#
Effect of Light Irradiation on the Diffusion Rate of the Charge Carrier Hopping Mechanism in P3HT–ZnO Nanoparticles Studied by μ^{+}SR

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}, and ZnO, are used as acceptors to transport electrons [10]. Previous studies have revealed that inorganic materials of nanoparticle size enhance optical absorption [12]. One material currently widely used is ZnO because it is easy to synthesize ZnO at nanoparticle sizes [13,14]. Another advantage of ZnO is that it is nontoxic compared with CdSe [10]. For electron mobility, ZnO has a higher value ($2\times {10}^{-3}$ cm

^{2}/V·s) than TiO

_{2}($1\times {10}^{-4}$ cm

^{2}/V·s) [15]. A high electron mobility facilitates efficient electron transport and produces high-efficiency solar cells [15,16,17]. In addition, ZnO nanoparticles have a lower conduction band than the lowest unoccupied molecular orbital (LUMO) of P3HT, which facilitates the transport of electrons from donor to acceptor [18]. Thus, a combination of P3HT and ZnO nanoparticles can be used to achieve the expected and improved performance in hybrid solar cells [16,17], although the PCE for the hybrid solar cells is still less than 1% [19].

^{+}SR) measurement is a suitable technique [21,22]. When a muon is implanted into the polymer sample, it interferes with the carbon double bonds in the polymer and forms muonium (the bound state of the positively charged muon and electrons), which gives rise to unpaired electrons and an accompanying polarization field, called the negative polaron, in the polymer chain. When the longitudinal magnetic field is applied to the sample, the polaron moves away and diffuses parallel (intra) and perpendicular (inter) to the polymer chain [23,24,25,26].

^{+}SR study, an active layer of hybrid solar cells of regio-regular P3HT–ZnO nanoparticles was measured with light irradiation, and it was found that at 10 K, the charge carrier transport was dominated by three-dimensional interchain diffusion [27,28], which differs from the μ

^{+}SR measurements without light irradiation, in which the three-dimensional diffusion was observed at the higher temperature of 25 K [29]. However, the values of the intrachain and interchain diffusion rates for the blended regio-regular P3HT–ZnO nanoparticles have not been reported. The diffusion rate of charge carrier transport needs to be estimated to obtain information about the number of charge carriers that can be transported either intra or interchain in order to estimate the solar cell’s efficiency. This is because solar cells’ efficiency strongly depends on the charge carrier mobility, which correlates with the diffusion rate. Hence, it is necessary to determine the diffusion rate in order to obtain solar cells with high efficiency.

^{+}SR), and the effect of light irradiation on the diffusion rate. By analyzing the μ

^{+}SR spectra, the hopping mechanism and the diffusion rate of the charge carriers in the sample can be calculated. The calculation and analysis were based on an empirical function using the equations relating to the relaxation rate data as a function of the H

_{LF}with the diffusion rates [30,31,32,33]. This paper is organized as follows: Section 1 is an introduction describing the state of the diffusion rates and the reason for choosing the regio-regular P3HT–ZnO nanoparticles as the material to be investigated. Section 2 explains the method for the material preparation and measurement of the μ

^{+}SR as well as the calculations and data analysis based on empirical functions. Section 3 presents the main results from the μ

^{+}SR data and discusses the analysis of the diffusion rate calculations. Finally, we present conclusions from this research in Section 4.

## 2. Materials and Methods

^{+}SR experiments in various longitudinal fields (LF) ranging from 0 to 395 mT, and at temperatures of 10 K, 15 K, 25 K, 50 K, and 300 K for samples of regio-regular P3HT–ZnO nanoparticles in conditions with and without white light irradiation (with a pulse-type flash lamp, 130 W, with 50 J per flash) at the RIKEN-RAL Muon Facility in the UK [27,28]. We collected 30 million events for every dataset.

^{+}SR measurements were the time-dependent asymmetry, and they were fitted using a simple exponential function as shown in Equation (1) [26,27,28,29,35,36,37,38,39].

_{LF}) at a certain temperature were obtained. The dependence of $\lambda $ on H

_{LF}can be refitted using the function of Equation (2) or (3) to obtain information on the direction of charge carrier hopping as previously reported [26,27,28,29,30,31,35,36,37,38,39]. If the field dependence (H

_{LF}) of $\lambda $ can be fitted properly using Equation (2), then the charge carrier hopping can be defined as one-dimensional intrachain hopping diffusion.

_{LF}) of $\lambda $ can be fitted properly using Equation (3), the charge carrier hopping can be defined as three-dimensional interchain hopping diffusion.

_{LF}, as shown in Equation (4) [30].

_{LF}dependence of $\lambda $ as shown in Figure 1 can be well fitted using Equation (2).

_{LF}, the $\lambda $ value is approximately constant as shown in Figure 1.

_{LF}is zero.

## 3. Results and Discussion

_{LF}as a result of the depolarization of the muonium state [40].

_{LF}of 10 mT are shown in Figure 3. When using light irradiation, the asymmetry shifts slightly higher due to the addition of energy that affects the depolarization of the muonium state, which may also affect the transport of charge carriers.

_{LF}dependence of the depolarization rate ${\lambda}_{1}$ of the regio-regular P3HT–ZnO nanoparticles with and without light irradiation at temperatures of 10 K, 15 K, 25 K, 50 K, and 300 K. The value of ${\lambda}_{1}$ was extracted from the fitting result for the asymmetry data using Equation (1). Without light irradiation, the dependence of H

_{LF}on ${\lambda}_{1}$ for temperatures of 10 K and 15 K showed a linear trend in a log–log plot that could be fitted using Equation (2), which indicates the direction of the charge carrier hopping of one-dimensional intrachain diffusion. For temperatures of 25 K, 50 K, and 300 K, the dependence of H

_{LF}on ${\lambda}_{1}$ is in accordance with Equation (3), which indicates the direction of the charge carrier hopping of three-dimensional interchain diffusion. With light irradiation, the dependence of H

_{LF}on ${\lambda}_{1}$ for all temperatures can be fitted using Equation (3), which shows the direction of the charge carrier hopping of three-dimensional interchain diffusion. It was found that, at temperatures of 10 K and 15 K, without light irradiation, the charge carrier hopping mechanism was dominated by one-dimensional intrachain diffusion. However, with light irradiation, the charge carrier hopping mechanism completely changed to three-dimensional interchain diffusion, confirming that the additional energy of light irradiation affects the direction of charge carrier hopping. A similar tendency was observed for the H

_{LF}dependence of ${\lambda}_{2}$ with and without light irradiation at temperatures of 10 K, 15 K, 25 K, 50 K, and 300 K, as shown in Figure 5. Although the tendency was the same, the value of ${\lambda}_{2}$ was much smaller than ${\lambda}_{1}$, therefore, for the present study, the fast component in the short time region of the depolarization rate (${\lambda}_{1}$) was analyzed in more detail, due to ${\lambda}_{1}$ providing more significant information than ${\lambda}_{2}$.

^{+}SR measurement without light irradiation, the parallel diffusion rate ranged from $1.39\times {10}^{15}$ to $0.09\times {10}^{15}$ rad/s. The parallel diffusion rate decreased with increasing temperature. The perpendicular diffusion rates were obtained starting from 25 K. It was found that the values increased with increasing temperatures. These results are consistent with our proposed model regarding the change in dimensionality obtained from the H

_{LF}dependence of ${\lambda}_{1}$ as described in Figure 4. When comparing the diffusion rate with that for regio-regular P3HT without ZnO nanoparticles, we found that the parallel diffusion rate in the present study was of the same order of magnitude, while the perpendicular diffusion rate was two orders of magnitude higher in the high-temperature range [32]. Moreover, compared with those of other conjugated polymers such as polyaniline (PANI), polypyridine, and polyphenylenevinylene (PPV), the parallel diffusion rates of regio-regular P3HT–ZnO nanoparticles are higher by up to three orders of magnitude, and the perpendicular diffusion rates are slightly higher than those of PANI and PPV at high temperature [41,42]. The increase in the parallel and perpendicular diffusion rates indicates that the addition of ZnO nanoparticles facilitates the transfer of charge carriers due to the different bandgaps of P3HT and ZnO nanoparticles. The energy level (LUMO) of P3HT is −3.3 eV, while the conducting band of ZnO nanoparticles is −4.2 eV [28]. The low value of the conduction band of ZnO nanoparticles makes the diffusion process easier, resulting in high values for both parallel and perpendicular diffusion.

^{+}SR measurement with light irradiation, the values of both parallel and perpendicular diffusion were obtained for all temperatures starting from 10 K. At 10 K and 15 K, the perpendicular diffusion rates were $0.95\times {10}^{10}$ and $1.13\times {10}^{10}$ rad/s, respectively. These values were not observed in μ

^{+}SR measurement without light irradiation. The parallel diffusion decreased with increasing temperature, whereas the perpendicular diffusion rate increased with increasing temperature. The parallel diffusion rates ranged from $2.28\times {10}^{14}$ to $0.88\times {10}^{14}$ rad/s while the perpendicular diffusion rates ranged from $0.95\times {10}^{10}$ to $1.79\times {10}^{10}$ rad/s. When light irradiation was performed, the parallel diffusion rate was lower by one order of magnitude than the diffusion rate without light irradiation at 10 K and 15 K. Meanwhile, at 25 K to 300 K, the diffusion rate was of the same order of ${10}^{14}$, as shown in Figure 6. For μ

^{+}SR measurement with light irradiation, the perpendicular diffusion rate increased slightly with increasing temperature compared with that for μ

^{+}SR measurement without light irradiation. It is indicated that the additional energy from light irradiation affects the diffusion, especially the charge diffusion in the perpendicular direction.

## 4. Conclusions

^{+}SR measurements with and without light irradiation. Without light irradiation, ${D}_{\Vert}$ decreased with increasing temperature, while ${D}_{\perp}$ was observed starting from 25 K and increased with increasing temperature. On the other hand, with light irradiation, the ${D}_{\perp}$ observed from 10 K indicated that the additional energy from light irradiation affected the diffusion, especially the charge diffusion in the perpendicular direction. The value of ${D}_{\Vert}/{D}_{\perp}$ for μ

^{+}SR measurement with and without light irradiation ranged from $2.40\times {10}^{4}$ to $0.49\times {10}^{4}$ and $1.70\times {10}^{4}$ to $0.57\times {10}^{4}$, respectively. A smaller value of ${D}_{\Vert}/{D}_{\perp}$ indicates a higher domination of charge carrier interchain diffusion.

^{+}SR measurements for active solar cell materials, such as P3HT, P3HT/PCBM, and P3HT–ZnO nanoparticles, have only determined the dimensionality of the charge carrier mobility; therefore, the diffusion rate has not been obtained. The value of the diffusion rate is required when a material is to be used in applications, especially for solar cell devices. By using this model, not only the dimensionality, but also the diffusion rate, can be exactly calculated and obtained from H

_{LF}-μ

^{+}SR measurements. Thus, researchers can use these two parameters in designing materials for applications, especially materials for producing high-efficiency solar cells. In addition, by using this model, we can also determine the diffusion rates for other materials such as poly(3-alkylthiophene) derivatives (poly(3-butylthiophene) and poly(3-octylthiophene)), which also have the potential to be used as active materials in solar cells. If the diffusion rates of other materials calculated using this model are higher than those of P3HT–ZnO nanoparticles, then these materials will become strong candidates for the active materials of solar cells.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Two regions of longitudinal field H

_{LF}dependence of relaxation rate $\lambda $ for high H

_{LF}and low H

_{LF}.

**Figure 2.**The asymmetry data for regio-regular P3HT–ZnO nanoparticles for various applied longitudinal fields without light irradiation at temperatures of (

**a**) 10 K, (

**b**) 15 K, (

**c**) 25 K, (

**d**) 50 K, and (

**e**) 300 K, and with light irradiation at temperatures of (

**f**) 10 K, (

**g**) 15 K, (

**h**) 25 K, (

**i**) 50 K, and (

**j**) 300 K.

**Figure 3.**Different asymmetry data for regio-regular P3HT–ZnO nanoparticles for 10 mT with (△) and without (▲) light irradiation at temperatures of (

**a**) 15 K and (

**b**) 25 K.

**Figure 4.**The longitudinal field dependence H

_{LF}of the relaxation rate ${\lambda}_{1}$ of the regio-regular P3HT–ZnO nanoparticles without light irradiation at temperatures of (

**a**) 10 K, (

**b**) 15 K, (

**c**) 25 K, (

**d**) 50 K, and (

**e**) 300 K and with light irradiation at temperatures of (

**f**) 10 K, (

**g**) 15 K, (

**h**) 25 K, (

**i**) 50 K, and (

**j**) 300 K.

**Figure 5.**The longitudinal field dependence H

_{LF}of the relaxation rate ${\lambda}_{2}$ of the regio-regular P3HT–ZnO nanoparticles without light irradiation at temperatures of (

**a**) 10 K, (

**b**) 15 K, (

**c**) 25 K, (

**d**) 50 K, and (

**e**) 300 K and with light irradiation at temperatures of (

**f**) 10 K, (

**g**) 15 K, (

**h**) 25 K, (

**i**) 50 K, and (

**j**) 300 K.

**Figure 6.**Temperature dependence of the diffusion rates in regio-regular P3HT–ZnO nanoparticles: (

**a**) parallel and (

**b**) perpendicular.

**Table 1.**The diffusion rates for regio-regular P3HT–ZnO nanoparticles at several temperatures without light irradiation obtained in this study.

10 K | 15 K | 25 K | 50 K | 300 K | |
---|---|---|---|---|---|

${D}_{\Vert}$ (×10^{15} rad/s) | $1.39$ | $1.35$ | $0.19$ | $0.16$ | $0.09$ |

${D}_{\perp}$ (×10^{10} rad/s) | $-$ | $-$ | $1.15$ | $1.25$ | $1.73$ |

${D}_{\Vert}/{D}_{\perp}$ (×10^{4}) | $-$ | $-$ | $1.70$ | $1.28$ | $0.57$ |

**Table 2.**The diffusion rates for regio-regular P3HT–ZnO nanoparticles at several temperatures with light irradiation obtained in this study.

10 K | 15 K | 25 K | 50 K | 300 K | |
---|---|---|---|---|---|

${D}_{\Vert}$ (×10^{14} rad/s) | $2.28$ | $1.83$ | $1.61$ | $1.19$ | $0.88$ |

${D}_{\perp}$ (×10^{10} rad/s) | $0.95$ | $1.13$ | $1.20$ | $1.38$ | $1.79$ |

${D}_{\Vert}/{D}_{\perp}$ (×10^{4}) | $2.40$ | $1.62$ | $1.34$ | $0.86$ | $0.49$ |

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**MDPI and ACS Style**

Pratikna, E.; Safriani, L.; Riveli, N.; Adiperdana, B.; Winarsih, S.; Aprilia, A.; Sari, D.P.; Watanabe, I.; Risdiana, R. Effect of Light Irradiation on the Diffusion Rate of the Charge Carrier Hopping Mechanism in P3HT–ZnO Nanoparticles Studied by μ^{+}SR. *Energies* **2021**, *14*, 6730.
https://doi.org/10.3390/en14206730

**AMA Style**

Pratikna E, Safriani L, Riveli N, Adiperdana B, Winarsih S, Aprilia A, Sari DP, Watanabe I, Risdiana R. Effect of Light Irradiation on the Diffusion Rate of the Charge Carrier Hopping Mechanism in P3HT–ZnO Nanoparticles Studied by μ^{+}SR. *Energies*. 2021; 14(20):6730.
https://doi.org/10.3390/en14206730

**Chicago/Turabian Style**

Pratikna, Eka, Lusi Safriani, Nowo Riveli, Budi Adiperdana, Suci Winarsih, Annisa Aprilia, Dita Puspita Sari, Isao Watanabe, and Risdiana Risdiana. 2021. "Effect of Light Irradiation on the Diffusion Rate of the Charge Carrier Hopping Mechanism in P3HT–ZnO Nanoparticles Studied by μ^{+}SR" *Energies* 14, no. 20: 6730.
https://doi.org/10.3390/en14206730