Simulation of a Charged Al2O3 Film as an Assisting Passivation Layer for a-Si Passivated Contact P-Type Silicon Solar Cells

In this paper, a charged Al2O3 tunneling film as an assisting for amorphous Si (a-Si) passivated contact layer is proposed and theoretically simulated for its potential application in improving a-Si passivated contact p-type (a-PC-p) solar cell. The concept is based on an Ag/n+ c-Si/p c-Si/Al2O3/p+ a-Si/Al structure. The key feature is the introduction of a charged Al2O3 layer, which facilitates the tunneling of holes through an Al2O3 insulator layer accompanied by the reduction of interface defect density (Dit). The negative charge in the Al2O3 layer makes the energy band of p-type c-Si bend upward, realizing the accumulation of holes and repelling of electrons at the c-Si/a-Si interface simultaneously. The influence of interface negative charges (Qit) between a-Si and c-Si, Al2O3 thickness, Al2O3 bandgap, interface defect density (Dit) at the a-Si/c-Si interface are systematically investigated on the output parameters of a-PC-p cells. Inserting a charged Al2O3 film between the c-Si/a-Si interface, a + 4.2% relative efficiency gain is predicted theoretically compared with the a-PC-p cells without the Al2O3 layer. Subsequently, the device performance under various temperatures is simulated, and the insertion of a charged Al2O3 layer obviously decreases the Pmax temperature coefficient from −0.336% /°C to −0.247% /°C, which is analogous to that of Heterojunction with Intrinsic Thin layer (HIT) solar cell. The above results demonstrate a better temperature response for a-PC-p cells with a charged Al2O3 layer, paving a road for its potential application in high-efficiency and high thermal stability a-PC-p solar cells.


Introduction
In recent years, the a-Si/c-Si passivated contact (a-PC) solar cell has attracted a great deal of attention due to its unique high V oc and its high efficiency. A famous example of the a-PC solar cell is the Heterojunction with Intrinsic Thin layer (HIT) solar cell which achieves very high conversion efficiency by using hydrogenated amorphous silicon (a-Si:H) to effectively suppresses recombination at the a-Si:H and crystalline silicon (c-Si) interface as well as at the metal contact [1]. Compared with traditional diffusion processed homo-junction solar cells, the most obvious advantages of the a-PC solar cell are its low deposition temperature (< 200°C) and better cell temperature coefficient (−0.25%) [2]. As is known to all, the device quality is mainly determined by factors including a-Si emitter quality and interface quality between a-Si and c-Si. Defect states at the a-Si/c-Si interface can cause strong interface recombination in an a-PC solar cell when the interface defect density is more than 1 × 10 13 cm −2 ·eV −1 . A low interface state in the mid-gap can be achieved by the insertion of intrinsic hydrogenated amorphous silicon. However, the narrow process window for depositing intrinsic hydrogenated amorphous silicon makes it very easy to grow epitaxially on the c-Si substrate [3]. The detrimental effect of an epitaxially grown interface usually causes a V oc of a-PC solar cell less than 600 mV.
The energy position within the bandgap and capture crosssection of the electron and hole determine the defects in the epitaxial film. Usually, the abruptness of the a-Si/c-Si interface without initial epitaxial growth is preferred. Therefore, a tunnel oxide insulator layer (usually SiO 2 ), is adopted to prohibit the epitaxial phenomenon and reduce recombination at the interface [4,5]. Generally speaking, the used SiO 2 should be as thin as possible to ensure the tunneling process (< 20 Å), while the interface passivation effect will be better if a thicker oxide layer is adopted. As a result, a trade-off between the tunneling process and interface passivation should be considered.
Most generally, a solar cell consists of a semiconductor material that absorbs light and then generates excess electrons and holes. The different contacts of a solar cell not only serve to collect the different types of charge carriers but also act as a semipermeable membrane such that one contact transmits electrons and blocks holes, while the other contact does exactly the opposite. In addition to being carrier-selective, the contacts should passivate the surface defects to make sure that the photo-generated carriers are collected before they recombine. Such contacts can therefore be defined as contact passivation [6]. There has recently been an increase in interest in the use of tunneling layers for contact passivation in singlejunction Si solar cells. The used a-Si stack layer in HIT solar cells [7] and SiO 2 /polycrystalline silicon stack layer [8] in high-efficiency n-type silicon solar cells are all, in fact, contact passivation structures. Therefore, the contact passivation structure is usually made of an ultrathin insulator layer and a highly doped semiconductor layer. The used insulator materials can be positively charged layers, i.e., a-SiN x : H [9] and thermal SiO 2 [10], which can lead to a high level of surface passivation on lightly doped n-and p-type c-Si, or negatively charged layer such as Al 2 O 3 [11]. Negative charges in Al 2 O 3 are particularly suited to passivate the backside of the p-type solar cell. It is expected that the negative charges in Al 2 O 3 can repel electrons and accumulate holes at the interface between a-Si and c-Si, which increases the probability of tunneling through the Al 2 O 3 layer. Aluminum oxide (Al 2 O 3 ) has recently been used as an alternative passivation material to conventional a-SiN x : H. The popularity of Al 2 O 3 can be explained by two important trends. First, the photovoltaic (PV) industry has recently been looking to improve the rear side of conventional screen-printed p-type Si solar cells by replacing the Al-back surface field (Al-BSF) with a dielectrically passivated rear [12][13][14]. The latter leads to lower surface recombination losses, better internal reflection, and reduced wafer bow for thin wafers [15][16][17]. The adoption of a passivated rear side is inevitable concerning the demand for higher efficiency and the use of thinner Si wafers. Though the ultrathin SiO 2 layer has been widely used in passivated contact (PC) solar cells, the use of an ultrathin Al 2 O 3 layer as a tunnel oxide layer in contact passivation structure is rarely reported. Therefore, there is a need for understanding parameters affecting tunneling, such as the influence of interface negative charges (Q it ) between a-Si and c-Si, Al 2 O 3 thickness, interface defect density (D it ) at the a-Si/c-Si interface.
In this paper, a p-type c-Si substrate a-Si passivated contact solar cell based on Ag/n + c-Si/p c-Si/Al 2 O 3 /p + a-Si/Al structure has been developed to analyze the influence of Q it between a-Si and c-Si, Al 2 O 3 thickness, Al 2 O 3 bandgap and D it at the a-Si/c-Si interface on a-PC cell performance using AFORS-HET software. The purpose of this paper is to investigate the influence of the charged Al 2 O 3 layer on a-PC cell's performance, so the reference cell is not optimized.

Tunneling Theory
For direct quantum tunneling, the electron tunnel current J e, tun calculation is based on the so-called Tsu-Esaki formula [18] in semiconductor-insulator-semiconductor (SIS) structures: where E min is the minimum conduction band edge energy allowing for tunneling, q is the elementary charge, m * is the tunneling effective mass in the semiconductors and h is Planck's constant. The transparency T(E) of the barrier gives the probability for an electron with the energy E to tunnel through the barrier. For known effective masses of silicon, the product outside the integration sign is a constant. The tunneling current is therefore controlled by the energy of the charge carriers, the quasi-Fermi levels and the transmission coefficient. The latter, which is the ratio between the outgoing and incoming flux, is found using the transfer matrix method to solve the Schrödinger equation. Here, the energy barrier height, the tunneling effective mass and the oxide thickness are important parameters. The above mentioned effective masses denote the conductivity effective masses.

Simulation Parameters
Numerical simulations are performed using the 1D simulation software "Automat FOR Simulation of HETerostructure" (AFORS-HET) developed at the Helmholtz Zentrum Berlin [19]. AFORS-HET solves one-dimensional semiconductor equations related to Shockley-Reed-Hall statistics. It utilizes the Lambert-Beer law based optical model for estimating the optical parameters. In the present simulation, metal contacts are assumed as a flat band and solar radiation AM 1.5 with a power density of 100 mW/cm 2 is considered as a light source.
The gap statistics of various types of a-Si:H layers and c-Si wafer are preset as default value in AFORS-HET software. Simulated cell architectures with the position of the added layers are presented in Fig.1. The input layer parameters are presented in Table 1.
At the back hetero-interface, defects are introduced using a 1 nm thick highly defective c-Si interfacial layer containing two Gaussian distributed density of states (DOS) [20]. The donor-like and the acceptor-like Gaussian distributions have their respective maximum at 0.56 eV and 0.76 eV above the valence band (E v ). Both distributions have a standard deviation of 0.2 eV and have electron and holes capture cross-sections (σ e , σ h ) of 1 × 10 −14 cm −2 . Their heights are adjusted to yield targeted equivalent interface defect densities (cm −2 ).
Regarding the carrier transport mechanism, we consider drift-diffusion for homo-interfaces (c-Si/c-Si) and thermionic emission with tunneling for hetero-interfaces (c-Si/a-Si:H).   Bandgap narrowing due to the high doping level of the added a-Si layer is considered. The electrical current through the interface between the two semiconductors is actually the current that would flow through a fictitious insulator layer by tunneling in this simulation using AFROS-HET software. The conduction mechanism in the simulated structure is hole tunneling from the valence band of the base p-type c-Si through the Al 2 O 3 layer, and into the p + a-Si:H layer. The effective mass of bulk Al 2 O 3 is 3-10 m 0 , while an effective mass of 0.33 m 0 has been found for tunnel thin layers [21]. So the input effective mass of Al 2 O 3 is set to 0.33 m 0 . Bulk Al 2 O 3 has a bandgap of about 8.8 eV in the crystalline phase. For amorphous Al 2 O 3 deposited by atomic layer deposition, 6.4 eV is reported [22]. This has been used unless stated otherwise. The dielectric constant and electron affinity values of the ultrathin Al 2 O 3 layer are set according to the results reported in the literature [22].

Results and Discussion
Along with the introduction of Aluminum oxide (Al 2 O 3 ) comes the introduction of atomic layer deposition (ALD) in the photovoltaic industry. ALD differs from conventional (plasma-enhanced) chemical vapor deposition methods by the strict separation of the precursor gases in two half-cycles during deposition, leading to a self-limiting layer-by-layer growth. The virtue of ALD is precise thickness control and very uniform and conformal deposition over large area surfaces. Generally speaking, the excellent passivation performance of ALD Al 2 O 3 originates from the combination of low D it (chemical passivation) and high Q it (field-effect passivation) [23]. The as-deposited thermal ALD Al 2 O 3 usually possesses a relatively low D it accompanied with a low value of Q it while the as-deposited plasma ALD provides high D it and high Q it . After annealing treatment, both ALD processes result in low D it ≤ 1 × 10 11 cm -2 [24,25]. Regarding the field-effect passivation, the thermal ALD Al 2 O 3 film exhibits very low Q it of the order of 10 11 cm −2 before annealing in contrast to plasma ALD with Q it of the order of 10 12 cm −2 . In addition, Also the highest Q it value for plasma ALD can reach 10 13 cm -2 [26][27][28] after annealing. Therefore, for ALD Al 2 O 3 film, Q it can be adjusted from 1 × 10 10~1 0 13 cm −2 by choosing different ALD processes and post-annealing treatment. To investigate the influence of Q it at p-type c-Si/ALD Al 2 O 3 interface on simulated a-PC-p cell's output parameters, Q it is adjusted from 1 × 10 10~1 0 13 cm −2 with D it fixed at 10 11 cm −2 . Figure 2 presents the simulated a-PC-p cell's Fig. 3 Influence of Al 2 O 3 thickness on simulated PC cell's output parameters. Bandgap, interface charges and interface defect density were fixed at 6.4 eV, −10 13 cm −2 and 10 11 cm −2 , respectively output parameters versus Q it . It is seen that the cell's performance is enhanced with increasing Q it from 10 10 cm −2 to 10 13 cm −2 . In the low Q it (< 10 12 cm −2 ) region, the amount of Q it is not enough to assist hole tunneling through the Al 2 O 3 layer, as a result of which low J sc and low FF appear. When Q it increases from 10 12 cm −2 to 10 13 cm −2 , J sc and efficiency increase while FF rarely changes. Therefore, it is suspected that enough amount of Q it can ensure the tunneling process even though a dielectric layer is used. This is consistent with the result reported in the literature [28].
As the ALD Al 2 O 3 layer thickness can influence the tunneling of carriers, various levels of Al 2 O 3 layer thickness are adopted to study its effect on simulated a-PC-p cell's output parameters (shown in Fig. 3). In order to understand how Q it affects the Al 2 O 3 layer of different thicknesses, Al 2 O 3 layers of various thicknesses with and without Q it are introduced (shown in Fig. 3). For the Al 2 O 3 layer without Q it , the cell's FF decreases rapidly from 80.89% to 49.33% with Al 2 O 3 thickness increasing from 0.2 nm to 0.4 nm. And FF, J sc and efficiency are reduced to 40.66%, 0.32 mA/cm −2 and 0.087%, respectively, when Al 2 O 3 thickness further increases to 1 nm. However, for the Al 2 O 3 layer with −10 13 cm −2 Q it , both FF and efficiency of the cell rarely change even when increasing Al 2 O 3 thickness to 1 nm. This demonstrates the vital role Q it plays in carrier tunneling. When Al 2 O 3 thickness exceeds 1 nm, the cell with −10 13 cm −2 Q it loses its J sc and efficiency rapidly, while its FF still rarely changes. Theoretically, the thicker an Al 2 O 3 layer is, the lower the tunneling probability (T(E)) for carriers will be. Therefore, a thinner Al 2 O 3 is desired for a high tunneling current. Besides, the added Q it facilitates the alignment of the energy bands for both c-Si and a-Si, and causes the accumulation of holes at their interface, which results in a higher built-in potential. Therefore, the enhanced built-in potential facilitates the tunneling of holes through the barrier.
According to the simulated results shown in Fig. 2 and Fig. 3, Q it at the c-Si/a-Si interface have a significant influence on carrier transport through the Al 2 O 3 dielectric layer. Q it can obviously maintain the successful tunneling of carriers without degrading the cell's performance. To figure out how Q it influences the transport of carriers through the Al 2 O 3 dielectric layer, band diagram and carrier distribution with the position of two different cells are calculated and compared. The Al 2 O 3 dielectric layer thickness for both cells is fixed at 1 nm. The only difference between the two cells is that one cell has a Q it of −10 13 cm −2 , while the other has a Q it of 0 cm −2 . As shown in Fig. 4 (a) and (b), the band diagram of the cell with a Q it of −10 13 cm −2 bends upward compared to the other cell, indicating (d) schematic band diagram illustrating how the charged Al 2 O 3 layer affecting the transport behavior of electrons and holes that the high Q it leads to an accumulation of holes at the interface. Figure 4 (c) shows the density of electron and hole at the c-Si/a-Si interface, a large number of holes with an order of 10 13 cm −3 accumulated on the c-Si side accompanied by a smaller amount of electrons for the cell with a Q it of 10 13 cm −2 . Cell with a Q it of 0 only has a much smaller amount of electrons and holes on the c-Si side. This reveals the fact that Q it can influence the carrier distribution at the c-Si/a-Si interface and thus the selective transport of carriers through the dielectric layer. Based on the above three figures, a schematic band diagram illustrating how the charged Al 2 O 3 layer affecting the transport behavior of electrons and holes is shown in Fig. 4  (d). As can be seen, the charged Al 2 O 3 layer behaves like a filter which can allow the transport of holes through it with repelling electrons backward.
The oxide bandgap (E g ) can also affect the magnitude of the effect caused by the charges. A difference in the bandgap of Al 2 O 3 has been found for different deposition methods, with variations from 6.2 eV to 7.0 eV found in the literature [29,30]. In Fig. 5, the simulated a-PC-p cell's four output parameters as a function of the Al 2 O 3 bandgap are shown for Q if value of −10 13 cm −2 . The cell's efficiency is mainly influenced by the change of J sc and FF. When E g is less than 6.7 eV, the decrease of efficiency along with increasing E g is due to the decrease of FF. However, when E g is bigger than 6.7 eV, the loss of efficiency is mostly determined by the decrease of J sc . It is expected that the barrier height at the c-Si/a-Si interface can be modeled by choosing the Al 2 O 3 layer of different E g . Therefore, selecting a bigger E g Al 2 O 3 layer means higher barrier height at the c-Si/a-Si interface, which results in a relatively low tunneling probability, and thus a low FF and a low J sc .
We know that the interface defect density (D it ) has a great influence on c-Si/a-Si interface recombination. The distribution of D it at the c-Si/a-Si interface is a superposition of states near band edges and states symmetrically distributing about a minimum near mid-gap. These states are surface pretreatment induced strain bonds, dangling bonds, bonds between adsorbates, and silicon surface atoms of different oxidation leading to several groups of interface states. The minimum value of these interface state distributions can be taken as a measure of the electronic quality of the wafer interface. Figure 6 shows the dependence of simulated a-PC-p cells' output parameters on D it . As can be seen, the output parameters of a-PC-p cells, whether with or without the charged Al 2 O 3 layer, tend to decrease with increasing D it . When D it is less than 1 × 10 13 cm −2 , the a-PC-p cell with charged Al 2 O 3 layer possesses a higher efficiency than that without charged Al 2 O 3 layer. However, the tendency operates in the opposite way when D it is over 1 × 10 13 cm −2 , indicating that the D it can have different effects on cell efficiency for different cells in different D it regions. As is known to all, D it at the a-Si/c-Si interface is more than 1 × 10 13 cm −2 and the Al 2 O 3 layer can supply a certain extent of interface passivation. Therefore, the a-PC-p cell's efficiency can be improved by inserting charged Al 2 O 3 at the a-Si/c-Si interface. Compared with directly deposited a-Si on the c-Si surface, the presence of the charged Al 2 O 3 can reduce D it and thus higher efficiency can be obtained. Figure 7 (a) shows a comparison of the I-V characteristics of a simulated cell with only a-Si and with a-Si plus Al 2 O 3 at c-Si/p + a-Si interface, assuming a fixed interface charge density (Q it ) of -1 × 10 13 cm −2 . The simulation shows that there is a large efficiency gain (4.2% relative) when changing from a pure a-Si to a-Si plus Al 2 O 3 (Q it = −1 × 10 13 cm −2 ) at the c-Si/ Al interface. Notably, there is a change of the I-V parameters of the solar cells, i.e., not only an improvement in V oc and J sc , but also a reduction in FF (see in the inset table in Fig. 7 (a)). V oc is improved by reducing the interface recombination within the hole collecting region. Compared with pure p + a-Si, the addition of a charged Al 2 O 3 layer can reduce a partial portion of D it by saturating some dangling bonds at the c-Si/p + a-Si interface (D it is reduced from 10 13 cm −2 to 10 11 cm −2 ). A relative J sc boost of 5.4% is observed for the cell with the Al 2 O 3 layer. Comparing the spectral response of simulated cell with only a-Si and with a-Si plus Al 2 O 3 at c-Si/p + a-Si interface, it is seen that the external quantum efficiency (EQE) increase from 800 nm to 1100 nm (seen in Fig. 7 (b)), which is the absorption region of the backside. Below 800 nm, the spectral response is almost the same. In the wavelength region from 800 nm to 1000 nm, EQE increases. As the front side is the same for both cells, the change of EQE between 800~1 000 nm must be due to the insertion of the Al 2 O 3 layer at the c-Si/p + a-Si interface. It is expected as light in this region is mostly absorbed in the 180 μm thick p-type base, Q it increases built-in potential at c-Si/p + a-Si interface which ultimately boosts the number of holes collected at the cell's backside. This can mostly stem from the enhanced interface passivation effect due to the Al 2 O 3 layer. Though a relative FF decrease of  3.0% occurs, which may be due to the insertion of 1 nm Al 2 O 3 layer, a high FF still maintains in comparison to the Al 2 O 3 layer without Q it (as discussed in Fig. 3). As discussed before, the cell with the Al 2 O 3 layer and Q it has a higher built-in potential, and thus enhances hole collection which leads to a relatively high FF.
To evaluate the device performance under various temperatures, the temperature response of the a-PC-p cells with and without charged Al 2 O 3 layer is shown in Fig. 8, where the efficiency can also represent the maximum output power. The temperature dependences of V oc , J sc , FF and efficiency are illustrated by Fig. 8 (a)-(d), respectively. As the temperature increases from 26.85°C to 76.85°C, J sc is enhanced; whereas both of V oc and efficiency drop; FF fluctuates as the temperature changes. Based on the simulated results, a linear fitting is adopted to calculate the temperature coefficients of V oc , J sc , FF and efficiency, respectively. The obtained temperature coefficients for both cells are listed in Table 2. As can be seen, the insertion of a charged Al 2 O 3 layer obviously drops the P max temperature coefficient from −0.336% /°C to −0.247% /°C, indicating that the output power degrades less with increasing working temperature. Simultaneously, the V oc temperature coefficient also drops for the better interface passivation of charged Al 2 O 3 layer. The above results demonstrated a better temperature response for the a-PC-p cell with a charged Al 2 O 3 layer, paving a road for its potential application in highefficiency and high thermal stability a-PC-p solar cells.

Conclusions
In this study, we theoretically investigate the charged Al 2 O 3 film as an assisting passivation layer in improving the performance of the p-type silicon-based a-Si passivated contact solar cell (Ag/n + c-Si/p c-Si/Al 2 O 3 / p + a-Si/Al structure). The purpose of the charged  Al 2 O 3 tunnel film is to realize the accumulation of holes and simultaneously to enhance the c-Si/a-Si interface passivation, which facilitates the tunneling of holes through the Al 2 O 3 insulator layer and the reduction of interface defect density (D it ) respectively. Through the systematic optimization of interface negative charges (Q it ) between a-Si and c-Si, Al 2 O 3 thickness, Al 2 O 3 bandgap, and interface defect density (D it ) at a-Si/c-Si interface, a + 4.2% relative efficiency gain is predicted theoretically compared with the a-PC-p cell without Al 2 O 3 layer. Based on the temperature-dependent investigation of output parameters of both a-PC-p cells, the decrease of the P max temperature coefficient from −0.336% /°C to −0.247% /°C is observed by the insertion of a charged Al 2 O 3 layer. The above results demonstrate the better performance of a-PC-p cell with a charged Al 2 O 3 layer, indicating its potential application in high-efficiency and high thermal stability a-PC-p solar cells.  Data Availability The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations
Research Involving Human Participants and/ or Animals Not applicable.
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Conflict of Interest
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.
The authors declare that they have no conflict of interest.