Optimizing Broadband Light Absorption in Thin‑Film Silicon Solar Cells with Double‑Sided Pyramid Gratings

Background

Advances in micro‑fabrication have made nanometer‑scale surface textures and engineered morphologies a cornerstone of next‑generation photovoltaics [1], [2]. For CS thin‑film solar cells, optimizing structural parameters is critical to push efficiencies toward the theoretical Yablonovitch limit [7]–[10]. Because each absorbed photon with energy above the band‑gap generates a single electron‑hole pair, the distribution of photon absorption across the cell’s layers determines the ultimate conversion efficiency. This paper focuses on how front pyramid gratings (FPG), rear pyramid gratings (RPG), and their combination (DSPG) influence photon absorption in the CS layer.

We decompose the total photon absorption A into three contributions: absorption in the front gratings (A_F), in the silicon bulk (A_Si), and in the rear gratings (A_R), as illustrated in Fig. 1. These satisfy the conservation relation R + T + A = 1. Importantly, A_Si is calculated differently for each structural variant.

Different structures of crystalline‑silicon (CS) thin‑film solar cells with or without pyramid gratings. a The bare crystal silicon (BCS). b The front pyramid grating (FPG). c The rear pyramid grating (RPG). d The double‑sided pyramid grating (DSPG). (A_F, A_Si, and A_R represent the light absorption of the front surface gratings, the CS part, and the rear surface gratings, respectively. H is the thickness of the CS layer; P₁, D₁, H₁ and P₂, D₂, H₂ represent the period, bottom diameter, and height of silicon pyramid of the front or rear surface, respectively)

Methods

Our simulations combine the net‑radiation method with effective‑medium approximation, a pairing that has consistently matched experimental data for silicon gratings [4], [11]. Figure 2 shows the multilayer system: an N‑layer stack with complex refractive indices N_i at each interface (i = 1…N‑1). Incoming and outgoing energy fluxes are denoted Q_i,a, Q_i,b, Q_i+1,c, and Q_i+1,d.

Schematic multilayer medium structure of the silicon pyramid gratings, with numbering convention of interfaces (1, …, i, …, N − 1), complex refractive index (N₁, …, N_i, …, N_N), and electromagnetic radiation fluxes (Q_i,a, Q_i,b, Q_i+1,c, Q_i+1,d, …)

Energy balance at each interface follows

{\n  Q_{i,a}=\tau_iQ_{i,c}
  Q_{i,b}=r_{i,i+1}Q_{i,a}+t_{i+1,i}Q_{i+1,d}
  Q_{i+1,c}=t_{i,i+1}Q_{i,a}+r_{i+1,i}Q_{i+1,d}
  Q_{i+1,d}=\tau_{i+1}Q_{i+1,b}
}

where r_i,i+1 and t_i,i+1 are the Fresnel reflectivity and transmissivity. The absorption attenuation of layer i is

\tau_i=\exp\left[-\alpha_i\,d_i/\cos\varphi_i\right]

with α_i = 4\pi k_i/\lambda and k_i the imaginary part of N_i. Assuming normal incidence Q_1,a=1 and zero outgoing flux at the rear Q_N,d=0, the absorption coefficient of layer i is A_i=Q_i,a−Q_i,c+Q_i,d−Q_i,b.

Effective refractive indices for the pyramid layers are obtained via the Bruggeman formula

\frac{f_1(N_{Si}^2-N_{Eff}^2)}{N_{Si}^2+2N_{Eff}^2}+
\frac{f_2(N_{Air}^2-N_{Eff}^2)}{N_{Air}^2+2N_{Eff}^2}=0

where f₁ and f₂=1−f₁ are the volume fractions of silicon and air. The total absorbed photon flux in layer i is then

\Phi_i=\int A_i\,F(\lambda)\,\lambda/(h_0c_0)\,d\lambda

with F(\lambda) the AM1.5 solar spectrum. The aggregate absorbed flux is Φ=\sum_i\Phi_i.

Results and Discussion

For a fair comparison, we set the CS layer thickness to H = 10 µm. The pyramid height and base diameter are fixed at H₁=H₂=200 nm and D₁=D₂=100 nm, respectively. The front grating’s period‑to‑diameter ratio is P₁/D₁=1. For the rear grating, we explore P₂/D₂=1 and 10. The double‑sided configuration combines these parameter sets.

Figure 3 summarizes the optical performance of each structure. The front gratings dramatically reduce broadband reflection and boost total absorption, especially in the short‑wavelength region (regions I and II). The rear gratings further suppress reflection in the infrared (region II) when P₂/D₂=10. Together, the DSPG can approach the Yablonovitch limit and achieve near‑zero reflection across the entire spectrum, a hallmark of black silicon. Interestingly, the rear gratings increase visible and near‑IR transmission, which may benefit photodetectors [9], [10].

Optical properties of different silicon pyramid grating structures compared to the BCS of the same thickness (BCS (H = 10 µm), FPG (P₁/D₁=1, H₁=200 nm), RPG (P₂/D₂=1 or 10, H₂=200 nm), DSPG (P₁/D₁=1, P₂/D₂=1 or 10, H₁=H₂=200 nm)). (a), (b), and (c) are the total light reflectivity, absorptivity, and transmissivity, respectively.

To dissect where photons are absorbed, we present three‑dimensional contour maps for the FPG and RPG structures in Fig. 4 and Fig. 5. These maps reveal that, for the FPG, increasing pyramid height enhances total absorption but eventually reduces silicon‑bulk absorption once the front layer becomes too tall. The optimal front‑grating geometry appears at P₁/D₁=1.05 and H₁=53 nm.

Contour maps of the photon absorption distribution in different parts for FPG structure. (a) The total photon absorption A. (b) The photon absorption of the front surface gratings A_F. () The photon absorption of CS part A_Si. (The dotted line in the illustration represents the absorption of BCS)

Contour maps of the photon absorption distribution in different parts for RPG structure. (a) The total photon absorption A. (b) The photon absorption of CS part A_Si. () The photon absorption of the rear surface gratings A_R. (The dotted line in the illustration represents the absorption of BCS)

For the RPG, a larger period‑to‑diameter ratio (P₂/D₂=10) coupled with a shorter pyramid height boosts infrared absorption by redirecting light back toward the active layer. However, the silicon‑bulk absorption remains largely unchanged because the rear gratings reflect many photons rather than capture them. Consequently, while the rear gratings improve total absorption, they do not enhance the effective absorption within the CS body.

Figure 6 consolidates the performance of four representative DSPG parameter sets. When the front grating’s ratio is too large (e.g., P₁/D₁=10 with H₁=10 nm), reflection increases and absorption drops. Only the configuration P₁/D₁=1.05, H₁=53 nm, paired with P₂/D₂=1.03 and H₂=170 nm delivers near‑zero reflection and maximal absorption across the spectrum. Yet, even in this optimal DSPG, the fraction of photons absorbed by the silicon bulk does not surpass that of the best FPG alone, underscoring that rear gratings offer limited benefit for bulk absorption.

Optical properties of four sets of different parameters for the DSPG (P₁/D₁=10, H₁=10 nm and P₂/D₂=1.03, H₂=170 nm or P₂/D₂=10, H₂=10 nm; P₁/D₁=1.05, H₁=53 nm and P₂/D₂=1.03, H₂=170 nm or P₂/D₂=10, H₂=10 nm) compared to the BCS (H=10 µm) and FPG (P₁/D₁=1.05, H₁=53 nm and P₁/D₁=10, H₁=10 nm). (a), (b), (c), and (d) are the total light reflectivity, transmissivity, absorptivity, and the absorptivity of CS part, respectively.

In summary, while the rear grating can tailor spectral response and reduce reflection, it offers negligible improvement in the effective absorption of the silicon bulk. The front‑grating geometry remains the critical lever for maximizing bulk absorption and achieving high‑efficiency, low‑reflection silicon solar cells.