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PLoS One. 2017; 12(8): e0182925.
Published online 2017 August 9. doi:  10.1371/journal.pone.0182925
PMCID: PMC5549970

Employment of single-diode model to elucidate the variations in photovoltaic parameters under different electrical and thermal conditions

Fahmi F. Muhammad, Data curation, Formal analysis, Methodology, Validation, Writing – original draft,1,* Mohd Y. Yahya, Conceptualization, Funding acquisition, Methodology,#2,* Shilan S. Hameed, Data curation, Formal analysis,3,4 Fakhra Aziz, Investigation,5, Khaulah Sulaiman, Investigation,6, Mariwan A. Rasheed, Conceptualization, Funding acquisition,#7 and Zubair Ahmad, Investigation, Validation8
Xiaosong Hu, Editor

Abstract

In this research work, numerical simulations are performed to correlate the photovoltaic parameters with various internal and external factors influencing the performance of solar cells. Single-diode modeling approach is utilized for this purpose and theoretical investigations are compared with the reported experimental evidences for organic and inorganic solar cells at various electrical and thermal conditions. Electrical parameters include parasitic resistances (Rs and Rp) and ideality factor (n), while thermal parameters can be defined by the cells temperature (T). A comprehensive analysis concerning broad spectral variations in the short circuit current (Isc), open circuit voltage (Voc), fill factor (FF) and efficiency (η) is presented and discussed. It was generally concluded that there exists a good agreement between the simulated results and experimental findings. Nevertheless, the controversial consequence of temperature impact on the performance of organic solar cells necessitates the development of a complementary model which is capable of well simulating the temperature impact on these devices performance.

Introduction

The most promising way to tackle the limiting supply of today’s main energy sources and their detrimental impact on the environment is to harness solar energy. It is imperative to evolve complement strategies into the process of solar energy conversion and its storage management. Supercapacitors or ultracapacitors [1, 2] are considered to be feasible reservoirs for the storage of solar electricity power and advanced power-source integration [3, 4]. Additionally, the utilization of solar energy has become instrumental in the state-of-art technologies, targeting the reduction of carbon dioxide emissions and cost-effectiveness. For instance, Hu et al. [5] explored the role of renewable energy and powertrain optimization in minimizing daily carbon emissions of plug-in hybrid electric vehicles (PHEVs). Very recently, the integration of photovoltaic arrays with battery energy storage of PHEV for smart home energy management was also elaborated [6]. In these contexts, the exploitation of photovoltaic (PV) technology to convert sunlight energy into electricity through solar panels is increasingly demanded by the public, industries and space program sectors [79]. This is mainly due to easy installation and low maintenance cost of solar panels compared with those of other electricity sources [10]. Solar panels are made from solar cells connected in series and parallel schemes in order to provide the desired current and voltage. It is known that the performance of solar cells can be affected by the change in temperature, sunlight intensity and aging [11, 12]. Therefore, it is crucial to have a model capable of simulating the real behaviour of solar panels, through which a comprehensive investigation on the devices parameters can be realized. Researchers have widely examined the single-diode and double-diode model to simulate solar cells characteristics and to determine the devices parameters [13, 14]. Comparatively, the single-diode model, which is also known as five parameters model, demonstrates reasonable accuracy and simplicity in the parameters estimation of various solar cell technologies [15]. This model comprises of an ideal diode connected in parallel with a constant current source and a shunt resistance bypassed to the external load through a series resistance. The implication of single-diode model allows us to perform sensitivity analysis on the solar cell parameters, thereby taking valuable strategies towards the improvement of modelling capabilities [16]. Simulations can be interestingly used to analyse solar cells and to predict various internal and external effects due to device changes or ambient conditions. Hence, they may promote device optimization and provide potential information regarding viable improvements.

Solar cell parameters including series resistance (Rs), parallel resistance (Rp) and ideality factor (n) can be readily extracted from the single-diode model [17]. These parameters describe the internal properties of the devices raising during the process of fabrication. In practical considerations, low Rs and high Rp values are favoured to achieve enhanced solar cell performance. One of the main challenges in front of researchers and users of solar panels is the difficulty of estimating the operational performance of these devices at modified internal and/or external parameters due to the impact of fabrication process, aging and ambient temperature. Therefore, it is of great importance to investigate and analyse the correlation between photovoltaic parameters, which are key performance measure of solar panels, and aforementioned internal/external parameters (electrical and thermal). Furthermore, results of such investigations can be highly beneficial for enhanced prediction strategy and model’s building in the optimization of energy management and power smoothing of solar PV systems [18, 19], while optimized PV plant is complicated by oscillating PV output due to uncertain environmental conditions, internal resistance variations and aging. The concepts might be further applicable when maximum power point tracking (MPPT) techniques are considered for delivering optimum power to the loads [20]. To the best of our knowledge, little attention has been paid to perform a systematic investigation on the variation of photovoltaic parameters due to the impact of broad modifications in the coefficients of solar cells having various efficiencies. Hence, the current work is intended to report on the employment of single-diode model to elucidate the variations in photovoltaic parameters under the influence of internal and external factors such as parasitic resistances, ideality factor and temperature. The main contribution of this work is to reveal and understand the important correlations between solar cell parameters and their photovoltaic performance along with temperature impact on the devices having various efficiencies, by which effective improvement approaches can be made upon the production of these devices.

Materials and methods

A prototype structure of solar cells is shown in Fig 1(A), in which the active layer is made of a p-n bulk heterojunction responsible for absorbing sunlight energy and producing free electrons and holes. The bottom electrode is responsible to collect free holes, while the top electrode receives free electrons. Fig 1(B) represents the single-diode model which is capable of well modelling the current-voltage (I-V) characteristics of solar cells, while Fig 1(C) shows the circuit simulator layout designed by using Multisim Power Pro. 10 electronic workbench software. The light activated current source (Ilight) depicts the amount of current generated in the cell when it is exposed to sunlight energy. The application of a load across the right side of the circuit gives rise to a voltage induction, which ultimately acts upon reducing the total amount of current passing through it in a reverse biased direction. Hence, the instantaneous average current in the load defines the characteristic current of the solar cell. From the electrical circuit, one can easily estimate the net current as follows:

I=Is[exp(VIRsnKBT/q)1]+VIRsRpIlight
(1)
Fig 1
A prototype architecture of solar cells (a), the equivalent circuit used to model the I-V characteristics of the devices (b), and workbench view of the simulated equivalent circuit by using Multisim Power Pro.10.

Where, Is is the saturation current of the diode under dark, KB is the Boltzmann’s constant, T is the temperature in Kelvin, q is electron unit charge, Rs and Rp are the series and parallel resistances of the device, respectively. The value of n in the equation defines the ideality factor, which is a measure of how closely the device follows the ideal p-n junction behaviour.

The methodology of the current work was implemented in two-fold; first, the equivalent circuit was sketched and simulated via the electronic workbench programming of Multisim Power Pro.10. In this simulation approach, the values of Rs and Rp were systematically altered, while the I-V characteristics was simultaneously recorded and stored by the grapher view to be exported into the MS excel file. Second, theoretical equations were compiled into the well-known Origin Pro 8 software in order to elucidate the implication of ideality factor (n) and cell temperature (T).

The saturation current was expressed using the equation reported by Messenger and Ventre [21]:

Is=Is,ref[TcTc,ref]3exp[1k(EgTrefEgTc)]
(2)

Where, Eg is the apparent energy gap of the cell’s active layer, Tc and Tref are the cell temperature and reference temperature, respectively. The Varshni equation [22] was also utilized to simulate the change of energy gap with temperature as follows:

Eg(T)=Eg(Tref)AT2T+B
(3)

Where, A and B are fitting parameters and are dependent on the active layer properties. Moreover, the impact of temperature on the light induced current at standard illumination (100 mW/cm2) was revealed through the following equation [13]:

IlightIlight(Tref) + μ(T − Tref)
(4)

Where, μ is the coefficient of temperature dependent light induced current.

Results and discussion

Variations in current-voltage (I-V) curve

Fig 2 shows the shape variation in the I-V characteristic of a simulated solar cell with efficiency of 10% at different series resistances (Rs). The value of Rs represents the sum of internal resistance, which includes the resistance of active layer and Ohmic contact of the device. It was seen that by increasing Rs, no obvious change was happened in the open circuit voltage (Voc). However, the increment in Rs has made a pronounced decrease in the short circuit current (Isc). This was observed to be in agreement with the results reported for inorganic and organic solar cells [23, 24]. The consequence of Isc variation with the change of Rs for various efficient solar cells is explored later. In practical considerations, the value of Rs for solar panels is usually deteriorated due to the impact of wire connections and aging, leading to unstable photovoltaic performance. Therefore, it is required to keep Rs within a minimal value during the device fabrication and installation in order to enhance the photo-generated current and to achieve the best possible performance. One might think of decreasing the thickness of devices active layer during fabrication, thereby reducing the value of Rs [25]. However, thickness reduction is not always a useful choice, especially for organic solar cells, in which a non-complementary photo-absorption is yielded when the thickness of the devices is kept below 200 nm [26, 27]. Other experimental approaches to reduce Rs can be achieved through a well interplayed donor-acceptor interfaces [28, 29] or by minimizing the contact resistance between the electrodes and active layer [30].

Fig 2
The impact of series resistance on the I-V characteristic curve of a simulated solar cell with efficiency of 10%.

Another internal electrical parameter affecting the performance of solar panels is the shunt or parallel resistance (Rp) of the devices, which takes into account the leakage of current at the donor-acceptor and active layer-electrode boundaries. The value of Rp is usually related to the charge recombination process (either to be geminate or non-geminate), of which the higher recombination rate, in forward bias connection, corresponds to the larger Rp value [31, 32]. In other words, the low carriers’ recombination rate under light illumination, i.e. without biasing, indicates the presence of a large Rp value for the device. Fig 3 shows the effect of Rp alteration on the I-V characteristic of a simulated device with 10% efficiency. A close inspection into the figure showed that the increase in Rp has made clear increment in both of Voc and Isc, while the increment rate of the Voc was seen to be higher in comparison with that of the Isc. It was practically evidenced that the insertion of PEDOT:PSS layer between the ITO and donor interface in organic solar cells (OSCs) has led to maximizing the value of Voc [25, 33]. Two theories are accentuated to define the origin of Voc, which are formulated from the difference of valence and conduction band levels between the donor and accepter materials as well as the difference of work functions between the top and bottom electrodes, respectively [34, 35]. Nevertheless, one cannot completely rely on these theories in order to elaborate the origin of Voc as the change in PEDOT:PSS thickness was seen to alter the value of Voc [36]. If the two aforementioned theories are fully applicable in OSCs then the impact of PEDOT:PSS thickness on Voc should not have been pronounced. This is because the level of energy band is not depended on the thickness. Besides, it was found that the difference in work function of the electrodes did not significantly change the value of Voc [37]. Therefore, the variation in Rp due to charge transfer, emission process and their recombination behaviour [38] might be more impressive to be correlated with the Voc response.

Fig 3
The impact of parallel resistance on the I-V characteristic curve of a simulated solar cell having efficiency of 10%.

Fig 4 shows the variation of I-V characteristic due to the change of temperature for a simulated solar cell with efficiency of 10%. The results showed a decrease in Voc and increase in Isc upon the rise of solar cells temperature, which is in compliance with the previous theoretical findings [39]. Experimentally, temperature effect produced similar variation trend in the Voc and Isc for almost all the types of inorganic solar cells [4042]. However, this was seen to be different for organic solar cells and the experimental results were in contradiction to that of the simulated ones. For instance, in the small molecular based OSCs [43] and ternary based ones [44], a decrease in the Isc was observed beyond 80 oC, while in the ternary devices, the value of Voc stayed relatively unchanged. However, the photovoltaic response in low temperature range, from 25 oC to about 80 oC, was found to be consistent with the simulated results [43, 45]. To conclude, this deviation between simulation and experimental results for organic solar cells requesting the development of a comprehensive model to simulate the temperature impact on these devices.

Fig 4
The impact of annealing temperature on the I-V characteristics of a simulated solar cell with efficiency of 10%.

Fig 5 shows the variation of I-V characteristic due to the change of ideality factor (n) for a simulated solar cell with efficiency of 10%. The value of n is a measure of how closely the device follows ideal p-n junction behaviour, by which valuable information regarding the charge transport and recombination process can be obtained. If the value of n = 1, only diffusion currents are flowing in the p-n junction, which corresponds to the band to band recombination process. However, if n = 2, the device currents are dominated by charge generation and recombination process, which require states near the middle of interface gap [46, 47]. In the region of large reverse bias, the recombination probability is ideally zero because of the existence of highly sufficient internal electric field to remove barriers against recombination, thereby guarantying a safe reach of free charge carriers to the electrodes. Therefore, it was seen that the Isc remained relatively unchanged by the increment of ideality factor. However, when the device is forward biased, the major recombination rate is increased, so the photo-generated current is up shifted exponentially. Wetzelaer et al. [48] reported that the ideality factor of trap-free solar cells (n = 1) is merely governed by bimolecular recombination rather than a trap-assisted recombination. Our numerical results showed that Voc was significantly affected by the change in ideality factor, in which the value of Voc was decreased with the reduction of ideality factor. Hence, we might speculate that the ideality factor is directly correlated with Rp. This is because the increment in Rp has also contributed in rising Voc (see Fig 3) and that Rp is inversely proportional to the charge recombination rate [46, 49]. Noteworthy, the simulated result estimated that recombination current at forward bias is higher for the devices with large ideality factor in comparison with those of the low ideality factor.

Fig 5
The impact of ideality factor on the I-V characteristics of a simulated solar cell with efficiency of 10%.

Variations in short circuit current (Isc)

Figs Figs668 show the effect of Rs, Rp and T alteration on the Isc of solar cells (CS)s with different efficiencies, respectively. The manipulation of various efficiencies for the devices in the simulation results was achieved by considering different energy gaps for the active layer materials, namely Eg = 1.2, 1.4 and 1.6 eV. The lower energy gap is resulted in higher photo-generated current, representing solar cells with higher efficiencies in comparison with those of higher energy gap at standard condition. From Fig 6, a linear inverse correlation of Rs with Isc was seen for various efficient devices in the low resistance range (region 1), while in the high range of Rs (region 2), this correlation showed an exponential decay. The linear region can be elucidated by the presence of a smooth transport of delocalized charge carriers as a result of low bulk resistance, which is activated by the influence of internal electric field. However, the increased bulk resistance promotes accumulated charge carriers between the electrode-active layer interfaces, whereby its role acting upon inducing a non-liner charge injection. Consequently, the highly efficient devices demonstrated a faster deviation from such linearity. It is worth to mention that the negative impact of Rs on the Isc is stronger in devices with high efficiency in comparison with that of the low efficiency ones. This can be ascribed to the effect of charge transport, which is governed by the space charge limited current (SCLC) [50]. The decrease of Isc with the increment in Rs can be understood as the internal resistance hindering the drift transport of free charge carriers towards the electrodes under the influence of internal electric field [47]. However, it is known that the increase in active layer thickness of inorganic solar cells is led to increase in Rs, the application of a thin layer of bathocuproine between Al electrode and active layer in OSCs has improved Isc [51]. Hence, it is evidenced that the increase in active layer thickness of OSCs does not always bring a negative impact on Isc. This is happened because of the enhanced donor-acceptor interface between the moieties constituents, which in turn facilitates efficient transport of free charge carriers. In contrast to the negative impact of Rs on the Isc, the effect of Rp was seen to be positive and showed a reverse trend (see Fig 7). Interestingly, the achievement of a relatively low practical Rp of about 200 Ω is enough to obtain a stable photo-current generation and deliver optimum Isc, provided that the series resistance of the cell is kept below 2 Ω. The value of Rs and Rp are regarded to be internal factors influencing the performance of solar cells, while temperature variations of the cell is considered as an external influence due to ambient temperature change or thermal annealing process. Fig 8 depicts the effect of cell temperature (T) on the Isc, in which a pronounced increase in the Isc was noticed versus temperature. This was occurred because of the enhanced thermal excitation of charge carriers, thereby reducing the active layer’s energy gap and hence promoting charge carriers transport. Noteworthy, the increment rate of Isc with temperature was theoretically found to be constant for solar cells with different efficiencies (see Fig 8), implying that the temperature impact on Isc is an energy gap independent phenomenon. However, the estimation of linearly increased Isc with T can only be applicable for inorganic solar cells, while for OSCs this was deviated from experimental evidences, as it was discussed previously in Fig 4.

Fig 6
The impact of series resistance (Rs) on the short circuit current (Isc) of solar cells with various efficiencies.
Fig 7
The impact of parallel resistance (Rp) on the short circuit current (Isc) of solar cells with various efficiencies.
Fig 8
The impact of cell temperature (T) on the short circuit current (Isc) of solar cells with various efficiencies.

Variations in open circuit voltage (Voc)

Figs Figs9911 show the effect of Rp, T, and n parameters on the Voc of solar cells with different efficiencies, respectively. One can notice that Voc is enlarged with the increase of Rp to appoint where a plateau region is observed beyond Rp = 200 Ω. The rise of Voc with Rp represents an increased potential barrier of the diode, at which the charge recombination process requires higher forward voltage to set off the photo-generated current under illumination in comparison with that of the low Rp devices. As Rp is related to the charge recombination process [31, 32], the complete saturation of Voc above Rp = 800 Ω indicating that Voc is limited by the recombination rate (the number of recombined charge carriers per time). Noticeably, similar recombination rate is speculated for devices with various efficiencies as long as they attain high enough parallel resistance of about Rp = 800 Ω. In support to the simulated results, experimental evidences showed that interplaying donor-acceptor ratio did not produce any obvious change in the Voc despite that the variation in Rp was appeared at values greater than 14.5 kΩ (290 Ω.cm2) [52]. As such, the impact of Rp on the Voc can be ruled out at Rp equals or greater than a threshold value of 800 Ω. Hence, during the fabrication process of solar cells special attention need to be paid in order to locate the parallel resistance beyond the threshold value. Furthermore, it was seen that the increased ratio of Rp/Rs did not change the Voc trend, but has made Isc to become constant faster. Based on the equation of single-diode model, Voc can be determined when the forward biased current is set to zero (I = 0). Hence, the expression for open circuit voltage is obtained from the explicit equation:

Is×exp(qVocnKBT)+VocRp=Ilight(open)+Is
(5)
Fig 9
The impact of parallel resistance (Rp) on the open circuit voltage (Voc) of solar cells with various efficiencies.
Fig 11
The impact of ideality factor (n) on the open circuit voltage (Voc) of solar cells with various efficiencies.

Where, Ilight(open) is the photo-generated current at open circuit condition. By having a high value of Rp in Eq 5, the second term on the left side of the equation can be neglected and Voc is no more dependable on Rp,

Voc=nKBTq×ln[Ilight(open)Is+1]
(6)

Eq 6 demonstrates that the higher Voc is related to the more efficient solar cell, as can be seen in Fig 9. On the other hand, a logarithmic decay in Voc with temperature (T) was seen (see Fig 10), which is inconsistent with Eq 6 in the sense that T is linearly proportional with Voc. This discrepancy can be concealed that Is is enlarged with the increase of T, thereby decreasing the value of Voc. Noteworthy, the results of Fig 10 show that the impact of temperature on Voc is less pronounced in the devices with high efficiency. Another parameter affecting Voc is ideality factor (n), as shown in Fig 11. Our numerical results showed that Voc is significantly affected by the change of ideality factor, in which the value of Voc is increased with the increase of ideality factor.

Fig 10
The impact of cell temperature (T) on the open circuit voltage (Voc) of solar cells with various efficiencies.

Variations in fill factor (FF)

The fill factor (FF) of a solar cell is defined by the ratio of maximum power (Pmax = Imax × Vmax), which is capable to be delivered to a load to that theoretically produced by the cell (Isc × Voc),

FF=Imax×VmaxIsc×Voc
(7)

It plays important role in controlling the efficiency of the cell and represents how easily the photo-generated carriers are extracted out of the cell. The shape of I-V curve can be a straightforward indication on how close to ideal the devices are fabricated, as the better the device performance the closer the I-V shape to a rectangle. Because FF is intricately influenced by many factors, it is the least understood parameter in solar cells. It has been claimed that the FF related shape of I-V curve is depended on the interface quality between the active layer and negative electrode. The S-kink shape in the fourth quadrant of I-V curve is almost due to a poor contact formation during the deposition of cathode electrode, which ultimately leads to unbalanced mobility of electron and hole and low minor surface recombination [46]. Therefore, a slow rate deposition of cathode electrode is practically requested to overcome these shortcomings. Recalling Fig 2, one can see that the I-V shape is convex, indicating the existence of small Ohmic contact between the cathode electrode and active layer. Consequently, the concave shape of I-V curve is expected to appear when there is a high barrier between the cathode electrode and active layer, by which charge accumulation occurs and inefficient exciton dissociation is obtained. The non-linear decrease of FF with the increase of Rs can be expressed by the following empirical equation [33]:

FF=FFref(1RsIscVoc)
(8)

Where, FFref is the reference fill factor of the solar cell at a defined Rs. Fig 12 shows the reduction of FF against the increment of Rs for solar cells with various efficiencies. There have been two points correspond to the Rs of 6 Ω and 80 Ω, respectively, at which the FFs of the devices are equal. This FF similarity indicated the presence of a shape consistency in the I-V curve regardless of the efficiency of the devices. Comparably, Eq 8 illustrates that the decrease rate in FF for highly efficient solar cells should be greater than that of the low efficient one (see Fig 12), which is again in agreement with the fact that the impact of Rs on Isc is more pronounced in solar cells with high efficiencies, as was shown in Fig 6. In contrast to that of the Rs effect, the increase in Rp was found to produce a non-linear increase in the FF, as shown in Fig 13. By considering the results of Figs Figs77 and and8,8, in which the values of Isc and Voc were increased with the rise of Rp, and upon the utilization of Eq 7, one can speculate that the FF should have been decreased with the increase of Rp as a result of increasing Voc. But this was seen not to be happened, elucidating that the increase of Rp has made changes in the I-V shape (see Fig 3) so that the value of maximum power point (Pmax) is become high. Consequently, the rapid rise in FF versus Rp is attributed to the weakened recombination rate of majority charge carriers, while that the internal electric field inducing the exciton dissociation is getting saturated with further increase of Rp.

Fig 12
The impact of series resistance (Rs) on the fill factor (FF) of solar cells with various efficiencies.
Fig 13
The impact of parallel resistance (Rp) on the fill factor (FF) of solar cells with various efficiencies.

Fig 14 shows the effect of cell temperature (T) on the fill factor of solar cells with various efficiencies. Overall, the increase in T depicted a decrease in FF, with its effect being more pronounced in the low efficiency devices compared with that of the high efficiency ones. Because of the complexity of FF dependence on the internal and external parameters affecting solar cells, there is not a generalized equation up to date by which the impact of T on the FF is being revealed. However, in its simple form, one can elucidate that the decreased FF against T is due to the change in the convexity shape of the I-V curve, in which the increment rate of Isc is more than the decrement rate of Voc so that Eq 8 can be safely held. Comparably, experimental results showed a non-monotonic change in the FF with the change of T [43, 53], indicating that the effect of T on the FF is complex, leading to a simultaneous tuning of the internal parameters such as Rs, Rp and n. Therefore, the solar cells whose temperature effect has resulted in the decrease of their Rs demonstrated enlarged FF upon thermal annealing. As shown in Fig 15, the increase in ideality factor produced a linear decrease in FF, with its stronger effect on the low efficiency devices. Since FF is a geometrical related parameter of I-V curve in the forward bias, we can conclude that the prevalence of the free charges recombination over their extraction is the major cause behind such decrement in the FF.

Fig 14
The impact of cell temperature (T) on the fill factor (FF) of solar cells with various efficiencies.
Fig 15
The impact of ideality factor (n) on the fill factor (FF) of solar cells with various efficiencies.

Variations in efficiency (η)

The power conversion efficiency (η) of solar cells is defined by the ratio of maximum electrical power (Pmax) to the optical power (Pin) of incident photons:

ɳ=PmaxPin=FF×IscVocPin
(9)

Figs Figs161619 show the theoretical impact of Rs, Rp, T and n on the efficiency of solar cells with different energy gaps of their active layers, respectively. The Rs and Rp parameters are generally correlated with the physical properties of the active layer and the architectural formation of the device. The increase in Rs was led to exponential decrease in efficiency, as shown in Fig 18, with its stronger detrimental impact on the devices with lower energy gap (higher efficiency). However, Rp increment has caused a positive exponential increase in the efficiency of the cells (see Fig 17). Therefore, in practical point of view, researchers should be curious about tuning the structure and morphology of the devices active layers in order to reduce the value of Rs and maximizing Rp. Fig 18 shows a general trend of decreasing efficiency of solar cell devices against temperature. This was found to be in agreement with the experimental investigations [41, 54]. The decrease in efficiency with temperature is attributed to increased internal carrier recombination rates, resulted from increased carrier concentrations. It can be seen from the simulated results that a low temperature profile of about 50 oC might have a positive impact on the efficiency enhancement of low performance devices. This was also found to be experimentally true for the OSCs operated at relatively low elevated ambient temperature of about 55 oC [55]. Therefore, it can be concluded that moderate temperature rise in the devices with high energy gap of their active layers can help improving the efficiency, while high temperatures are acted upon deteriorating the efficiency and decreasing the devices performance [56, 57]. Fig 19 shows that the increase in ideality factor of the active layers has caused a linear increase in the devices efficiency. Despite an obvious decrease in the FF with the increase of the ideality factor (see Fig 15), the efficiency of the solar cells was yet enhanced. This can be concealed that the increase in ideality factor has caused a reasonable increase in Voc, thereby improving the power conversion efficiency of the devices based on Eq 9. It is worth mentioning that when a real photovoltaic module is simulated, the ideality factor of the series connected cells should be summed up [13]. Therefore, in such a case the increment in the ideality factor is counted for the increased number of string cells, which by then the efficiency of the solar module is expected to be remained constant [58]. In our discussion, the ideality factor variation, shown in Fig 19, is considered to be due to other factors such as fabrication process, aging and temperature change for a single compact solar cell or solar module. Noteworthy, the exponential correlations of PV panel efficiency with enlarged internal resistance and temperature elevation, shown in Figs Figs1616 and and18,18, can be interestingly included into the existed models [18, 19] when an improved optimization of energy management and power smoothing of solar PV systems are targeted. This is because the optimized PV plant is complicated by oscillating PV output due to uncertain environmental conditions, internal resistance variations and aging.

Fig 16
The impact of series resistance (Rs) on the efficiency (η) of solar cells with various energy gaps of their active layer.
Fig 17
The impact of parallel resistance (Rp) on the efficiency (η) of solar cells with various energy gaps of their active layer.
Fig 18
The impact of cell temperature (T) on the efficiency (η) of solar cells with various energy gaps of their active layer.
Fig 19
The impact of ideality factor (n) on the efficiency (η) of solar cells with various energy gaps of their active layer.

Conclusions

The single-diode modelling approach was employed to correlate the parasitic resistances, temperature and ideality factor with the photovoltaic parameters of solar cells. The impact of series resistance (Rs) was seen to be detrimental on the performance of the devices, especially on the devices with small energy gap of their active layers. On the contrary, an increased parallel resistance (Rp) is practically requested because of its positive impact on rising Voc and Isc of the devices. The achievement of Rp = 800 Ω was found to be enough to produce a stable Isc and Voc (S1 Table). Noteworthy, the increment rate of Isc with temperature was theoretically found to be constant for solar cell devices with different efficiencies, implying that the temperature impact on Isc is an energy gap independent process. Our numerical results showed that Voc is decreased with the reduction of ideality factor and increased temperature, while Isc remained relatively unchanged by the increase of ideality factor. The rapid rise in FF versus Rp was attributed to the weakened recombination rate, while the internal electric field inducing the exciton dissociation is become saturated with further increase of Rp. Because of the complexity of FF dependence on the internal and external parameters affecting solar cells, there is no a generalized equation up to date, by which the impact of T on the FF is being revealed. Comparably, the experimental evidences showed a non-monotonic decrease in the FF upon thermal annealing, indicating that the effect of T on the FF was indirect and was made through the tuning of the internal features such as Rs, Rp and ideality factor. There was a general simulation trend of decreasing efficiency of solar cells versus temperature (S1 Table). It was concluded that moderate temperature rise in the devices with high energy gap of their active layers can help improving the efficiency, while high temperatures are acted upon deteriorating the efficiency and decreasing the devices performance

Supporting information

S1 Table

Data analysis and calculation of the main findings.

(XLSX)

Acknowledgments

Authors acknowledge the financial support in part by Research University Grant (RUG), UTM Malaysia (Vot: Q.J130000.21A2.03E00), and in part by the University of Human Development.

Funding Statement

This work was financially supported in part by Research University Grant (RUG), UTM Malaysia (Vot:Q.J130000.21A2.03E00), and in part by the University of Human Development. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Data Availability

Data Availability

All relevant data are within the paper and its Supporting Information files.

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