3.1.

Room-Temperature Current Density versus Voltage Characteristics in the Dark and under Illumination

Figure 2 presents a comparison of the illuminated current density (J_L) versus voltage (V) characteristics at room temperature of the AlPcCl/C₆₀-based heterojunction photovoltaic devices fabricated with the two types of interfacial layers. We observe a significant increase in the open-circuit voltage from V_OC = 0.61 V using the PEDOT:PSS interfacial layer to V_OC = 0.81 V for the device with the MoO₃ layer. The corresponding device fill factor also increased from 0.49 to 0.55. However, the short-circuit current is reduced for the device fabricated with MoO₃ compared to PEDOT:PSS from 4.21 to 3.47 mA/cm². Nevertheless, the observed increase in V_OC and FF results in a significant improvement in the power-conversion efficiency from 1.33 to 1.64%.

To understand the differences in the J–V characteristics presented in Fig. 2, we use the typical equivalent circuit model developed to describe photovoltaic devices.⁶ In this model, the photocell is described by a diode in parallel with a current source, J_ph, and a parallel resistance R_p, all connected in series with the resistance R_s. The diode represents the rectifying donor-acceptor heterojunction and is characterized by the reverse-bias saturation current density J_S, and the diode ideality factor n. J_ph(V) is the voltage-dependent photogenerated current density present in the device under illumination, and it becomes zero for devices measured in the dark. The parallel resistance R_p is related to leakage currents due to pinholes or other imperfections during device fabrication or to intrinsic recombination processes present in the active layers. The series resistance R_s accounts for the organic layer resistance together with the contact resistance formed between each of the interfaces present in the device. With this model, the current density (J) as a function of the applied voltage is given by the generalized Shockley diode Eq. 1,

Note that Eq. 1 describes the illuminated current density (J_L) when J_ph ≠ 0 and the dark current density (J_d) for J_ph = 0. In our analysis, we estimate the photocurrent as J_ph = J_L − J_d.

The experimental J_d versus V curve is fitted to Eq. 1 to obtain the diode parameters R_s, R_p, n, and J_s. The fit to the room temperature J_d – V for both devices is presented in Fig. 3. Good agreement of the fit with the data is obtained using the diode parameters listed in the caption to Fig. 3. When the PEDOT:PSS interfacial layer is replaced with the MoO₃ interfacial layer, the reverse-bias saturation current J_s decreases by two orders of magnitude from 9.48 × 10⁻⁷ mA/cm² to 7.84 × 10⁻⁹ mA/cm². As we will show later, such a decrease in J_s can explain the elevated V_OC measured from the device with the MoO₃ interfacial layer.

An expression for the V_OC can be extracted from Eq. 1 by setting J = 0. For R_s ≪ R_p this yields,

The device fill factor can also be calculated from the diode parameters of Eq. 1. In general, FF is obtained numerically. However, the following empirical estimates were previously shown to be good approximations of the numerical values when V_OC > 10nk_BT^{5, 6}, where the normalized quantities are defined as v_OC = qV_OC/nk_BT, r_S = R_s/R_CH, and r_p = R_p/R_CH. The characteristic resistance is given by R_CH = V_OC/J_SC.

We compare the experimentally measured V_OC with that given by Eq. 2 using the fitting parameters obtained from the dark current characteristics described above. From Fig. 3(b), we estimate J_ph(V_OC) = 1.16 mA/cm² for the MoO₃ device and J_ph(V_OC) = 0.31 mA/cm² for the PEDOT:PSS device. Using Eq. 2, and noting that the first term dominates over the other two terms for the quantities inside the bracket, the expected open-circuit voltage for the device with a PEDOT:PSS interface is V_OC = 0.60 V, whereas the one with a MoO₃ interface has V_OC = 0.82 V. These estimates are in very good agreement with the experimental values of 0.61 and 0.81 V, respectively, suggesting that the equivalent circuit model is applicable in describing the devices’ photovoltaic characteristics at room temperature.

We now account for the observed fill factor in both devices. Using the estimate of V_OC derived from the dark diode characteristics, the ideal fill factor (FF_O) calculated from Eq. 3 is FF_O = 0.80 for the MoO₃ device and FF_O = 0.74 for the PEDOT:PSS device. Correction associated with the different series resistance yields FF_S = 0.79 for the MoO₃ device and FF_S = 0.73 for the PEDOT:PSS device, demonstrating negligible effect of R_s on FF. The large value of R_p extracted from the dark J_d–V characteristic from both devices also results in negligible correction to the fill factor. However, the linear increase of J_ph at large negative applied voltage [seen in Fig. 3(b)] suggests another R_p contribution to FF under illumination condition. Estimating this light-induced parallel resistance from the slope of the linear part of the J_L–V curve, we obtain R_p ≈ 850 Ω cm² for the MoO₃ device and R_p ≈ 538 Ω cm² for the PEDOT:PSS device. Using these values, the fill factor calculated from Eq. 3 is FF = 0.61 for the MoO₃ device and FF = 0.55 for the PEDOT:PSS device, values that are comparable to the corresponding measured device fill factor. This analysis shows that FF is controlled by the ideality factor and saturation current of the diode as well as a light-induced R_p contribution. The latter could come from photoconductivity of the donor and/or acceptor layers.⁷

The measured J_ph versus V characteristics for the two different interfacial devices under investigation are presented in Fig. 3(b). In the inset of Fig. 3(b), J_ph is plotted against the effective voltage across the device, V_C–V, where V_C is the compensation voltage defined as the voltage where J_ph = 0. V_C is 0.62 V for device fabricated with a PEDOT:PSS interfacial layer, while V_C = 0.86 V for a MoO₃ interfacial layer device. We note that a scaling factor of 0.75 was used to multiply J_ph for the MoO₃ devices. Surprisingly, the shape of the photocurrent for both devices is nearly identical demonstrating that the photocurrent generated within the device is determined by the effective voltage, V_C–V, consistent with the absence of space-charge formation in the donor and acceptor layers. Thus, the differences that we observe in the J_ph–V curves can be attributed to the differences in the built-in field imposed by the presence of the anode interfacial layers. To gain further insight into the origin of the V_OC, we explore the photovoltaic characteristics of both devices at various temperatures and intensities of the incident light.

3.2.

Temperature and Power Dependence of the Open-Circuit Voltage

Figure 4 compares the temperature dependence of the open-circuit voltage for both devices under different illumination intensities. For a given incident illumination intensity, we observe a linear increase in V_OC as the temperature decreases from 300 to 140 K. A maximum value for V_OC is achieved at ∼140 K in both devices. Figure 4 shows this value is 1.05 V for the device fabricated with MoO₃ layer [Fig. 4(a)], whereas it is 0.65 V for the device with the PEDOT:PSS interfacial layer [Fig. 4(b)]. These observations indicate that the maximum V_OC value is strongly dependent on the nature of the anodic interfacial layer, while its position on the temperature scale seems to be determined by the properties of the donor/acceptor heterojunction. Upon further cooling, we observe a decrease in V_OC for both devices. The insets show the comparison of the temperature dependence of V_OC and the compensation voltage, V_C, in both devices. V_OC coincides with V_C for T < 140 K with both decreasing by nearly the same value of ∼0.1 V at the lowest temperature. For T > 140 K, V_OC < V_C with the MoO₃ device manifesting a larger offset than that of the PEDOT:PSS device.

Figure 4 also reveals a clear dependence of V_OC on the incident light intensity that is observed for T > 140 K in both devices. At <140 K, this power dependence disappears. Figure 5(a) presents a semilogarithmic plot of V_OC versus P, where P is the incident light intensity at three representative temperatures. The experimental data can be fitted with a linear function, and the slope can be compared to k_BT/q. The extracted slope decreases rapidly with temperature from 1.20k_BT/q (0.80k_BT/q) at T = 290 K to 0.92 k_BT/q (0.69k_BT/q) when T = 200 K and 0.52k_BT/q (0.47k_BT/q) at T = 150 K for the MoO₃ (PEDOT:PSS) device. Equation 2 relates the observed power dependence of V_OC to that of J_ph(V_OC). Assuming that the measured photocurrent at V = V_OC obeys the power-law dependence, J_ph(V_OC) = J_T(P/P_o)^α, where the parameter J_T depends only on temperature, then V_OC is given by

Figure 5(b) shows a double-logarithmic plot of J_ph(V_OC) versus P. We observe an experimental power low dependence of J_ph(V_OC) with the exponent strongly decreasing with temperature. Extracting α from Fig. 5(b) and combined with the slope of V_OC versus ln(P) determined from Fig. 5(a), the diode ideality factor can be obtained using Eq. 4. The results of this analysis at various temperatures and their comparison to n derived from the J_d versus V characteristics are displayed in Fig. 6. Good agreement between the two values of n is illustrated in Fig. 6, corroborating our assumption of the power-law dependence of J_ph(V_OC) with P as well as demonstrating that the equivalent circuit model is a good representation of the data.

3.3.

Discussion

We have shown above that the observed variation in V_OC associated with different interfacial layers at the anode of AlClPc/C₆₀ bilayer organic photovoltaic devices is related to the diode saturation current density J_s. Earlier works on inorganic p-n homojunctions and heterojunctions have shown that J_s results from the dominant transport process associated with the p-n junction.⁸ For devices with finite thickness, recombination at the electrode interfaces can also influence J_s. In p-n homojunctions, finite thickness correction leads to J_s = J_SOF, where J_SO is the saturation current density for an infinitely thick diode and

where W is the depletion width associated with the band-bending at the p-n junction, S is the surface recombination velocity at the electrode interface, and D and L are the diffusion coefficient and diffusion length of the minority carrier at the interface.⁹ Applying Eq. 5 for the organic heterojunction with W ≪ L (Ref. 10), then J_s ≈ (J_SOL/D)S. Recall that J_s is nearly two orders of magnitude lower in the device with the MoO₃ interface than that with the PEDOT:PSS interface. In the approximate expression for J_s, the quantities J_SO, L, and D are the same in both devices. Thus, S at the MoO₃/AlClPc interface is significantly lower than the one associated with the PEDOT:PSS/AlClPc interface. Such difference between the surface recombination velocities of the respective interfaces accounts for the variation in the open-circuit voltage observed in AlClPc/C₆₀ bilayer photovoltaic devices.

An early work by Rand⁷ demonstrated that, in bilayer organic photovoltaic devices, V_OC approaches its maximum value at low temperatures. Our current work demonstrates that this maximum value coincides with the compensation voltage V_C. Malliaras et al.¹¹ showed that V_C at low temperatures is a measure of the diode built-in potential V_bi. We find that V_bi is higher in the device where MoO₃ is used as an interfacial layer. Neglecting excitonic corrections, the maximum V_OC (or V_bi) in organic photovoltaic devices is given by the difference between the energetic positions of the donor highest-occupied molecular orbital (E_HOMO) and the acceptor lowest-unoccupied molecular orbital (E_LUMO) (Refs. 7, 12). Measurements using ultraviolet photoelectron spectroscopy report values of 5.3 eV (Ref. 2) and 5.4 eV Ref. 1) for E_HOMO in AlPcCl and 4.1 eV Ref. 13) and 4.5 eV (Refs. 1, 2) for E_LUMO in C₆₀. These values suggest that the maximum attainable V_OC for AlPcCl/C₆₀ heterojunction devices is ∼ 0.8 to 1.3 V. The data in Fig. 4 illustrate that this expected maximum V_OC is achieved in the MoO₃ device in which it is observed that V_OC = 1.05 V at T = 140 K, indicating negligible voltage losses at the MoO₃/AlPcCl interface. The observed higher maximum V_OC (and V_bi) in the MoO₃ device compared to that in the PEDOT:PSS device is consistent with the low surface recombination velocity in the former as described earlier.

An unusual feature of the data presented in Fig. 4 is the apparent peak seen in the V_OC versus T curves at T = 140 K in both devices. Both devices manifest a drop from this peak V_OC value by about δV_OC = 0.1 V as the temperature is lowered to T = 30 K, suggesting that the effect is associated with the p-n heterojunction at the AlPcCl/C₆₀ interface. This observation indicates a voltage loss contribution of the AlPcCl/C₆₀ heterojunction to V_OC. We argue that the presence of photoexcited charge carriers at high temperatures screens the electrostatic band bending at this p-n heterojunction reducing its deleterious effect on V_OC.