3HT, can be seen, nevertheless only minor impact of the P3HT absorption on the photogeneration in this wavelength range is noticeable. The photogeneration quantum yield decreases with increasing light wavelength in accordance with the absorption spectra of pristine PCBM in this range. Despite the similarity of shapes of the ϕ(λ) curves, values of the photogeneration quantum yield are very different for negative and positive polarization. For the PCBM+5%PMMA system the ϕ(λ) values in the range 240 nm - 550 nm for positive polarization are ca. twice as high as for negative one (Fig. 2A.). In the case of the PCBM+5%PS the ϕ(λ) plots are similar and they reached approximately similar values, but for reverse polarizations of the sample (Fig. 2A and 2B.). Such effect can be caused by the creation of different charge carrier traps in polymer phases near the PCBM-polymer junction – preferably for holes in the PS and preferably for electrons in the PMMA. Above the wavelength equal ca. 550 nm the photogeneration quantum yield was detectable, but very low (Fig. 2). It is understandable because in C60 and PCBM below the threshold energy Eth (2.2 - 2.3 eV)31,53 extrinsic photogeneration prevails and probability of dissociation of electron-hole pairs is very low. The PCBM+5%P3HT system charged negatively exhibits photogeneration efficiency ca. 2 times higher than for positive polarization (Fig. 2C). This difference can be related to the effective dissociation of excitons at the PCBM/P3HT junction and transfer of electrons from the excited P3HT species to the PCBM molecules which is the main phenomenon causing high power conversion efficiency in the P3HT:PCBM 1:1 OPVDs.10,16,23 One should note also, that due to very high electron affinity of PCBM and energetically deep-lying LUMO at ca. 4.2 eV, electron transport in such system is not affected by a presence of electron traps in P3HT. It was shown by Nicolai et al.54 that in all conjugated polymers, also in P3HT, exist



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common electron traps, centered at ca. 3.6 eV below the vacuum level and most likely related to hydrated oxygen complexes, (H2O)2–O2. Further, more detailed studies on electric field dependence of photogeneration quantum yield were conducted at the wavelength 410 nm (hν ≈ 3 eV). Kazaoui et al.53 reported that in the range 2.3 - 3.75 eV charge carriers in C60 derivatives are generated by field assisted dissociation of charge-transfer (CT) states. It was shown, that intermolecular CT states can contribute to the photogeneration of free charge carriers.33 Selection of this particular wavelength is justified by the fact, that for λ = 410 nm the calculated photogeneration quantum yield ϕ(λ) reaches similar values (in the range 0.004-0.008 [electron/photon]

–

see

Fig.

2)

for

positively

charged

PCBM+5%PMMA

and

PCBM+5%P3HT samples, as well as for negatively charged PCBM+5%PS system. Theoretical models19,32,55 and experimental investigations56,57,58,59,60 of photogeneration of charge carriers in organic photoconductors show that for low electric field the photogeneration yield has very low values which are almost independent of electric field. However, one can find reports where monotonical decrease of ϕ with declining electric field is described. This discrepancy between theoretical model prediction and experimental results is not fully understood. One of possible explanation is that while the photogeneration yield at low electric field is indeed independent of the electric field strength, the drift velocity of the photogenerated charge carriers is so low, that probability of bimolecular recombination and/or trapping is high and it increases considerably with decreasing field strength.57,61,62 The electric field dependences of the photogeneration quantum yield ϕ(F) determined experimentally for PCBM+5%PMMA, PCMB+5%PS and PCBM+5%P3HT systems are shown in Fig. 3. For all the samples ϕ depends very strongly on electric field in the entire investigated range.


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By means of formulas (3) - (5) and the least squares method the theoretical curves based on the Onsager photogeneration model32 were fitted to the experimentally determined relationships ϕ(F). The fitting procedures were made assuming 5 different radial distribution functions of the thermalization distance gR(r0) (eq. (6) - (10)). The best fit was achieved for experimental points corresponding to electrical field higher than 2⋅106 V/m. From this one can conclude that for the electric field below 2·106 V/m the trapping and recombination pheneomena play dominant role in the photodischarge process; it is pronounced especially for the PCBM+5%PMMA system, cf. Fig. 3. The r0M, η0 and r0exp parameters (see eq. (8)) for the best achieved fits are presented in Table 2. Table 2. Parameters for the best fits of the theoretical curves based on the Onsager photogeneration model for different radial distribution functions of the thermalization distance gR(r0): η0 - charge carriers primary photogeneration quantum yield; r0M - distance between electron and hole for which gR(r0) takes the maximum; r0exp - expected values of the thermalization lengths (see eq. (8)). gR(r0)

Dirac delta

Gauss

Exponential

r2exponential

Heaviside

η0

0.16±0.08

1.0±0.3

1.8±0.8

1.0±0.2

1.0±0.4

r0M [nm]

2.5±0.3

1.2±0.1

0.64±0.05

0.76±0.02

2.5±0.2

r0exp [nm]

2.5

1.35

---

1.14

1.25

The radial distribution functions of thermalization distance gR(r0), plotted with the determined parameters r0M, are presented in Fig. 4A.



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In a case of the Dirac delta distribution, the meaning of the parameter r0M is the thermalization distance between electron and hole in the coulomb-bound charge pairs. If we assume close packing of the PCBM molecules, as schematically illustrated in the top part of Fig. 4, then the distance r0M = 2.5 nm indicates that the centroid of the thermalized electron is located on the next but one PCBM molecule to the PCBM molecule being the geminate recombination center (GRC). This value is similar to the r0M = 2.4 which was obtained by Hahn et al.31, who have studied IQE for the layers made of C60 and PCBM molecules. The primary photogeneration yield η0 corresponds to the probability of thermalization of electronhole separated at distance r0M. Thus, the determined value of η0 ≈ 0.16 for Dirac delta distribution (Table 2) indicates that only 0.16 fraction of the excitons can produced electronhole pairs that are able to dissociate. The best fit of experimental data by the theoretical model with assumed exponential distribution function gives unrealistic primary photogeneration quantum yield equal 1.80. This result will be recalled in the Discussion for the analysis of photogeneration mechanism in PCBM. For

other

functions:

Heaviside,

Gaussian

and

r2exponential

the

primary

photogeneration yield η0 was fund to be around 1. For these distribution functions, according to Onsager’s 1938 theory the thermalization length r0 of the coulomb-bound pairs depends on external electric field F and on temperature T (cf. eq. 5). Basing on parameters r0M and η0, and on the equation (11) the formula for relative photogeneration yield (ηrel) is given by:

ηrel (r0 , F ) =

η (r0 , F ) ηmax (r0 max , F )

(15)

where r0max is the thermalization length, for which the quantum photogeneration yield has the highest value for a given value of electrical field F.


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For all tested distribution functions at low electric field (F ≤ 107 V/m) the thermalization length r0max is around 2,5 nm, close to the discussed above thermalization length found with assumed the Dirac delta distribution (Figs. 4B, 4C and 4D). With increasing electric field the r0max value decreases for all the distribution functions except the Dirac delta function, for which it is independent of electrical field. With increasing electric field probability of dissociation increases and even the electrons localized at very short distances from GRC can dissociate. For the Gauss and r2exponential distribution function, for the highest electric field strengths (F > 1010 V/m), the centroid of the thermalized electron which can undergo dissociation is located on the PCBM molecule next to the GRC molecule. When the F → ∞ the distance r0max(∞) tends to the value r0M that is characteristic of given distribution function gR(r0) (see Fig. 4A, 4C and 4D). For the thermalized charge pairs the mean coulomb binding energy (Ecoul) can be written as Ecoul = e/4πεε0rS. The dependences of rS and of Ecoul(rS) on electric field are presented in Fig. 5. Initially, at low electric field range, the increasing electric field doesn’t influence the separation length rS and coulomb-bound energy Ecoul for all distribution functions. The values of rS and Ecoul depend on the assumed distribution function gR(r0) and have specific values: 28 nm and 98 meV for r2-exponential function, 25 nm and 110 meV for Gauss and Dirac delta functions and 22 nm and 130 meV for Heaviside function, respectively. These values of separation length rS correspond to second or third PCBM molecule away from the GRC molecule (Fig. 4B, 4C and 4D). For the threshold electric field Fth = 1.8⋅108 V/m the most probable thermalization length was r0th ≈ 19.3 nm and did not depend on the assumed distribution function gR(r0); one can see in Fig. 5, that all the curves cross at the same point. This “isosbestic point” corresponds to the coulomb bound energy Ecoulth ≈ 0.15 eV. When electric field strength tends to infinity the expected value rS(∞) will



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correspond to PCBM molecule next to the GRC (Fig. 5). The distance rS(∞) will then approach the expected values r0exp, which for different functions gR(r0) are given in Table 1. 4. Discussion Fullerene C60 is well known as an electron conducting material since long time63 and it shows relatively high electron mobility, of the order of ca. 1 cm2/V/s as determined from fieldeffect-transistor characteristics64. However theoretical, as well as experimental investigations have shown that fullerene derivatives, like o-xylene C60 monoadduct65 and PCBM66 are ambipolar semiconductors, able to transport both electrons and holes. We have also observed a hole and electron transport in the PCBM+5% PMMA and PCBM+ 5% PS mixtures, where the polymeric additive are insulators and the transport of charge carriers can occur only in the PCBM phase. As one can see in Fig. 1 the mobility of electrons and holes in PCBM was high enough to study photogeneration of charge carriers using the xerographic discharge method for positively as well as negatively polarized samples. Spectral response of the photogeneration quantum yield follows the shape of the absorption spectra of PCBM for all investigated samples, irrespectively of the used polymer additive (Fig. 2). One can assume also, that charge carriers are transported only via the PCBM phase. Nevertheless kind of the added insulating polymer affects significantly dependence of the photogeneration quantum yield on the sign of the applied electric field. It is probably due to creation of the traps for holes in the PS33 and for electrons in the PMMA67, as suggested already in the Results section. In order to apply model based on the Onsager’s 1938 theory of geminate recombination, one has to postulate apriori a mathematical form of radial distribution function of thermalization length gR(r0) (eq. (3)-(7)). Using Dirac delta distribution function it is assumed that the thermalization distance r0M and primary photogeneration quantum yield η0


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are parameters characteristic of a particular type of photoconductor and does not depends on the electric field.51,57,68,69 An occurrence of a single, precisely defined value of r0M can have physical meaning only when the thermalization distance is much larger than the size of a molecule. For instance, Meltz (1972) and Borsenberger (1972) analyzed the charge carries photogeneration phenomenon in pristine poly(N-vinylcarbazole) (PVK) and in PVK photosensitized by the 2,4,7-trinitrofluorenone molecules. They used the Onsager 1938 model with the Dirac delta distribution function of thermalization length and determined r0M in the range from 2.2 nm to 2.5 nm. This distance is much larger than the size of the carbazole group together with the adjacent PVK mer, within which the separation of electrons and holes occur, which can be estimated to be below 0.5 nm. The discrete value of thermalization distance r0M, calculated for the Dirac delta distribution function, is comparable to the size of two PCBM molecules (Fig. 4A), what is realistic. On the other hand one should remember, that within one molecule of PCBM, which has a diameter of ca. 1.1 nm, a cloud of delocalized π electrons is constituted.70,71 Additionally the densely packed PCBM molecules may form strongly interacting dimers, within which electrons can be delocalized.72,73 It might also be expected that as the strength of electric field will increase, the center of the delocalized electron wave function will shift away from the recombination center. In fact such effects should be taken into account when Onsager 1938 model is used to analyze photogeneration in any fullerene based material, irrespectively of the assumed distribution function of thermalization distance r0M. Therefore one should keep in mind limited accuracy of the analysis presented in this work, as well as those in other published works in which these effects were not considered. The exponential distribution function (eq. (5)) also allows fitting the experimentally determined dependences of the photogeneration quantum yield η on electric field F, as shown in Fig. 3. However, as indicated already earlier, the primary photogeneration quantum yield



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reaches physically meaningless value η0 > 1, what’s more the relative photogeneration yield has maximal value for r0 < rPCBM (Table 2), it means for the thermalized electron which would be localized on the GRC molecule. This is unrealistic, since such electron would undergo immediately geminate recombination. The Heaviside step function predicts that electrons cannot undergo thermalization at a distance exceeding the value of r0M ≈ 2.5 nm, what is similar value to that obtained for the Dirac delta distribution function. However the thermalization probability is the same for all distances lower than r0M, including the area occupied by the GRC molecule, what is evidently unrealistic, as discussed above. The dependence of the relative photogeneration yield ηrel on thermalization length changes considerably with increasing electric field (Fig. 4 C); for low electric fields, below 107 V/cm, only electrons thermalized at the largest distances, close to r0M, will avoid geminate recombination and dissociate, contributing to photocurrent. With increasing electric field more and more electrons localized at shorter distances will dissociate, and finally for the highest fields, above 1011 V/cm, almost all thermalized electrons will dissociate and the ηrel(r0) function (Fig. 4C) will mimic the rectangular shape of the gR(r0) function (Fig. 4B). A comparison of the r0M and η0 parameters obtained by using the Dirac delta, Heaviside and Exponential distribution functions with closely packed PCBM molecules (as illustrated in Figs. 4A and 4B) indicates, that the predominant part of the thermalized electrons is located in an area occupied by the first and the second molecules adjacent to the GRC molecule. More appropriate for description of distribution of thermalization lengths in the granular structure of PCBM, are the Gaussian and r2-exponent distribution functions. One can assume that position of center of mass of the delocalized electron occurs at some distance


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from the recombination center, where the thermalization probability is the highest. In fact this distance should be integral multiplicity of the center-to-center distance between the adjacent PCBM molecules. Figs. 4D and 4E show that for low electric field, in the range 104 - 107 V/m, the most efficient photogeneration of charge carriers occurs when thermalized electrons are located at the molecule next but one to the GRC molecule (molecule no. 2 in Fig. 4). As one can see on figures 4C, 4D and 4E, for all considered distribution functions the highest relative photogeneration yield for low electric field is found for electrons located at the distance near r0 = 2.5 nm, and their average Coulombic binding energy varies from 100 meV to 130 meV (Fig. 5). It can be concluded that the parameters of the Onsager 1938 model which were determined using the Dirac delta distribution function (r0M = 2.5 nm and Ecoul = 110 meV) describe the photogeneration mechanism relatively well for low electric field in the range 104 - 107V/m. Only when the electric field exceeds a value of about 107 V/m, then significant differences in predictions given by different assumed distribution functions can be observed (Fig. 4 and Fig. 5). For Gauss and r2-exponential distribution functions the thermalized electrons located closer than 2.5 nm to the GRC play a dominant role in the photogeneration process. When the electric field strength is higher than 2⋅108 V/m, the maximal value of the relative photogeneration yield ηrel is for the thermalized electrons located on the molecule next to the GRC (Fig. 4). The separation length rs (see eq. (12)) calculated for the infinite electric field is equal to the expected value of the thermalization distance r0exp (see Fig. 5 and Table 2) and corresponds to the distance between centers of adjacent molecules dPCBM which for PCBM is about 1.1 nm74,75 (Table 2 and Fig. 4C and 4D). Considering Gauss and r2exponential distribution functions the best fit for the measured data was obtained for η0 ≈ 1. It



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implies that almost all of the photogenerated electrons were located at a molecule adjacent to the GRC. For the Heaviside, Gauss and r2-exponential distribution functions for the electric field F ≈ 2·108 V/m the threshold separation length rsth is independent of gR(r0) and equal approximately 1.9 nm (Fig. 5). It can therefore be assumed that the “isosbestic point” seen in Fig. 5 corresponds to the rsth characteristic of PCBM. The rsth value can be correlated with the electron-hole thermalization distance corresponding to the quanta of light threshold energy hν = Eth = 2.25 eV (Fig. 2A and 2C) which determines the limit value between the intrinsic and extrinsic photogeneration.17 If the electric field exceeds Fth = 2·108 V/m, then electrons thermalized at the molecule next to the GRC give dominating contribution to the photogenerated charge carriers. For F < 2·108 V/m the majority of free charge carriers will come from electrons localized at distances greater than 1.5·dPCBM from the recombination center. In other words, if the electric field is lower than 2·108 V/m the separation length rs of electrons which can dissociate is higher than 1.9 nm and an inefficient extrinsic photogeneration dominates. Efficient intrinsic photogeneration phenomena occur for electric field higher than 2·108 V/m. The energy of the electron bonded with the recombination center by the Coulomb binding energy Ebi is equal to Ebi = Eg - Ecoul,17 and the Ecoul energy between the thermalized electron and the GRC at the rsth distance is given by Ecoulth = e/4πεε0rsth. For the studied systems Ecoulth ≈ 0.15 eV and Eth ≈ 2.25 eV (Fig. 2) and thus assuming Ebi = Eth, the determined band gap width is equal Eg = 2.4 eV. The obtained Eg value is very close to the electrical band gap Eg = 2.37 eV determined for PCBM by photoemission and inverse photoemission techniques by Guan et al.35 On the other hand this value is slightly lower than Eg = 2.45 eV, estimated by Hahn et al.31 They have analysed the dependence of the IQE ratio on the electric field in PCBM and in C60 photoexcited with light of energies hν in the range


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2.25 eV to 2.35 eV. However they have taken into account the Onsager model 1938 with Dirac delta distribution function, and this can account for the slightly overestimated Eg value. When the PCBM molecule is excited by a light with energy equal to the optical energy gap hν = Eopt, the Coulomb binding energy EcoulPCBM is given by the equation: EcoulPCBM = Eg - Eopt. Assuming that Eg = 2.4 eV and Eopt = 1.85 eV,31 the obtained value of EcoulPCBM is equal to 0.55 eV. This energy corresponds to the distance 0.52 nm and it is equal to a half of the distance between centers of mass of the densely packed PCBM particles.74,76 The determined values of the Coulomb binding energy Ecoul, the energy of the bandgap Eg and the radius rPCBM of the PCBM molecule are consistent with the data reported in the literature. Such coherence is a strong argument in favor of describing the charge carrier photogeneration phenomenon in PCBM by means of the Onsager’s 1938 theory with the application of Gauss or r2-exponent distribution functions of thermalization length. It should however be noted, that the analysis was made on a basis of photogeneration of charge carriers in the electric field strength not exceeding 2·107 V/m. Analysis of the results presented on Figs. 3, 4 and 5 indicates, that more reliable determination of the distribution function would require photoconductivity measurements at very high electric field, significantly greater than 108 V/m, however such measurements are very difficult due to limited electric breakdown strength of PCBM layers. A significant increase in the photogeneration efficiency occurred when PCBM was mixed with a small amount of P3HT, cf. Fig. 2 and Fig.3. It can be concluded that admixture of P3HT results in formation of the p-n junctions with a sufficiently enough extended interphase surface that promotes dissociation of excitons formed in PCBM (the diffusion path of an exciton in PCBM is at least 5 nm15). It is plausible, since it was shown in the literature4 that excitons photogenerated in the PCBM phase diffuse towards PCBM-polymer junction and in



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consequence the holes transfer from the HOMO level of the PCBM excited molecule to the HOMO level of the polymer. Commonly accepted mechanism consisting in transfer of photoexciting electron from the LUMO level of polymer to the LUMO level of a PCBM molecule23 in our case is of minor importance due to diminutive amount of P3HT. Situation is different in the OPV with a 1:1 mixture of P3HT and PCBM illuminated by light with wavelength above 410 nm, since in this case light is absorbed almost entirely by the P3HT phase. The diffusion of excitons generated in the P3HT phase and their dissociation at the P3HT-PCBM boundary4,15,23 has a decisive impact on the photovoltaic effect. The photogeneration mechanism at the P3HT-PCBM junction can be described using the OnsagerBrown model. Photogeneration of charge carriers occurring in the PCBM phase contributes also to the photovoltaic effect in OPV31,77,78 however, it is very weak. Poor photogeneration efficiency of charge carriers in PCBM results from low intensity of the internal electric field in the P3HT + PCBM 1:1 solar cells.79,80 Electric field does not exceed the value of 108 V/m, and under such conditions most of the thermalized charge carriers in PCBM are localized at the molecule adjacent to GRC and their release requires electric field higher than 2·108 V/m (Fig. 6). 5. Summary The above presented discussion of the obtained results, as well as an analysis of the literature data allow to propose mechanism of dissociation of excitons in the PCBM+P3HT mixtures illuminated with light of energy hν > 3eV. In the first step the created excitons in a form of electron-hole pairs bound by Coulomb interactions diffuse to neighboring PCBM molecules. The migrating excitons dissipate energy and therefore the electron-hole distance increases gradually until it reaches thermalization length r0. The thermalized charge carriers are localized with the highest probability at the distance r0M corresponding to a center of the


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PCBM molecule next to the geminate recombination center - GRC. Only few thermalized charge carriers can reach the next but one PCBM molecules; an amount of charge carriers localized still further is negligible. In the next step the thermalized pair can undergo geminate recombination or dissociate into free charge carriers. The dissociation may occur at the n-p junction, what can be described by the Onsager-Braun model18,19,23, or by autodecomposition of the electron-hole pair as foreseen by the Onsager 1938 model32. In both cases probability of dissociation increases with increasing strength of external electric field. Fig. 6 presents schematically the proposed photogeneration mechanisms. In an absence of external electric field, all thermalized charge carriers are located inside potential well, and according to the Onsager 1938 model32, only charge carriers localized at distances exciding two radii of the PCBM molecule (r > 2rPCBM, see Fig. 6A) can avoid geminate recombination. Since only small population of charge carriers can reach such distance, the yield of the autonomous photogeneration in the PCBM phase is very low, and practically only dissociation at the n-p junction, i.e. at the PCBM-P3HT interface, is possible. In a presence of external electric field, the potential barriers decrease, and according to the Poole-Frenkel model81, radius of the potential well decreases with increasing strength of external electric field: rP-F = sqrt(e/4πεε0F). This effect is illustrated schematically on diagrams in Figs. 6B, 6C and 6D. With increasing electric field more and more thermalized charge carriers are localized outside the potential well and can avoid geminate recombination. However for the electric field lower than the threshold value Fth = 2·108 V/m, probability of autonomous dissociation of charge carriers which are thermalized at the most probable distance r0M is still very low, and prevails the dissociation at the PCBM-P3HT interface. For electric fields higher than Fth = 2·108 V/m, the radius of potential well rP-F decreases to value below 1.2 nm, which is close to the most probable distance r0M. Therefore



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much more thermalized charge carriers are localized outside the potential well, as shown in Figs. 6C and 6D. This results in increasing probability of dissociation of charge carriers thermalized close to the GRC. For high electric field the probability of dissociation at the PCBM-P3HT junction also increases, however actual number of charge carriers dissociating at this junction decreases, due to competing very efficient dissociation occurring in the PCBM phase. This is because the diffusion time of an exciton to the PCBM-P3HT interface is longer than the thermalization time, and in high electric field most of the thermalized charge carriers dissociate immediately. The presented above model explains also an origin of the observed experimentally threshold value of the photon energy hν = Eth ≈ 2.25 eV, below which photogeneration in fullerene based materials decreases abruptly.17,52 According to Kohler et al.17 this photon energy determines the transition between the intrinsic and extrinsic photogeneration. However in the experiments reported in literature, in which this threshold value was determined, the external electric field was much below the determined by us threshold value Fth ≈ 2·108 V/m. Therefore, dissociation was efficiently occurring only for small population of charge carriers, which were thermalized at relatively large distance r > 2rPCBM; most of the thermalized charge carriers were localized inside the potential well and they were undergoing geminate recombination. According to our model, the observed experimentally threshold value of the photon energy Eth ≈ 2.25 eV corresponds to a difference between the electric gap energy Eg and the average electron-hole pair Coulomb binding energy Ecoulth ≈ 0.15 eV, as determined at the threshold electric field Fth (cf. Fig 6A and 6B). This gives the electric gap energy value Eg = 2.4 eV, in an accordance with literature data.31,35 Such agreement with the independent experimental results, together with the previously described correctly evaluated


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size of the PCBM molecules (rPCBM = 0.52 nm) present strong evidences supporting the proposed by us model.

ACKNOWLEDGMENTS This work was funded by the Polish Ministry of Science and Higher Education under the "Diamond Grant" No. DI2012 022342. J.U. acknowledges support from the grant funded by the National Science Centre in Poland No. 2013/09/BST5/03521.

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A

PCBM + 5% PMMA PCBM + 5% PS PCBM + 5% P3HT

Vp [V]

10 5 0

0

10000

20000

30000

-5 -10 t [ms] 1.0

B

0.5

Iphrel [a. u.]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.0 0

1000 2000 3000 4000

-0.5 -1.0

t [ms]

Fig. 1. (A) Examples of the surface potential decays Vp(t) for PCBM+5%PMMA, PCBM+5%PS and PCBM+5%P3HT systems illuminated with light of wavelength λ = 410 nm and following values of the light intensity: nf = 1.1·1014 photon/s for PCBM+5%PMMA, 5·1013 photon/s for PCBM+5%PS, and 4.6·1013 photon/s for PCBM+5%P3HT; (B) the relative photocurrents Iphrel for the same systems.



600

700 300

PCBM+5%PMMA

0.006

0.004

[nm] 600

PCBM+5%PS

Vp>0

Vp>0

Vp 3 eV: (A) without the external electric field some photogenerated excitons can diffuse to the PCBM/P3HT junction, where CT complexes are formed and then can dissociate, however most of the excitons are thermalized with electron-hole separation distance lower than the threshold separation length rsth and undergo geminate recombination; (B) under low electric field, below the threshold field Fth, only a small part of charge carriers will thermalize at a distance > rsth and then dissociate; most of charge carriers will undergo geminate recombination; for high (C) and very high (D) electric field, exceeding the threshold field Fth, also the charge carriers localized on the PCBM molecules next to the geminate recombination centre will dissociate. For symbol description see the text.


Page 43 of 43

P3HT

E

Interface

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


PCBM

rsth

F=Fth

rPCBM

r

0 thermalization

excitons

LUMO e _

Ecoulth

LUMO e

Eth

EcoulPCBM

CT

S1

+ HOMO h

exciton diffusion

Eg extrinsic

intrinsic

Eopt

rP-F =r0M

S0 efficiency:

low/ negligible

low

high


Photogeneration of Charge Carriers in (Phenyl-C61-butyric Acid

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