  Since thin-film silicon solar cells have limited optical absorption, we
explore the effect of a nanostructured back reflector to recycle the unabsorbed
light. As a back reflector we investigate a 3D photonic band gap crystal made
from silicon that is readily integrated with the thin films. We numerically
obtain the optical properties by solving the 3D time-harmonic Maxwell equations
using the finite-element method, and model silicon with experimentally
determined optical constants. The absorption enhancement relevant for
photovoltaics is obtained by weighting the absorption spectra with the AM 1.5
standard solar spectrum. We study thin films either thicker ($L_{Si} = 2400$
nm) or much thinner ($L_{Si} = 80$ nm) than the wavelength of light. At $L_{Si}
= 2400$ nm, the 3D photonic band gap crystal enhances the spectrally averaged
($\lambda = 680$ nm to $880$ nm) silicon absorption by $2.22$x (s-pol.) to
$2.45$x (p-pol.), which exceeds the enhancement of a perfect metal back
reflector ($1.47$ to $1.56$x). The absorption is enhanced by the (i) broadband
angle and polarization-independent reflectivity in the 3D photonic band gap,
and (ii) the excitation of many guided modes in the film by the crystal's
surface diffraction leading to enhanced path lengths. At $L_{Si} = 80$ nm, the
photonic crystal back reflector yields a striking average absorption
enhancement of $9.15$x, much more than $0.83$x for a perfect metal, which is
due to a remarkable guided mode confined within the combined thickness of the
thin film and the photonic crystal's Bragg attenuation length. The broad
bandwidth of the 3D photonic band gap leads to the back reflector's Bragg
attenuation length being much shorter than the silicon absorption length.
Consequently, light is confined inside the thin film and the absorption
enhancements are not due to the additional thickness of the photonic crystal
back reflector.
