Absorption enhancement of GaInP nanowires by tailoring transparent shell thicknesses and its application in III-V nanowire/Si film two-junction solar cells

Xinhua Li; Tongfei Shi; Guangqiang Liu; Long Wen; BuKang Zhou; Yuqi Wang

doi:10.1364/OE.23.025316

1. Introduction

Due to their potential to realize low cost and high energy conversion efficiency solar cells, semiconductor nanowire array (NWA) is a topic of intense research for photovoltaic applications [1,2 ]. Compared to conventional solar cells, the integration of NWAs to photovoltaic (PV) applications has many advantages. By combining its intrinsic anti-reflection and efficient absorption enhancement, NWA can achieve near perfect light absorption with reduced material usage [3]. Meanwhile, many kinds of semiconductor NWA have been experimentally integrated onto low-cost substrates, which can substantially reduce the final cost of cell fabrication [4,5 ]. More interestingly, the nanowire (NW) configuration allows the pn junction of the photovoltaic cell to be arranged in the radial direction. Therefore, each individual pn junction wire in the cell is long in the direction of the incident light, allowing for maximum light absorption, but thin in the orthogonal direction, thereby allowing for effective carrier collection [6].

In view of the advantages aforementioned, recently, many efforts have been made on fabricating NWA solar cell based on axial and radial single pn NW junction [7–9 ]. Meanwhile, considering the fact that many kinds of III-V NWAs have been successfully prepared on hetero-substrates(such as Si) [4,5 ], the concept of multi-junction solar cell can also be used in the design of photovoltaic devices. Due to NWA structures having a high tolerance of lattice mismatch, more material choices are enabled in the design of multi-junction solar cells based on NWA structures. Recently, a two-junction cell comprised of a III-V NWA on an active Si substrate was theoretically demonstrated to have the photovoltaic performances comparable to thin-film multi-junction cells [10–13 ]. However, from the reported optical simulation results, it is evident that either a high filling ratio or a large height for the NWA is required to maintain high absorption [12,13 ]. This causes more consumption of earth's scarce materials (especially group III source elements). In addition, the absorption of the NWA depends strongly on its’ geometry [11,13 ]. Hence, precise geometry control on the NWA is needed to balance the absorption of the top NWA and bottom active Si substrate. These factors increase the complexity and manufacturing price of PV fabrication. To seek future technology pathways for high efficiency and low-cost multi-junction solar cells, further optical-and electrical optimization is still needed, to aim for high tunable absorption [14] and less consumption of source materials.

In this paper, to find a low-cost but effective way to adjust the absorption in III-V NWA, a non-absorbing transparent layer is proposed to be coated onto the outer surface of the photoactive NWA. First, the influence of the thickness of the coating layer on the optical absorption of the NWA was thoroughly analyzed by using finite-difference time-domain (FDTD) simulations. Second, to find an optimized geometry, the ultimate photocurrents were calculated to maximize the light absorption capability of the III-V NWA/Si two-junction solar cells in the solar spectrum. The maximum detailed balance efficiencies of the III-V NWA/Si two-junction solar cell were then obtained by considering the current matching between two sub cells. Finally, in order to investigate the electrical properties of the solar cells, the photo-generated rates of the two-junction cell under optimized coating conditions were incorporated into the electrical simulation. The effects of the transparent shell on the electrical properties of the two-junction cell are discussed.

2. Methods

The structural morphology of the investigated two-junction solar cell distributed in a square geometrical configuration is presented in Fig. 1(a) . An active Si substrate with the thickness of 500μm is used as the bottom cell of the proposed two-junction solar cell, on which surface oxide is coated. In this simulation, we set the thickness of surface oxide on Si substrate at 10nm, which is an optimized condition for the real experimental growth of III–V NWs to obtain near 100% vertical yields [15]. From the iso-efficiency curves reported by Bosi et al, a two-junction cell with optimum efficiency of 38.8% (1 Sun, AM1.5 G) consists of a bottom bandgap close to that of Si (1.12 eV) and a top bandgap near 1.7 eV. Hence, we chose Ga_0.35In_0.65P (E_g = 1.7eV, λ_g = 729.5nm) as the top cell to form dual-junction solar cell with the bottom Silicon cell [16]. As shown in Fig. 1(a), GaInP NWAs are vertically arranged on the bottom Si substrates. On the side faces of the GaInP NWA, a non-absorbing transparent layer is uniformly coated. Recently, Czaban et al. have reported a GaAs NW/SiO₂ coating structure fabricated by the transparent coating deposition and top coating removal process [17]. Their processing route can also be used to obtain the core-shell structure we proposed. The complex refractive indices used to describe the optical property of materials (i.e. SiO₂, GaInP, MgF₂, Si₃N₄) used in this simulation are taken from the Ioffe n&k Database [18]. The parameters of the structure are the period of the square lattice P, the filling ratio D/P and the transparent coating thickness T. In our previous published paper, we selected a geometry of diameter (D) of GaInP NW = 100nm, length (L) of GaInP NW = 2 µm, D/P = 0.5 for the NWA by considering the optimization of light absorption and the ease of devices’ fabrication. This setting enables the top subcell to achieve near perfect light absorption and produces a high and closely matched photocurrent [12]. Previously, it has been demonstrated by N Anttu that the absorption in III-V NWAs can be optimized by increasing D until the resonant absorption through the HE₁₁ mode red-shifts to close to the bandgap wavelength of the III-V nanowire material [14]. One can obtain a rough approximation for the resonance condition by using π(D/2)n_NW2π/λ = 2πm, where m = 1 corresponds to the resonant absorption condition of the HE₁₁ waveguide resonance [19,20 ]. For the bare GaInP NW, D≈132nm correspond to optimized diameter, which can cause the resonant peak near the bandgap wavelength of GaInP. However, for GaInP/SiO₂ core-shell structure, the transparent shell increases the total diameter of the NW. Hence, to make the resonant peak near the bandgap wavelength of GaInP, the diameter of core GaInP NW must be less than 132nm. Meanwhile, to make the simulated results comparable to our previous published result, we fixed D and L of GaInP NWs to 100nm and 2µm and simulate the optical absorption property of NWA by varying D/P. It should be noted that the D/P mentioned in this paper refers to the ratio of GaInP NW’s D to the period of lattice P. By placing periodic boundary conditions, the three-dimensional optical simulations were carried out in a unit cell to model the periodic square-array by using the software package FDTD SOLUTIONS (Lumerical, Inc.). The two-dimensional modal analyses of NWA with core shell structure were performed with the MODE Solutions software package (Lumerical Solutions, Inc.) Three types of physical quantities: the mode profile, coupling efficiency and effective index were computed to characterize the supported Bloch modes. The device behaviors of the proposed two-junction solar cell under AM1.5G illumination (ASTM G-173-03) [21] were simulated by the Sentaurus device physics simulator, a package of the TCAD software suite (Synopsys, Inc). The terminal current-voltage characteristics of the two-junction cell after the addition of non-absorbing transparent layer were emphatically investigated.

Fig. 1 (a) The schematic diagram and simulated unit of core-shell GaInP/SiO₂ NWA/Si film two-junction solar cell modeled in this study. (b)Absorption (c)Reflection (d)Transmission of GaInP NWA (D/P = 0.2) with various SiO₂ coating thicknesses.(e) optical absorption properties of GaInP NWA coated with transparent dielectric materials (MgF₂, Si₃N₄) and transparent conductive oxide (Indium tin oxide, ITO), the coating thicknesses are set at 70nm.

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3. Results and discussion

To investigate the effects of the transparent coating on the optical properties of the top GaInP NWA, we select SiO₂ coating, which is a typical transparent dielectric layer and simulate the absorption, reflection, transmission of NWA by varying the SiO₂ coating thickness. For the uncoated GaInP NW, the absorption remains at a high value above 0.8, when the incident wavelength is less than 380nm. As the incident wavelength is increased to around 425nm, an absorption dip (marked as A in Fig. 1(b)) could be observed from the absorption curve. Above 425nm, the absorption is increased gradually to a peak value of near unit, when the incident wavelengths rise to a critical wavelength of 525nm (marked as B in Fig. 1(b)). Then, the absorption of NWA decrease gradually back to zero as the incident light wavelength is increased to the absorption edge of the GaInP semiconductor. For the GaInP NWA/ SiO₂ coating system, from Fig. 1(b), the absorption dip gradually becomes shallow, and the dip position A shifts from 425nm to a longer wavelength of 530nm, as the SiO₂ coating thickness is increased to 70nm. Another feature noticeable in the absorption spectra is that the critical wavelength B also undergoes a red shift to longer wavelengths with the increasing of SiO₂ coating thickness. Besides the redshift of dip position A and critical wavelength B, the overall absorption increase substantially as the thickness of shell is increased to 70nm, which is attributed mainly to the reduction of transmission and reflection. The absorption enhancement can be attributed to the weakness of However, further increasing the coating thickness to 90nm will cause decrease of absorption, due to enhanced reflectance (<380nm, Fig. 1(c)) and transmission (>580nm, Fig. 1(d)). Besides SiO₂, we also compare the optical properties of GaInP NWA coated with other typical transparent dielectric materials (MgF₂, Si₃N₄) and transparent conductive oxide (indium tin oxide, ITO) with their refractive index ranging from 1.3 to 2.2 [18]. As shown in Fig. 1(e), similar absorption enhancement could be observed for NWs coated with these transparent layers.

In order to understand the propagation of light in the NWA/transparent shell systems, the electrical field distributions in the uncoated GaInP NWA and GaInP NWA coated with 30nm SiO₂ shell at three typical wavelengths were simulated. As plotted in Fig. 2(a) , at the wavelength of 450nm, the incident light is concentrated to several lobes in the uncoated GaInP NWA, with small amounts reaching the Si substrate. At the incident wavelength of 550nm, the incident light is concentrated near the top and sides of the NW. The electrical field intensity has almost approached zero before reaching the Si substrate. At the longer wavelength of 650nm, when the incident photon energy is close to the optical bandgap of the GaInP, the incident light is strongly distributed within the area between NWs, with small amounts of the electrical field confined within the photo-active GaInP NW. When the 30nm SiO₂ shell is coated, obvious reduction in the electric field intensity (especially for 450 and 650nm) could be observed above the top of NWA. This implies the reflection of GaInP NWA/ SiO₂ system is reduced, which stems mainly from the improved optical impedance matching between air and NW due to the presence of an additional low-index coating layer. Meanwhile, at the aforementioned wavelengths, as the 30nm SiO₂ shell is coated, more intensive photo-excited electric fields are concentrated in the photoactive GaInP NWs. The effect of the transparent coating on the absorption of core GaInP NW can be intuitively understood by the electrostatic approximation [19,20 ]. As proposed by N Anttu et al., the incident electric field intensity is screened from the interior of the NW by the factor of |E_core /E_inc| ² = |2ε_ext /(ε_ext + ε _core)| ² [20]. For bare GaInP NW, this factor is equal to 0.0178 at the incident wavelength of 650nm, by taking the dielectric function of the vacuum exterior to the NW as ε_ext = 1 and the dielectric function of GaInP NW ε _core≈13.96 + 1.04i. Because the absorption is proportional to |E_core|², the absorption in bare GaInP NW is limited, due to the strong electrostatic screening caused by the high refractive index of the NWs [19]. Comparatively, when the SiO₂ shell with dielectric function value between the vacuum and GaInP semiconductor (the exterior ε _coat = 2.13) is considered, |E_core/E_inc|² = |2ε_ext/(ε_ext + ε_coat)|²|2ε_coat /(ε_coat + ε_core)|² = 0.027. Hence, by introducing a dielectric function with a value between that of the GaInP and the vacuum exterior, the electrostatic screening of the incident electric field from the interior of GaInP NW can be weakened. To quantitatively study the absorption enhancement at the incident wavelength of 650nm, we calculated the average electric field <|E_xy|²> in the x-y cross section of GaInP NW as a function of axial position along the NW axis. As shown in Fig. 2(b), the <|E_xy|²> for both uncoated NW and NW with a 30nm SiO₂ coating were obtained. The mean value of the electric field inside the uncoated NWs was <|E_xy|²> = 0.291 (calculated as the average of <|E_xy|²> over Z). For the NWs with a 30 nm thick coating, <|E_xy|²> = 0.649. Hence, the 30nm SiO₂ coating causes a 2.23 times larger <|E_xy|²> inside the GaInP NW, which coincides well with the absorption enhancement (2.23 times) at this wavelength as shown in Fig. 1(b). Obviously, below the absorption cutoff of the GaInP NWA, the SiO₂ coating can serve as a non-absorbing dielectric shell, which drastically reduces the reflection and increases the absorption of the vertical semiconductor NWs.

Fig. 2 (a) The electrical field intensity distribution in uncoated GaInP NWA and GaInP NWA coated with 30nm SiO₂ shell at three typical wavelengths. (b) Average electric field <|E_xy|²> in the x-y cross section of GaInP NW as a function of axial position (Z, where the bottom of the NW was set as the zero point and the top of the NW as −2μm) of the NW (<|E_xy|²> was normalized to the maximum value in the NW with 30nm SiO₂ coating shell).

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To understand the underlying mechanism responsible for the special light absorption features of GaInP NW(absorption dip and cutoff and their redshifts with the increasing of SiO₂ coating thickness), a two-dimensional modal analysis of GaInP NWA was carried out to obtain the mode profile and effective index of the supported Bloch modes. Meanwhile, the power coupling efficiency is determined to examine the absorption mechanism in detail. The power coupling efficiency is defined as the fraction of the power of the incident light coupled to the propagation mode of the optical system:

η_{i} = \frac{{| \iint φ_{s y s} (x, y) ϕ_{_{i}}^{*} (x, y) d x d y |}^{2}}{\iint φ_{s y s} (x, y) φ_{_{s y s}}^{*} (x, y) d x d y \iint φ_{i} (x, y) φ_{_{i}}^{*} (x, y) d x d y}

Where φ_sys is the optical electric field of the input light and φ_i is the electric field of the modes [22,23 ]. It has to be noted that in Eq. (1), the power coupling efficiency is not an exact projection of the powerflow onto the eigenmodes, because the optical modes in the nanowire array are not orthogonal in the power-flow projection [14].

Figures 3(a) and 3(b) show the coupling efficiency evolution of the fundamental mode and the key mode. In this study, we find that the two absorbing modes have at least an order of magnitude stronger coupling than that of all other modes and herein dominate the absorption of the GaInP NW. At short wavelengths, the coupling efficiency of the fundamental mode is low, which implies the poor spatial overlap of this mode with normal incident plane wave. The key mode on the other hand has a much more efficient coupling because of the good impedance match between the mode and free space background. At longer wavelengths, these two modes evolve in distinctive ways. Beyond a critical wavelength of 525nm, with the modal field concentrated in both NWs and air between, the fundamental mode has a good coupling with the plane waves and herein dominates the absorption (Fig. 3(c)). Comparatively, above the critical wavelength, the key mode cannot be efficiently excited, resulting in poor coupling efficiency of this mode with the incident light. As the SiO₂ coating is added, more intense fields are concentrated in the photoactive inner GaInP NW (Fig. 3(d)). Since the absorption is proportional to the energy density in the photoactive material, it is therefore possible to obtain an efficient modal absorption when SiO₂ is coated onto the surface of the Si NW. It is interesting to note that the crossing points of the coupling efficiencies between the calculated two absorbing modes shift to 562nm for NWs coated with 30nm SiO₂. The shifts coincide with the redshifts of the critical absorption wavelength as shown in Fig. 1(b).

Fig. 3 (a)-(b) The relative power coupling efficiency of the fundamental mode and key mode for the GaInP NWA without coating and 30nm SiO₂ coating. (c)-(d) The electric field intensity distributions of the two modes at four selected wavelengths. (e)-(f) The absorption coefficient of the fundamental mode and key mode of the GaInP NWA with different coating thicknesses. (g) The contribution of the key mode (green solid line), fundamental mode (blue solid line) to the overall absorption, the absorption summed by the absorption of the two Bloch modes(black dotted line) and the FDTD simulation absorption (red dotted line) for the NWA with different SiO₂ thicknesses.

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Figures 3(e) and 3(f) show the absorption coefficient ( $α_{i} = \frac{4 π k_{i}}{λ}$ , $k_{i}$ is the imaginary part of the effective refractive index of the Bloch mode) of the fundamental mode and key mode as a function of coating thickness. For the key mode, the absorption coefficients exhibit a dip in the wavelength range from 350 to 750nm. It should be noted that, according to Beer’s law, when the absorption coefficient is above 2 × 10⁴ cm⁻¹, near unity light absorption (above 0.98) could be obtained by considering the length of the NWs of 2μm (grey area above the dashed line in Fig. 3(e) and 3(f)). Comparatively, the absorption coefficient of the fundamental mode decrease gradually when the wavelength increases.

To understand the absorption behavior of the NW quantitatively, the absorption of the NWA Bloch modes with different SiO2 thicknesses is computed by:

A = \sum_{i = 1, 2} η_{i} (1 - e^{- α_{i} L})

Where η_i is the coupling efficiency of the supported mode,

α_{i}

is the absorption coefficient of the supported Bloch mode and L the length of NW (2μm) [22]. Fig. 3(g) shows the calculated modal absorption of GaInP NWA at different coating thicknesses. At the shorter wavelength region, the key mode has much larger coupling efficiency (as illustrated in Fig. 3(a) and 3(b)) and dominates the absorption, so that the absorption spectrum (Fig. 1(b)) of the NWA essentially follows the key mode’s absorption character. Near the critical wavelength, these two supported modes have comparable coupling efficiency and both contribute with a significant amount to the overall absorption of NWs. Above the critical wavelength, the couplings of incident lights in the fundamental mode become predominant and herein the overall absorption drops gradually. From Fig. 3(g), one can find good coincidences (dip A and cutoff positions B and their redshifts with the increasing of SiO₂ coating thickness) are obtained between the modal analysis method and the 3D FDTD simulation absorption. Similar absorption enhancements and redshift of absorption cutoff wavelengths have also been reported in InP NW coated with Al₂O₃ shell [20]. As observed by N. Anttu et al. [20], an resonant excitation of the HE₁₁ waveguide mode causes substantial increase of absorption in InP NW. Meanwhile, the resonance wavelength of the HE₁₁ waveguide mode exhibits a redshift with the thickness of Al₂O₃ coating [20]. From Fig. 3 (g), one can also observe small variations between the absorption calculated by FDTD and the summed modal absorption. One reason for this discrepancy could be the phase difference between the propagating modes, which is not considered in Eq. (2) [24, 25 ]. Another possible reason could be the interaction between the forward propagating Bloch modes, the absorption is dependent on |E|² and this term gives cross-terms between the fundamental and key mode [14]. Such cross-terms are not taken into account in Eq. (2). Furthermore, the backward propagating Bloch modes after reflection of light at the NWA/Si interface can interfere with the original forward propagating modes [14]. Such reflected back-ward propagating modes can give rise to additional cross-terms which gives rise to z-dependence beyond the simple exponential dependence shown in Eq. (2). These factors can cause the modal absorption summed by Eq. (2) deviate from the absorption calculated by FDTD.

From the above discussion, it is clear that the light absorption of the NWA/ transparent coating structure is quite sensitive to structural parameters. To significantly enhance absorption of the NWA, the thickness of the transparent coating must be optimized. In addition, in the design of a two-junctional cell, the current density is limited to the smallest current generated in each subcell, since the NW and Si sub-cells are connected electrically in series. Hence, to obtain the maximum power conversion efficiency, the absorption of the solar spectrum in each sub cell must be rationally assigned to achieve the current matching. To determine the optimized geometric configuration, we calculate the ultimate photocurrent by assuming that all photo-generated carriers can contribute to the photocurrent:

J_{p h} = \frac{e}{h c} \int λ A (λ) I (λ) d λ .

where e is the elementary charge, h is the Plank’s constant, c is the speed of light, I(λ) is the AM1.5G spectrum, and A(λ) is the absorption in top NWA cell and bottom Si sub cell separately [26,27 ]. For top NWA subcell, A(λ) is the absorption of GaInP NW/ SiO₂ structure calculated by FDTD simulation. The ultimate photocurrents as function of the coating thickness and filling ratio of NWA are shown in Fig. 4(a) . At D/P = 0.25 and coating thickness of 70nm, the ultimate photocurrent reaches a maximum of 19.5 mA/cm², which is about 28.2% higher than that for bare GaInP NWs (15.2 mA/cm²) with the same diameter and filling ratio. Furthermore, this photocurrent is 1.2 mA/cm² higher than that of bare NWs with high D/P of 0.5, which was proved to have an optimized absorption at this NW’s D and L [12]. Obviously, a much improved light absorption could be obtained, when SiO₂ shell with an appropriate thickness is coated onto the GaInP NWs. When the incident wavelength is above 1030nm, the absorption length of Si material is greater than the thickness of the bottom Si cell(500μm). This implies the incident light with its wavelength above 1030nm can go through the bottom Si cell and cause absorption loss. To take into account the finite absorption ability of the bottom Si cell, we calculated the absorption of the bottom Si cell by:

A_{S i} (λ) = T (λ) {1 - \exp [- α_{S i} (λ) Z]}

where T(λ) is the 3D FDTD simulated transmission of NWA obtained above,

α_{S i}

is the absorption coefficient of Si and the term

\exp [- α_{S i} (λ) Z]

is referred to as the transmission loss from an effective optical length Z of Si thin film. It has to be noted that, the periodic NWA on the top of the bottom Si cell can act as a diffraction grating: the propagation of light is not strictly that of a plane wave in the Si substrate. As compared with the normally incident plane wave, the diffracted orders show a larger absorption coefficient and cause the absorption enhancement in the bottom Si cell. Hence, the photocurrent calculated by Eq. (4) can be taken as a lower limit for the absorption in the bottom Si cell. From Eq. (3), one can obtain the photocurrents of the bottom cell vary between 18.1 to 22.6 mA/cm². With a geometry of D/P = 0.3 and T = 70nm, the integrated absorption from the NWA and the Si sub-cell each produces a photocurrent of 19.0 mA/ cm², corresponding to the current matched condition. It is very interesting to note that, stemmed from the low reflection of this NWA/SiO₂ coating structure, the overall photocurrent of the two-junction NWA/Si solar cell at the current matching geometry can reach 38 mA/cm², which corresponds to absorb 95% incident light in solar spectral range between 300 and 1100nm. This photocurrent is much higher than the calculated photocurrents (18.3 mA/ cm²) in our previous reports, where the uncoated GaInP NWs with the same diameter but much higher filling factor(0.5) are suggested to maintain high absorption of incident solar light [12]. Our results indicate that diluted GaInP NW with proper choice of SiO₂ coating thickness can absorb more light than that for bare high density NWA. This causes less raw material consumption in cell fabrication. In addition, another important feature can be obtained from Fig. 4(a) is that, at a fixed geometry of the photoactive GaInP NW(D/P, H), the photocurrent in top NWA can be adjusted through changing the SiO₂ coating thickness(for example, from 13.8 to 19.1 mA/cm² at D/P of 0.3). Hence, in the design of a two-junction cell, the condition of current matching in III-V NWs/Si multi-junction can be fulfilled by adjusting the coating thickness. Such an optimization process for current matching differs much from our previous reported results for III-V NWs/Si solar cells, in which precise NWA geometry control is needed for the design of this type of series-connected photovoltaic devices [12]. From the published results of NW growth, to precisely control NWA’s geometry, complicated growth parameters’ monitor is required [20,28 ]. Comparatively, it is much easier to obtain the SiO₂ coating preparation by secondary processing technology, such as evaporation, sputtering et al. [17]. This can help reduce the complexity and manufacturing price of III-V NWs/Si solar cell fabrication. To gain more direct insight into the photovoltaic conversion ability of the proposed two-junction cell, we further evaluate the detailed balance efficiency at different NWA geometries. We use the J-V characteristic of an ideal diode to describe the electrical properties of each subcell:

V_{i} (J) = \frac{k_{B} T}{q} \ln [\frac{(J_{p h, i} - J)}{J_{0, i}} + 1] i = 1, 2

where

J_{p h, i}

is the ultimate photocurrent related to the light absorption of each sub cell,

J_{0, i}

is the reverse saturation current density [11]. In this study,

J_{0, i}

is calculated by assuming that the only loss process in the dark is the radiative relaxation of electrons through spontaneous emission, which is in detailed balance with the absorption of ambient blackbody radiation at room temperature [11].

J_{0, i} = \frac{2 π e}{h^{3} c^{2}} \int_{E_{g, i}}^{\infty} \frac{E^{2}}{\exp (\frac{E}{k_{B} T})} d E

Considering that two-junction solar cells are connected in series, the total J-V curve can be obtained from

Fig. 4 (a)The ultimate photocurrents of the top GaInP NWA sub cell (yellow curve) and bottom Si sub cell (red curve). (b) The detailed balance efficiencies of GaInP NWA/Si film two-junction cell with different NW geometry.

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V_{t o t a l} (J) = V_{1} (J) + V_{2} (J)

The achieved detailed balance efficiencies under different NW’s geometries are shown in Fig. 4(b). The maximum efficiency limit (34.6%) is achieved at a filling factor of 0.3 and coating thickness of 70nm. This result is 7.1% higher than our previous reported detailed balance efficiency (32.3%) for the bare NWA(D/P = 0.5)/Si film two-junction solar cell [12]. Note that in our study, the emissivity of a perfectly absorbing bulk cell is used for calculating the reverse bias saturation current density of top NWA solar cell. However, as pointed out recently by N Anttu et al by the angular dependent emission calculation, the NWA solar cell emits fewer photons than the bulk cell at thermal equilibrium [29]. This weaker emission decreases the reverse bias saturation current density and allows for a higher V_oc for the NWA cell. Hence, for the top NWA solar cell, the reverse bias saturation current density obtained by Eq. (6) in this study can be taken as the upper limit of N Anttu et al’s results. Correspondingly, the achieved detailed balance efficiencies in Fig. 4(b) give only a lower limit to the efficiency of the proposed two-junction solar cell.

Based on the above analyses, one can find that a transparent shell with proper thickness can improve optical absorption and herein facilitate the detailed balance efficiency enhancement of the proposed cell. In this paragraph, we will focus on discussing the effect of the transparent coating on the performance of the two-junction cell. In the electrical simulation, we propose a composite coating structure (Fig. 5(a) ), which is composed by an inner dielectric shell (Note that there is no dielectric coating on top of the NWs.) and an outer conductive ITO coating. The transparent dielectric materials (SiO₂) and transparent conductive oxide (ITO) have the refractive index ranging from 1.3 to 2.2, which lie between the refractive index of Si and air. These transparent coatings can cause absorption enhancement in the core GaInP NWs (Fig. 1(e)), when they are separately coated onto the outer surface of GaInP NW. Similar absorption enhancement (Fig. 5(b)) could also be observed, when these two transparent materials are combined into a composite coating. Meanwhile, in the design of photovoltaic devices, both the optical absorption and electrical properties (surface passivation of dielectric coating) must be taken into account. Amongst the materials studied, SiO₂ meets the aforementioned criterion. Hence, in this study, we selected SiO₂ as the inner coating layer of the NWs. The proposed NWA/Si tandem two-junction cell with its structure more feasible for actual fabrication is shown in Fig. 5(a). The tunnel diode connecting the top GaInP NWA and bottom Si cell was assumed to be perfect (i.e., resistive or optical absorption losses were neglected). To calculate the terminal current-voltage characteristics of the solar cell, optical generation profiles are firstly calculated from optical simulations then incorporated into the electrical tool. The optical generation rates, $G_{opt}$ , are obtained from the divergence of the Poynting vector:

G_{opt} = \frac{r e a l (\nabla • S)}{2 ℏ ω} = \frac{ε^{''} {| E |}^{2}}{2 ℏ}

where ε” is the imaginary part of the complex permittivity and E is the electric field. The AM1.5G spectrum is divided into 80 discrete wavelengths (10nm intervals), from 310 to 1100 nm. For the top GaInP NWA, three-dimensional optical generation under AM1.5G illumination can be modeled by superimposing the spectrally resolved single wavelength optical generation rates (weighted by the power in the solar spectrum) from FDTD simulation output. To obtain the 3D optical generation profiles in the top sub cell, FDTD simulation was performed on NWA with composite coating structure. The coating structure is composed by an inner SiO₂ dielectric shell and an outer conductive ITO coating. For the bottom Si cell, the two-dimensional optical generation is calculated by the Beer-Lambert absorption model. The current-voltage behaviors of each sub cell are calculated, using the drift diffusion carrier transport model. Note that in this simulation, photo-generated carriers are collected by ITO, which is in direct contact with GaInP at the top of NW. No tunneling of carriers through the SiO₂ shell is considered. Electrical simulation takes into account doping dependent mobility, Auger, radiative, and Shockley-Reed-Hall (SRH) recombination. Detailed electrical parameters used in the device performance simulation were listed in Table 1 . Considering the fact that the addition of transparent layer onto the outer surface of GaInP only changes the surface condition of the NWA, in this study, we focused on investigating the effects of surface recombination velocities (SRV) on the output characteristics of top NWA subcell.

Fig. 5 (a) Schematic diagram and optical generation rates in the proposed two-junction solar cell. (b) The variation of V_oc and J_sc with SRV. (c) The J-V characteristic of the bottom Si sub cell, top NWA sub cell and series connected two-junction cell at SRV = 2 × 10⁴ cm/s(after passivation).

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Table 1. Detailed parameters used in the device performance simulation

View Table

Figure 5(c) shows the variation of the open-circuit current (V_oc) and the short-circuit current (J_sc) with SRV. When SRV increases from 0 to 5 × 10⁶cm/s, J_sc decreases substantially from 18.88 to 14.15mA/cm². Compared with the cell with a perfect surface, about 25% of the photo-generated photocurrent is annihilated. Obviously, when the surfaces are not properly treated, a large amount of photo-generated carriers will recombine at the surface of the NWA. As expected, when J_sc decreases with the increase of SRV, the V_oc of the top NWA subcell drop correspondingly. Hence, in the top NWA solar cell, the surface recombination is responsible for the annihilation of minority carriers and determines the performance of the proposed NWA cell. A relative low SRV must be ensured to satisfy the current matching condition between the two series connected sub cells. Referred from the publication in III-V film, some compact dielectric material, including Si₃N₄, SiO₂, can be used as effective surface passivation layer to reduce surface defects density in III-V film. For GaInP, the SRV value as low as 2 × 10⁴ cm s⁻¹ can be obtained by careful sulphur and dielectric layer passivation [30]. Considering this, in this work, an ideal SRV(2 × 10⁴ cm s⁻¹) was selected and taken into electrical simulation of top NWA cell. The simulated J-V characteristics of the two-junction III-V GaInP NWA/Si thin film solar cell are shown in Fig. 5(d). As can be seen from Fig. 5(c), J_sc keep at a high value of 18.83mA/cm², which is close to the ultimate photocurrents. This implies most of the photo-generated carriers can be extracted and reach the electrode. Benefitting from optical absorption enhancement and surface passivation effect of dielectric layer(SRV = $2 \times 10^{4} cm \cdot s^{- 1}$ ), the net J-V characteristic yielded $J_{sc} = 18.72 mA \cdot {cm}^{- 2}$ , $V_{oc} = 1.88 V$ , $FF = 0.85$ and $η = 29.9 %$ .

4. Conclusion

In conclusion, a non-absorbing transparent coating is used to improve the efficiency of GaInP NWA/Si film solar cells. On the optical side, the addition of transparent coating layers allows for better light absorption in the GaInP NW. It is demonstrated the diluted GaInP NW with a proper choice of transparent coating thickness can absorb more light than that of a bare NWA. Therefore, more GaInP material is saved in the design of III-V NWA(uncoated)/Si film two-junctional cell. Furthermore, through adjusting the coating thickness of the SiO₂ coating in the top NWA sub cell, the condition of current matching between top III-V NWA and Si film sub cell can be easily fulfilled. From the detailed balance calculation, at an optimized size, the proposed III-V NWA/Si film two-junctional cell exhibits a promising detailed balancing efficiency of 34.6%. On the electrical side, some transparent dielectric coatings(Si₃N₄ or SiO₂, for example) can serve as a surface passivation layer of top GaInP NWA to reduce surface recombination. This can further ensure the stable and promising device performance of the proposed cell. Obviously, the combination of low-cost coating, easy adjustment of photocurrent in each sub cell makes this III-V NWA/Si film solar cell worthy of further investigation.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 51472247) and the Natural Science Foundation of Anhui province (Grant No.1308085MA10).

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	Parameter	Description	Values
GaInP NW	d	p-doped core diameter	60 nm
	D	n-doped shell diameter	100 nm
	L	NWs height	2µm
	P	period of the NWs unit	333nm
	μ_n	Electron mobility	480cm⁻²/vs
	μ_p	Hole mobility	22.5cm⁻²/vs
	SRV	NWs surface recombination velocity	from 0 to $5 \times 10^{6} cm \cdot s^{- 1}$
	$τ_{SRH}$	SRH recombination lifetime	10ns
SiO₂ shell		Thickness	60nm
ITO coating		Thickness	10nm
Si substrate		Thickness	400μm
	The doping profile of n-type emitter and p-type back surface field layer are modeled using a Gaussian function with a peak doping concentration of $2 \times 10^{19} {cm}^{- 3}$

Absorption enhancement of GaInP nanowires by tailoring transparent shell thicknesses and its application in III-V nanowire/Si film two-junction solar cells

Abstract

1. Introduction

2. Methods

3. Results and discussion

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (5)

Tables (1)

Equations (8)

Optics Express