1. Introduction

Study of solar cells has become increasingly important due to the upcoming energy shortage and various environmental problems [1,2]. When making these devices, special care must be taken to reduce the Fresnel reflection occurring at the interface between air and absorbing layers [3]. For instance, over 30 percent of the energy impinging on bare silicon surface is reflected and wasted because of the high refractive index of silicon. Traditional anti-reflective (AR) coatings consist of alternative layers with different refractive indices [4]. Reflection at different interfaces within the AR films interfere destructively when the optical thickness of each layer is λ/4. These kinds of AR layers usually work in narrow bands which cover only small portions of the solar spectrum. The optimization of AR performance involves precise control of refractive index and thickness of each layer of the films [5,6].

An alternative for reducing reflection is sub-wavelength structures. Using methods such as nanoimprinting [7,8] and nanosphere lithography [9–11], various structures have been fabricated for AR coatings. Sub-wavelength pyramidal and honeycomb structures were fabricated on silicon substrates with colloidal lithography followed by a reactive ion etching process. Reflection less than 1.5% were obtained with optimal structural parameters [9]. Inspired by the structures in the corneas of nocturnal moths [12], sub-wavelength nipple arrays were directly patterned on silicon using spin-coated silica colloidal monolayers as etching masks [13]. The resulted textures showed excellent AR properties over a wide range of wavelenghs. Sub-wavelength structures can also be patterned on transparent substrates. Using close packed nanoparticle arrays as masks, plasma etching was performed to generate nanopillar arrays on quartz substrates. Effects of structure parameters on AR performance were analyzed in detail [14]. Numerical methods such as rigorous coupled-wave analysis (RCWA), finite element method (FEM), and finite-difference time domain (FDTD) method [9,15] are often used to study the optical properties of these structures.

The main idea of sub-wavelength structures is to generate a graded refractive index between air and substrates, therefore, Fresnel reflection can be supressed [16,17]. From this point of view, random structures can also be used for AR coatings as long as the structures are sub-wavelength in scale [18].Black silicon can be fabricated with different etching process with or without masks [19]. The nano-structures on the silicon surface effectively suppress reflection, so the silicon substrates appear black.

Besides directly made on substrates, sub-wavelength structures can also be fabricated on additional coating layers. Using a square array of TiO₂ nano-cylinders, an average reflectivity (weighed over the AM1.5 solar spectrum in the 420~980 nm spectral range) of 2.8% was demonstrated [20]. With carefully controlled synthesis process, TiO₂ nano rods dramatically reduced the reflection of silicon substrates [21]. Along with suppressing reflection, AR layers may have additional functionalities such as passivation [7] and self cleaning [22,23].

In this paper, we present a simple method to make TiO₂ AR layers on top of silicon substrates. We use radio frequency plasma to etch the surfaces of TiO₂ films and get wage-like textures. The etched films can effectively suppress the reflection to 2.9~4.6% at the wavelength range of 400~800 nm. We analyze the optical properties with a 3D FDTD method, and attribute the enhanced AR effect to increased roughness of the TiO₂ surfaces. TiO₂ is one of the most widely used materials for AR coatings due to its properties such as high refractive index, excellent visible and near infrared transmittance, chemical resistant and stable, good mechanical properties, non-toxic, and low cost [24–26]. High efficient and low cost methods of making TiO₂ AR layers can be very helpful to the development of solar cells.

2. Experiments

The experiments started with commercial polycrystalline TiO₂ films [27]. The films were prepared on silicon wafers by the Chemical Vapor Deposition (CVD) method. They were well crystallized in the anatase form. The surface morphology was examined by scanning electron micrographs (SEM, Hitachi S-4500). It is clear that the film is composed of well faceted nanocrystals that are stacked in random directions [Fig. 1(a)]. The microcrystals are hundreds of nanometers in size. The thickness of the film is about 800 ~ 900 nm [Fig. 1(c)].

 

Fig. 1 Micrographs of the TiO₂ films: (a) top view of the unetched film, (b) top view of the etched film, c) cross section of the unetched film, (d) cross section of the etched film.

Download Full Size | PDF

We used CF₄ plasma to etch the TiO₂ film to modify its surface morphology. This method has been proved to be an efficient way for roughening surfaces of TiO₂ films [27]. After 40s etching, we got a structure shown in Figs. 1(b) and 1(d). Wedge like structures are formed in the process. Some wedges may stack together and form wedge arrays, but both the sizes and directions of the wedges are generally random [Fig. 1(b)]. The typical lateral size of a single wedge from the top view is about 300 nm*80 nm, [Fig. 1(b)]. The average height of the wedges is around 600 nm [Fig. 1(d)], which is a little smaller than the original thickness of the film.

We measured the reflection with a UV-Vis spectrometer (Shimadzu UV-2450) attached with an integrating sphere (ISR-2200). The schematic of the configuration inside the integrating sphere is shown in Fig. 2(a). The measurement beam impinges on the sample at an 8 ° incident angle. Both of the specular and diffuse reflection are collected. The measured results are shown in Fig. 2. In the wavelength range of 400 ~ 800 nm, the reflection of a bare silicon substrate is above 30% (blue dashed line). The reflection of a TiO₂ film as purchased varies from 3% to 8%. The oscillations in the reflection are due to the interference between the reflection at air/TiO₂ and TiO₂/Si interfaces (red dotted line). After 40 s etching process, the reflection of the TiO₂ film droped to 2.9~4.6% at the wavelength range of 400~800 nm, meanwhile, the oscillations in the reflection no longer exist (black solid line). We can tell from the black surface of the etched film that the incident light is trapped and absorbed [Inset of Fig. 2].

 

Fig. 2 (a) Schematic of the configuration inside the integrating shpere. (b) Measured reflection of bare a Si substrate, unetched TiO₂ film, and etched TiO₂ film. Inset shows the photograph of etched TiO₂ film.

Download Full Size | PDF

3. Numerical simulation

Qualitatively, the AR effects can be attributed to the graded refractive index. Since the lateral size of the wedge-like structures are smaller than wavelengths in the 400~800 nm region (especially, the width of the structures are only around 80nm, well below the wavelengths), the TiO₂ film can be evaluated with the effective medium theory [13,15]. From the top of TiO₂ film to the bottom, the ratio of TiO₂/air increases continuously. As a result, there is graded refractive index inside the TiO₂ layer.

In order to understand the underlying physics of the experimental results, we numerically simulated the optical properties with the finite-difference time-domain (FDTD) method (Lumerical FDTD Solutions). The configuration of the simulation is demonstrated in Fig. 3. A plane wave source with a wavelength range of 400~800 nm is placed 1200 nm above the top surface of silicon substrate. A reflection monitor (frequency domain filed and power monitor) is placed 100 nm above the source. The plane wave propagates downwards to the AR structure, so that both the specular and diffuse reflection are collected by the reflection monitor. A field profile monitor (frequency domain filed and power monitor) is placed perpendicular to the surface of substrate. The electric field profiles in the cross sections are recorded in the frequency domain.

 

Fig. 3 Schematic of the configuration in FDTD simulations

Download Full Size | PDF

We constructed 4 models of TiO₂ layers [Fig. 4] on silicon substrates and calculated the corresponding reflection. The refractive index of TiO₂ in the simulation follows the dispersion formula [28]:

Therefore, the refractive index varies from 2.45 to 2.69 in the wavelength range of 400~800 nm. We believe that the key factor of the AR effects is the roughness of the film surfaces, so random roughness is used to simulate the textures of the TiO₂ film surfaces [Fig. 1]. The roughness used in the simulation is characterized by the root-mean-squre (rms) roughness (σ_rms) and correlation length (l_c). The correlation function is

The simulated reflection of the bare silicon substrate [Fig. 4(a)] is above 30% (blue dashed lines in Fig. 5), which is in accordance with the measured result [blue dashed line in Fig. 2(b)]. When the silicon substrate is covered by a flat TiO₂ film [Fig. 4(b)], we can expect AR effect because the refractive index of TiO₂ is between the refractive indices of air and silicon. Following the conventional strategy of single-layer AR coating, the thickness of the TiO₂ layer is set to be 60 nm, so that the optical length is nL = λ/4 at the wavelength of 600 nm. The calculated reflection is shown with cayan dot-dashed line in Fig. 5(a). The minimum reflection is about 5% at the wavelength of 600 nm, while the reflection increases at other wavelengths, such as 38% at the wavelength of 400 nm. The calculated reflection is similar to the reported experimental results [29].

 

Fig. 4 Illustration of the sub-wavelength structures used in numerical sumulation, (a) bare Si substrate, (b) flat TiO₂ film, (c) TiO₂ film with roughness of rms=80 nm, (d) TiO₂ film with roughness of rms=200 nm.

Download Full Size | PDF

 

Fig. 5 Comparison between the measured and simulated reflection of TiO₂ films, (a) film as purchased, (b) film etched for 40 s by CF₄ plasma.

Download Full Size | PDF

The AR effect enhances when roughness is introduced to the surface of the film. We used σ_rms = 80 nm and l_c = 100 nm [Eq. 2] to generate random roughness shown in Fig. 4(c). In this case, the subwavelengh textures on the surface generate gradually varing effective rafractive index [16] in the vertical direction, so that the reflection can be further reduced. The simulation result is shown with the black solid line in Fig. 5(a). The reflection reduces to below 10%, which is in accordance with the experimental result of the unetched film [red dotted line].

We increased the rougness of the surface to σ_rms = 200 nm, and got a rougher film shown in Fig. 4(d). The average thickness of the film is also reduced to 400 nm. This model is used to simulate the roughened and thinner film after the etching process [Figs. 1(b) and 1(d)]. The simulated result is shown with the black solid line in Fig. 5(b). The calculated reflection is round 4%, which is in accordance with the experimental result of the etched film [red dotted line]. The gradient of the effective refractive index reduces with the increase of the roughness. That leads to the improvement of AR effect.

Using numerical simulation, we can see the effects of the surface roughness on the propagation of light [Fig. 6]. The top surface of silicon substrate was defined as the z = 0 nm position, and the plane wave source propagating along the −z direction was placed at z = 1200 nm. The field monitor is 2-D Y-normal and placed at the position of y=500 nm [Fig. 4]. The electric field (|E|²) distributions were calculated at the frequency of 500 THz (which corresponds to the wavelength of about 600 nm in the air). The electric field intensity above the source is contributed by the reflection. Without TiO₂ layer, there is considerable intensity above the air/Si interface owing to the high reflection of the bare silicon substrate [Fig. 6(a)]. With a smooth TiO₂ film, the reflection is reduced, that leads to less electric field intensity above the air/TiO₂ interface [Fig. 6(b)]. When roughness is introduced to the TiO₂ films, we can hardly see any electric field intensity above the air/TiO₂ interface [Figs. 6(c) and 6(d)]. Because of the AR effect generated by the rough films, we can also see more electric field intensity in the silicon substrates. The sub wavelength strucures in the rough films induce modifications of the electric field distribution, and the field intensity is no longer uniform along the x direction.

 

Fig. 6 Simulated Electric field distribution (|E|²) in the cross sections near the surfaces, (a) bare Si substrate, (b) flat TiO₂ film, (c) TiO₂ film with rms= 80 nm (d) TiO₂ film with rms=200 nm.

Download Full Size | PDF

The simulated results are in good accordance to the experimental results, the remaining differences between them can be attributed to the following reasons: owing to the limitation of computing power, we generated random structure in a small area (1 µm²) then used periodic boundary conditions; there are fine structures at the surface of the microcrystals and wedge like structures in TiO₂ films [Fig. 1], which can further modify the near field optical properties.

4. Discussion

We believe that the method presented here is helpful to improve the performance of silicon solar cells. Firstly, the reflection is suppressed to below 4.6%, while the reflection of a conventional textured silicon surface is above 10% [25,30]. The etched film exhibits AR effects in the whole visible band, while conventional single-layer AR coatings, such SiN [31], TiO2, and ITO [32], can minimize reflection in a narrow band. Secondly, excellent AR effects can be obtained with elaborate structures such as moth-eye structures [9], black silicon [19], and TiO₂ arrays [20], however, the fabrication processes usually involve multi-step procedures, and the parameters need to be precisely controlled. Mask-free dry etching is relatively easy to implement. Thirdly, textured surfaces of substrates may have more charge recombination sites and need additional passivation [33], while the AR coating in this paper does not destroy the silicon surface. Fourthly, CVD and dry etching are widely used industrial methods, so we may expect high throughput and process speed. Meanwhile, the cost of TiO₂ AR coating is relatively low compared to materials such as ITO. The method presented here can be integrated into the current fabrication process of silicon solar cells. The idea for generating graded refractive index can even be applied to already finished solar cells. Finally, in standard commercial photovoltaic modules, solar cells are commonly encapsulated with polymers such as ethylene vinyl acetate (EVA) [34]. The wedge-like structure may maintain their shapes after encapsulation. Moreover, because the high refractive index of TiO₂, the encapsulated structures may still generate graded refractive index. However, owing to the modification of environmental refractive index, more study is needed to optimize the nanostructures to keep the excellent AR effects. The method presented in this paper may also be applied in optical devices such as LEDs and detectors.

5. Conclusion

We have investigated the AR effects of TiO₂ films on top of silicon substrates. The polycrystalline TiO₂ films were roughened by an mask-free ething process, then exhibited broad band AR properies. We numerically analyzed the reflection of the films with the FDTD method, and showed that the AR performance can be attributed to random roughness. TiO₂ layers reduce the contrast of refractive index between air and silicon substrates. The rough surfaces of TiO₂ films further reduce the gradient of the refractive index and improve AR performance.