Photovoltaics (or solar cell) has been an active area for research and development, driven by the world's constantly increasing needs for power. Among the current solar technologies, thin film solar cell promises lower cost, but at the expense of lower power conversion efficiency. The efficiency of thin film solar cell can be improved using light confinement schemes commonly referred to as light-trapping. In this thesis, we develop novel light-trapping schemes utilizing photonic crystals (PCs). The optical modeling is performed with a rigorous scattering matrix approach, where Maxwell's equations are solved in Fourier space, and simulations are carried out on parallel computation environment. Although the concepts apply to any thin film solar cell structures, hydrogenated amorphous silicon (a-Si:H) single junction thin film solar cell is used for simulation due to widely available optical property data.;In the solar cell structure we design, a one dimensional (1D) photonic crystal or distributed Bragg reflector (DBR) is used as back reflector. The DBR consists of alternating layers of SiO2 and Si or Indium Tin Oxide (ITO) and Si to provide high reflectivity with little loss. A layer of two dimensional (2D) photonic crystal slab between the a-Si:H absorber layer and the DBR can diffract light at oblique angles, so that total internal reflection can occur inside the absorber layer. The light path length inside the absorber layer will be greatly increased, so will the absorption. The parameters for photonic crystals are optimized through computer simulations to obtain the maximum absorption and path length enhancement. The simulations show significantly enhanced photon harvesting between 600--775 nm below the band edge. The path length enhancement can reach several hundred at resonant peaks, far exceeding the classical limit predicted for randomly roughened scattering surfaces.