Insights into Backscattering Suppression in Solar Cells from the Helicity-Preservation Point of View

We show that the antireflection performance of nanoparticle arrays on top of solar-cell stacks is related to two conditions: a high enough degree of discrete rotational symmetry of the array and the ability of the system to suppress crosstalk between the two handednesses (helicities) of the electromagnetic field upon light-matter interaction. For particle-lattice systems with a high enough degree of discrete rotational symmetry $2\pi /n$ for $n\ge 3$, our numerical studies link the suppression of backscattering to the ability of the system to avoid the mixing between the two helicity components of the incident field. In an exemplary design, we optimize an array of ${\mathrm{Ti}\mathrm{O}}_2$ disks placed on top of a flat heterojunction solar-cell stack and obtain a threefold reduction of the current loss due to reflection with respect to an optimized flat reference. We numerically analyze the helicity-preservation properties of the system, and also show that a hexagonal array lattice, featuring a higher degree of discrete rotational symmetry, can improve over the antireflection performance of a square lattice. Importantly, the disks are introduced in an electrically decoupled manner such that the passivation and electric properties of the device are not disturbed.

Figure 1

(a) Reflectance from dual-symmetric systems with rectangular ($C_2$) and square ($C_4$) rotational symmetries under normal incidence. The systems are made of hypothetical materials with electric permittivities ${ϵ}_r$ equal to those of natural materials and whose magnetic permeabilities are set to ${\mu }_r={ϵ}_r$ to achieve perfect duality symmetry. The natural materials and geometry are as follows: a semi-infinite $c$-$\mathrm{Si}$ substrate, an absorbing 300-nm-thick film of c-Si, an 8-nm-thick layer of passivating $a$-$\mathrm{Si}$ (intrinsic and $n^{+}$-doped), an ITO layer of 50-nm thickness, and ${\mathrm{Ti}\mathrm{O}}_2$ disks with a height of 100 nm and a diameter of 300 nm. The $C_4$ unit cell parameter is $a=500\mathrm{nm}$. The $C_2$ unit cell parameters are $a_x=806.5\mathrm{nm}$ and $a_y=310\mathrm{nm}$. The unit cells of the systems are schematically shown in the inset. (b) Reflectance from the system with square ($C_4$) rotational symmetry. Colors correspond to different ratios of relative permeability with respect to relative permittivity.

Figure 2

(a) Reflectance versus wavelength for a standard flat HJT solar cell with optimized ITO thickness and for an optimized nanocoated structure. The incident field is a normally incident plane wave with right-handed polarization (helicity $-1$). (b) Normalized reflected powers of EM fields of both helicities $P_{+}$ and $P_{-}$ for the square array comprised of ${\mathrm{Ti}\mathrm{O}}_2$ disks placed on the top surface of HJT solar cell. The system is schematically shown in the inset; lattice constant $a=500\mathrm{nm}$. The layers comprising the substrate are as follows: a semi-infinite $c$-$\mathrm{Si}$ substrate, an absorbing 300-nm-thick film of c-Si, a 8-nm-thick layer of passivating $a$-$\mathrm{Si}$ (intrinsic and $n^{+}$-doped), an ITO layer of 50-nm thickness. The ${\mathrm{Ti}\mathrm{O}}_2$ disks have a height of 100 nm and a diameter of 300 nm.

Figure 3

(a) Normalized specularly reflected powers of EM fields of both helicities $P_{+}$ and $P_{-}$ for an isolated nanodisk on top of the HJT solar-cell-layer stack under normal incidence of illumination with a right-handed polarized plane wave (helicity $-1$). The system is schematically shown in the inset and has the same parameters as in Fig. 2 except that we consider here an isolated disk and not an array. (b)–(d) Polar plots of the far-field intensities at wavelengths $\lambda =300$, 500, and 600 nm, respectively. The far-field intensities are computed in a plane that contains the cylinder axis of the disk.

Figure 4

(a) Reflectance from a nanocoated substrate for $C_4$ (bold lines) and $C_6$ (dashed lines) lattices under normal incidence. The electric permittivity of the substrate and disks correspond to those of $c$-$\mathrm{Si}$ and ${\mathrm{Ti}\mathrm{O}}_2$, respectively. Colors correspond to different ratios of relative permeability with respect to relative permittivity. (b) Reflectance from a $c$-$\mathrm{Si}$ substrate nanocoated with a ${\mathrm{Ti}\mathrm{O}}_2$ disk array for different symmetries in the case of natural materials (${\mu }_r=1$): rectangular ($C_2$), square ($C_4$), and hexagonal ($C_6$) lattices. The lattice constants are $a_x=625\mathrm{nm}$, $a_y=400\mathrm{nm}$ for $C_2$, $a=500\mathrm{nm}$ for $C_4$, and $a=500\mathrm{nm}$ for $C_6$.

Figure 5

Refractive index $n$ and extinction coefficient $k$ of a passivation layer comprised of intrinsic $a$-$\mathrm{Si}$ and $n^{+}$-doped $a$-$\mathrm{Si}$.