This paper presents an experimental investigation into the light trapping within silicon wafers textured by upright random pyramids. In prior studies, the conventional approach to simulating random pyramids agrees poorly with experimental data at wavelengths greater than 1000 nm in which internal light trapping becomes significant. In this work, we show that expanding the optical simulation to include Phong scattering (with an exponent of 25) improved the agreement between simulation and measurement in regard to hemispherical reflectance, transmittance, and absorptance over the range of 1000-1200 nm. The best-fit Phong exponent was not significantly altered by substrate waviness, structure symmetry, or deposition of a dielectric layer. Thus, the value of the Phong exponent determined in this study is applicable to a variety of different samples textured with upright random pyramids. In addition, the simulated angular reflectance at 532 nm shows a closer agreement with the experimental results in literature when Phong scattering is included.