2. Electrical Modeling and Simulation of a Solar Cell
2.1. Modeling
The operation of a photovoltaic (PV) solar cell can be represented using an equivalent electrical circuit
[2] | Nandhini Kullampalayam Murugaiyan, Kumar Chandrasekaran, Premkumar Manoharan, & Bizuwork Derebew. Leveraging opposition-based learning for solar photovoltaic model parameter estimation with exponential distribution optimization algorithm. Scientific Reports, 14, Article number: 528(2024). https://www.nature.com/articles/s41598-023-50890-y |
[3] | B. S. S. Ganesh Pardhu, & Venkata Reddy Kota. A novel HRMO-AOA approach for a grid integrated wind-solar PV system with a 5-level NPC inverter. Results in Engineering, 23(2024), 102582. https://doi.org/10.1016/j.rineng.2024.102582 |
[2, 3]
(see
Figure 1). In this model, the cell is considered as a current generator. The current source
represents the photogenerated current under light irradiation. Two diodes,
and
, respectively model the generation-recombination phenomena in the space-charge region and the diffusion current of carriers in the neutral regions.
The equivalent circuit also includes:
1) A series resistance , which accounts for internal ohmic losses within the cell (notably at the metallic contacts, the emitter, and the substrate);
2) A parallel resistance
(or shunt resistance), which models leakage currents due to crystalline defects, impurities, or edge effects within the cell, particularly in the bulk or near the junction
[1] | Jan Haschke et al. (2018). Silicon heterojunction solar cells: Recent technological development and practical aspects – from lab to industry. Solar Energy Materials and Solar Cells, 187, 140–153. https://doi.org/10.1016/j.solmat.2018.07.034 |
[2] | Nandhini Kullampalayam Murugaiyan, Kumar Chandrasekaran, Premkumar Manoharan, & Bizuwork Derebew. Leveraging opposition-based learning for solar photovoltaic model parameter estimation with exponential distribution optimization algorithm. Scientific Reports, 14, Article number: 528(2024). https://www.nature.com/articles/s41598-023-50890-y |
[1, 2]
.
By applying Kirchhoff’s laws to the equivalent circuit shown in
Figure 1, the current I delivered by the cell can be expressed as the algebraic sum of the different currents flowing through the circuit:
Where:
I: Output current.
: Photocurrent.
: Generation/recombination current in the space charge region (SCR).
Diffusion current in the quasi-neutral regions.
Resistive loss current.
The diode current is expressed as:
The shunt current is expressed as:
The total current becomes:
(4)
Where:
Saturation current density of diode related to carrier diffusion in the quasi-neutral regions of the base and emitter.
Saturation current density of diode related to the generation/recombination current in the space charge region.
Series and shunt resistances, respectively.
Ideality factors of diodes and , respectively.
Boltzmann constant
Elementary charge
T: Temperature (K)
V: Voltage across the cell (V)
2.2. Electrical Performance Parameters of a Photovoltaic Cell
When a photovoltaic (PV) cell, module, or array is exposed to illumination, a characteristic relationship between the generated current and the applied voltage appears: the I-V curve. This curve serves as the "identity card" of the PV device and is used to determine its key electrical performance parameters, commonly referred to as photovoltaic parameters
[2] | Nandhini Kullampalayam Murugaiyan, Kumar Chandrasekaran, Premkumar Manoharan, & Bizuwork Derebew. Leveraging opposition-based learning for solar photovoltaic model parameter estimation with exponential distribution optimization algorithm. Scientific Reports, 14, Article number: 528(2024). https://www.nature.com/articles/s41598-023-50890-y |
[3] | B. S. S. Ganesh Pardhu, & Venkata Reddy Kota. A novel HRMO-AOA approach for a grid integrated wind-solar PV system with a 5-level NPC inverter. Results in Engineering, 23(2024), 102582. https://doi.org/10.1016/j.rineng.2024.102582 |
[4] | Mohamed Saleck Heyine. Performance analysis of a 50 MWp grid-connected photovoltaic solar power plant of SOMELEC. Doctoral Thesis, University of Nouakchott (2023). |
[2-4]
, including the fill factor (FF), open-circuit voltage
, short-circuit current density
, and efficiency
.
i) Short-Circuit Current
The short-circuit current corresponds to the current generated when the voltage across the cell is zero. It depends on several factors, including temperature, the wavelength of the incident radiation, the active surface area of the cell, and the carrier mobility. The short-circuit current is proportional to the light intensity received and represents the maximum current the cell can produce.
ii) Open-Circuit Voltage
The open-circuit voltage is the voltage measured when the current is zero (I = 0), meaning the cell is connected to an infinite resistance load. This voltage depends on several factors: the cell type, the materials composing the active layer, the nature of the interfaces between this layer and the electrodes, and the light intensity received.
Where:
: Thermal voltage
T: Absolute temperature
q: Elementary charge
k: Boltzmann constant.j/k
Photocurrent
Saturation current
iii) Power P
Under constant ambient operating conditions (illumination, temperature, etc.), the electrical power P (in watts) delivered by a photovoltaic cell is given by the product of the direct current III and the direct voltage V across its terminals:
Where:
P(W): Power measured at the PV cell terminals
U(V): Voltage across the PV cell terminals
I(A): Current measured at the PV cell terminals
iv) Fill Factor (FF)
The fill factor is a dimensionless parameter used to assess the quality of a photovoltaic module. It reflects the cell's performance through the shape of its I-V characteristic. The fill factor is the ratio between the maximum power delivered by the cell and the theoretical maximum power defined by the product of the open-circuit voltage and the short-circuit current .
Where:
Maximum power delivered by the PV cell
, : Voltage and current at the maximum power point
The fill factor depends on the cell design, the PN junction quality, the material properties, and the resistivity of the metallic contacts.
v) Conversion Efficiency
The efficiency of a photovoltaic cell is defined as the ratio between the maximum power Pmax delivered by the cell and the incident light power Pinc per unit area. This efficiency can be improved by optimizing the fill factor (FF), the short-circuit current , and the open-circuit voltage .
(10)
Where:
: Incident light power
S: Cell surface area
The fill factor alone already provides valuable insight into the overall cell performance, as it reflects the cell's ability to efficiently convert light energy into electrical energy.
4. Results and Discussion
The electrical performance of a heterojunction photovoltaic (PV) solar cell strongly depends on the thickness of the different layers that compose it.
In this section, we analyze the influence of the emitter layer thickness on the cell’s performance using the TCAD-SILVACO Atlas simulator. The two key parameters of the p+-doped hydrogenated amorphous silicon emitter layer (p+-a-Si:H), namely its thickness and its dopant concentration, are studied as the main variables.
Initially, the emitter layer thickness was varied from 2 nm to 20 nm for different base thickness values, while keeping the dopant concentration and the other physical parameters of the device constant. The study focused on the evolution of the following key parameters: the open-circuit voltage , the fill factor (FF), the short-circuit current density , and the overall conversion efficiency.
4.1. PV Parameters as a Function of FSF Thickness
The heavily doped front surface field (FSF) layer [(p
+)-a-Si:H] plays a major role in the performance of heterojunction solar cells
[5] | Djicknoum Diouf. Silicon heterojunction photovoltaic cells with interdigitated back contact structure. Doctoral Thesis, Université Paris Sud 11(2010). |
[5]
.
With the aim of optimizing this layer, we conducted a study on the variation of its thickness in this section. We simulated several heterojunction solar cells (with different crystalline silicon (c-Si) base thicknesses) for various emitter thicknesses ranging from 2 to 20 nm.
i) Cell Efficiency (η) as a Function of FSF Thickness
As shown in
Figure 3, increasing the thickness of the front emitter layer (FSF) from 2 nm to 5 nm significantly improves the efficiency, reaching a maximum of 23.5% at 5 nm. This improvement is attributed to better light absorption, particularly at longer wavelengths, which is characteristic of hydrogenated amorphous silicon (p
+-a-Si:H).
However, beyond this optimal thickness, further increases lead to two detrimental effects: a growing opacity of the layer, which limits light penetration into the deeper layers, and an increase in minority carrier recombination, which reduces the extractable current. This phenomenon is explained by the reduction in diffusion length L, which is directly related to carrier lifetime and diffusion coefficient D according to the following relation:
This equation highlights the importance of minimizing recombination mechanisms in the emitter layer to maintain high efficiency, especially when its thickness increases.
Thus, excessive thickness not only reduces the collection current but also results in significant optical losses due to internal absorption
[6] | M. N. Kateb, S. Tobbeche, & A. Merazga. Influence of μc-Si:H tunnel recombination junction on the performance of a-Si:H/μc-Si:H tandem solar cell. Optik, 139(2017), 152-165. https://doi.org/10.1016/j.ijleo.2017.04.061 |
[7] | Venkanna Kanneboina, Ramakrishna Madaka, & Pratima Agarwal. High open circuit voltage c-Si/a-Si:H heterojunction solar cells: Influence of hydrogen plasma treatment studied by spectroscopic ellipsometry. Solar Energy, 166(2018), 255-266. https://doi.org/10.1016/j.solener.2018.03.068 |
[8] | Chedia Aliani, Monem Krichen, & Abdelaziz Zouari. Effect of the front metal work function on the performance of Si:H(n+)/a-Si:H(i)/c-Si(p) heterojunction solar cells. Journal of Computational Electronics, 18(2019), 576–583. https://doi.org/10.1007/s10825-019-01324-4 |
[6-8]
. Optimizing the emitter layer thickness is therefore essential to balance efficient light absorption and minimal recombination losses, ensuring maximum cell efficiency. The results of this study are presented in
Figure 3.
Figure 3. Impact of varying FSF layer thickness on cell efficiency.
ii) Short-Circuit Current Density () as a Function of FSF Thickness
Figure 4 shows the evolution of the short-circuit current density
as a function of the emitter layer thickness (p
+-a-Si:H) in a heterojunction photovoltaic cell. For thicknesses between 2 nm and 5 nm, the current density increases rapidly. This improvement is attributed to enhanced material quality of the hydrogenated amorphous silicon layer, which becomes more homogeneous and less prone to electronic defects as its thickness increases. This better quality promotes the efficient generation and collection of photogenerated carriers.
Within this thickness range, the series resistance progressively decreases due to the reduction of contact barriers and the improved conductivity of the emitter layer. At the same time, the parallel resistance increases, indicating a reduction in leakage currents associated with parasitic recombination. These combined effects contribute to more efficient current extraction.
Beyond 5 nm, the current density continues to increase more slowly until it reaches a plateau. This trend is explained by the increasing optical opacity of the emitter layer, which absorbs a growing fraction of the incident light without significantly contributing to useful carrier generation. Moreover, greater thickness increases the transit time of minority carriers, raising the probability of recombination before reaching the ohmic contacts.
The optimal thickness, identified around 5 nm, therefore represents a compromise between the optical absorption capacity of the layer, its electronic quality, and the management of series and parallel resistances. Excessive thickness beyond this threshold induces optical and electronic losses that gradually degrade cell performance. The results of this study are presented in
Figure 4.
Figure 4. Impact of varying FSF layer thickness on cell current density.
iii) Open-Circuit Voltage () as a Function of FSF Thickness
Figure 5 shows a progressive decrease in the open-circuit voltage
as the thickness of the emitter layer (p
+-a-Si:H) increases. This degradation in
is mainly due to intensified recombination mechanisms, particularly at the interfaces. Increasing the FSF thickness raises the defect density within the layer and at the interfaces, promoting minority carrier recombination especially holes from the (n)-c-Si substrate via interfacial trap states.
When the thickness becomes excessive, bulk recombination dominates, causing a significant loss of open-circuit voltage. In contrast, a thinner, well-passivated emitter layer effectively limits both surface and bulk recombination, resulting in an increase in
. Optimizing this layer’s thickness is therefore essential to maintain a high open-circuit voltage, a key parameter in the overall performance of photovoltaic cells. The results of this study are presented in
Figure 5.
Figure 5. Impact of varying FSF layer thickness on cell open circuit voltage.
iv) Fill Factor (FF) as a Function of FSF Thickness
The fill factor (FF) progressively decreases as the thickness of the emitter layer (FSF) increases (
Figure 6). This degradation is primarily due to the increase in recombination within the p
+-a-Si:H layer, which directly influences the internal resistivity of the FSF and, consequently, the ohmic losses. Excessive thickness thus impairs the cell’s ability to maintain an optimal current-voltage curve shape, which is essential for achieving a good fill factor.
The combined analysis of the evolution of the fill factor, the open-circuit voltage , the short-circuit current density , and the efficiency shows that a thickness of approximately 5 nm provides the optimal balance for maximizing overall cell performance.
Simulation results demonstrate that the front emitter layer (FSF) thickness plays a decisive role in the performance of heterojunction solar cells. A thin layer (around 5 nm) simultaneously optimizes the short-circuit current density., the open-circuit voltage , and the fill factor (FF), leading to a maximum efficiency of 24%. At this thickness, the layer offers an ideal compromise between optical absorption, low opacity, effective interface defect passivation, and minimized bulk and surface recombination.
In contrast, increasing the thickness beyond this optimal value raises the layer’s resistivity, enhances recombination, degrades
and FF, and limits potential performance gains. This result underlines the importance of emitter layer thickness optimization to ensure efficient and stable cell operation. The results of this study are presented in
Figure 6.
Figure 6. Impact of varying FSF layer thickness on cell form factor.
The variation in FSF thickness has a significant influence on the overall photoelectric characteristics of the cell.
4.2. PV Parameters as a Function of FSF Doping
The emitter layer (a-Si:H) plays a particularly critical role in the performance of photovoltaic solar cells. It is essential to evaluate the effect of its doping concentration on the overall cell performance. For this purpose, the doping concentration was varied within the range of to . For the other layers c-Si (absorbing layer) and a-Si:H (rear layer) the doping concentrations were set to to , respectively.
i) Effect of FSF (Front Surface Field) Emitter Layer Doping
The upper p
+-n junction, formed between the p
+-doped hydrogenated amorphous silicon emitter layer (p
+-a-Si:H) and the n-type crystalline silicon absorbing layer (n-c-Si), induces an electric field within the space charge region, establishing a potential barrier favorable to charge carrier separation
[9] | Souad Tobbeche & Mohamed Nadjib Kateb. Simulation and optimization of silicon solar cell back surface field. Materials Science, 21(4) (2015), 575-581. http://dx.doi.org/10.5755/j01.ms.21.4.9565 |
[10] | K. Bendjebbara, W. L. Rahal, D. Rached, & S. Bahlouli. Numerical analysis of metal-semiconductor junctions ITO/p-a-Si:H and n-c-Si/Al on silicon heterojunction solar cells. Optik, 212(2020), 164741. https://doi.org/10.1016/j.ijleo.2020.164741 |
[11] | Duy Phong Pham, Sangho Kim, Sehyeon Kim, Sunhwa Lee, Anh Huy Tuan Le, Jinjoo Park, & Junsin Yi. Ultra-thin stack of n-type hydrogenated microcrystalline silicon and silicon oxide front contact layer for rear-emitter silicon heterojunction solar cells. Materials Science in Semiconductor Processing, 96(2019), 1-7. https://doi.org/10.1016/j.mssp.2019.02.017 |
[12] | T. F. Schulze, C. Leendertz, N. Mingirulli, L. Korte, & B. Rech. Impact of Fermi-level dependent defect equilibration on Voc of amorphous/crystalline silicon heterojunction solar cells. Energy Procedia, 8(2011), 282-287. https://doi.org/10.1016/j.egypro.2011.06.137 |
[9-12]
.
This section focuses on optimizing the performance parameters of heterojunction solar cells, specifically the conversion efficiency, short-circuit current density , open-circuit voltage , and fill factor (FF) as a function of the doping level of the emitter layer (p+-a-Si:H), under constant temperature conditions of 300 K.
ii) Effect of Emitter Doping on Cell Efficiency (η)
A low photovoltaic cell efficiency is observed (
Figure 7) when the doping concentration of the emitter layer (p
+-a-Si:H) is relatively low, around 10
17 cm⁻³. As the doping level increases, the efficiency improves in a nearly linear manner.
This improvement is explained by the evolution of the Fermi level positions. At low doping levels, the difference between the Fermi levels of the two materials forming the junction (p+-a-Si:H/n-c-Si) is larger, which limits the internal electric field and reduces the efficiency of charge carrier separation and collection.
Conversely, increasing the dopant concentration in the emitter layer reduces this gap, thereby strengthening the electric field at the junction and improving charge separation. This configuration promotes better collection of photogenerated carriers, resulting in higher cell efficiency. The effect of emitter layer doping on the efficiency of heterojunction photovoltaic solar cell is illustrated in
Figure 7.
Figure 7. Evolution of cell efficiency as a function of FSF layer doping.
iii) Effect of Emitter Doping on Short-Circuit Current Density ()
The analysis of
Figure 8 reveals an increase in the short-circuit current density
with the rise in the emitter layer doping level. This improvement is mainly attributed to the modification of the electric field profile at the p
+-n junction.
When the doping concentration in the p+-a-Si:H layer increases, the electric field induced in the space charge region becomes more intense due to the higher concentration of fixed charges on both sides of the junction (in the p+ emitter and the n-type base). This enhanced field lowers the effective potential barrier that minority carriers must overcome.
Under these conditions, photogenerated carriers in the n-c-Si base are more efficiently driven towards the junction, which significantly improves their collection. Thus, the current density increases with doping, reflecting improved charge transport and reduced recombination losses in the junction region. The effect of emitter layer doping on the current density of heterojunction photovoltaic solar cell is illustrated in
Figure 8.
Figure 8. Evolution of cell current density as a function of FSF layer doping.
iv) Effect of Emitter Doping on Open-Circuit Voltage ()
The curves in
Figure 9 show a positive correlation between the doping level of the emitter layer (p
+-a-Si:H) and the open-circuit voltage
. As the dopant concentration increases, a progressive improvement in
is observed.
This trend is explained by the fact that higher doping levels in the emitter lead to a reduction in the diffusion potential, which enhances the separation of the quasi-Fermi levels. This configuration allows for more effective separation of photogenerated carriers and limits recombination at the junction, contributing to the increase in open-circuit voltage. The effect of emitter layer doping on the open circuit voltage of the heterojunction photovoltaic solar cell is illustrated in
Figure 9.
Figure 9. Evolution of cell open-circuit voltage as a function of FSF layer doping.
v) Effect of Emitter Doping on the Fill Factor (FF)
Increasing the doping concentration in the emitter layer (p
+-a-Si:H) results in a nearly linear improvement in the fill factor (FF) (
Figure 10). This evolution is explained by the reduction in emitter resistivity, which is directly related to the increased doping.
Indeed, electrical resistivity is inversely proportional to the concentration of free carriers, so higher doping improves the conductivity of the emitter layer. This enhanced conduction reduces internal ohmic losses, optimizes charge transport, and thus contributes to improving the fill factor.
The study highlights the strategic importance of the doping level of the emitter layer (p+-a-Si:H) in optimizing the performance of heterojunction solar cells. A gradual increase in dopant concentration simultaneously improves the open-circuit voltage , the short-circuit current density , and the fill factor (FF), leading to a significant enhancement in overall conversion efficiency.
These improvements can be explained by several combined mechanisms:
1) The reduction in emitter layer resistivity, which improves electrical conduction and reduces ohmic losses.
2) The strengthening of the electric field at the junction, which promotes charge separation and collection.
3) The decrease in diffusion potential, which contributes to the increase in .
As a result, well-optimized doping maximizes the electrical performance of the cell while maintaining a balance between passivation, conduction, and charge transport. However, it should be noted that excessively high doping levels may, beyond a certain threshold, induce additional recombination or structural disorder, justifying the need for precise optimization.
Simulation results confirm that the thickness of the front emitter layer (FSF) plays a crucial role in the performance of heterojunction solar cells. A thin layer (around 5 nm) simultaneously optimizes the short-circuit current density , the open-circuit voltage , and the fill factor (FF), leading to a maximum efficiency of 23.5%. At this thickness, the layer provides an excellent balance between optical absorption, low opacity, effective interface defect passivation, and minimized bulk and surface recombination.
Conversely, increasing the thickness beyond this value raises the layer’s resistivity, promotes recombination, degrades and FF, and limits performance improvement.
Recent studies by Khairuddin et al. (2023) demonstrated that excessive emitter layer thickness increases recombination, thereby reducing efficiency, while well-calibrated doping optimizes charge transport without compromising passivation
[13] | N. S. Khairuddin et al. The effects of thickness and doping concentration on the solar efficiency of GaNp-Si based solar cells. Chalcogenide Letters, 20(12) (2023), 629-637. |
[13]
. Additionally, Zhang et al. (2022) achieved an efficiency of 26.45% by simultaneously optimizing the thickness and doping of the a-Si:H(n) emitter layer, which improved both the fill factor and open-circuit voltage
[14] | Y. Zhang et al. Emitter layer optimization in heterojunction bifacial silicon solar cells. Journal of Semiconductors, 43(12) (2022), 122701. |
[14]
. The effect of emitter layer doping on the form factor of the heterojunction photovoltaic solar cell is illustrated in
Figure 10.
Figure 10. Evolution of cell form factor as a function of FSF layer doping.
Varying the FSF doping significantly influences the overall photoelectric characteristics of the cell.
4.3. Effect of the Band Gap Energy on Photovoltaic Parameters
The band gap energy
is a key parameter influencing the performance of photovoltaic solar cells
[11] | Duy Phong Pham, Sangho Kim, Sehyeon Kim, Sunhwa Lee, Anh Huy Tuan Le, Jinjoo Park, & Junsin Yi. Ultra-thin stack of n-type hydrogenated microcrystalline silicon and silicon oxide front contact layer for rear-emitter silicon heterojunction solar cells. Materials Science in Semiconductor Processing, 96(2019), 1-7. https://doi.org/10.1016/j.mssp.2019.02.017 |
[14] | Y. Zhang et al. Emitter layer optimization in heterojunction bifacial silicon solar cells. Journal of Semiconductors, 43(12) (2022), 122701. |
[11, 14]
. Studies by Steiner et al. (2023)
[15] | M. A. Steiner et al. Modeling and design of III-V heterojunction solar cells for enhanced performance. National Renewable Energy Laboratory (2023). |
[15]
and Taguchi et al. (2005)
[16] | M. Taguchi et al. Obtaining a higher Voc in HIT cells. Progress in Photovoltaics: Research and Applications, 13(6) (2005), 481-488. |
[16]
have shown that an appropriately selected
value maximizes charge separation while minimizing thermal losses.
In this study, we analyzed the impact of different values, considering various emitter layer thicknesses to evaluate their combined effect on the key performance parameters of the cell, namely: open-circuit voltage , short-circuit current density , fill factor (FF), and conversion efficiency.
i) Effect of Band gap Energy on Efficiency (η)
Figure 11 illustrates the combined impact of the band gap energy
and the thickness of the emitter layer on the efficiency of photovoltaic solar cells. The results show that cells with a larger band gap in the emitter layer are generally less efficient. This decrease is due to the fact that photons with energy lower than the band gap are not absorbed, reducing the amount of light converted into electrical energy.
Conversely, cells with a smaller band gap absorb a greater portion of the solar spectrum but incur significant thermal losses due to the excess energy of photons beyond the absorption threshold. There is thus an optimal band gap that maximizes efficiency by balancing effective absorption and minimizing thermal losses.
Additionally, a regular and significant increase in efficiency is observed for all cells, regardless of the band gap, as the FSF thickness increases up to approximately 3 nm, beyond which efficiency stabilizes. However, when the thickness exceeds this value, cells with a large band gap experience a marked performance drop, while those with a smaller band gap remain relatively stable, with minimal sensitivity to thickness variations.
These observations suggest that cells with larger band gaps are more sensitive to thickness variations, possibly due to a reduction in recombination probability facilitated by a more direct transition of charges between the conduction and valence bands. This configuration makes these cells less effective at higher thicknesses due to reduced absorption and weakened charge transport.
Nevertheless, we achieved an efficiency of 24% for a heterojunction photovoltaic solar cell with a front emitter gap of less than 1.7 eV and a thickness between 5 and 7 nm. The evolution of the efficiency of a heterojunction photovoltaic solar cell with different emitting layer band gap values as a function of the front layer thickness are shown in
Figure 11.
Figure 11. Evolution of Efficiency as a Function of FSF Thickness for Different Band gap Energies.
ii) Effect of Band gap Energy on Current Density ()
The results show that reducing the band gap energy (
) leads to an increase in the short-circuit current density (
) when the emitter layer thickness (FSF) is between 2 nm and 3 nm (
Figure 12). In this range, cells with a smaller
exhibit broader absorption capacity, which enhances carrier generation and consequently results in higher current.
Beyond a 3 nm thickness, the current density becomes nearly constant regardless of the band gap, suggesting a saturation of absorption and generation mechanisms. However, for a cell with a band gap of 1.75 eV, a rapid drop in is observed starting from a thickness of 13 nm, indicating a degradation of carrier collection beyond this limit.
Generally, increasing the band gap reduces the number of absorbed photons since only those with energy higher than the band gap can be converted, leading to a decrease in current density. Conversely, a lower band gap allows absorption of a larger portion of the solar spectrum, increasing carrier generation and the current produced by the cell. The evolution of the current density of a heterojunction photovoltaic solar cell with different emitting layer band gap values as a function of the front layer thickness are shown in
Figure 12.
Figure 12. Evolution of the current density as a function of FSF thickness for different band gap energies.
iii) Effect of Band gap Energy on Open-Circuit Voltage ()
The open-circuit voltage () is strongly affected by variations in band gap energy (). It varies positively with decreasing bandgap energy when the FSF layer thickness is between 2 nm and 3 nm. With a thickness greater than 3 nm, cells with a small band gap maintain a stable. , while those with medium and large band gaps show a decrease.
The depends directly on the minimum energy required to excite an electron into the conduction band. A large band gap in the FSF layer reduces the number of absorbed photons, theoretically increasing. . However, excessive band gap combined with increased FSF thickness significantly limits photon absorption, restricting carrier generation and paradoxically leading to a reduction in .
Optimizing both the band gap width and emitter layer thickness is essential to maximize this parameter. The open circuit voltage evolution of a heterojunction photovoltaic solar cell with different emitter layer band gap values as a function of the front layer thickness are shown in
Figure 13.
Figure 13. Open-circuit voltage variation as a function of FSF thickness for different band gap energies.
iv) Effect of Band gap Energy on Fill Factor (FF)
Like other photovoltaic parameters, the fill factor (FF) is also influenced by the band gap energy (
Figure 14). For emitter layer thicknesses between 2 nm and 3 nm, a sharp and uniform decrease in FF is observed regardless of the band gap value.
Beyond 3 nm, behavior diverges depending on the band gap: cells with a low band gap show FF stabilization, while those with a large band gap experience a significant decline. This degradation is attributed to two combined factors:
1) A more challenging energy barrier, hindering carrier transport;
2) Increased diffusion length, associated with reduced emitter layer conductivity, resulting in higher resistivity and thus a lower FF.
The observed trends align with findings from other similar studies
[12] | T. F. Schulze, C. Leendertz, N. Mingirulli, L. Korte, & B. Rech. Impact of Fermi-level dependent defect equilibration on Voc of amorphous/crystalline silicon heterojunction solar cells. Energy Procedia, 8(2011), 282-287. https://doi.org/10.1016/j.egypro.2011.06.137 |
[13] | N. S. Khairuddin et al. The effects of thickness and doping concentration on the solar efficiency of GaNp-Si based solar cells. Chalcogenide Letters, 20(12) (2023), 629-637. |
[12, 13]
, confirming the strong link between band gap energy, material conductivity, and photovoltaic cell performance.
The study highlights the critical role of the emitter layer band gap energy () in the operation and optimization of heterojunction solar cells. The results show that overall cell performance is highly sensitive to the band gap value, particularly in configurations with thin emitter layers (between 2 nm and 3 nm).
Reducing the band gap enables better solar spectrum absorption, increasing but potentially leading to higher thermal losses and reduced stability beyond certain thicknesses. Conversely, an excessively high restricts photon absorption, decreasing and potentially affecting FF due to increased resistivity and challenges in efficient carrier extraction.
Regarding open-circuit voltage (), a moderate value combined with an optimized emitter layer thickness maximizes this parameter. The fill factor tends to be relatively stable at low but significantly degrades at high and large thicknesses, indicating increased electronic transport limitations.
During our simulations, we initially used indium tin oxide (ITO) as the front layer, following conventional heterojunction solar cell structures. However, simulations with reduced ITO thickness did not yield convergent or exploitable results. To overcome these numerical difficulties and continue the structural parameter analysis, we temporarily substituted ITO with a silicon dioxide (SiO2) layer, which stabilized the simulations and provided coherent results in terms of carrier profiles and overall performance.
It should be emphasized that this substitution is not intended for real-world fabrication since SiO
2 is an insulating material and does not fulfill the necessary conduction functions. Our approach is exploratory, aimed at analyzing the cell's sensitivity to front layer thickness and identifying underlying physical trends. Further detailed modeling with appropriate TCO parameters or experimental validation will be required in future work. The evolution of the form factor of a heterojunction photovoltaic solar cell with different emitting layer band gap values as a function of the front layer thickness are shown in
Figure 14.
Figure 14. Form factor evolution as a function of FSF thickness for different bandgap energies.
The results observed in Section 4.3 are consistent with those of Sehyeon Kim un, Park Hyeongsik et al
[17] | Sehyeon Kim, Hyeongsik Park, & Duy Phong Pham. Design of front emitter layer for improving efficiency in silicon heterojunction solar cells via numerical calculations. Optik, 235(2021), 166580. https://doi.org/10.1016/j.ijleo.2021.166580 |
[17]
, confirming the close link between the band gap energy and the electrical properties of photovoltaic cells.