1. Introduction

Light management is crucial to solar cell design as it increases the path length of light in the absorber layer, thereby enhancing the probability of electron-hole pair generation. By engineering the reflective and refractive properties of the solar cell surfaces, we can trap light within the active region to achieve physically thin, but optically thick solar cells.

Texturing the surface of solar cells is an effective light management technique, providing both light trapping and anti-reflection properties [1–5]. The operational spectrum of a single junction silicon solar cell is from 300nm to 1200nm. In the ultraviolet and visible spectrum where the photon energy is well above the band gap energy of silicon, all light coupled into the Si is absorbed before reaching the rear side of the cell. In contrast, in the near-infrared region the probability of a band transition of a photon-excited electron reduces significantly. At these wavelengths, surface textures can preferentially direct light into the solar cell at angles outside the escape cone of silicon, resulting in light trapping and increased absorption.

As solar cell technology becomes increasingly competitive, accurately estimating the light trapping induced current enhancement at an early stage of solar cell fabrication is very important. It is therefore highly desirable to have a technique that accurately assesses optical absorption enhancement, with the ability to distinguish between band-to-band absorption and parasitic absorption [6, 7]. Conventional methods such as photo-thermal deflection and reflection/transmission measurements (A = 1-R-T) provide inaccurate estimates of photo-current generation as they inevitably include parasitic absorption [8].

In a solar cell, only photons that excite an electron from the valence band to the conduction band contribute to the photo-current generation. In the inverse process electron-hole pairs recombine and photons are emitted via band-to-band radiation, which can be directly quantified from the measured photoluminescence (PL) spectrum [7, 9–13]. Therefore, by studying the PL spectrum of silicon wafers, we can derive the portion of the absorbed photons that lead to effective electron-hole generation. In a silicon wafer, both carrier densities and the optical properties of the sample determine the PL intensity at a given wavelength. The carrier densities of the sample determine the internal generation rate of emitted photons, while the optical properties determine the probability of a photon escaping the sample and contributing to the measured spectrum [14]. There are a number of studies in the literature that model the spectral distribution of photo/electroluminescence emission of silicon wafers or solar cells [9–12, 15]. The relationship between spectral photoluminescence intensity per energy interval and band-to-band transition absorptivity can be described as follows [10, 11, 14]:

In Eq. (1), C is constant proportionality, ε_F.C-ε_F.V is the difference of the quasi-Fermi energies, k is the Boltzmann constant, T is temperature in Kelvin, and ћω is the photon energy. Quantifying the absolute absorptance A_BB that generates electron-hole pairs in a silicon wafer can provide a quick and accurate estimation of the maximum possible current density J_sc in a solar cell without the need for a p-n junction and current extraction. The methods of obtaining the absolute absorptance of silicon solar cells and wafers from electroluminescence spectra and photoluminescence spectra have been experimentally demonstrated by Trupke et al. and Barugkin et al. [7, 10].

In this contribution, we extend the method of extracting A_BB from PL spectra, previously applied to plasmonic structures only, to evaluate light trapping and quantify the light trapping efficiency (LTE) [16] for a range of promising structures (shown in Fig. 1) in crystalline Si wafers. With the above mentioned method, the band-to-band absorptance is extracted from the photoluminescence spectrum of silicon wafers with different light trapping structures. By integrating the extracted band-to-band absorptance over the AM1.5G photon flux spectrum, we calculate the J_sc of the silicon wafer with each type of structure. We then compare the J_sc of each sample to the J_sc of an ideal Lambertian model to evaluate the LTE.

 

Fig. 1 Schematic diagram of double side textured silicon wafer and SEM images of various types of texture structures: (1) metal-assisted etched texture (side view); (2) reactive ion etched texture (angle view); (3) random pyramid texture (side view) and (4) plasmonic Ag nanoparticles on silicon wafers (top view).

Download Full Size | PDF

2. Experiment

We study a range of light trapping structures on monocrystalline silicon wafers: double side random pyramids texture (RAN) with anti-reflection coating (AR), double side metal-assisted etched texture (MET) [17] with AR coating, double side reactive ion etched texture (RIE) [18] and a structure with front RIE/rear RAN textures (RIE/RAN). For comparison, we also include a sample with RIE on the front and plasmonic Ag nanoparticles plus diffuse back reflector (Ag/DR) on the rear side [7, 19]. Float zone, <100>, 260 µm, 3Ω•cm, N-type silicon wafers are used for all experiments. The details of the fabrication procedure of each structure are as follows:

In order to use the PL spectrum to extract the absorptivity, one needs to assume a homogenous electron and hole distribution in the wafer [8–10]. Therefore samples with high minority carrier lifetimes, i.e., with minority carrier diffusion length much longer than the wafer thickness, are used in this experiment. To fulfil the need for high minority carrier lifetimes, all the textured silicon wafers are passivated with 20nm atomic layer deposited (ALD) Al₂O₃ followed by a forming gas anneal (FGA) at 400 °C for 30 minutes. This gives an average lifetime of 1ms at an injection level of 1 × 10¹⁵cm⁻³. For the RAN and MET samples, we deposit 60nm of plasma enhanced chemical vapor deposited (PECVD) SiN_x on top of the Al₂O₃ film forming an Al₂O₃/SiN_x stack AR coating on the front side of each sample.

To take the photoluminescence spectra, we illuminate the samples at room temperature (295K) with a 785nm, 252 mW free running laser diode source at close to normal incidence (shown in Fig. 2). The emitted photoluminescence is focused and transmitted into a double-grating monochromator with 600 grooves/mm and 1000nm blaze, and detected with a liquid nitrogen cooled InGaAs detector in the wavelength range of 900nm to 1400nm. A long pass filter with a cut-off wavelength of 800nm is used to prevent any laser light reaching the detector. An optical chopper with a frequency of 500Hz and a lock-in amplifier is used to amplify the signal of the final spectrum. A Perkin Elmer 1050 spectrophotometer with an integrating sphere detector is used to measure the reflectance R and transmittance T of the samples in the wavelength range of 300 to 1200nm. A diffuse reflector with reflectance above 95% is attached on the rear side of each sample for both PL and spectrophotometer measurements.

 

Fig. 2 Schematic diagram of the system set-up for photoluminescence measurement.

Download Full Size | PDF

According to Eq. (1), the photoluminescence spectrum can be divided by (ћω)²exp(-ћω/kT) to obtain the relative A_BB as a function of wavelength (Fig. 3). The absorptivity that we extract is only relative as the PL is measured in arbitrary units. This is converted into absolute values by normalizing the relative A_BB to the value of 1-R in the wavelength range of 950nm to 1000nm, where the two spectra have an overlapping region. Here R is the front surface reflectance measured with the spectrophotometer.

 

Fig. 3 (Right Y-axis) Photoluminescence spectra of a planar silicon wafer and the RIE/RAN sample as a function of wavelength. (Left Y-axis) The absorptivity of the two samples extracted from the PL spectra.

Download Full Size | PDF

The wavelength range of 950nm to 1000nm is chosen for converting the relative A_BB into absolute values based on two requirements: first, the PL emission must be sufficiently strong to minimize uncertainty; second, the absorption measured by the spectrophotometer should be dominated by band-to-band absorption. The Si wafers have detectable luminescence spectra down to wavelengths of ~900nm but the spectra are relatively noisy below 950nm. Above 950nm the measured PL intensity is sufficiently strong to provide accurate data for normalization. This sets the lower wavelength bound for the analysis. The upper wavelength bound for normalization is determined by parasitic absorption (e.g. free carries absorption, absorption in the back reflector) which starts to become significant above 1000nm in the wafers being studied. Below 1000nm, the free-carrier absorption contribution is negligible [10] and light is fully absorbed in the Si wafer before reaching the back reflector. Thus it is valid to assume that absorption is dominated by A_BB for wavelengths <1000nm. Extracted PL absorption spectra do not vary significantly provided the normalization wavelength is in the range of 950nm to 1000nm. We note that the upper wavelength bound would have to be reduced for thinner Si wafers in order to meet the requirement of no light reaching the rear reflector, but the lower bound would remain. Thus there is likely to be a minimum wafer thickness for which this normalization approach can be applied.

In order to quantify the absorption in the Si wafers as well as estimating the photocurrent generation, we can use Eq. (2) to calculate the maximum possible current density J_sc of each structure by integrating the absorption spectrum over the AM1.5G solar spectral photon flux density ($\Phi (\lambda )$) from ${\lambda }_1$ = 300nm to ${\lambda }_2$ = 1200nm. The absorptance from 300nm to 1000nm is derived from 1-R-T, and the PL extracted absorptance from 1000nm to 1200nm is used to exclude parasitic effects.

In Eq. (2), $q$ is the elementary charge, $\lambda$ is wavelength, and $A_{BB}$ stands for the band-to-band absorptance.

The light trapping efficiency (LTE) chart compiled by Schuster et al. [16] is a credible benchmark to assess the performance of light trapping structures regardless of the substrate property and thickness. Similar to our previous demonstration of fraction of Lambertian enhancement (FLE) [7, 21], LTE can be used to isolate the light trapping property of textures from their anti-reflection properties and highlight the texture-induced current enhancement in the weakly absorbing band gap region. To quantify the light trapping, we use the definition of light trapping efficiency introduced by Schuster et al. [16]:

Here J_max is the maximum current density determined experimentally by 1-R-T and PL absorptance measurements; J_ref is the modelled value of the current from the silicon sample with the same front reflectance as J_max and a 100% rear reflector; and J_Lam and J_MB are modelled currents of an ideal Lambertian reflector [4] and a 100% specular reflector respectively, both with zero front reflection loss. To isolate the light trapping properties from the anti-reflection effect of the textured samples, the numerator J_max-J_ref represents the light trapping induced current gain and the denominator J_Lam-J_MB indicates the maximum improvement in current with an ideal Lambertian structure. Therefore, LTE determines the extent to which the measured sample approaches an ideal Lambertian light trapping structure. To calculate light trapping efficiency, one has to be aware of that the LTE is only valid when J_max and J_ref have the same front reflection losses.

3. Results and discussion

Figure 3 shows the PL spectra (red) and extracted absorptance spectra (blue) of a silicon wafer with planar surfaces on both sides (solid) and a silicon wafer with the RIE/RAN texture (open). As shown in the graph (right Y axis), the surface properties have a strong impact on the PL intensity and spectrum shape. The PL intensity of the textured wafer is substantially higher than the planar wafer as the textures increase the light absorption in the bulk. Compared to planar surfaces, the textured surfaces can couple the light more effectively into the silicon and increase the absorption capacity of the solar cell. As a result, the amount of emitted photons will increase significantly. A red shift of 30nm of the peak intensity is also seen in the PL spectra of RIE/RAN as well as in the literature [14] compared to the planar sample. This is due to the randomization of the path of the photons in the textured sample which leads to a higher escape probability for long wavelength light. Using the method mentioned in the previous section, the band-to-band absorptance spectra of a planar wafer and a wafer with RIE/RAN structure are extracted and presented in the left Y axis of Fig. 3. Both spectra have been normalized to the spectrophotometer measured 1-R at 1000nm for each sample. The absorption enhancement of RIE/RAN sample compared to the planar sample is due to the combined optical effects of RIE and RAN textures. RAN increase the absorption in silicon by providing a certain amount of anti-reflection and excellent light trapping properties, while the RIE further reduces the front reflection loss to almost 0%. Therefore, by combining these two structures on a silicon wafer and using the PL technique to evaluate the optical performance, we can increase the absorption in the silicon wafer significantly. More quantitative analysis of this structure will be performed later in the paper.

Spectrally resolved electroluminescence of solar cells has been used to model their external quantum efficiency with the opto-electronic reciprocity between the photovoltaic and photon emission properties of silicon [22–24], where the splitting of the quasi-Fermi levels in Eq. (1) is replaced by the junction voltage applied to the solar cell. In order to validate the accuracy of the PL technique, we use it to extract the absolute absorptance of a high efficiency back-contact (BC) solar cell [25] and compare the extracted absorptance spectrum with the measured external quantum efficiency (EQE). Figure 4 shows the A_BB and EQE of a BC solar cell. The circle represents A_BB, while the triangle is the conventional 1-R-T absorptance measured with a spectrophotometer. The blue solid line represents the EQE measurement of the cell. We can see the A_BB value is very close to the EQE of the cell from 1000nm to 1200nm, as opposed to the conventional optical characterization method (1-R-T) using a spectrophotometer, which clearly highlights the shortcomings of the 1-R-T approach. The 1-R-T measurement is significantly higher than the EQE in the range of 1000nm to 1200nm which clearly indicates the existence of parasitic absorption in the 1-R-T measurement. The EQE of the solar cell is affected by the absorption in the active layer as well as the probability of charge carrier collection within the device, which can potentially results in EQE$\le$A_BB [22, 24]. Considering the fact that the BC cell we use in this study is a high efficiency device and the carrier collection efficiency is close to 100%, the absorptance A_BB extracted from PL is very close to the EQE of the cell. Therefore, the method of extracting A_BB using the PL signal can provide much more accurate current prediction compared the conventional 1-R-T method which can easily overestimate the absorption in the region where light trapping plays a significant role. The 1-R-T measured absorptance is higher than the EQE in the range of 300nm to 600nm mostly due to the absorption of the light in the Al₂O₃/SiN_x anti-reflection coating layer.

 

Fig. 4 External quantum efficiency (EQE, blue line) and spectrophotometer measured (R&T) absorptance (triangles), PL extracted absorptance (circles) of a back contact silicon solar cell.

Download Full Size | PDF

With the validation performed in the previous paragraph, the technique of extracting A_BB from the PL spectrum is applied to the wafers with different types of light trapping structures as well as a wafer with a planar surface. The absorptance spectra extracted from R&T measurements from 300nm to 900nm are shown in Fig. 5(a). While all three textures notably reduce the front reflection losses, RIE texture provides a broadband excellent anti-reflection effect across both the ultraviolet and visible wavelengths. RAN and MET have wavelength dependent reflection loss while MET performs better in the spectrum below 400nm due to the existence of a larger fraction of nano-scale textures which are more effective at coupling short wavelength light into the silicon.

 

Fig. 5 (a): Absorptance of wafers with various light trapping structures measured with a spectrophotometer. (b): Band-to-band absorptance extracted from photoluminescence spectra of wafers with different light trapping structures.

Download Full Size | PDF

The extracted A_BB of the samples in the long wavelength range are shown in Fig. 5(b). Black solid squares represent A_BB of a 260µm wafer with planar surfaces, which serves as a baseline in this study with maximum J_sc of 3.4mA/cm² from 990nm to 1200nm. The double side RIE sample shows excellent broadband anti-reflection properties but the least light trapping contribution of the test structures (J_sc = 4.9mA/cm²). This is likely due to the high aspect ratio of the nano-structures of RIE textures which is more effective at scattering the short wavelength light than the long wavelength light [26]. Double side MET performs better than RAN in terms of overall anti-reflection in the range of 300nm to 900nm but has same light trapping properties (5.4mA/cm² for both). Therefore, by combining RIE and RAN one can benefit from both excellent anti-reflection of RIE and light trapping properties of RAN textures. As shown in Fig. 5(b) with green solid squares, RIE/RAN performs the best (5.8mA/cm²) among all the structures clearly demonstrating low reflection loss of RIE and highly randomizing property of RAN. In a recently reported work by Ingenito et.al., a similar structure with the combination of RIE/RAN textures and a distributed Bragg reflector provides the implied photo-generated current density up to 99.8% of the 4n² limit [1] on a thin silicon solar cell [26]. As an innovative structure alternative to RAN, Ag/DR provides excellent light trapping without increasing the surface recombination at the rear side [7]. The combined structure of RIE and Ag/DR can also provide excellent light trapping performance (5.7mA/cm²) comparable to RIE/RAN`s (5.8mA/cm²).

Using the maximum possible photocurrent for each sample obtained by integrating the combined absorptance spectra over the solar spectrum from 300nm to 1200nm, and modelled values of J_ref, J_Lam and J_MB, we calculate the LTE of RIE/RAN and RIE-Ag/DR and compare them with the LTE of other reported light trapping structures shown in Fig. 6. In order to ensure consistency of LTE values and a fair comparison among different solar cells, we only choose the cells with J_ref values reported in [16]. For the rest of the cells in [16] where J_ref is not known and J_MB is used as a reference value, the value of J_max - J_MB includes the optical impacts from both anti-reflection and light trapping properties. We think it will be an inconsistent comparison of LTE values with other structures of which the LTE represents the light trapping properties only. Therefore, the LTE of those cells are not presented here.

 

Fig. 6 Light trapping efficiency of RIE only (orange downward triangle), RIE/RAN (red star) and RIE-Ag/DR (green upward triangle) on silicon wafers using the LTE figure of merit introduced by Schuster [16]. The blue colored circle, diamond and cross are LTE of solar cells calculated from the data from [15].

Download Full Size | PDF

The light trapping efficiency of different solar cells with various thicknesses is shown on Fig. 6. The scattered circles indicate the LTE of monocrystalline solar cells that are calculated from experimentally measured values of J_max and J_ref. The scattered diamonds are the LTE of monocrystalline solar cells with numerically calculated J_max and J_ref. The scattered crosses represent an experimentally derived light trapping efficiency of microcrystalline silicon thin film solar cells. The red star and green upward triangle are the LTE of RIE/RAN and RIE-Ag/DR calculated from the PL extracted absolute absorption. Monocrystalline silicon wafers with RIE/RAN and RIE-Ag/DR can provide a LTE of 55% and 52% respectively which are both well above the reported values in Fig. 6 with similar wafer thicknesses. The double side RIE texture provides only 18% LTE (shown as orange downward triangle), which is significantly lower than the LTE of the other two structures from this work presented in the graph. Thus, the RIE texture by itself has very weak scattering properties at longer wavelengths, but the light trapping efficiency can be improved dramatically to 55% by integrating it with light trapping structures that effectively scatter the light with long wavelengths. For crystalline silicon solar cells, the numerically calculated results generally show higher LTE compared to the experimental results, which indicates that certain losses exists in the experimental value of J_sc. However, as validated in Fig. 4, the method we demonstrate here can provide close estimation to the actual current in silicon cells, even though we are extracting the short circuit current density from wafers rather than complete solar cells. Therefore, it is useful to compare the light trapping performance of our structures with other experimentally derived LTEs of solar cells on the graph.

The light trapping efficiency proposed by Schuster et al. [16], and used in this work tries to do compare the LTE independently of the substrate thickness by defining the LTE as the ratio of the absorption enhancement due to the light trapping structure as compared to the enhancement due to an ideal Lambertian structure. However, thin film cells clearly outperform thicker wafer cells by this measure of LTE. Whether this is due to thicker cells already being close to their limiting current, and thus having less space for improvement, or whether the LTE definition is not a fair comparison for cells of vastly different thickness is still not clear. Nevertheless, our results show excellent light trapping efficiency compared to cells of similar thickness.

4. Conclusion

We use the band-to-band absorption extracted from photoluminescence spectra to calculate the maximum possible current for a standard silicon wafer. This technique allows the rapid comparison of a wide variety of light-trapping structures without distortions in the measured absorption due to parasitic effects that occur when extracting absorption from reflection and transmission measurements. The light trapping properties of several structures including reactive ion etched textures, metal-assisted textures and random pyramid textures are experimentally evaluated with this technique. By fabricating a silicon wafer structure with RIE and RAN textures on the front and rear side respectively, we demonstrate a light trapping structure with near ideal absorption in the ultraviolet and visible spectrum and a LTE of 55% in the near infrared region of the solar spectrum.