Three-dimensional backside mirrors patterned by microscale hemispheres were proposed to enhance the light extraction efficiency (LEE) of light-emitting diode (LED) chips. In a thorough investigation, various design parameters, including duty ratio, pattern materials, concave/convex pattern style, aspect ratio, types of mirrors, and chip configurations, were studied using the Monte Carlo ray tracing method. The square lattice of hemispheres with various radius and lattice constants was designed. It is shown that the close-packed hemisphere pattern is preferred. Several materials, including SiO2, polystyrene, sapphire, ZnO, GaN, and TiO2, were selected for the pattern layer. Generally, the optimized pattern material is the substrate material. Comparing the LEE induced by a concave pattern and a convex pattern, it is shown that the former benefits a higher LEE. Various aspect ratios of the spherical caps were also discussed. As the height of the cap increases, the LEE increases or decreases for a concave pattern or a convex pattern, respectively. Considering various mirrors, it is shown that the LEE increases with the increasing of the integral reflectivity of backside mirrors. Finally, the optimized structure parameters for backside mirrors were used in different chip configurations. In the case that of all lights extracted from LED chips were calculated, the LEE can be enhanced by 52%, 135%, and 173% for conventional, flip-chip, and thin-film LED chips, respectively. If only the lights that escaped from the top surface were calculated, the LEE can be enhanced by 65%, 209%, and 263% for conventional, flip-chip, and thin-film LED chips, respectively.