Due to the exhaustion of traditional energy sources and serious need for the energy, replacement of new and clean energy is a vital task for scientists. In recent years, solar energy due to its availability and abundance is being considered as a replacement for energy. During last five years, perovskite solar cell has absorbed scientist’s attention from all parts of the world[1-7] and recently power conversion efficiency of close to 20% is reported [8, 9]. As a very important component for perovskite solar cells, wide band gap materials such as TiO2 for their unique characteristics such as wide range of applications, controllable framework compositions and tunable pore sizes have attracted scientists [10-13]. Up until now for application in dye sensitized solar cells, TiO2 with different morphologies such as nanoparticles [14, 15], nanowires [16, 17], nanosheets , nanotubes [19, 20], spheres [21, 22] and some other mesoscopic structures [23-27] has been used. Another way to improve characteristics of TiO2 as an electrode is doping. For this purpose, TiO2 can be n-type doped to improve charge collection and electron transport properties. One of the elements that were used as a dopant with different concentrations (up to a doping level of 20 mol%) to enhance TiO2 performance is Niobium (Nb) [28-32]. To date, few researches on application of Nb-doped TiO2 have been done to improve the conversion efﬁciency of dye-sensitized solar cells (DSSCs) [30, 33]. To the best of our knowledge, however, there is no experimental or theoretical study for application of Nb- doped TiO2 in perovskite solar cell. To control the junction characteristics and enhance the charge transport properties of TiO2 electrode, Nikolay and co-workers work on lightly doped (from 0.5 to 3 mol% Nb) TiO2  and an increasing in the photocurrent of DSSCs with lightly doped (from 2.5 to 10 mol% Nb) TiO2 were concluded by Lu and co-workers .
Buffer layer plays an important role in cell’s efficiency, so choosing a suitable buffer layer is very important for creation of an efficient perovskite solar cell . The band gap , stability , and charge transport property  can be tuned by doping different concentrations of Nb into the TiO2 structure.
In this study, our aim is to show that application of Nb-doped TiO2 could improve the efficiency of Provskite solar cell. As experiment has shown before, Lightly Nb-doped TiO2 will result in widening band gap . In this work the effect of band gap widening, effects of operating temperature and thickness variation of Nb-doped TiO2 as a buffer layer on performance of Provskite solar cells are investigated. For this purpose, we considered a doping level of 1.5, 2.5 and 3 mol%. For base electronic properties of simulated pure and doped TiO2, experimental results and parameters are used [33, 39].
In this work, SCAPS version 3.2.01(a Solar Cell Capacitance Simulator) software which is a one dimensional solar cell simulation program is used. This software is developed at Department of Electronics and Information Systems (ELIS) of the University of Gent, Belgium . The simulated perovskite solar cell has layer configuration with transparent conductive oxide (TCO)/ blocking layer (TiO2)/ absorber/ and hole transport material (HTM) layers. The considered materials for the mentioned layers are fluorine doped SnO2 (SnO2:F), pure and doped TiO2 , CH3NH3PbI3-XCl3 and spiro-OMeTAD, respectively. For TiO2, the effect of the Niobium dopant with the concentrations of 1.5, 2.5 and 3 mol% into TiO2 is considered  and accordingly the electron affinity of the layer are varied too. The descriptions of base parameters are available in Table 1, and Table 2 which shows the base parameter set for different layers of the simulation that have been used in this study. The thicknesses of layers are chosen based on experimental works on perovskite solar cell. To consider interface recombination, the interface layers INT1 and INT2 were defined from reference . In this study, to obtain carrier diffusion lengths (Ln and Lp) of 1 μm that is similar to that of for experimental work, the value of defect parameters for all layers are considered identical and defect density for absorber is assumed equal to Nt= 2.5 × 1013 cm3.
RESULTS AND DISCUSSION
Effect of doping concentration
To simulate the effect of doping concentration into the buffer layer of perovskite solar cell, we considered the effect of Niobium dopant on the energy band gap of the TiO2 layer. The data for band gap energy that are used in simulations are chosen from experimental results . The amount of Niobium into the TiO2 layer and the energy band gap of the pure and doped layers are available in Table. 3.
Fig. 1 shows the fill factor (FF) and efficiency (η) for different doping concentrations. As it can be seen from the Fig. 1, cell efficiency and FF for doped samples are improved. The calculated cell’s efficiency for pure cell is 15.52% and for 1.5, 2.5, and 3 mol% Nb-doped cells are 15.71%, 17.39% and 18.26%, respectively. The value of FF increased from 71.43% for pure TiO2 to 84.25% for 3.0 mol% Nb- doped layer. Also, FF for 1.5 and 2.5 mol% Nb-doped are 79.09% and 83.77%, respectively. As it can be seen from table 3, adding Niobium as a defect into TiO2, caused the band gap widening for doped TiO2 layer. This can be explained by the difference in band gap energy of anatase (with Eg= 3.2 ev) and rutile (with Eg= 3.0 ev) phases. The use of Niobium into the TiO 2 structure facilitates the formation of anatase phase and prevents the formation of rutile phase [33-36]. The shift in the conduction band minimum position toward the LUMO of the absorber may enhance the electron injection from the absorber to the conduction band of TiO2. Also, another reason for improvement in cell’s performance is existence of oxygen vacancies into the structure and on the surface of TiO2 that is independent from the band gap energy. Oxygen vacancies on the surface of and inside TiO2, give p-type characteristics to the structure. Utilization of Niobium into the TiO2, because of its tendency for attracting extra oxygen, Niobium reduces the oxygen vacancies and strengthens the n-type characteristics of the layer.
Fig. 2 shows open circuit voltage (Voc) and short circuit current density (Jsc) of the cells with different Niobium doping levels. By doping Nb into the TiO2 structure, minimum conduction band level of TiO2, because of band gap widening, moves toward the LUMO level of the absorber. Closeness of minimum conduction band of TiO2 to LUMO level of the absorber facilitates electron injection from the absorber into the TiO2 layer and consequently improves the Jsc of the cell. Higher carrier concentrations at TCO layer and HTM layer Improve Voc too. However, calculations of our simulation (Fig. 2) show a rapid strange decline in Voc from pure TiO2 layer to 1.5 mol% Nb-doped sample. On the other hand, comparing pure and doped cells, a rapid and irrational rise for FF (From 71.43% for pure layer to 79.09% for doped layer) is seen too.
Effect of Buffer Thickness
In this section, the effect of the thickness of the Nb-doped TiO2 layer on the performance of the perovskite solar cell is investigated. The Thickness of this layer as a buffer layer was considered 100 nm in order to study the effect of dopant on cell’s performance. To study the effect of doped buffer’s thickness on the cell, the thickness of 1.5 mol% Nb-doped layer is changed from 50nm to 300 nm in this simulation. The results for efficiency and FF have been shown in Fig. 3. Based on the information from Fig. 3, increase in thickness of the Nb-doped TiO2 layer has a negative impact on the cells efficiency. However, the FF of the simulated cell is improved.
Fig. 4 demonstrates the results for Voc and Jsc. It has been shown in Fig. 4 that by increasing thickness of the doped buffer layer, the Jsc of the cell goes toward the lower current density values. Possible reason is that photon loss is happening when the thickness is increasing. In fact, each photon is carrying energy and when the thickness of the layer is increased, the numbers of absorbed photons by the layer are increased too. Accordingly the number of photons that have been transferred from the buffer layer to the absorber would decrease too. Therefore, reduction in the number of photons inside the absorber layer would cause the Jsc to fall down and consequently reduce the efficiency.
Spectral of solar cell with variable thickness of Nb-doped TiO2 buffer layer are shown in Fig. 5. From Fig. 5, it can be found that by enlarging the thickness, the incident photon to electron efficiency (IPCE) of the cell is being reduced (especially for short wavelengths). So, thicker buffer layer would cause for the absorption in short wavelengths and consequently the loss in absorption edge would happen.
Effect of Temperature
Temperature plays a vital role in the performance of solar cells. The variation of temperature could have intense influence on the efficiency of solar cell. In this study, up to now, all the calculations were done at 300 K. In this section, our aim is to study the effect of the temperature on the performance of the perovskite solar cell with Nb- doped TiO2 buffer layer. For this purpose, the operating temperature has been changed from 300 K to 325, 350, 375 and 400 K. Fig. 6 illustrate that how the temperature variation could affect the efficiency and fill factor of the cell. As it can be found from Fig. 6, when the operating temperature is increased from 300K to 400K, the efficiency of the cell is dramatically reduced from 18.26% to 14.07%.
Actually, temperature could affect Physical parameters such as the electron and hole mobility as well as carrier concentration and band gap of the layers. Higher temperature can also lead to the production of more electrons into the conduction band that leads to the higher short circuit current density (Jsc). On the other hand, the band gap energy at higher temperatures would reduce and this would increase the recombination rate of mobile electrons and holes between the valance band and the conduction band which finally leads to the reduction in Jsc. Also, Voc decreases at higher temperatures, whereas it increases with increasing in band gap. The results from our simulation (Fig. 7) have proven the experimental results. For the perovskite simulated cell, from 300K to 400K the Voc decreased from 0.965V to 0.79V, while the short circuit current density is not significantly changed.
The efficiency of the Nb-doped TiO2 perovskite solar cell by increasing the operating temperature from 300 K to 400K has been reduced by 22.9%.
The effect of the temperature on perovskite solar cell with pure TiO2 layer has been studied too. The results in Fig. 8 shows that the efficiency of the cell with pure buffer layer is reduce too. By an increase in temperature from 300 K to 400 K, the efficiency of the cell declined from 15.52% to 11.47%. The efficiency of the cell for 325, 350 and 375 K are 14.49%, 13.48%, and 12.48%, respectively.
For the cell with pure buffer layer, reduction in efficiency with increase in operating temperature would occur faster than that of for the solar cell with Nb-doped TiO2 buffer layer. Therefore, at higher temperatures, perovskite solar cell with Nb-doped TiO2 buffer is more stable than the cell with pure TiO2 buffer layer. The results for the impact of the temperature on the efficiency of doped and pure buffer layers are shown in Fig. 9. The reduction rate in efficiency for pure perovskite solar cell is 26.09%, while the rate for the cell with Nb-doped buffer is 22.9%.
Effect of Niobium dopant concentration into the TiO2 buffer layer and its effect on the performance of the perovskite solar cell are studied. The cell’s efficiency increased from 15.52% to 18.26% with doping level of 3.0 mol%. Also, the effect of thickness on doped TiO2 buffer layer and effect of operating temperature on the performance of the perovskite solar cell with doped and pure buffer layers are investigated too. Optimum thickness for the cell with doped buffer layer is around 50nm to 100 nm. In general the operating temperature has negative effect on cell’s performance. The efficiency of the cell with pure and doped buffer layers decreased from 15.52% to 11.47% (with 26.09% reduction) and 18.26% to 14.07% (with 22.9% declination), respectively. Therefore, the cell with doped buffer layer shows better stability at higher operating temperatures.
The authors would like to thank Professor Marc Burgelman, Department of Electronics and Information Systems, University of Gent for the development of the SCAPS Software package and allowing its use.
CONFLICT OF INTEREST
The authors declare that there is no conflict of interests regarding the publication of this manuscript.