1. INTRODUCTION

Nanowire (NW) antireflective coating has a significant effect in reducing the reflection of light; thus, it is especially important and widely used to improve the light trapping capability in the field of crystal silicon (CS) solar cells [1,2]. Several studies have reported that optical absorption performance of NW solar cells is greatly influenced by the NW geometric parameters, such as the NW diameter, length, arrays density, volume filling ratio, etc. [3 –6]. The optimal optical properties of NW solar cells can be obtained by reasonably modulating these parameters. Most of the studies have considered the NW antireflection coating and CS substrate as a whole and mainly focus on how to minimize the light reflection ($R$) and transmission ($T$) to increase the light absorption ($A$) by $A=1-R-T$. There is no doubt that the light trapping performance of CS solar cells is significantly enhanced after etching a NW antireflection layer, but it is often to neglect the difference of light absorption distribution between the NW antireflection layer ($A_{\mathrm{NW}}$) and CS body ($A_{\mathrm{Si}}$) where $A=A_{\mathrm{NW}}+A_{\mathrm{Si}}$, as shown in Fig. 1(a).

 

Fig. 1. (a) Distribution of light absorption ($A_{\mathrm{NW}}$ and $A_{\mathrm{Si}}$ are light absorption of antireflection layer and CS, respectively). (b) Structure diagram of NW arrays ($D$ is the NW diameter, $L$ is the period length, and $T$ is the thickness of CS). (c) Shapes of NW (I, cylindrical, $m=0$; II, parabolic truncated conical, $m=0.50$; III, convex conical, $m=1.0$; IV, conical, $m=2.0$; V, concave conical, $m=4.0$).

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In this paper, compared with the naked CS, the enhancement factor of efficient light trapping $E_T$ and effective light absorption $E_A$ are defined as follows:

2. SIMULATION METHODS

The net radiation method (NRM) [7,8] and effective medium approximation (EMA) [9,10] are used in our theoretical calculations. NRM is suitable for illustrating the transmission, absorption, and reflection characteristics of a multilayer medium for incident radiation based on its good matching between simulation and experimental results. As shown in Fig. 2(a), a system of $N$ layers, a, c and b, d represent the incoming and outgoing light radiation, respectively. The interfaces are labeled $i=1,\dots ,N-1$, where $i$ is the total number of interfaces, and $N_i$ is the refractive index of the $i$th medium. The relations between the outgoing and incoming energy fluxes ($Q$) at each interface can be expressed in terms of the reflection at the interface and the transmission passing through the medium. For every interface $i$, there are four equations:

 

Fig. 2. (a) Schematic multilayer structure, with numbering convention of interfaces ($1,\dots ,i,\dots ,N-1$), refractive index ($N_1,\dots ,N_i,\dots ,N_N$), and energy fluxes ($Q_{i,a},Q_{i,b},Q_{i+1,c},Q_{i+1,d},\dots$). (b) Schematic representation of silicon NW and effective multilayer structure.

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The effective multilayer structure of silicon NW is shown in Fig. 2(b), and the refractive indices of different NW layers can be solved by the EMA formula:

Before starting the calculations, related parameters are assumed as follows: the NW array’s density $\rho$ is set as $100{\mathrm{\mu m}}^{-2}$, so the array’s period length $L=100\mathrm{nm}$; the maximum value of NW bottom diameter $D=L=100\mathrm{nm}$ and the NW length $H=1.0\mathrm{\mu m}$; the thickness of CS substrate $T=100\mathrm{\mu m}$; the layer thickness $d_i=10\mathrm{nm}$, and it is also the minimum step in calculating.

3. RESULTS

First, taking the NW antireflection layer and the CS body as a whole, the effect of different shapes of NW arrays on optical performance is studied. As shown in Fig. 3, compared with the naked CS, there is a better light trapping effect with the NW antireflection coating than without it. Among the five NW shapes, the shape of “I” (the cylindrical NW) has the weakest ability to lower the light reflection, and the other tapered NW has better antireflection capability, as shown in Figs. 3(a) and 3(b). This means that the bigger top cross-sectional area will block the light incidence [3,11]. Furthermore, the shape of “III” (the convex conical NW) has better antireflection and absorption capability than others, as seen in Figs. 3(d) and 3(e). For the whole structure, the light absorption is enhanced for wavelengths less than 1.17 μm; for the longer wavelength region, the more the light antireflection, the more the light transmission because the light in this wavelength range cannot be absorbed by CS, as shown in Figs. 3(c) and 3(f). For the five NW shapes, if taken as a whole, the ranking order of light trapping performance is $\mathrm{III}>\mathrm{IV}>\mathrm{II}>\mathrm{V}>\mathrm{I}$. This result is consistent with previous research findings and the conclusion that the tapered Si NW has strong light trapping ability [12,13].

 

Fig. 3. (a)–(c) Calculated reflectivity, absorptivity, and transmissivity of the CS substrate covered with NW antireflection coating compared with the naked CS. (The five simulation shapes: I, cylindrical; II, parabolic truncated conical; III, convex conical; IV, conical; V, concave conical, respectively.) Right inset (d)–(f): partially enlarged corresponding to the left.

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The NW antireflection coating can enhance light trapping characteristics, but, in the meantime, the increased surface recombination losses represent a handicap for high-efficiency solar cells [11]. Therefore, our concern is about how to increase the amount of photons that be absorbed after the surface texturization. In our research, the absorbed photons are divided into two parts: ${\mathrm{\Phi }}_{\mathrm{NW}}$ and ${\mathrm{\Phi }}_{\mathrm{Si}}$, which are absorptivity of photon flux (APF) of NW antireflection coating and CS body, respectively. Here, for comparison’s sake, it is assumed that the photons, which are absorbed by NW antireflection coating, are used to compensate for surface recombination losses and that the photons, which are absorbed by the CS body, can be efficiently utilized and completely converted into electron-hole pairs. Thus, for $A_{\mathrm{Si}}$, a higher value is better, and, for $A_{\mathrm{NW}}$, a lower value is better. The differences of light absorptivity and APF between the NW antireflection layer and CS body are shown in Fig. 4. For shape of “I,” as a whole, although there is a little contribution to the light trapping effect than that of naked silicon, which can be seen in Fig. 3(a), there is little enhancement in improving the light absorption in the CS body and even worse than naked CS, as seen in Figs. 4(b) and 4(d). The main cause of this situation is that the NW antireflection layer has absorbed part of the photons. For other shapes, obviously, the NW antireflection layer basically absorbs part of the high-energy photons. The light absorptivity and APF show a decreasing trend with decrease in NW volume, and the absorption peak declines and appears to shift to the shorter wavelength, as shown in Figs. 4(a) and 4(c). Other high-energy photons, which are not absorbed by the NW antireflection layer, enter the CS body and are absorbed by it, as shown in Figs. 4(b) and 4(d). In this sense, the light trapping ability of NW antireflection coating is further enhanced, and the NW has a similar effect on the antenna [14,15].

 

Fig. 4. (a) and (c) Light absorptivity $A_{\mathrm{NW}}$ and absorptivity of photon flux (APF) ${\mathrm{\Phi }}_{\mathrm{NW}}$ of silicon NW coating, respectively. (b) and (d) Light absorptivity $A_{\mathrm{Si}}$ and absorptivity of photon flux (APF) ${\mathrm{\Phi }}_{\mathrm{Si}}$ of CS body compared with the naked silicon under AM, respectively. 1.5 spectrum.

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As previously mentioned, our concern is about how to increase the amount of photons that can be absorbed by the CS body compared with the naked CS, and this is what the NW antireflection layer really does. To make the difference between them more intuitionistic, a 3D illustration is necessary.

There is an important parameter, the ratio of the NW diameter to the array period length, i.e., $D/L$. This parameter is closely related to the effective refractive index of the NW antireflection layer, which affects the change of photon absorption. variations of the enhanced factors $E_T$ and $E_A$ under different geometric parameters are studied and shown in Fig. 5. First, for the cylindrical NW shown in Figs. 5(a) and 5(f), only when the value of $D/L$ is in the range of 0.69–0.82 and $H$ is greater than 0.440 μm, there is improved best light trapping property and $E_T$ is the biggest and near 0.21, which is consistent with the present results [3]. However, under these conditions, $E_A$ is less than zero and cannot compete with the naked CS. It means the NW alone absorbs all of the photons, instead of being absorbed by the CS body. For $E_A$, its maximum value is near 0.13 only when the value of $D/L$ is in the range of 0.70–0.89, $H$ is less than 0.300 μm, and, under the same conditions, $E_T$ is only about 0.17, less than 0.21. This implies that better light trapping does not translate into better light absorption. Next, for other NW shapes, values of $E_T$ are greater than that for the shape of “I” under the same conditions, and, for the shape of “III,” it can reach the biggest value of 0.52. Among them, $E_T$ of shape of “III” has a little advantage as compared with others shown as the larger area, where $E_T$ is greater than 0.5, as shown in Fig. 5(c). It reflects the parabolic contours of NW having least resistance to the flow of photons and improves the light absorption. Quite unexpectedly, $E_A$ of shape of “III” is not the largest, while $E_A$ of shape of “V” is the largest of about 0.31, as shown as the larger area, where $E_A$ is greater than 0.3, as shown in Fig. 5(j). Through the analysis, it can be concluded that photon absorption is not only related to the NW volume but also on the NW shape, which mainly depends on the small tip and the larger base [13,16]. The number of photons, which should be absorbed by the NW antireflection layer, is reduced due to the unique NW morphology, so there are more photons penetrating through the NW antireflection layer and then absorbed by the CS body.

 

Fig. 5. (a)–(e) Contour map of enhancement factor $E_T$ under different values of $H$ and $D/L$, which are corresponding to NW shape of “I,” “II,” “III,” “IV,” and “V” having the circle cross section. (f)–(j) Contour maps of enhancement factor $E_A$ under different values of $H$ and $D/L$, which are corresponding to NW shape of “I,” “II,” “III,” “IV,” and “V” having the circle cross section.

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Several conclusions can be reached through analysis of Fig. 5. First, the tapered NW (shape of “II,” “III,” “IV,” and “V”) has better optical properties than the cylindrical NW (shape of “I”), no matter for light trapping or effective light absorption. Second, with longer NW, there is better light trapping ability [17,18] but poor effective light absorption. Third, for the tapered NW, the larger the ratio of $D/L$ and the closer it is to equal 1, the better are the light trapping and effective light absorption. The third conclusion implies that the best arrangement for the NW arrays is that the NW should be arranged closely and without gaps. Therefore, the square cross-section NW arrays are considered next.

With the NW array density unchanged, the performances of light trapping and effective light absorption of square cross-section NW are studied and are shown in Fig. 6. Compared with the circle cross-section NW shown in Fig. 5, there is a tendency of blueshift for both $E_T$ and $E_A$ corresponding to the maximum value of their optimal properties. Under the same conditions, the square cross-section NW arrays have the larger values of $E_T$ and $E_A$ than does the circle cross-section NW. Among the five shapes of NW, in the same way, the shape of “V,” whose apparent shape is like the Eiffel Tower’s, has the most obvious advantage.

 

Fig. 6. (a)–(e) Contour map of enhancement factor $E_T$ under different values of $H$ and $D/L$, which are corresponding to NW shape of “I,” “II,” “III,” “IV,” and “V” having the square cross section. (f)–(j) Contour map of enhancement factor $E_A$ under different values of $H$ and $D/L$, which are corresponding to NW shape of “I,” “II,” “III,” “IV,” and “V” having the square cross section.

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4. CONCLUSIONS

We have investigated the optical absorption of silicon NW-based solar cells, which can be divided into two parts: the light absorption of the surface NW arrays; the CS body. The main function of the antireflection layer is to reduce light reflection and increase light transmission; the CS substrate is the main place where photons are absorbed and converted. Computer simulations demonstrate that the NW arrays can increase the optical absorption, and it depends on not only the NW diameter, length, and volume filling ratio but also on the shape of the cross section. By studying the circular and square cross-section NW, based on the definition of enhancement factors $E_T$ and $E_A$, we found that silicon NW, which is shaped like the Eiffel Tower, has the largest amount of photon absorption even when its light trapping capability is not the best. Therefore, the enhancement factor $E_A$ should be considered as the key index in the design of a light-trapping structure.