Introduction

Clean energy refers to the energy that the pollution production and greenhouse gas production are not sought. The tendency toward clean energies is extended day by day, due to the saturation of life environment by the pollutions of oil, gas and fossil fuels. One of the advantages of the clean energy is the preservation of the environment. The sun is one of the important and obvious sources of the free energy, clean and free from the destructive effects of environmental, which it has long been applied in the different ways by human. In recent years, the application of this type of energy source has caused solar cells to come. A solar cell is a device that converts the energy of sun by photovoltaic effect (direct conversion of solar power to electricity) without the connection to an external voltage source [1]. The technologies of the silicon solar panels are growing and increasing yields. But, they are not preferred due to the high energy consumption in the production processes in high temperatures and carbon dioxide production. In contrast, the organic and polymeric solar cells with the improvement of efficiency are built at ambient temperature, and their production speed is very high. In these types of device, the tenacity for the silicon solar cells is being raised. The technology of polymer sun cells has also not the limitation of raw materials in comparison with the technology of thin layers. In action by increasing the efficiency and the stability of polymer cells, it will be caught the competition field in the market of solar electricity. The primary reason for this success is low weight and high flexibility of these cells [2].

The solar cell is made of different layers. Solar cells are divided into two types of inorganic and organic, due to the type of materials that applied in the active layer of the cell. The most important parts of OSCs are donor (D) and acceptor (A) materials. Among the essential materials of the donors and acceptors could point to the conductive polymers and fullerene derivatives [3].

So far, various materials are applied in creating solar cells that have different efficiency and costs for the making. For instance, the efficiency increased dramatically and decreased costs by changing new dyes or using different nano particles such as selenium nanoparticles and employing other nano structure on FTO (fluorine-doped tin oxide). Solar cells created from organic materials have lower efficiency in comparison with other pairs. But, this type of solar cell has generally various advantages such as easy manufacture, flexibility, lightweight and low cost for making [3,4,5,6,7,8,9,10].

Polymer Solar Cells (PSC) are generally flexible solar cells, because of their polymer platforms. The first sample of PSCs was made by the research group of Tang et al. PSC is a combination of thin layers covered on polymer sheet or strip. Sometimes these cells act as a combination of the donor, an acceptor–donor and acceptor (D–A) systems. They have potential functions in artificial photosynthesis processes, photovoltaic devices, molecular electronics, solar cells based on polymer, organic semi-conductive materials, organic conduction and the materials with non-linear optical properties [11, 12]. The engineering of each system D–A should be included in an integrator full of electron donor and acceptor with electron shortage property. Fantastic properties may have resulted in the combination of D–A sections, such as the production of charge transfer intramolecular space with low energy that it could be increased the length of active conjugation using highly polar molecules.

Boron-nitride (BN) has different allotropes. The polymorph hexagonal boron-nitride (h-BN) is the most important and stable one among BN allotropes. In general, graphite analogs have a layer structure that it is soft and slippery. For this reason, it has high usage as lubricant and filler for cosmetics. Compound BN is not present in nature, and it reacts through an artificial combination from B element, boric acid (H3BO3) and boron oxide (B2O3) with different resources of nitrogen such as N2, ammonia gas (NH3) and urea (CO(NH2)2). Then, BN is applied as a practical substance with different types in a wide range by much effort in the field of modern process technology. BN is a suitable selection as the right product for manufacturing photovoltaic devices notably solar cells, because of the considerable structural specification. This compound is an ideal substance for using in photovoltaic devices, because of the presence of a direct and adjustable band gap for all effective solar spectrum wavelengths [11, 13].

These substances are generally made through weak ultra-molecular actions such as Van der Waals forces and π–π interactions in solid phase. A hard aromatic structure will be formed by a combination of D–A parts together, which it can help to reinforce the energy decline of reformation and also two polar π–π intramolecular actions. Hence, this type of molecule can have an essential role in organic field-effect transistors (OFET) as semi-conductive part or ambipolar type. Aromaticity had a significant role in D–A combination systems, especially when the donor is tetrathiafulvalene (TTF). Aromatic combinations have shown more thermodynamic stability in CH compounds, due to their resonance and aromaticity effects toward saturated pairs, and it will decrease system energy [13].

The internal mechanism of polymer photovoltaic cells is done through several following steps: (1) Light absorption: Light is absorbed in the organic layer and makes electron–hole pairs (excitons). The properties of natural layer absorption should be matched with solar spectrum. (2) Exciton split: Then they should be isolated. It means the charge will be separated. An inverse trend called charge recombination should be correctly limited due to being efficient in charge isolation. (3) Charge transport: The charges that are not separated (hence they don't renew exciton split) should be run in an organic layer under the electric field. This is made with the equality of fermi energies of two electrodes. (4) Charge collection: At last, although many considerable types of research being done about increasing photoelectric properties of colors in the experiment, the understanding mechanism steps is a challenge, the electrical charges should be collected in the electrodes. One of the considerable properties of this type of target molecules (as indicated in recent DFT computation) includes into the determination of the location of the low electron-free energy balance (adapted with the highest occupied bonding molecular orbitals; HOMO) and with the lowest unoccupied antibonding molecular orbitals (LUMO) in the molecules with conjugation of π-system, despite of analyzing D–A sections in a framework. The cyclic voltammetry of the HOMO–LUMO gap of the discussed thin layer has approximately determined about 1.1 eV [13].

The separation of both exciton and recombination charge is related to the reaction of charge transfer, and it can be estimated the kinetic of this charge transfer using the Marcus theory [14].

Furthermore, Marcus' theory is extensively applied for the description of the dynamics of charge transfer and charge recombination in each D–A system, including Organic solar cells (OSCs) [15].

Although, this theory ignores tunneling effects, which it can help to the electron transfer process (especially in low temperatures), but it is reliable based on this assumption that the system should reach transfer space to receive transfer situations [16].

Another analysis is 3D real space of transfer density (TD) and charge difference density (CDD), which it is applied for the analysis of the charge and energy transfer in several conjugated polymers. A combination of 2D and 3D real space analysis is extensively applied for the study of the properties of the excited state of polymers [17]. There are several key parameters to consider designing the small molecule donors to be paired with fullerene acceptors in solution that processed bulk-heterojunction (BHJ) solar cells. The stages include: (a) the strong optical absorption were desired to maximize photon harvesting that extends into the near-IR region (λmax should be centered around 700 nm, the region of maximum photon flux) and extinction coefficients (ε) greater than 50,000 M−1 cm−1; (b) relatively deep HOMO energy levels from − 5 to − 5.5 eV to maximize open circuit voltages, while still matching commonly used high work function anodes; (c) relatively planar structures to promote intermolecular π–π interactions, which they are important for achieving high charge carrier mobility; (d) sufficient solution viscosity and solubility to enable thin film formation via solution deposition; and (e) synthetic procedures that are simple, high yielding and highly tunable to ensure both gram quantities could be made. In this way, the molecular libraries can be created. The several research groups have developed a series of solution-processing with small molecules by these considerations that challenge those of the very best polymers in solar cell applications [18].

This study was reported an electric transport measurement across a graphene-BN hetero structure [19, 20]. The DFT and TD-DFT calculation methods were implemented to examine four donor–acceptor systems as OSCs based on hole–electron theory. Alpha-sexithiophene and scandium-doped open edge BN were selected as D–A, respectively. Actually, by applying, this theory was tried to predict, simulate and calculate the distance of charge or electron transfer between two parts. In addition, according to the obtained and discussed results and applying some important correlate theories and rules (such as Marcus' theory, Plank’s formula and Rehm−Weller equation) some discussed complexation process about organic solar cells were simplified and categorized. Figure 1 has shown the predicted first studied system.

Fig. 1
figure 1

Predicted general structure of OSC in this study, including D and A part (cavity transmitters and acceptors)

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Computational methods and procedures

One of the main aims of this investigation is designation an appropriate D–A system applicable in OSCs. Accordingly, and by a literature review, Sc-doped open edge BN was implemented as NFA (non-fullerene acceptor). The vacant d-orbitals in scandium (Sc) as well as monolayer sp2 hybridization of BN facilitate charge and electron acceptance from donors [20, 21]. Semi-conductive conjugated polymers can be applied in the place of donors since they are normally good hole transporters. A sexithiophene is a conjugated polymer popular in generation of solar cells to date [22]. In Fig. 2, the structures of D1-Sc@BN to D4-Sc@BN were optimized via B3LYP and LANL2DZ basis set functions in DFT method at ground state and gas phase under standard conditions. According to this Figure, detailed structure of 1 consists of apart species of D1-Sc@BN. The structures of D2-Sc@BN to D4-Sc@BN include two, three and four D parts, respectively, with an A-part namely Sc@BN in all of them. The systems variety is a key to the superefficient system; in synthesis and production of these nano cells, generation of side products is inevitable. So, the monitoring operation of these products would be helpful to efficiency of OSC. The HOMO and LUMO energy levels of donor, acceptor and OSCs were calculated in the ground state [23].

Fig. 2
figure 2

The structures D1-Sc@BN to D4-Sc@BN were optimized via B3LYP and LANL2DZ basis set functions in DFT method

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The electron localization function (ELF) is a visual parameter for electron density investigations. In fact, it demonstrates probability of the electron presence in proximity of reference electrons with the same spin. ELF apparently isolates electrons in valance layer and cores, which it is advantageous to OSCs operation comparison and exploration of electron density variations. In this investigation, the region around Sc in Sc@BN and the OSCs were just studied to determine the better contrast [24].

Since Sc@BN is capable of accepting charge and electron, it could be applied as an acceptor in D–A systems, such as OSCs and organic light-emitting diode (OLEDs). Evaluation of charge and electron transfer in excited state was carried out by means of TD-DFT calculations to demonstrate D → A charge transfer. Another goal is to approach absorption and diffusion spectra to determine the charge transfer in OSCs (Fig. 2) by CAM-B3LYP method and LANL2DZ base set. CAM-B3LYP method as a modified B3LYP is satisfactorily precise in the excited state. This method has attracted the attentions gathering for the organic compounds with similar costs [20]. Charge transfer was accomplished based on electron–hole theory for the first five excitation possessing minimum energy. The electron transfer kinetic between D and A species was obtained by implementing Marcus theory [25] and the defined wavelength. All DFT and TD-DFT calculations were performed by Gaussian 09 software although some were based on Multiwfn 3.3.9, VMD 1.9.2 and GaussSum [26,27,28,29].

Marcus theory is the common place in donor–acceptor (D–A) electron transfer phenomenon. It is widely known for its interesting anticipations with respect to the electron transfer kinetic in previous decades. Using the maximum wavelength (λmax) for charge transfer (CT) as well as Planck and Rehm−Weller equations with some other physical and chemical parameters of D–A were calculated to investigate the electron transfer kinetic such as activation free energy of electron transfer. The potential variance of the ET process was also calculated. The data caused by D–A charge transfer that was produced based on the absorption wavelength. These calculations were fulfilled by good approximation considering the minimum energy required for the charge transfer.

Results and discussion

The donor–acceptor (D–A) systems were evaluated for application as OSC after optimizations (see Fig. 2). This investigation attempts to apply effective and modern visual parameters to achieve better perception. ELF electron densities for Sc@BN or the sole “A” part and the four D–A systems were provided in Fig. 3. These images display apparently that part A has specially donated electron in Sc-doped region, which they show electron density at the ground state. This area is capable of electron and charge transfer due to semi occupied d-orbitals. The shape shows increasing charge density on Sc atom after addition of part D, while it is significantly reduced in D–A system (Fig. 3e, number 4). These images are compatible with HOMO and LUMO orbitals.

Fig. 3
figure 3

ELF for regions accepting Sc@BN in a Sc@BN; b D1-Sc@BN; c D2-Sc@BN; d D3-Sc@BN and e D4-Sc@BN

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In fact, only the scandium impurity area on the BN plate was studied by two purposes. First of all, it was investigated the changes in the BN area, and also some empty orbitals of Sc atoms would be filled by electron donation of BN. It is important to note that this part of the BN plate has the highest load capacity in the entire exponent [30]. On the other hand, examining alphasixtufen polymers due to their optimization and rotation angle did not show us a technically accurate comparison, and it might even be confusing. But, comparing the scandium regions in the discussed structures has just offered a complete relative analogy for all OSCs with BN@Sc and effect on each other.

Absorption of the irradiated light in UV–Vis region of D1-Sc@BN systems was investigated over the study. It is evident that due to the donor structure the major portion of the high energy transfers is of type S0 → S1 (n → π*) and S0 → S2 (π → π*), which it has sulfur LPs (lone pairs) and π-bonds of C=C, as well as acceptor with sp2 hybridization. The charge transfers occur at the second stage. It should be noted that in the explored OSC systems, not only the absorption range but also the photonic transfers from donor to acceptor were great importance (transfers that lead to electrical current in OSCs). The different results were derived for each of the discussed OSC [30]. Figure 4 refers to absorption spectrum of donor and acceptor solely and all the OSCs. Examination of photoinduced electron transfer (PET) and photoinduced charge transfer (PCT) absorption was discussed in the following sections. In the classical solar cells, there is a direct relationship between wavelength and amplitude of absorption and their performance, which they are generally made by solid crystals. But, in the organic solar cells, increasing the absorption wavelength does not mean increasing efficiency. Sometimes, these wavelengths are not able to perform PCT or PET due to the lower energy.

Fig. 4
figure 4

The calculated UV–Vis spectra for Sc@BN; D1-Sc@BN; D2-Sc@BN; D3-Sc@BN and D4-Sc@BN

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Electron or charge transfer would be defined as a process in which the excited electron transfers from an excited donor molecule to an acceptor species (equation I). This process has namely kown as the hole transfer in hole–electron (HE) theory as well.

$${\text{D}}^{*} + {\text{A}} \to {\text{D}} + {\text{A}}^{*}$$
(1)

This process includes different mechanisms but the calculations in accordance with Spin Winner rule with the assumption of a constant system total spin are allowed via an electron transfer mechanism for every individual excitation state [31]. The simplest condition for the electron transfer including fluorescent photoinduced electron transfer (PET) and photoinduced charge transfer (PCT) are sole donor and absorption by acceptor to cause a new excitation state. It may calculate by hole–electron (HE) theory [32, 33]. The pathway of the electron transfers in D1-Sc@BN.OSC was shown in Fig. 5. This transfer was considered for the third excitation state, and those relevant to the first five excitations was reported in Table 1.

Fig. 5
figure 5

Charge transfer between D and A for third excitation state of OSC D1-Sc@BN

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Table 1 The charge transfer (CT) results on electron-hole theory for the first to five excitation states OSCs (D1-Sc@BN; D2-Sc@BN; D3-Sc@BN and D4-Sc@BN)
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Parameter D in Table 1 refers to the center-to-center distance (Å) of the hole part and the electron orbitals, and “s” is the overlap integral of the aforementioned orbitals, while the maximum overlap is considered as one. In these calculations, the ideal state for charge transfer occurs in presence of light with s = 0.22. According to the obtained results, the charge transfer D → A was just happened in OSCs D1-Sc@BN and D2-Sc@BN, which it is bolded in Table 1. Therefore, D1-Sc@BN in two excitation states possesses has five charge transfer abilities the longest of which it is averagely 9.81 Å. Also, D2-Sc@BN transfers the charge in an excitation state. The absorption spectra and wavelengths generated by the PET, and PCT processes were listed in Table 2. According to Table 2, the best charge transfer for D1-Sc@BN was at 298.1 and 279.55 nm in the third and fifth excited states. The severities (f) of each were 0.0016 and 0.0709, respectively. On the other hand, the best charge transfer for D2-Sc@BN in the fifth excited state at the wavelength 487 nm has a severity of 0.0019. These results are confirmed in third excitation state of D1-Sc@BN system in Fig. 6 (as color plot for excited regions through transition density matrix (TDM) technique). In Fig. 6a, TDM graph with 13 atoms in each step was displayed. Addition of heat map (Fig. 6b) of HE orbitals and a comparison based on these two parameters, charge transfer route and length can be conveniently derived, which it is detailed in the next section. Effective absorption range for the electrical current production in OSCs has shown in Fig. 7, in which the highest efficiency based on domain, and rate of absorption wavelength refers to D1-Sc@BN. The two OSCs capable of charge transfer and electrical current have eventually effective absorption range of 300–400 nm.

Table 2 The severity and wavelengths generated by the PET and PCT processes for OSCs D1-Sc@BN–D2-Sc@BN based on Hole–Electron theory
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Fig. 6
figure 6

a TDM of OSC D1-Sc@BN in the third excitation state with atomic structure; b Heat map for hole and electron orbitals and their overlap in the third excitation state of OSC D1-Sc@BN

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Fig. 7
figure 7

Absorption range for OSCs D1-Sc@BN–D3-Sc@BN which leads to PET and PCT

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The photoinduced electron transfer (PET) and photoinduced charge transfer (PCT) processes for OSCs D1-Sc@BN-D2-Sc@BN were demonstrated in Fig. 8. Accordingly, blue orbitals are holes and the red ones play the role of electrons. Every transfer refers to a unique excitation state, and levels of the major participants as well as their orbitals were included. As expected, the electron transfers from part D to part A occurred in two OSCs. PET and PCT include n → π* and π → π* charge transfers, respectively. The process in D1-Sc@BN was of types PET and PCT. D2-Sc@BN in fifth excitation state refers to PET and PCT, which it has taken place in 371.50 nm. The transfers in D3-Sc@BN were solely the PET, which it has occurred in fourth and fifth excitation states at wavelengths of 325.84 and 325.47 nm. These transfers from the viewpoint of absorption domain (see Fig. 7), and the process rate has the least efficiency compared to two other structures, in which transfers were only occurred in donor region. So, it would not be applied as OSC.

Fig. 8
figure 8

Hole-Electron orbitals and the portion of participant orbitals in excitation; a D1-Sc@BN n-state = 3; b D1-Sc@BN n-state = 5 and c D2-Sc@BN n-state = 5

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The electron transfer kinetic in D–A systems can be calculated with a good approximation using Marcus theory the results like the explored OSCs. In Table 3 was shown the obtained results. Application of Planck’s equation No. 2 leads to free energy of the electron transfer; since in two OSCs, PET and PCT processes are evident in the first five excitation states. The absorption wavelength for these transfers may be equalized to λmax in electron transfer [34].

$$\Delta G_{{{\text{et}}}}^{\# } = \, hc/\lambda$$
(2)
Table 3 The activation energies of electron transfer (ΔG#et), electron transfer kinetic (ket), free energies of electron transfer (ΔGet) and potential variance (ΔE) caused by photon absorption in the OSCs
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Constant values in the electron transfer kinetic ket can be calculated through Eq. 3 after achieving activation free energies of electron transfer ΔG#et. Furthermore, the free energy electron transfer of OSCs could be calculated via Eq. 4 (electron transfer Marcus theory) [35, 36].

$$k_{{{\text{et}}}} = \, k_{0} \exp ( - \Delta G_{{{\text{et}}}}^{\# } /RT)$$
(3)
$$\Delta G_{{{\text{et}}}}^{\# } = (L/4)(1 + \Delta G_{{{\text{et}}}}^{^\circ } /L)^{2}$$
(4)

Finally, Eq. 5 (Rehm−Weller) and the free energies electron transfer lead to estimation of electrode potential variance in calculation conditions, which it is in gas phase, for every OSC.

$$\Delta G_{{{\text{et}}}}^{^\circ } = e\left[ {E_{{\text{D}}}^{^\circ } - E_{{\text{A}}}^{^\circ } } \right] - \Delta E^{*} + \omega_{1}$$
(5)

Rehm−Weller equation foresees free energy variations between electron D–A according to the above formula in which “e” is the electrical charge, \(E_{{\text{D}}}^{^\circ }\) and \(E_{{\text{A}}}^{^\circ }\) are reducing potentials of electron and acceptor, ∆E* is mono and triple excitation energy, and ω1 is the required work for putting D–A into the ET distance [33].

According to the results in Table 3, the highest electron transfer kinetic refers to the third excitation state in D1-Sc@BN system (16.790 × 10–43 m s−1), which it requires the least energy for this electron transfer process. The calculations in relevant conditions (gas phase) show that this electron transfer can cause a potential variance (difference between electrodes connected to A and D) of 2.206 eV by absorption of wavelength 298.71 nm. Therefore, potential variance of two species can be forecasted by close similarity using excitation wavelength to execute electron transfer process. In addition, the obtained results of the calculation for D2-Sc@BN system revealed that potential variance of 2.210 eV can be produced by absorption of wavelength 297.92 nm. Results for the fifth excitation state of D1-Sc@BN show the highest potential variance among all discussed systems. Although, the calculations accounting the location of electron orbitals in a small portion of part A (Figs. 6b and 8b), this system cannot be highly applicable.

Conclusions

Sc-doped open edge BN is a structure with reasonable capacity for charge or electron acceptance in optical reactions. This and/or similar structures may be highly potential in replacing costly materials especially from the environmental viewpoint. In this work, four different D–A systems with the acceptor base were examined, and the results revealed that only D1-Sc@BN and D2-Sc@BN systems were capable of the electron and charge transfer due to light absorption. In all discussed systems, poly alpha-sexithiophene was applied as the electron donor in different contents. Effective absorption for charge transfer in two OSCs was in range 300–400 nm, in which both of them had one or two electron transfer process leading to the electrical current, and the largest transfer distance referred to D1-Sc@BN with an average value of 9.81 Å. The electron transfer kinetic of OSCs was subsequently calculated in good approximation via Marcus theory, where the results accompanied by Planck’s equation led to calculation of free energy of the electron transfer. Finally, electrode potential variance in calculation conditions namely the gas phase was estimated for each OSCs applying Rehm−Weller equation. These values for D1-Sc@BN and D2-Sc@BN were 2.3 and 2.2 eV, respectively. The highest electron transfer kinetic refers to the third excitation state in D1-Sc@BN system, which it requires the least energy for this electron transfer process. The results of the calculations for D2-Sc@BN system revealed that the potential variance of 2.21 eV can be produced by absorption of wavelength 297.92 nm. According to the obtained results and applying some important correlate theories and rules (such as Marcus' theory, Plank’s equation and Rehm−Weller formula), some discussed complexation process about organic solar cells was simplified and categorized. Due to the absorption wavelength range, the designed cells were far from ideal form. But, selection and construction of these predicted cells has usually applied as a composite and mosaic systems. It means that several different solar cells (each operating in a different wavelength range) have placed next to each other to create a high-performance solar cell. Furthermore, the aim of this investigation was primarily to demonstrate the potential of Sc–BN as a non-fullerene receptor in the construction of new organic cells. In addition, the efficiency of the system could be increased to an acceptable level by replacing different substituents on poly-six thiophene and testing them.