Previously, we demonstrated a large format 1024 × 1024 corrugated quantum well infrared photodetector focal plane array (C-QWIP FPA). The FPA has a cutoff at 8.6 μm and is BLIP at 76 K with f/1.8 optics. The pixel had a shallow trapezoidal geometry that simplified processing but limited the quantum efficiency QE. In this paper, we will present two approaches to achieve a larger QE for the C-QWIPs. The first approach increases the size of the corrugations for more active volume and adopts a nearly triangular pixel geometry for larger light reflecting surfaces. With these improvements, QE is predicted to be about 35% for a pair of inclined sidewalk, which is more than twice the previous value. The second approach is to use Fabry-Perot resonant oscillations inside the corrugated cavities to enhance the vertical electric field strength. With this approach, a larger QE of 50% can be achieved within certain spectral regions without using either very thick active layers or anti-reflection coatings. The former approach has been adopted to produce a series single color FPAs, and the experimental results will be discussed in a companion paper. In this paper, we also describe using voltage tunable detector materials to achieve multi-color capability for these FPAs.