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Abstract
One of the most important and challenging loss factors of photovoltaics is the heat production of energetic carriers excited by high energy incident photons. The present work shows that if carriers are extracted at their high energies before cooling down due to scattering, the conversion efficiency can be noticeably enhanced. To increase the efficiency of a single-band gap solar cell in this work, selective energy contacts are introduced to a p-i-n structure to extract hot carriers. A selective energy contact solar cell is made up of many collecting contacts with particular energy differences from the conduction band of the cell. In other words, each contact could extract carriers with a special range of energies. The concept of selective energy contact solar cells is to collect high energy carriers, i.e. electrons in this case, within a range of energies onto external electrodes before they cool down. The comparison between conventional solar cells and selective energy contact solar cells shows a significant enhancement in electron collection and efficiency. Based on simulation results, it is observed that the efficiency of the selective energy contact solar cell has been enhanced substantially exceeding almost twice as much as a conventional solar cell’s and reaching a significant 34% efficiency.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ever-increasing global energy demand has forced human beings to search for other limitless and clean energy sources instead of fossil fuels [1,2]. Sunlight is the most important thermodynamic resource of energy for the earth because it is renewable and has the capability of conversion to electricity by photovoltaic devices [3]. Over several past decades, the efficiency of solar cells has improved through the works of many researchers; however, the limits on solar energy conversion still exist. Fundamental limits of efficiency of solar energy harvesting have been extensively studied and the solutions proposed have been profoundly investigated to decrease these limitations [4–16]. In fact, the main problem of photovoltaic devices is their cost which is still many times higher than fossil fuels [17]; thus, low cost and high-efficiency cells are still among the biggest challenges [18–20].
According to the detailed balance limit of Shockley and Queisser [4], the maximum attainable efficiency for bandgap energy of 1.12eV under one sun illumination is about 30% [21]. The values acquired for the efficiency of solar cells using different technologies and materials are lower than theoretical limits. For instance, the best modern efficiency reported for silicon is about 25% according to NREL’s 2020 chart [22]. Yet numerous models of solar cells are developed to deal with efficiency and cost issues.
Critical detailed balance limit [4] assumptions are about the purity of the materials used in the cell, the number of junctions, the concentration of sunlight to the cell, and the levels beyond which photon conversion is prevented. Several studies have attempted to explain the impact of the number of bandgaps [8,23–29], material quality, and light concentrations [30–34].
According to this theory, about 37% of sunlight is converted to heat, 18% passes through the cell, 4% gets lost by Carnot and emission losses, 11% gets lost by Bultzman loss and finally, 30% will be converted to electricity. It should be noted that these results are approximate [35]. Based on the laws of thermodynamics, the number 30 is indeed the maximum achievable efficiency for a single junction c-Si solar cell under one sun illumination. However, other losses are impacting the performance of the cell such as reflection, ohmic losses, material impurities, etc. Reaching the Shockley-Queisser limit of solar cell conversion efficiency requires some features which are explained in [36,37].
Thermodynamic calculations reveal that single-junction solar cell conversion efficiencies can reach around 66% under one–sun illumination if the excess energy of hot photo-generated carriers is used before they cool to the lattice temperature [38].
To collect a large amount of solar spectrum, multi-junction structures are a solution to surpass Shockley-Queisser’s limit of single-junction solar cells. As the number of junctions increases, the potential conversion efficiency increases asymptotically to 65% at one-sun [38]. The optical concentration of the incident light also increases the density of photo-generated carriers in the semiconductor. Thus, 85% efficiency could theoretically be achieved for an infinite number of junctions at the maximum optical concentration in the detailed balance limit [5,11].
With a global production share of about 90%, Silicon is by far the most dominant photovoltaic technology [39] due to its abundance and environmentally friendly nature. Silicon can be used in crystalline or amorphous form. A multi-crystalline silicon cell has an efficiency of 21%-25% [40]. The amorphous silicon alloy can be used to make thin sheets of Silicon; however, the amorphous structure impedes the flow of electrons and holes and degrades more quickly [41]. Crystalline silicon is a weak absorber of long wavelengths; therefore, crystalline silicon solar cells must have a thickness of more than 40-$\mu m$ to enable efficiency exceeding 20% [42]. Then efficiency has to be high to get an economical cell. Solar cells made of c-Si have reached 26.7% photoconversion efficiency using 165µm-thick Si wafers [43,44]. Regarding this, different technologies have been used to optimize silicon solar cells [21,45–48].
Here, the rate of loss related to the heat production of energetic carriers has been investigated prepossessing 37% of total induced light from the sun. Having this phenomenon in mind, via reducing this amount of loss, total achievable efficiency is enhanced and even go beyond the detailed balance limit. To this end, in this work, based on the appropriate energy selectivity of carriers, the efficiency of the proposed solar cells can be enhanced. Improving energy selectivity of the solar cell by accomplishing selective energy contacts results in better extraction of different energy ranges and better carrier management.
2. Proposed selective energy contact solar cell
Only a small fraction of the incident solar energy converts to electrical power in a solar cell. Loss processes constrain the efficiency of a conventional solar cell to the detailed balance limit which is not considered as an optimum efficiency for solar cells. There are two kinds of loss mechanisms in a single junction solar cell. Recombination caused by impurities, ohmic losses, and unwanted absorption are examples of extrinsic yet avoidable losses. The fundamental limitation of energy conversion represents an intrinsic loss that is unavoidable as well. However, the Shockley-Queisser limit has mentioned and considered this loss and its processes earlier. The dominant amount of intrinsic loss contributes to heat generation in a solar cell’s structure. Heat generation corresponds to the transmission of two types of photon groups into the cell. One of them is the photons with energy levels lower than the bandgap which lacks the energy required to excite electrons and whose energy is transferred to phonons in a structure. This process comprises about 18% of the c-Si solar cell’s loss. The other type includes photons with energy levels higher than the bandgap. High energy photons create free carriers known as hot carriers in a solar cell. These photons have excess energy compared to the bandgap; thus, they cause carriers to excite to levels above the band edge resulting in hot carriers. Hot carriers release their energy over bandgap to cool down to band edge to get extracted and participate in energy conversion. The extra energy is then transferred to phonons and contributes to the process of heat generation in a device leading to a temperature rise and causing an inevitable impact on the performance of the solar cell. This respective loss possesses about 37% of the c-Si solar cell’s energy conversion [35].
As mentioned above, carriers generated in a conventional solar cell, lose energy by cooling down from their prior situation to the band edge by optical phonon emission. These energetic carriers can contribute to a higher conversion efficiency if there is a way to prevent them from cooling down and extract them at their elevated energy eliminating thermalization loss. In this paper, a model is proposed to tackle the hot carrier loss developed from energetic photons to achieve higher conversion efficiency in a conventional solar cell.
This method attempts to minimize this loss by introducing a way to extract carriers before cooling down and losing energy. By utilizing this method, the solar cell would be capable of extracting carriers excited by a wide range of photons before losing energy as phonons. This process could be done by adding other collecting contacts to the structure of a conventional cell. These contacts should be capable of extracting hot carriers before thermalization. In this case, foresaid contacts are devised in a way to be within the range of hot carriers to extract a fraction of them. These supplement contacts, known as selective energy contacts (SECs), have an energy level higher than the original contact of the solar cell and each contact is allowed to extract a particular range of hot carriers at their initial level. The number of SECs and the energy range should be optimized.
Since these SECs choose a fraction of hot carriers, an energy range is defined for each contact to extract them separately and autonomously. The SECs are devised in levels above conduction band edge and below valance band edge; so these energy differences allow higher voltages to be attained from the cell and hence higher efficiencies would be achievable in addition to extraction improvement.
For simplicity, in this research, a conventional p-i-n c-Si solar cell using two SEC has been investigated. As mentioned earlier, the electrons generated by high energy photons have been excited to higher energy levels than the bandgap and the conventional solar cell is not capable of extracting these carriers due to their high energy. The most important kind of loss happens when these carriers lose energy to cool down. By accomplishing SECs to extract hot electrons, one of the main energy losses of the solar cell can be reduced significantly.
To realize the modeling of SECs in solar cell, one back contact on the n-side of the cell is considered to collect total hole current as conventional solar cell and on the p-side, where the sunlight induces two different contacts are considered as front contacts of the solar cell for collecting electrons. The common geometry of the p-i-n c-Si solar cell structure using two SEC has been illustrated in Fig. 1. The generated electrons are collected by the corresponding SEC according to their energies. In other words, the electrons which their energy are lower than the energy of the second SEC, have been collected by the first SEC (is indicated as orange contact in Fig. 1), and the electrons with energies higher than the energy of the second SEC are collected by the second one (the blue contact in Fig. 1).
Fig. 1. Schematic diagram showing the structure of the p-i-n c-Si solar cell consisting of two SEC. The i-layer is fully depleted. The p+-layer is used as a front surface field reducing the front surface recombination velocity along with upper layers which are not represented here. The n+-layer is used as a back surface field reducing the back surface recombination velocity. ${x_p}$ is the width of intrinsic region on the p-layer side, ${x_n}$ denotes the width of intrinsic region on the n-layer side. These widths are dependent on the voltage across the cell. The ${w_p} - {x_p}$ (${w_n} - {x_n}$) is thickness of p-layer (n-layer). Hot electrons are extracted via two SECs. The first contact (the second contact) which is for low (high) energy electrons is depicted in orange (blue) and has the current of J1 (J2) and voltage of V1 (V2).
Moreover, the Global AM1.5 spectrum approximately from 300nm to 1100nm has been considered as incident light according to the c-Si absorption range, and it is illustrated in Fig. 2(A). Also, the energy band diagram of the structure and the generated carrier spectrum has been depicted in Fig. 2(B).
Fig. 2. A) The global AM1.5 spectrum (${\cong} 1000{\; \boldsymbol{W}}.{{\boldsymbol {m}}^{ - 2}}$) and spectral absorption of c-Si. B) Energy band diagram of proposed two SEC p-i-n solar cell and density of minority electrons generated in conductance band. Blue color stands for high energy; blue district in (A) is associated with blue region in (B), in (A) blue district indicates high energy wavelengths which causes to create high energy electrons illustrated in blue in (B). Likewise orange district in (A) denotes low energy photons which is associated with low energy electrons indicated in orange in (B).
As stated before, there are two groups of electrons from the point of view of this study: low energy and high energy electrons. The electrons (indicated as orange in Fig. 2(B)) generated by photons in which their energy is higher than the bandgap of the c-Si and lower than the second SEC level (indicated as orange in Fig. 2(A)) are considered as low energy electrons and get collected by first SEC (orange contact). Besides, the second SEC (blue contact) is supposed to collect high energy electrons including all the electrons generated by photons in which their energy is higher than the second SEC (shown as blue in Figs. 2(A) and (B)). The parameter for the second SEC level is considered as ΔE whose value significantly determines the performance of the solar cell. This implies varying ΔE causes a change in SEC’s ranges likewise in the number of electrons they can extract. As ΔE ascends in level, the range of the first SEC increases and it extracts more electrons as well. The optimum value of ΔE should be obtained to maximize conversion efficiency. The wavelength associate with ΔE is λΔ where photons having wavelengths lower than it is considered as high energy photons and induce electrons with energies higher than ΔE.
3. Modeling of the proposed selective energy contact solar cell
Similar to conventional solar cells, to investigate the figure of merits in the proposed selective energy contact solar cell (SEC-SC), the continuity equations have to be solved. To this end, to calculate the current densities, the carrier distribution in each layer has to be obtained considering the continuity equations for electrons and holes with appropriate boundary conditions [49–52]. Minority carrier transport parameters obtained from continuity equations critically affect the operation and performance of solar cells [53,54]. In particular, important parameters of solar cells which are open-circuit voltage (Voc) and photo-generated current density (J) depend on these equations [55]. It should be mentioned that the Shockley-Read-Hall mechanism is considered for the recombination process for all layers of SEC-SC and no shadow effect, reflectance and resistance is indeed assumed on this simulation. Furthermore, considering the Global AM1.5 spectrum as incident light on the p-layer of SEC-SC, the optical generation rate is defined as,
As stated above, two SECs are utilized for collecting the generated electrons in the p-layer of SEC-SC. Hence, considering two groups of electrons according to Fig. 2(B), the minority electron density distributions of each group can be obtained by solving the continuity equation for the electrons of each SECs in the p-layer of SEC-SC, and are given as
By substituting Eqs. (6), (7), (9), and (10) into Eq. (8), the total current density of each SEC can be obtained,
4. Simulation results and discussion
As mentioned earlier, one of the most important factors that affect the efficiency of solar cells is heat production due to hot carriers. Based on the proposed method in the previous section, this source of loss can be compensated by adding two SECs to a conventional solar cell to prevent hot carriers from losing energy as heat. To evaluate the performance of a proposed SEC-SC, current vs. voltage (I-V) characteristics can be obtained by considering Eq. (11). According to the I-V characteristic, many common parameters of the proposed SEC-SC such as ${J_{sc}}$, ${V_{oc}}$, maximum power and total efficiency of the solar cell are investigated.
In this section, the results of analytical-numerical simulation in MATLAB are represented based on the model described in the previous section. To this end, the general parameters of the SEC-SC utilized in the simulation are given in Table 1. According to parameters in [50], a set of modifications to suits this p-i-n model are proposed in a solar cell surface of 100cm2. Total width of cell is about 325µm. The N-layer width is 300µm and p-layer width is 0.3µm. The i-layer width is chosen in a way that it suits the structure and it is 25 µm. The only varying parameter is ΔE, the energy difference of two SECs, whose effect on the performance of the cell is still being investigated.
The I-V characteristics of the conventional solar cell and SEC-SC for various values of ΔE are depicted in Fig. 3. As illustrated in this figure, the green curve is the I-V characteristic of the conventional solar cell, the orange, and the blue curves are the I-V characteristics of the first and the second SECs in the proposed SEC-SC, respectively. Based on the simulation results for the conventional solar cell (green curve) the short-circuit current of 345A/m2, the open-circuit voltage of 0.67V, and the efficiency of 17.36% are obtained. Besides, it is shown that as ΔE shifts to the higher energies, the short-circuit current density of the first SEC is increased while the short-circuit current density of the second one is decreased. Furthermore, the open-circuit voltage of the second SEC is enhanced by increasing ΔE.
Fig. 3. The I-V characteristics of the conventional solar cell and SEC-SC for ΔE=0, 0.4eV, 1eV, 1.6eV. The green curve is the I-V characteristic of the conventional solar cell. The Orange color stands for the I-V characteristics of the first SEC. By increasing ΔE, the short-circuit current of first SEC is increased. For second SEC which is shown in blue, as ΔE shifts to the higher energies, the short-circuit current decrease and the open-circuit voltage is increased. The simulation parameters are listed in Table 1.
Table 1. The parameters of SEC-SC
The dependency of the short-circuit current density, the open-circuit voltage, maximum attainable power of each SEC, total maximum attainable power of SEC-SC, the efficiency of each SEC, and the total efficiency of the SEC-SC, on the energy difference between two SEC (ΔE) are demonstrated in Fig. 4. It is shown that as ΔE increases, according to Fig. 2(B) the first SEC extracts more electrons and an ascending current density is expected for this SEC. By extracting more electrons through the first SEC as ΔE increases, the second SEC extracts fewer electrons; thus, the current density for this contact is decreased. The variation of the short-circuit current density corresponding to two SEC versus increasing ΔE is illustrated in Fig. 4(A).
Fig. 4. The dependency of short-circuit current density, open-circuit voltage and the efficiency of the SEC-SC on the variation of ΔE; (A) The short-circuit current density of two SEC of the SEC-SC versus ΔE. (B) The open-circuit voltage of two SEC of the SEC-SC versus ΔE. (C) The maximum attainable power of each SECs and the total maximum attainable power of SEC-SC versus ΔE. (D) The efficiency of each SECs (${\eta _1},{\eta _2}$) and the total efficiency of SEC-SC ($\eta $) versus ΔE. The simulation parameters are listed in Table 1.
The open-circuit voltage of the second SEC ascends as the enhancing of the energy level of ΔE from 0 to 3eV, while the open-circuit voltage of the first SEC does not change noticeably. Figure 4(B) illustrates the variation of the open-circuit voltage of SECs versus ΔE. On the other hand, Fig. 4(C) illustrates the maximum attainable power of each SEC as ΔE increases. As shown in this figure; the maximum power of the first SEC increases as ΔE goes higher; yet, the maximum power of the second SEC reaches a peak at the beginning and then decreases. Eventually, the sum of the maximum powers of two SECs forms up the SEC-SC’s total maximum attainable power. (The green curve in Fig. 4(C)) illustrates the total maximum attainable power of the SEC-SC as ΔE varies.
Variation of efficiencies of SECs and the total efficiency of SEC-SC versus ΔE behave extremely similarly to variation of maximum power according to ΔE. Figure 4(D)) shows the efficiency of two SEC and the total efficiency of SEC-SEC as ΔE increases. The optimum values for the maximum power and maximum efficiency are obtained when the energy difference between two SEC is ΔE=0.61eV where the maximum power and maximum efficiency of SEC-SC are 341W/m^2 and 34.11% respectively. Whereas in comparison to conventional solar cells, SEC-SC shows a significant improvement, the I-V and P-V characteristics of the proposed SEC-SC at the optimum condition are enhanced where these characteristics in ΔE=0.61eV is demonstrated for each SEC in Fig. 5.
Fig. 5. The I-V and P-V characteristics of two SECs in the optimum performance; when $\Delta {\textbf {E}} = 0.61\; {\textbf {eV}}$. (A) First SEC (${J_{sc}} = 131.52\; ({A/{m^2}} ),\; {V_{oc}} = 0.634\; V\; ,\; {P_{max}} = 60.12\; W/{m^2}$). (B) Second SEC (${J_{sc}} = 215.19\; ({A/{m^2}} ),\; {V_{oc}} = 1.437\; V\; ,\; {P_{max}} = 281.03\; W/{m^2}$)
5. Conclusion
In this paper, the efficiency of the proposed SEC-SC has been enhanced as a result of collecting the energetic carriers excited by high energy photons, preventing one of the important loss factors in a solar cell. A wide range of electrons is generated by the induced photons in the conduction band of a solar cell. These electrons cannot be extracted spontaneously and they have to cool down to band edges to get extracted and participate in energy conversion. The excited electrons are collected by the SECs before cooling down and losing heat to the cell structure, leading to the enhancement of efficiency. To this end, the analytical modeling for the introduced SEC-SC has been developed. Based on the simulation results, the modification of the conversion efficiency of the proposed SEC-SC almost 34% has been substantiated by comparing it with a conventional solar cell efficiency of around 16%.
Disclosures
The authors declare that they have no conflicts of interest.
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