Citation for published version (APA): Mihailetchi, V. D. (2005). Device physics of organic bulk heterojunction solar cells s.n.

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1 University of Groningen Device physics of organic bulk heterojunction solar cells Mihailetchi, V.D IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2005 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Mihailetchi, V. D. (2005). Device physics of organic bulk heterojunction solar cells s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date:

2 3 Photocurrent generation in bulk heterojunction solar cells Abstract In this chapter, the photogeneration in organic donor/acceptor photovoltaic cells is discussed, with emphasis on the mechanism of charge dissociation and the consequences of an unbalanced charge transport on photocurrent generation. It is demonstrated that the photocurrent in conjugated polymer:fullerene blends is dominated by the dissociation efficiency of bound electron-hole pairs at the donor/acceptor interface. A model based on Onsager s theory of geminate charge recombination is proposed, which explains the observed fieldand temperature dependence of the photocurrent in polymer:fullerene blends. At room temperature only 60% of the generated bound electron-hole pairs in MDMO-PPV:PCBM blends are dissociated and contribute to the short-circuit current, which constitutes a major loss mechanism in photovoltaic devices based on this material system. With respect to the charge transport, it is demonstrated that the photocurrent reaches the fundamental space-charge limit when the difference in electron and hole mobility exceeds two orders of magnitude. The experimental photocurrents reveal all the characteristics of a space-charge limited photocurrent; a one-half power dependence on voltage, a three-quarter power dependence on light intensity, and a one-half power scaling of the voltage at which the photocurrent switches into full saturation with light intensity. The main results of this chapter have been published as: (a) V. D. Mihailetchi, L. J. A. Koster, J. C. Hummelen, P. W. M. Blom, Physical Review Letters 93 (2004), ; (b) V. D. Mihailetchi, J. Wildeman, P. W. M. Blom, Physical Review Letters 94 (2005),

3 40 Chapter 3: Photocurrent generation in bulk heterojunction solar cells 3.1 Photocurrent in polymer:fullerene blends Introduction The primary process of photocurrent generation in organic donor/acceptor photovoltaic cells is the generation of excitons after absorption of light, either by the donor or by the acceptor. The excitons diffuse in either of the domains towards the polymer (donor)-fullerene (acceptor) interface where rapid charge transfer will occur [1]. After dissociation, a geminate pair of a hole at the donor and electron at the acceptor is formed. Due to the low dielectric constants (ǫ r ) of the molecular materials and polymers (ǫ r ranges typically from 2 to 4), these electron-hole (e-h) or polaron pairs are strongly bound by Coulomb interaction, with binding energies of typically several tenths of an electron volt. In order to generate a photocurrent, the bound e-h pairs must dissociate into free charge carriers and subsequently move to the electrodes before recombination processes take place. In the bulk heterojunction devices using MDMO-PPV and PCBM as donor and acceptor, respectively, an external quantum efficiency of more than 50% has been reported [2]. Many fundamental aspects regarding the operation of these devices are presently under strong debate: It has been observed that the photocurrent under short circuit conditions (J SC ) is relatively weakly dependent on temperature [3]. This has been attributed to either the temperature dependence of the charge transport in combination with recombination with shallow traps [4] or space-charge effects [5]. The voltage dependence of the photocurrent in bulk heterojunction devices has to our knowledge not been addressed, so far only recently a device model for photocurrent in bilayer devices has been developed [6]. Another important issue is the origin of the relatively large external quantum efficiencies in spite of the strong Coulomb binding between the e-h pairs in organic materials. In this section, a model is presented that consistently explains the voltageand temperature dependence of the photocurrent in PPV:PCBM bulk heterojunction devices. It is demonstrated that at voltages V close to the compensation voltage V 0 (V 0 -V <0.1 V), implying a small electric field in the device, the photocurrent linearly increases with voltage. For V 0 -V >0.1 V the photocurrent enters the saturation regime, as expected for weak recombination. In this regime the photocurrent is governed by the field- and temperature dependent dissociation of e-h pairs according to Onsager s theory of ion pair dissociation [7, 8]. For large (reverse) voltages > 10 V the photocurrent becomes field- and temperature independent, implying that every generated bound e-h pair is dissociated into free carriers by the applied field. From the observation of the fully saturated current we obtain that under short-circuit conditions only 60% of the bound e-h pairs in an MDMO-PPV:PCBM based photovoltaic device is dissociated Photocurrent-voltage characteristics The measurements were performed on 20:80 wt. % blends of MDMO-PPV:PCBM sandwiched between two electrodes (see Section 3.3) with different work func-

4 3.1. Photocurrent in polymer:fullerene blends 41 J [A/m 2 ] J D J L J ph =J L -J D V OC V V [V] Figure 3.1: Current density under illumination (J L), in the dark (J D), and calculated net photocurrent (J ph ); J ph =J L-J D. The arrows indicate the open-circuit voltage (V OC) and the compensation voltage (V 0) determined when the J ph =0. tion to generate an internal electric field, necessary to separate the photogenerated charges. The devices were illuminated by a white light halogen lamp with an intensity of 800 W/m 2, in inert (N 2 ) atmosphere. A reverse voltage sweep from 1 V down to -15 V has been applied and the current density under illumination (J L ) has been recorded for a temperature range of 210 K K. In order to determine the net photocurrent, the current density in the dark (J D ) was also recorded. The experimental photocurrent is given by J ph =J L -J D. From the resulting J ph -V characteristics the compensation voltage (V 0 ) at which J ph =0 was determined, as is shown in the Figure The origin of the field-dependent (reverse bias) photocurrent In Figure 3.2 J ph is plotted, at room temperature, on a double logarithmic scale against the effective voltage across the device, given by V 0 -V. For a small effective voltage (V 0 -V <0.1 V) the photocurrent increases linearly with the effective voltage, which has not been noticed before, and then tends to saturate. At higher reverse voltage (V 0 -V >1 V) the photocurrent further increases with increasing voltage. In order to qualitatively understand this behavior, let us first consider the situation in which recombination of free charge carriers as well as spacecharge effects can be neglected. In that case the internal field in the device is given by E=(V 0 -V )/L, where V is the applied voltage. Without recombination the photocurrent through the external circuit is [9]: J ph = qgl, (3.1) where q is the electric charge, G the generation rate of e-h pairs, and L the thickness of the active layer. Thus in case of no recombination and a constant generation rate G of e-h pairs J ph is independent of V, as shown in Figure 3.2 by the dotted line. However, Sokel and Hughes (SH) [10] pointed out that this result

5 42 Chapter 3: Photocurrent generation in bulk heterojunction solar cells diffusion drift J ph [A/m 2 ] V 0 -V [V] Figure 3.2: Room temperature J ph -V characteristics of an MDMO-PPV:PCBM 20:80 device as a function of effective applied voltage (V 0-V ) (open circles), for a device with thickness of 120 nm. The solid line represent calculated photocurrent from Equation 3.2 using G= m 3 s 1, whereas, the dotted line represent drift current calculated from the Equation 3.1 using the same G. is incorrect at low bias voltages because diffusion currents have been neglected. Using the same approximation as above, but including diffusion, SH found an analytical solution for the photocurrent: [ exp(qv/kb T) + 1 J ph = qgl exp(qv/k B T) 1 2k ] BT, (3.2) qv where qgl is the saturated photocurrent, k B is the Boltzmann constant and T is the temperature, respectively. The solutions of the Equations 3.1 and 3.2 are shown schematically in Figure 3.2 together with the experimental data. Using a G of m 3 s 1, Equation 3.2 fits the experimental data at low effective fields, indicating that diffusion plays an important role in the experimental photocurrent. It should be noted that the photocurrent given by Equation 3.2 is independent of the mobility of either electrons or holes, since for none or very weak recombination the carrier lifetime will always exceed the transit time. It appears from Figure 3.2 that for effective voltages exceeding 1 V the experimental photocurrent does not saturate at qgl but gradually increases for larger effective voltages. An important process which has not been taken into account into the Equations 3.1 and 3.2 is that not all the photogenerated bound e- h pairs (represented by G max ) dissociate into free charge carriers. Only a certain fraction of G max is dissociated into free charge carriers, depending on field and temperature, and therefore contributes to the photocurrent J ph. Consequently, the generation rate G of free charge carriers can be described by: G(T,E) = G max P(T,E), (3.3) where P(T, E) is the probability for charge separation at the donor/acceptor interface.

6 3.1. Photocurrent in polymer:fullerene blends A model for charge carriers dissociation at donor/acceptor interface The photogeneration of free charge carriers in low-mobility materials has first been explained by the geminate recombination theory of Onsager [7, 8]. Onsager calculated the probability that a pair of oppositely charged ions in a weak electrolyte, that undergo a Brownian random walk under the combined influence of their mutual Coulomb attraction and external electric field, would escape recombination. An important addition to the theory has been made by Braun [11], who stressed the importance of the fact that the bound e-h pair (or charge transfer state) has a finite lifetime, as schematically depicted in Figure 3.3. The bound e-h pair, formed after the dissociation of an exciton at the donor/acceptor interface, can either decay to the ground state with a rate constant k F or separates into free carriers with an electric-field dependent rate constant k D (E). The decay rate (k F ) is dominated by phonon-assisted non radiative recombination [12]. Once separated, the charge carriers can again form a bound pair with a rate constant k R, as shown schematically in Figure 3.3. Consequently, free carriers which are captured into bound pairs may dissociate again during the lifetime of the bound pair. Therefore, long lived charge transfer states act as a precursor for free charge carriers. It has been demonstrated that after generation, bound e-h pairs in PPV:PCBM blends can still be detected after microseconds and even milliseconds, depending on temperature [13, 14]. Furthermore, Onsager s theory as discussed here was extensively applied in the past to describe photogeneration in pure and sensitized conjugated polymers [15, 16]. It should be noted that Onsager s model describes charge dissociation in three dimensions. This is also applicable to bulk heterojunction cells since the length scale of morphology, typically two times the exciton diffusion length (10-15 nm), is in the order of Onsager radius of 17 nm. In Braun s model the probability that a bound polaron pair dissociates into free charge carries at a given electric field E and temperature T is given by: P(T,E) = k D (E) k D (E) + k F. (3.4) Based on Onsager theory for field-dependent dissociation rate constants for weak electrolytes [7, 8], Braun derives k D (E) for dissociation of a bound pair Figure 3.3: Schematic diagram of charge carrier separation at interface between polymer (donor; D) and fullerene (acceptor; A).

7 44 Chapter 3: Photocurrent generation in bulk heterojunction solar cells to be [11]: k D (E) = k R 3 4πa 3 e E B k B T [1 + b + ] b23 b b , (3.5) with a the initial separation of bound e-h pair at the interface, b=q 3 E/8πǫ 0 ǫ r k 2 B T 2, and E B the e-h pair s binding energy. For low mobility semiconductors electronhole recombination is given by Langevin: k R =q µ /ǫ 0 ǫ r, where ǫ r is spatially averaged dielectric constant and µ the spatially averaged sum of electron and hole mobilities. Furthermore, in disordered materials as conjugated polymers and fullerenes it is unlikely that all donor/acceptor separations (a) would be the same [17]. As a consequence, Equation 3.4 should be integrated over a distribution of separation distances P(T,E) = N F P(x,T,E)F(x)dx, (3.6) 0 where P(x,T,E) is the probability that an electron and hole generated at a distance x, temperature T, and field E, will escape recombination; F(x) is a distribution function of donor-acceptor separations, and N F is a normalization factor for the function F(x). The F(x) was assumed to be F(x) = x 2 e x2 /a 2, with N F = 4/π 1/2 a 3 [17]. The bulk dielectric constant is ε r =3.4 (which was taken as the spatial average dielectric constant of PPV and PCBM). The final parameters required in the model are the mobilities of the charge carriers in the 20:80 blends of MDMO-PPV:PCBM, which have been determined (in Chapter 2 of this thesis) to be µ e = m 2 /Vs and µ h = m 2 /Vs, at room temperature. Combining Equations 3.3 and 3.6 the generation rate of producing free electrons and holes in blends of MDMO-PPV:PCBM for any temperature and electric field can be calculated. It should be noted that Equation 3.3 involves only two adjustable parameters: the initial separation of e-h pairs a, and the ground state recombination rate k F, since all the other parameters were experimentally determined Comparing the model with the experimental photocurrent Figure 3.4(a) (solid lines) shows the calculated photocurrent from Equation 3.1 as a function of temperature, including the calculated field-dependent generation rate G(T, E). Using a=1.3 nm, and a room temperature recombination lifetime k 1 F =1 µs, the calculations consistently describe the field- and temperature dependence of the experimental data in the saturation regime (V 0 -V >0.3 V). In the inset of Figure 3.4(a) the spatial distribution F(x) is shown for a=1.3 nm corresponding to a mean e-h separation distance of typically 1.5 nm. In Figure 3.4(b) the (normalized) temperature dependence of the predicted- and experimental photocurrent is plotted, for two different effective voltages of 0.01 V and at short-circuit. The excellent agreement at both voltages demonstrates that the activation energy of the photocurrent is completely dominated by the rate of producing free electrons and holes (G) from the internal donor/acceptor

8 3.1. Photocurrent in polymer:fullerene blends 45 J ph [A/m 2 ] 10 1 (a) 295 K 270 K 250 K 230 K K x [nm] F(x) V 0 -V [V] J ph /J ph (295 K), G/G(295 K) 1 (b) 0.8 =35.4 mev 0.6 =94.1 mev 0.4 J ph /J ph (295 K) G/G(295 K) /T [K -1 ] Figure 3.4: (a) Temperature dependence of the photocurrent (symbols) versus effective applied voltage (V 0-V ) for a device of 100 nm thickness. The solid line represents the calculated photocurrent from Equation 3.1 using field dependent generation rate G(T, E). The inset shows the spatial distribution F(x) for a=1.3 nm. (b) Normalized experimentally photocurrent (J ph ) and normalized calculated generation rate [G(T, E)] from Figure 3.4(a), as a function of 1/T, taken in linear regime at 0.01 V (full symbols) and at short circuit (empty symbols). The activation energies are written on the figure. interface. It should be noted that the activation energy of G [shown in Figure 3.4(b)] arises from the combined effect of the distribution of binding energies, the temperature dependence of both charge carrier mobility and decay rate k 1 F as well as the effect of applied field, and therefore it does not reflect directly the bound e-h pair activation energy. As shown in Figure 3.4(a) at high effective voltages of typically 10 V the photocurrent saturates and becomes field- and temperature independent. At these voltages all bound e-h pairs are separated and the maximum photocurrent J sat =qg max L is reached. By comparing the photocurrent with the experimentally observed J sat the dissociation efficiency can be read directly from Figure 3.4(a). Under short-circuit conditions (V=0 V) only 60% of the bound e-h pairs dissociate, and at the maximum-power-point (V=0.64 V) this efficiency even further decreases to 52%. This incomplete dissociation of generated bound e-h pairs under operating conditions is therefore a main loss mechanism in solar cells based on PPV:PCBM blends. As a next step, the generation rate G(T,E) is combined with Equation 3.2, as shown in Figure 3.5 by the dotted line, for 295 K. It is observed that this approach underestimates the photocurrent in the low voltage regime. This apparent discrepancy arises from the fact that the analytical model has been deduced for blocking contacts [10]. However, in case of Ohmic contacts (as the devices presented here), the internal electric field in the device is slightly modified due to the band bending created by the accumulation of the charge carries at the interface. This effect is negligible at high reverse bias (in the saturation regime), but it has a significant effect at voltage close to V 0 (in the linear regime). Therefore, the use of Equation 3.2 together with G(T,E) will not entirely fit the experimental data of the devices with Ohmic contacts. Furthermore, the analytical model does not include the effects of space charge and recombination. Therefore, we

9 46 Chapter 3: Photocurrent generation in bulk heterojunction solar cells J ph [A/m 2 ] K 250 K V 0 -V [V] Figure 3.5: Experimental photocurrent (J ph ) as a function of effective applied voltage (V 0-V ) of MDMO-PPV:PCBM 20:80 device (symbols), at 295 and 250 K. The solid line represents the numerical calculation including diffusion, field dependent of generation rate G(T, E) and recombination, for a device with thickness of 120 nm. The dotted line represents calculated J ph from Equation 3.2 using G(T, E), at 295 K. have developed an exact numerical model that calculates the steady-state charge distributions within the active layer with Ohmic contacts by solving Poisson s equation and the continuity equations, including diffusion and recombination of charge carriers at donor/acceptor interface. This numerical model describes the full current-voltage characteristics in the dark and under illumination, including the field dependent generation rate G(T, E) [18]. Figure 3.5 shows the experimental photocurrent (symbols) together with the numerical calculation (solid lines) for two different temperatures. At both temperatures, using the same parameters as presented above, the calculated photocurrent fits the experimentally data over the entire voltage range Conclusion In this section, the photocurrent in 20:80 blends of MDMO-PPV:PCBM solar cells has been interpreted using a model based on Onsager s theory of geminate charge recombination. The model explains the field- and temperature dependence of the photocurrent in a large voltage regime. The long lifetime of 1 µs is a precursor for the high external quantum efficiencies observed in MDMO- PPV:PCBM blends. Under short-circuit conditions, at room temperature, only 60% of the bound e-h pairs are separated and contribute to the photocurrent. 3.2 Space-charge limitation in organic solar cells Introduction When a semiconductor is exposed to photons with an energy larger than the band gap, charge carriers are produced. With a built-in field or an externally

10 3.2. Space-charge limitation in organic solar cells 47 applied bias these charge carriers can be separated, thereby producing a photocurrent in an external circuit. The efficiency of photocurrent generation depends on the balance between charge carrier generation, recombination, and transport. The extraction of photogenerated electrons and holes from a semiconductor has been treated by Goodman and Rose [9]. With non-injecting contacts the external photocurrent becomes saturated when all photogenerated free electrons and holes are extracted from the semiconductor. This implies that the mean electron and hole drift lengths w e(h) =µ e(h) τ e(h) E are equal or longer than the specimen thickness L; with µ e(h) the charge carrier mobility of electrons (holes), τ e(h) the charge carrier lifetime and E the electric field, respectively. In this case no recombination occurs and the saturated photocurrent density is given by Jph sat=qgl [9]. However, as is shown in Section 2.1, if either w e<l or w h <L or both are smaller than L, space-charge will form and recombination of free charge carriers becomes significant. In the following, this specific case will been analyzed with more details Goodman and Rose approximation Suppose that the e-h pairs are photogenerated uniformly throughout the specimen and that the charge transport is strongly unbalanced, meaning that w e w h. As is demonstrated in Section 2.1, in a semiconductor with w h w e and w h <L, the holes will accumulate to a greater extent in the device than the electrons, altering the electric field. As a consequence, the electric field increases in the region (L 1 ) near the anode, enhancing the extraction of holes, as is shown schematically in Figure 2.1(b). In Section 2.1 it has been shown that if w h w e, the length of the region L 1 is given by the mean hole drift length (L 1 = µ h τ h V 1 ). Since almost the entire voltage V drops on the region of hole accumulation (V 1 V ) and the photocurrent generated in this region is substantially the total current, it follows directly that [9]: J ph = qgl 1 = qg(µ h τ h ) 1/2 V 1/2. (3.7) It is evident that in the region L 1 the accumulated holes are not neutralized by an equal density of electrons, which results in a build-up of positive spacecharge. Goodman and Rose pointed out that there is a fundamental limit to be expected for the build-up of space-charge in a semiconductor at high intensities; The electrostatic limit of hole accumulation is reached when the photocurrent generated in this region, J ph =qgl 1, is equal to the space-charge limited current: J SCL = 9 8 ε V1 2 0ε r µ h L 3, (3.8) 1 where ε 0 ε r is the dielectric permittivity. By equating qgl 1 with Equation 3.8 it follows that the length of the region L 1 in this space-charge limited (SCL) regime is given by: L 1 = (9ε 0 ε r µ h /8qG) 1/4 V 1/2 1. (3.9)

11 48 Chapter 3: Photocurrent generation in bulk heterojunction solar cells Since V 1 V, the maximum electrostatically allowed photocurrent that can be extracted from the device is [9]: ( 9ε0 ε r µ ) h 1/4G J ph = q 3/4 V 1/2. (3.10) 8q Comparison of Equations 3.7 and 3.10 show that both in the absence and presence of the space-charge limitation J ph scales with the square-root of the applied voltage and is governed by the slowest charge carrier mobility, although the physical reasons of this are distinctly different. Experimentally, both regimes can be discriminated by investigating their dependence on G. To our knowledge, the existence of SCL photocurrents has not been demonstrated experimentally in semiconductors so far Experimental evidence In order to observe SCL photocurrents a semiconductor should fulfil a number of requirements: First, the amount of photogenerated charge carriers should be large, meaning a large G and a long carrier lifetime τ e(h) after dissociation of the e-h pairs. Furthermore, the charge transport should be strongly unbalanced, leading to the formation of space-charge regions. Finally, the slowest charge carrier should have a low mobility such that the photocurrent can reach the SCL current inside the space-charge region. A material system that fulfills most of these demands are blends of conjugated polymers (electron donor) and fullerene molecules (electron acceptor) [19]. In these blends light absorption leads to the production of excitons that subsequently dissociate at the internal interface by an ultrafast electron transfer ( 45 fs) from excited polymer to fullerene [1]. Since the created electrons and holes are spatially separated the back-transfer process is very slow leading to long-lived charge carriers, in the microsecond to millisecond range [13, 14]. In combination with the large internal donor/acceptor interface these bulk heterojunctions enable a large generation rate of long-lived charge carriers. As is explained in the previous section, the important quantity which determines the formation of space-charge in photoconductors, is the difference in the µτ product of electrons and holes. The most investigated system of polymer/fullerene solar cells are blends of MDMO-PPV and PCBM. The main recombination process found in these devices is bimolecular recombination of photogenerated free electrons and holes (as discussed in Section 3.1), resulting in an equal electron and hole lifetime. Therefore, a large mobility difference between electrons and holes is required for the generation of a SCL photocurrent in this system. However, it turns out that the hole mobility of MDMO-PPV inside the blend is enhanced by a factor of 400 as compared with the pure material (see Section 2.3). The resulting mobility difference of only one order of magnitude is not sufficient to induce a SCL photocurrent. As demonstrated in Section 2.3, when symmetrical substituted PPV is used (such as BEH 1 BMB 3 -PPV), the hole mobility in polymer phase is hardly affected by the presence of PCBM, resulting in an increased mobility difference between electrons and holes in the blend. The measurements here were performed on 20:80 weight percentage blends of

12 3.2. Space-charge limitation in organic solar cells µ [m 2 /Vs] /T [K -1 ] Figure 3.6: Experimental charge carrier mobility of the electrons (µ e; ) and holes (µ h ; ) as a function of temperature T. The µ e and µ h have been determined from space-charge limited measurements on 20:80 blends of BEH 1BMB 3-PPV:PCBM. BEH 1 BMB 3 -PPV:PCBM sandwiched between two electrodes with asymmetric work function, which are non-injecting under reverse bias operation. In order to investigate the photocurrent in blends of BEH 1 BMB 3 -PPV:PCBM, knowledge about the hole and electron mobility in the polymer and fullerene phases is indispensable. In Chapter 5 is shown that the electron and hole mobilities in a blend can be determined from dark current-voltage measurements by using suitable electrodes which either suppress holes or electrons. In Figure 3.6 the experimental electron and hole mobilities in 20:80 blends of BEH 1 BMB 3 - PPV:PCBM are shown as a function of temperature (1/T ). It is observed that at room temperature the electron mobility in the PCBM phase (µ e = m 2 /Vs) is a factor of 125 larger than the hole mobility in the BEH 1 BMB 3 -PPV phase (µ h = m 2 /Vs). This low hole mobility originates from a hopping process between localized sites, which consist of conjugated polymer chain segments. Due to strong disorder there is a variation in the on-site energies, reducing the coupling between these localized states [20, 21]. Since PPV and PCBM have different energetic disorder, the activation energy of charge carrier mobility is different in the case of electrons (0.18 ev) and holes (0.35 ev). Consequently, as the temperature decreases the difference between µ e and µ h becomes larger. For example, at 210 K the difference between experimental µ e and µ h increases to a factor of 2000, thereby strongly unbalancing the transport in these blends. Figure 3.7(a) shows the experimental J ph as a function of V 0 -V in a 20:80 blend of BEH 1 BMB 3 -PPV:PCBM, for a temperature range of 210 K- 295 K. It is observed that for V 0 -V < 0.06 V J ph shows a linear dependence on voltage, due to the competition between drift and diffusion of photogenerated free charges to the electrodes, as discussed in the Section 3.1. However, above 0.06 V the experimental J ph clearly shows a square-root dependence on voltage for all measured temperatures, as is predicted by the Equations 3.7 and 3.10 for very different µ e and µ h. Furthermore, as the temperature decreases, the square-root part of the J ph extends to larger voltages, since the difference between µ e and µ h be-

13 50 Chapter 3: Photocurrent generation in bulk heterojunction solar cells J ph [A/ m 2 ] (a) K 270 K 250 K 230 K K V 0 -V [V] J ph [A/ m 2 ] 10 (b) 1 V sat L=275 nm T=210 K V 0 -V [V] Figure 3.7: (a) Temperature dependence of the photocurrent (symbols) in a 20:80 blend of BEH 1BMB 3-PPV:PCBM versus effective applied voltage (V 0-V ) for a device of 275 nm thickness illuminated at an intensity of 800 W/m 2. The solid lines represent the square-root dependence of the photocurrent J ph on effective voltage, used here as a guide for the eye. (b) Incident light power (ILP) dependence of the photocurrent (J ph ) versus the effective voltage (V 0-V ) measured at T =210 K. The solid (thick) lines represent the calculated J ph from Equation 3.10 using µ h = m 2 /Vs, ε r=2.6 and G ILP, where ILP was varied from 800 to 60 W/m 2. The arrow indicates the voltage (V sat) at which J ph shows the transition to the saturation regime. comes larger. At even larger voltages ( 0.8 V at 295 K) the J ph shows a clear transition to the saturation regime, where it becomes limited by the field- and temperature dependence of the generation rate G(E, T) (Equation 3.3). These results are distinctly different than in the case of MDMO-PPV:PCBM blends, where no square-root dependence of J ph is observed, as a result of the more balanced transport (see Section 3.1). The important question is whether J ph from Figure 3.7(a) is limited by the space-charge (Equation 3.10) or by the mobilitylifetime product given by Equation 3.7. The unique test to distinguish between the two processes is to investigate the dependence of J ph on G, since a different dependence is predicted by Equations 3.7 and A direct way to change the amount of photogenerated charge carriers is to vary the light intensity. We have demonstrated in the Section 3.1 that in the absence of SCL the J ph in reverse bias is described by J ph =qg(e,t)l. Furthermore, for these non-scl devices J ph closely follows a linear dependence with light intensity [22, 23]. Combining these two observations it follows that G is proportional with light intensity in these type of devices. Therefore, the SCL photocurrent is expected to scale with a 3/4 power dependence on light intensity (Equation 3.10). Figure 3.7(b) shows the J ph -(V 0 -V ) characteristics, of the same device from Figure 3.7(a), as a function of incident light power (ILP), measured at 210 K. This temperature was chosen because the J ph shows the largest square-root regime, but the same effect is present also at room temperature. The ILP was varied from 800 W/m 2 (upper curve) down to 60 W/m 2 using a set of neutral density filters. It appears from Figure 3.7(b) that the J ph shows weaker light intensity dependence in the square-root regime as compared with the saturation regime. Figure

14 3.2. Space-charge limitation in organic solar cells (a) shows, in the double logarithmic plot, the experimental J ph taken from Figure 3.7(b) as a function of ILP for two different voltages, at V 0 -V =0.1 V in the square-root regime and at V 0 -V =10 V in the saturation regime. The slope S determined from the linear fit (lines) to the experimental data amount to S=0.76 in the square-root part and S=0.95 in the saturation part at high voltages. Furthermore, the SCL photocurrent predicted by Equation 3.10 is compared with the square-root part of the experimental current in Figure 3.7(b) (solid lines). Note that Equation 3.10 contains parameters as charge carrier mobility of the slowest species (µ h in this case), the relative dielectric permittivity ε r of BEH 1 BMB 3 -PPV, and the generation rate G of e-h pairs. Since µ h was experimentally measured (Figure 3.6) and ε r of 2.6 was found from impedance spectroscopy experiments, we can fit G at the highest light intensity. Using Equation 3.10 we can predict the photocurrent at all other light intensities. As shown in Figure 3.7(b), the predicted photocurrents (solid lines) are in excellent agreement with the experimental data. The 1/2 power dependence of J ph on voltage and 3/4 dependence on ILP is a strong indication for the occurrence of a SCL photocurrent in this materials system. Another way to confirm the presence of a SCL photocurrent is to consider the voltage V sat at which J ph switches from the square-root dependence to the saturation regime. This transition occurs when the hole accumulation region L 1 becomes equal to the device thickness L. A schematic band diagram of this case is shown in Figure 2.1(b). Thus the Equation 3.9 gives the value for V sat to be: ( ) 1/2 8qG V sat = L 2. (3.11) 9ǫ 0 ǫ r µ h From Equation 3.11 it appears that in case of a SCL photocurrent V sat scales with the square-root of light intensity. In contrast, in the absence of a spacecharge limit (Equation 3.7) the transition voltage will be independent on light intensity [9]. In Figure 3.7(b) the voltage V sat at which the transition occurs is J ph [A/ m 2 ] 10 1 J V 0 -V=10 V J V 0 -V=0.1 V S = 0.95 S = 0.76 (a) Incident Light Power [W/ m 2 ] 10 1 V sat [V] S=0.53 (b) Incident Light Power [W/ m 2 ] Figure 3.8: (a) Incident light power (ILP) dependence of the photocurrent J ph taken from Figure 3.7(b) at an effective voltage of V 0-V =0.1 V and V 0-V =10 V (symbols). (b) Saturation voltage (V sat) versus ILP as determined for Figure 3.7(b). The slope (S) determined from the linear fit (solid lines) to the experimental data is written on the figure.

15 52 Chapter 3: Photocurrent generation in bulk heterojunction solar cells determined from the crossover point of the square-root dependence and the extrapolated saturation part, as indicated by the arrow. From Figure 3.7(b) it is already demonstrated that V sat shows a clear variation with light intensity. In Figure 3.8(b) V sat is plotted in double logarithmic scale as a function of ILP. A slope S=0.51 is found, being in agreement with the space-charge limited prediction (of 0.5) from Equation This is a further conformation that the photocurrent in 20:80 blends of BEH 1 BMB 3 -PPV:PCBM devices is truly limited by space-charge effects Analytical prediction for the conversion efficiency The SCL photocurrent is the maximum electrostatically allowed current that can be generated into the external circuit of any solar cell. A J ph limited by spacecharge effect also has a strong impact on the power conversion efficiency of this type of solar cells. For a photovoltaic device (Figure 3.7) the output power density is given by P(V )=J ph (V OC -V ) V, where V OC is the open-circuit voltage (V OC V 0 ). For a device under space-charge limitation the J ph (V OC -V ) is given by Equation Thus P(V ) (V OC -V ) 1/2 V, which reaches its maximum (P max ) at V =V max =( 2 3 )V OC. Hence, from Equation 3.10 we obtain: ( ) 1/4 P max = qg 3/4 9ǫ0 ǫ r µ h 2 3/2 V 8q 33/2 OC. (3.12) The fill factor (FF) of the photovoltaic cells is calculated from the ratio: FF = J maxv max J SC V OC 100%, (3.13) where J max V max =P max and J SC is the short-circuit current (applied voltage V = 0 V). Combining Equations 3.10 and 3.12 gives the maximum possible value of the FF for a solar cell limited by the space-charge to be: FF = 2 100% = 38.49%. (3.14) 33/2 From Figure 3.7 and Equation 3.11 it is observed that J ph is limited by the buildup of space-charge for effective voltages V 0 -V <V sat, and is space-charge-free for V 0 -V V sat. The J SC of the solar cells is given at the effective voltage of V 0 - V V OC (which is 0.8 V for the experimental data presented here). Thus, for the V sat >V OC, the J SC will fall into the space-charge limitation (square-root dependence on V ) and it will approach a 3/4 light intensity dependence (Equation 3.10). Consequently, the solar cell performance is fully limited by space-charge effect (Equations 3.12 and 3.14). In order to reduce the effect of the space-charge on device performance, the V sat should be strongly reduced (V sat 0 V). From Equation 3.11 it is observed that V sat is mostly influenced by the film thickness L and the light intensity (or G). A device could be space-charge-free under normal operation condition (1 Sun illumination), but become space-charge limited at higher light intensity or in thicker films, as long as there is a difference between electron and hole mobility to build-up the space-charge accumulation.

16 3.3. Experimental section 53 Equations 3.12 and 3.14 qualitatively predict the maximum electrostatic allowed FF and power conversion efficiency (η=100% P max /ILP) of any solar cell limited by space-charge. It is important to note that for a quantitative analysis the effect of diffusion, recombination, field-dependent generation rate G(E) and the effect of a non uniform electric field should be taken into account. For example, as has been shown in this chapter, a linear dependence of J ph -(V 0 -V ) characteristics is observed at very low effective voltages (close to V 0 or V OC ) due to diffusion. Such a linear dependence increases the maximum attainable FF of the solar cell under space-charge limitation (Figure 3.7) to a value of approximatively 42%. A recent numerical model developed by Koster et al. incorporates these processes and a quantitative fit to the experimental data can be given [18] Conclusion In this Section, we demonstrated the existence of a fundamental limit of the photocurrent in semiconductors. The photocurrent in 20:80 blends of BEH 1 BMB 3 - PPV:PCBM solar cell devices reaches this electrostatic limit already under normal operational conditions (0.8 sun). The experimental photocurrents obey all features characteristic for the space-charge limited regime: The photocurrent is proportional with a 1/2 power dependence on voltage and a 3/4 power of light intensity. Furthermore, the saturation voltage varies as the one-half power of the light intensity. These results give further insight in the mechanism of photoconduction in semiconductors and are valuable for the design of new materials in organic photovoltaic devices. 3.3 Experimental section Materials: The material used were MDMO-PPV synthesized via the Gilchroute, PCBM (received from University of Groningen), a 25:75 random copolymer of poly[2,5-bis(2 -ethylhexyloxy)-co-2,5-bis(2 -methylbutyloxy)-1,4-phenylene vinylene] (BEH 1 BMB 3 -PPV; for molecular structure see Figure 2.14), PE- DOT:PSS from Bayer AG (Baytron P VP Al 4083), LiF and Al from Aldrich. Glass plates (3 cm 3 cm) covered with 160 nm patterned ITO resulting in 4 different device areas (0.1, 0.15, 0.33, 1 cm 2 ) were used for device preparation. Device Preparation: The ITO covered glass substrates were wet-cleaned by rubbing with soap, rinsing with water, and ultrasonic cleaning in acetone and propanol. The substrates were further UV-ozone treated and a layer of PE- DOT:PSS was subsequently spin-coated on the pre-cleaned ITO, using a Convac spin-coater. The PEDOT:PSS layer was dried at an elevated temperature. The samples were then inserted into a glove box filled with nitrogen. An active layer was then spin-coated using a Karl Suss spin-coater following by the evaporation of the metal top electrode which consist of a thin LiF (1 nm) layer toped with Al (100 nm) to complete the devices. The active layer consist either of a 20:80 weight percentage blend of MDMO-PPV:PCBM spin-coated from a chlorobenzene solution (with a concentration of 3.3 mg PPV/mL), or by a 20:80 weight percentage blend of BEH 1 BMB 3 -PPV:PCBM spin-coated from a ortho-

17 54 Chapter 3: Photocurrent generation in bulk heterojunction solar cells dichlorobenzene solution (with a concentration of 8.0 mg PPV/mL). In order to determine the electron and hole mobility in blends of BEH 1 BMB 3 -PPV:PCBM (Figure 3.6), the devices were prepared and characterized similar to that described in Section 5.5. Device Characterization: All measurements were performed under a nitrogen atmosphere. J-V measurements were performed with a Keithley 2400 Sourcemeter. In forward bias ITO electrode was positively biased. The devices were illuminated at the transparent ITO electrode using a halogen lamp with a spectral range of nm calibrated using a Si diode. Light intensity dependence was measured by varying the light power using a set of neutral density filters with a constant optical density over the spectral range of the light source. Subsequently, the resulting spectrum of each filter-lamp combination was recorded and integrated over the absorption spectrum of the active layer, which gives the intensity. Therefore, the generation rate (G) of electron-hole pairs is proportional to the light intensity (G ILP).

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