10.1.2.1 Photo-CELIV technique
Charge carrier mobility in bulk heterojunction solar cells has been studied using a ToF technique , or calculated from the transfer characteristics of an FET . These experiments showed that the electron mobility (PCBM phase) and the hole mobility (conjugated polymer phase) in the photoactive blend is fairly balanced, which is counterintuitive to experiments performed on the pristine materials. Space charge limited current measurements showed that the mobility of injected holes in the pure MDMO-PPV thin films is several orders of magnitude lower than injected electrons in PCBM thin films . Recent ToF studies performed on MDMO – PPV:PCBM 1:2 blends concluded that the mobility is unbalanced, the electron mobility being at least two orders of magnitude higher than the hole mobility . The apparent discrepancy between the above examples shows that the straightforward experimental determination of mobility using currently available methods is problematic.
The ToF technique is limited to a rather thick sample (~1 pm at the absorption maximum), which is at least 3-10 times higher than the optimum thickness of bulk heterojunction solar cells requires. Both mobility and solar cell performance may exhibit strong morphology dependence. The morphology may vary depending on the film preparation conditions, e. g. concentration of the solution, drying time, etc. In addition, the concentration of charge carriers in a ToF technique is limited to 10 % of the capacitive charge, which limits the concentration in a typical device configuration to n ~1014 cm-3. This concentration is at least 2-3 orders of magnitude lower than the charge carrier concentration in a solar cell under AM1.5 illumination conditions.
Mobility values obtained by FET measurements seem to fit better the predictions of numerical simulations of current density and voltage curves of bulk heterojunction solar cells . Nevertheless, the FET technique, in which the motion of electric field induced charge carriers is monitored near the surface of an insulator, also has serious limitations. First of all, the mobility obtained by the FET technique may also be strongly dependent on the morphology of the film. The morphology of the phase separated network near the insulator may be altogether different to the bulk. Moreover, the direction of the motion of charges in an FET is perpendicular to the direction of motion in a sandwich type photodiode, and the presence of anisotropy of mobility, such as observed in  could not be distinguished a priori.
The recombination dynamics of the photogenerated charge carriers in a blend of electron donor and electron acceptor materials have been studied by various optical techniques, such as light induced electron spin resonance (LESR) , photoinduced absorption (PIA) , photoinduced reflection/absorption (PIRA)  and transient absorption (TA) . In these optical techniques, the charge carrier induced changes of the absorption of the films (-AT) is monitored either by a modulation technique (PIA) or followed in a time resolved experiment (TA). The recorded signals are often very dispersive, especially at low temperatures and low frequencies or long timescales. Although the nature of these long lived photoexcitations is of practical importance, optical techniques cannot directly distinguish between mobile or deeply trapped, immobile charge carriers. For example, transient absorption experiments on the blend MDMO-PPV:PCBM showed power law decay of the -AT/T signal with an exponent of a = 0.4 in the ps to ms timescale . Power law decay indicates a broad distribution of lifetimes due to strong dispersion. Moreover, optical techniques are typically applied on films without electrodes; therefore operational devices cannot be easily studied.
Information on the recombination processes in operational bulk heterojunction solar cells is often obtained indirectly by the incident light intensity dependence of the short circuit current . Scaling factors close to one indicate that the short circuit current is not limited by second order recombination processes, such as bimolecular (nongeminate) recombination. In the latter case, an exponent close to 0.5 is expected. Unfortunately, this experiment provides little information on any first order recombination processes, which scale linearly with light intensity. Examples of such first order recombination processes are trap mediated (quasi-) monomolecular recombination or recombination due to accumulated space charge.
Both the charge carrier mobility (p) and the lifetime (t) can be determined simultaneously in operational bulk heterojunction solar cells using the photo-CELIV technique. In this technique, charge carriers are photogenerated by a short laser flash, followed by either extraction of the charge carriers under the intrinsic electric field and/or recombination. The intrinsic field may be compensated by the application of a forward bias offset voltage minimizing the external photocurrent and forcing recombination (flat band conditions). The remaining charge carriers can be extracted by a linearly increasing voltage pulse after a certain delay time (tdel).
The three different stages of the photo-CELIV technique are illustrated in Figure 10.22. Initially (stage 1), charge carriers are photogenerated via photoinduced charge transfer. During the second, equilibration, stage, the charge carriers recombine under zero electric field conditions. The zero field condition is achieved by compensating the built-in field of the device by the application of a forward bias offset voltage (E0ffset). Simultaneously, the charge carriers may relax towards the tail states of the distribution. In stage 3, the remaining charge carriers are extracted by a reverse bias voltage pulse. From the time the extraction current reaches its maximum, the mobility is calculated, and by calculating the concentration of extracted charge carriers versus delay time, the recombination kinetics are studied.
Figure 10.22 The three main stages of the photo-CELIV technique: (1) charge generation, (2) charge recombination and energy relaxation, (3) charge extraction.
The effect of Uoffset on the recorded photo-CELIV curves is shown in Figure 10.23. The sandwich type device used for this study is a typical of a bulk heterojunction solar cell (ITO/PEDOT – PSS/MDMO-PPV:PCBM 1:4/Al). The MDMO-PPV was prepared by the sulfinyl precursor route according to Scheme 10.2. The device (active layer thickness 265 nm) exhibited a power conversion efficiency of 1.8 % as determined using a calibrated solar simulator unit. The absorption coefficient of the photoactive layer at 532 nm excitation wavelength is 4 x 104 cm-1, corresponding to OD ~1, and thus bulk generation of charge carriers. The delay time (rdei) between the light pulse and the linearly increasing voltage ramp (A = 4 V/10 ц-s) was 5qs.
Under short-circuit conditions (0 V applied voltage), most of the photogenerated carriers exit the device prior to the reverse bias voltage pulse under the influence of the built-in field of the device (photoconductivity). Applying 0.9 V, the photocurrent upon photoexcitation is minimal (flat band conditions), and the extraction current due to the reverse bias voltage pulse is increased. Finally, the photocurrent turns to negative when Uoffset > 0.9 V, which indicates that the charge carrier motion is electric field driven. In addition, significant injection current flows, shown by the nonzero offset current, and the injected charge carriers are also extracted under the CELIV pulse together with the photogenerated ones. Experimentally, Uoffset is chosen close to the built-in field of the device, yet slightly smaller in order to avoid dark injection, which complicates the evaluation of the photo-CELIV curves. It is worth mentioning that the built-in field could be more precisely compensated in devices without PEDOT-PSS hole
Figure 10.23 The effect of Uoffset on the recorded photo-CELIV curves at 5 q. s fixed delay time.
injection layers. Nevertheless, no significant difference in the mobility values and its time and concentration dependence has been observed between devices with and without PEDOT-PSS.
Figure 10.24 A, shows recorded photo-CELIV curves as a function of delay time. The Uoffset during these measurements was 0.75 V. The maximum of the extraction current decreases with increasing delay time, indicative of charge carrier recombination, and tmax shifts slightly to longer times . The extraction current at all applied delay times decreases till the capacitance current step value, which shows that the majority of the photoinduced charge carriers are extracted in these photo-CELIV experiments. In Figure 10.24 B, the photo-CELIV transients recorded at varying light intensities and at fixed 5 ps delay time are shown. The maximum of the extraction current is constant until the threshold light intensity of ~ 1 pJ cm-2 pulse-1 and decreases constantly at lower light intensities. In contrast to the results obtained by the delay time dependent measurements, tmax at various light intensities remains almost constant. Finally, in Figure 10.24 C, the photo-CELIV curves recorded as a function of the maximum of the applied voltage pulse (Umax) at fixed 15 ps delay time and fixed light intensity are shown. The tmax value is shorter when the maximum of the voltage pulses is increased indicating the voltage (field) dependence of the mean charge carrier velocity.
The obtained mobility values are plotted versus delay time in Figure 10.25 A. The mobility decreases with tdel until 10 ps, and remains almost unchanged for longer delays. In Figure 10.25 B, the mobility is plotted as a function of the concentration of charge carriers obtained by the intensity dependent photo-CELIV measurement. Clearly, the rather strongly increasing mobility at short time delays in Figure 10.25 A, does not correspond to the weak concentration dependence of the mobility. Figure 10.25 C shows the voltage (field) dependence of the mobility for two different delay times: (i) 5 ps and (ii) 15 ps. The electric field dependence of the mobility at longer delay times is a typical positive dependence, as expected for an amorphous semiconductor, yet at short delays it shows an anomalous negative dependence. This comparison shows that the time dependent mobility at shorter time delays is not related to the charge carrier concentration (occupational density) dependence of the mobility alone, which is expected to play a role in disordered semiconductors due to e. g., trap filling effects. It may be related to time dependent energy relaxation of the charge carriers at short timescales.
The number of extracted charge carriers is calculated by integrating the extraction current transients, and plotted versus the delay time in Figure 10.26. The concentration decay is fitted using a time dependent (dispersive) recombination as :
— = – p(t )n2 (10.9)
where p(t) is the time dependent recombination coefficient. The time dependence of в (t) can be directly calculated using the data shown in Figure 10.26 as:
„ dn /dt
and the values are shown in the inset of Figure 10.26. A power law time decay following p(t) = e0t-(1-Y), where у characterizes dispersion, is found. The solution to Equation 10.9 by substituting в(t) = Pot-(1-Y) yields
time / s
Figure 10.24 Recorded photo-CELIV curves as a function of (A) delay time, (B) incoming light intensity at fixed 5 |as delay time, and (C) applied maximum voltage (Umax) at fixed 15 |as delay time and fixed light intensity. Reprinted with permission from Figure 1, A. Mozer et al., Applied Physics Letters, 86, 112104, Charge transport and recombination in bulk heterojunction solar cells studied by the photoinduced charge extraction in linearly increasing voltage technique. Copyright (2005), American Institute of Physics.
Figure 10.25 The mobility values versus (A) delay time, (B) charge carrier concentration determined from intensity dependent measurement, and (C) square root of the electric field at (a) 15 |as delay time and (b) 5 |as delay time.
where n(0) is the initial (t = 0) concentration of photogenerated charge carriers and tb = (Y/(n(0)$}))1/Y is an ‘effective’ bimolecular lifetime. The obtained fitting parameters are в(0) = 6 x 10-11 cm3 s-1, tb = 1.7 x 10-6 s, n(0) = 9 x 1015 cm-3 and y = 0.99, the latter indicating a nondispersive (time independent) bimolecular recombination at room temperature. Temperature dependent photo-CELIV studies showed that the nondispersive bimolecular recombination law observed at room temperature (y = 0.99) changes significantly when the temperature is decreased, e. g., y = 0.47 at 120 K indicative of a highly dispersive (time
Figure 10.26 Concentration of the charge carriers calculated from delay time dependent photo-CELIV curves versus tdel. The inset shows |3(t) versus tdel calculated according to Equation (10.5).
dependent) recombination process. Moreover, the ‘effective’ bimolecular lifetime tb decreases with increasing temperature, (~319 ps at 120 K) clearly showing that the recombination is a thermally activated process with calculated activation energy of ~80 meV.
The simultaneous determination of mobility (p) and lifetime (t) using the photo-CELIV technique gives surprising results when compared to previous transient absorption (TA) studies. The different recombination law calculated from delay time dependent photo-CELIV as compared to the TA measurement of Refs. [22, 87] might arise from the fact that the concentration decay of all the charge carriers including the immobile ones is probed in the transient absorption experiment. On the other hand, only charge carriers with reasonable mobility are extracted in the photo-CELIV experiment. From the end of the extraction pulse extraction current it is estimated that the number of unextracted, deeply trapped charge carriers is minimal at room temperature. The important question, therefore, is whether these long living charge carriers can also be extracted under operational conditions in bulk heterojunction solar cells, or in other words, whether the рт product determined by the photo-CELIV technique can properly describe the measured current density versus voltage curves of bulk heterojunction solar cells.