Graphene quantum dots (GQD) and edge-functionalized GQDs as hole transport materials in perovskite solar cells for producing renewable energy: a DFT and TD-DFT study

This study investigated the potential suitability of graphene quantum dots (GQD) and certain edge-functionalized GQDs (GQD-3Xs) as hole transport materials (HTMs) in perovskite solar cells (PSCs). The criteria for appropriate HTMs were evaluated, including solubility, hole mobility, light harvesting efficiency (LHE), exciton binding energy (Eb), hole reorganization energy (λh), hole mobility, and HTM performance. It was found that several of the compounds had higher hole mobility than Spiro-OMeTAD, a commonly used HTM in PSCs. The open circuit voltage and fill factor of the suitable GQD and GQD-3Xs were found to be within appropriate ranges for HTM performance in MAPbI3 PSCs. GQD-COOH and GQD-COOCH3 were identified as the most suitable HTMs due to their high solubility, small λh, and appropriate performance.


Introduction
2][3] The PSC has emerged as a transformative technology in the realm of photovoltaics, exhibiting a signicant improvement in efficiency from 3.7% to 25.8% within a very short timeframe.This remarkable progress positions PSCs as a strong contender to conventional silicon solar cells. 4,5PSCs oen have a light-absorbing level positioned between the HTM and the electron transport material (ETM).
The primary function of the HTM is to assist in the extraction of holes while impeding charge recombination at the interface between the HTM and the perovskite layer. 6In order to be deemed appropriate for use in PSCs, HTMs must possess signicant attributes like extraordinary hole transport capacity and conductivity, high mobility, a HOMO level that is wellaligned with the valence level of the perovskite material, favorable solubility to facilitate processability and cost-effectiveness. 7,8The effectiveness of a PSC device is signicantly affected by the choice of HTMs since they full many crucial functions.There are two primary functions of HTMs.Firstly, they serve to alter the energy barrier height that exists between the active layer and the electrode.Secondly, they create a specialized contact for the carriers.Furthermore, it is important to note that HTMs play a crucial role in providing a protective barrier, effectively safeguarding the active layer from any physical or chemical interactions that may arise between the electrode and the active layer.In addition, these entities play a crucial role in enhancing the process of charge transmission and collecting, hence contributing to the overall efficiency of the device.Finally, it should be noted that the use of HTMs has a remarkable role in enhancing the stability of both the active layer and the electrode.This aspect holds immense importance as it directly inuences the overall stability of the device. 4,8piro-OMeTAD, scientically referred to as 2,2 ′ ,7,7 ′ -tetrakis-(N,N-di-p-methoxyphenylamine), the compound known as 9,9 ′ -spirobiuorene has been more favored as a HTM in the advancement of PSCs.This is primarily attributed to its stable amorphous structure, capacity to generate thin lms, and favorable electrical conductivity subsequent to doping. 9-13However, the high cost involved in its synthesis has prompted researchers to explore alternative materials. 14Fortunately, several simple and inexpensive alternatives for HTMs have been successfully developed, including uorene, 15 phenylamines, 16 carbazole, 17,18 furan, 19 azine, 20 silolothiophene, 21 and azomethine. 224][25][26][27][28] The rst discovery of these entities occurred in 2004 by Xu et al.Subsequent investigations have been conducted to gain insights into their synthesis, characterisation, and prospective applications. 27,29CQDs are renowned for their remarkable stability and conductivity, little toxicity, and ecologically benign characteristics, making them very appealing for a different type of applications. 27,28raphene quantum dots (GQDs) have received most attention in contemporary discourse as a variant of CQDs.1][32] However, it is possible to functionalize them in order to alter their features, such as adjusting the band gap, to cater to diverse applications.Carbon quantum dots (Cdots) are carbon atoms at the periphery of GQDs that have been fully saturated with hydrogen atoms. 33C-dots have been the subject of substantial research due to their potential uses, notably in the eld of photocatalysis.Numerous studies have shown the ability of carbon dots (C-dots) to function as exceptionally procient photocatalysts, exhibiting remarkable catalytic efficacy.][36] In recent times, there has been a growing attention in the use of CQDs, with a particular focus on GQDs, as highly efficient HTMs in the PSC.][39] A technique for producing nitrogen-functionalized graphene quantum dots (NGQDs) with adjustable optical properties was developed by Testsuka et al.Incorporating NGQD layers into optoelectronic devices, such as perovskite solar cells and hybrid phototransistors, signicantly improved their performance. 37atta et al. employed density functional theory to examine a range of pristine and functionalized hexagonal GQDs and reported that GQDs functionalized with -OH and -COOH were effective for hole transport in MAPbI 3 as a PSCs. 38Furthermore, Sorli et al. investigated the potential of 360 different coronene derivatives as small GQDs for hole transport, using both theoretical and experimental methods. 39The present study aims to utilize DFT to examine the impact of the edge substitutions on the efficiency of GQDs as HTMs in perovskite solar cells.
This study investigates the potential of Graphene Quantum Dots (GQD) and a particular kind of edge-functionalized GQDs, referred to as GQD-3Xs, as Hole Transport Materials (HTMs) with prospective applications in PSCs.The careful choice of suitable heterojunction materials (HTMs) plays a pivotal role in optimizing the overall performance of PSCs.In order to assess the appropriateness of these materials, a thorough set of criteria is used, including solubility, hole mobility, light harvesting efficiency (LHE), exciton binding energy (E b ), hole reorganization energy (l h ), hole mobility, and hole transport material (HTM) performance.The method used in our study encompasses a series of methodical inquiries aimed at comprehensively characterizing the material characteristics and evaluating the performance of Graphene Quantum Dots (GQDs) and Triple-Doped Graphene Quantum Dots (GQD-3Xs) inside the framework of PSCs.
The Berny optimization algorithm 40 was used to optimize the GQD and 9 functionalized GQDs.During the optimization process, we selected maximum force, RMS force, maximum displacement, and RMS displacement thresholds of 4.5 × 10 −4 Hartree/Bohr, 3.0 × 10 −4 , 1.8 × 10 −3 Bohr, and 1.2 × 10 −3 , respectively.The inuence of dichloromethane solvent were studied by employing conductor-like polarizable continuum model (C-PCM) method. 41Imaginary frequencies were not found in the frequency calculations performed on pristine and functionalized GQDs.The UV-visible (UV-Vis) spectra were obtained using time-dependent density functional theory (TD-DFT) calculations. 42Natural bond orbitals analysis 43 accompanied with Chemcra 1.7 (ref.44) were employed to study and draw molecular orbitals of pristine and functionalized GQDs. [47] where, f abs max is the oscillator strengths for the maximum absorption peak.E g is dened as the gap energy between the HOMO and LUMO whereas E opt is optical bandgap which is the gap energy between electronic ground state and rst excited state.

Geometry, solubility, and dipole moment
The optimized geometries of the considered pristine and edge functionalized graphene quantum dots (GQD and GQD-3X, Paper RSC Advances X = CH 3 , COOH, COOCH 3 , NH 2 , NMe 2 , OH, OMe, SH, and SMe) in gas phase have been depicted in Fig. 1.In the development of organic electronic devices, solubility is a critical characteristic of HTMs.This term describes the capacity of a substance to dissolve in a specic solvent and form a homogenous solution.The signicance of solubility lies in its impact on the ability to create a thin lm of the material, which is a crucial element for the efficient performance of electronic devices. 51The formula DE solvation = E solution − E gas was utilized to obtain the solvation energies of HTMs, where E solution and E gas , respectively, represent the molecular energies in the solvent and gas phase. 47The solvation energies of the GQD and GQD-3Xs in dichloromethane solvent have been imported in Table 1.The results indicate that the HTMs with the highest solvation energies are GQD-3COOH, GQD-3COOCH 3 , and GQD-3NH 2 , with values of −14.45, −12.92, and −11.68 kcal mol −1 , respectively.These ndings indicate that GQD-3COOH, GQD-3COOCH 3 , and GQD-3NH 2 possess the greatest solubility among the HTMs considered.This phenomenon can be attributed to the strong hydrogen Fig. 2 The HOMO and LUMO schema of the GQD and GQD-3Xs.
bonding ability of the -COOH, -COOCH 3 , and -NH 2 substituents with dichloromethane.Table 1 also reports dipole moments of GQD and GQD-3Xs in gas phase and dichloromethane solvent.An inverse relationship exists between dipole moment and electron-carrier mobility.A high dipole moment indicates a low in electroncarrier mobility, while simultaneously improving the mobility of hole-carriers, 52 improving organic electronic devices performance.GQD is a nonpolar compound due to its symmetric structure, which results in a lack of dipole moment.However, the introduction of edge functionalization can break its symmetry and enhance its dipole moment and polarity.Among the GQD-3Xs considered, GQD-3COOH and GQD-3COOCH 3 have the highest polarity, with dipole moments of 6.20 and 6.78 D in gas phase, respectively.Furthermore, dissolving GQD-3Xs in dichloromethane can increase their polarities.
Other factor which plays an signicant role in the transport of charge carriers in materials, including hole transport materials used in organic electronic devices is polarizability. 52,53In the context of hole transport materials, polarizability can affect the mobility of charge carriers, including holes, within the material.Materials with high polarizability tend to have a higher interaction with electric elds, which can enhance the mobility of holes and improve the performance of devices such as organic solar cells.As seen in Table 1, the polarizability of GQD increases by replacing three edge hydrogens with selected substituents.Among these substituents, the highest polarizability is observed when hydrogens are replaced with the -S(CH 3 ) substituent.

Frontier orbital levels
The transportation of holes through a HTM is intricately connected to the energy levels of its HOMO and LUMO orbitals, which exert a profound inuence on the overall efficacy of a PSC.The schemas of HOMO and LUMO of the considered GQD and GQD-3Xs in dichloromethane solvent have been illustrated in Fig. 2. Also, Table 2 reports the energies of HOMO and LUMO of the considered GQD and GQD-3Xs.To be suitable for PSC applications, a molecule must possess a HOMO level that is higher than that of the valence band (VB) the perovskite.MAPbI 3 (methylammonium lead iodide) is a perovskite material that has been widely studied for its potential use in solar cells.5][56] The VB of MAPbI 3 was measured to be −5.43 eV. 57As reported in Table 2, the HOMO energies of all GQD and GQD-3Xs are higher than HOMO level of MAPbI 3 , indicating GQD and GQD-3Xs may be appropriate HTMs for MAPbI 3 based solar cells.Another critical requirement for HTMs in PSC applications is their capacity to transport holes to the Au cathode.To fulll this criterion, the HOMO level of the HTM should be situated below the Fermi level of the Au cathode, which is −5.1 eV. 58As seen in Table 2, the HOMO energy levels of GQD-3COOH and GQD-3COOCH 3 are less than the Fermi level of Au cathode.An important observation to make is that, GQD-3COOH and GQD-3COOCH 3 possess HOMO energies that are more profound than Spiro-OMeTAD's HOMO energy of −5.20 eV. 59As a result, it is plausible to anticipate that GQD-3COOH and GQD-3COOCH 3 are more suitable for use as HTMs compared to Spiro-OMeTAD.
In addition to proper position of HOMO, the LUMO level of a suitable HTM need to be located higher than the conduction band of MAPbI 3 perovskite (−3.93 eV). 57Preventing the ow of photo-generated electrons from the MAPbI 3 layer back towards the Au electrode is the key reason for this requirement. 47As observed in Table 1, the LUMO levels of all considered GQD and GQD-3Xs are positioned upper than the conduction band of MAPbI 3 perovskite.

UV-spectra and exciton binding energy
The UV-visible spectra for the GQD and GQD-3Xs were obtained using TD-DFT at the mentioned level.Table 3 provides the electronic conguration of the rst and most intense absorption lines, while Fig. 3 displays the calculated UV-visible spectra with a half width at half height (HWHH) of 0.33 eV.The UV spectra of GQD and GQD-3Xs exhibit three signicant peaks: a short peak in the 600-650 nm range, and two intense peaks in the 350-450 nm and 250-350 nm ranges.The short peaks are attributed to the S0 / S1 electron excitation, which corresponds to electron excitation from HOMO to LUMO.The most intense absorption lines in the UV-visible spectra of GQD and GQD-3Xs, except for GQD-3NH 2 , GQD-3N(CH 3 ) 2 , GQD-3OH, and GQD-3SCH 3 are attributed to S0 / S6 electron excitation.S0 / S7 electron excitation accounts for the most intense absorption lines in GQD-3NH 2 , GQD-3N(CH 3 ) 2 , and GQD-3OH and S0 / S9 corresponds to the most intensive absorption line in GDQ-3SCH 3 .Furthermore, the light harvesting efficiencies (LHEs) of the GQD and GQD-3Xs using eqn (1) presented in Table 4 demonstrate their suitable light absorption capabilities.As seen, the most LHEs correspond to GQD and GQD-CH 3 with value of 0.99 while GQD-NH 2 and GQD-3N(CH 3 ) 2 have the lest LHE with value of 0.87.
The required energy for S0 / S1 excitation corresponds to optical bandgap (E opt ).As shown in eqn (2), the difference between E g and E opt is the exciton binding energy (E b ) which indicates the strength of the coulombic attraction between the excited electron and the hole. 46A large exciton binding energy implies a strong electron-hole interaction, which can result in reduced charge separation efficiency and decreased device performance, particularly for solar cells, where efficient charge separation is critical for high power conversion efficiency.Conversely, a small exciton binding energy can indicate weak electron-hole interactions, facilitating efficient charge separation and transport, making the material more suitable for optoelectronic applications.The E b of the GQD and GQD-3Xs were found to be within the range of 0.17 to 0.19 eV (Table 4), indicating weak electron-hole interactions and high charge transfer in these materials.

Hole reorganization energy and hole mobility
The hole reorganization energy (l h ) is the energy change that occurs in a system when it undergoes structural relaxation following the loss of electrons. 60l h is calculated by: E + 0 and E + are the cationic energies of optimized neutral and cationic structures, respectively.Also, E 0 + and E 0 denote the neutral energies of optimized cationic and neutral structures.Minimizing the l h is crucial for achieving high charge carrier mobility in organic semiconductors. 60Table 5 presents a comparison of the l h values for GQD and GQD-3Xs.The table indicates that, with the exception of GQD-3N(CH 3 ) 2 and GQD-3NH 2 , the l h values of GQD and GQD-3Xs are all less than l h values of Spiro-OMeTAD (163.31meV (ref.8, 47, 60 and 61)), suggesting that they may have a better mobility than Spiro-OMeTAD.
The most stable molecular structure pairs of GQD and GQD-3Xs, and the Einstein ration were used for modeling their hole mobility: where e, K B , and T indicate unit electronic charge, Boltzmann constant (8.61733034), and temperature (298 K), respectively.r i is centroid to centroid distance.Also, k h,i and P i are the hole hopping rate and hoping possibility, respectively, and are obtained employing following equations: 62  In eqn (5), n h is transfer integral and proximately obtained by: 8 The hole mobility along with hole hopping rate, transfer integral, and centroid to centroid distance of the considered GQD and GQD-3Xs have been listed in Table 5.As seen, the hole mobility of all considered GQD and GQD-3Xs is more than calculated and experimental hole mobility values of Spiro-OMeTAD (2 × 10 −4 to 6 × 10 −3 cm 2 V −1 s −1 ). 51,62,63Among them, GQD, GQD-3SCH 3 , and GQD-3COOH have the most hole mobility with values of 2.45, 1.10, and 0.89 cm 2 V −1 s −1 , respectively.

Performances of PSCs
The performance of PSCs are proportional to their open circuit voltage (V OC ) and ll factor (FF) as described in following equation: 64 PC f V OC FF V OC and FF can be calculated by eqn ( 6) and ( 7): 65 In this case, MAPbI 3 perovskite is considered as acceptor and the GQD and GQD-3Xs are donors.9) and (10).
Table 6 presents a summary of the results obtained from evaluating various criteria for HTMs in the case of GQD and GQD-3Xs, and compares them to Spiro-OMeTAD.It is evident from the table that only GQD-3COOH and GQD-3COOCH 3 meet all the necessary criteria to be considered suitable HTMs.Additionally, these GQD-3Xs exhibit higher hole mobility and open circuit voltage compared to Spiro-OMeTAD.Consequently, GQD-3COOH and GQD-3COOCH 3 can be effectively utilized as efficient HTMs for perovskite solar cells.

Conclusion
In this study, the suitability of graphene quantum dot (GQD) and certain edge functionalized GQDs (GQD-3Xs, where X = CH 3 , COOH, COOCH 3 , NH 2 , NMe 2 , OH, OMe, SH, and SMe) as HTMs in PSCs was studied using DFT and TD-DFT.Specic criteria must be met for a compound to be considered an appropriate HTM in PSC, including the positioning of the HOMO of the HTM higher than the valence band (VB) of the perovskite, equal to or lower than the Fermi level of the gold cathode, and the LUMO energy level of the HTM higher than the conduction band (CB) of the perovskite.For this study, MAPbI 3 perovskite, which is widely used in PSCs, with VB and CB energy levels of −5.43 and −3.93 eV, respectively, was selected.Among the GQD and GQD-3Xs considered, the DFT calculations clari-ed that the HOMO levels of GQD and GQD-3Xs except for GQD-3COOH and GQD-3COOCH 3 were located higher than the Fermi level of Au cathode.As a result, these compounds do not meet the criteria, and they are not suitable as HTMs in PSC.
Solubility is a critical characteristic of HTMs in the development of organic electronic devices.The solubility of GQD and GQD-3Xs in dichloromethane was investigated in this study.It was found that GQD-COOH and GQD-COOCH 3 had the highest solubility, but these compounds did not meet the criteria to be used as suitable HTMs in PSCs.Among the compounds that met the criteria, GQD-3OH and GQD-3OCH 3 had the best solubility.The LHE and E b of GQD and GQD-3Xs were determined by analyzing their UV-visible spectra.Among the compounds that met the criteria, their LHE was found to be greater than 0.87, indicating their potential for effective light harvesting.The calculated E b values fell within the range of 0.17 to 0.19, suggesting their potential for efficient charge separation.The investigation of the hole reorganization energies (l h ) and the hole mobility of GQD and GQD-3Xs revealed that the hole mobility of all compounds considered may be higher than Spiro-OMeTAD and other benzene derivatives commonly used as HTMs in PSCs.Additionally, the V OC and ll factor (FF) of the GQD and GQD-3Xs that can be used as HTMs fall within the ranges of 0.57 to 1.07 V and 0.74 to 0.89, respectively, indicating their appropriate HTM performance in MAPbI 3 PSCs.Overall, due to its high solubility, small l h , and appropriate performance, GQD-COOH and GQD-COOCH 3 were found to be the most suitable HTMs among the compounds considered in this study.

Table 3
The main electronic configuration (MEC), wavelength (l), oscillator strength (f), and the possibility of electronic configuration (P) of the first and the most intensive absorption lines of the GQD and GQD-3Xs.The H is HOMO and L is LUMO © 2023 The Author(s).Published by the Royal Society of Chemistry RSC Adv., 2023, 13, 29163-29173 | 29167 Paper RSC Advances

Table 4
HOMO-LUMO bandgap energy (E g ), optical bandgap energy (E opt ), oscillator strength of the most intensive absorption line (f max ), exciton binding energy (E b ), and light harvest efficiency (LHE) of the GQD and GQD-3Xs

Table 5
Hole reorganization energy (l h ), hole hopping rate (k h ), transfer integral (n h ), centroid to centroid distance (r), hole mobility (m), open circuit voltage (V OC ), and fill factor (FF) of the GQD and GQD-3Xs

Table 6 A
summary for the comparison of GQD and GQD-3Xs in various criteria of HTMs a H1 = E HOMO (HTM) − E HOMO (perovskite).b H2 = E Fermi (Au) − E HOMO (HTM).c L1 = E LUMO (HTM) − E LUMO (perovskite).d Negative sign indicates that the compound is not a suitable HTM. e Calculated by eqn (