Full 3D numerical modeling is undertaken on light-emitting diode structures with patterned surfaces represented by regular, pseudorandomly disordered, and uniformly distributed random arrays of square holes to investigate both grating and random scattering phenomena. Unlike typical roughened surface LEDs, no recycling mirror is present below the source, enabling straightforward implementation in existing device designs. The period or feature width of the arrays is varied and the output emission intensity calculated. A maximum enhancement factor of $\sim 2$ is seen for both a disordered pattern with an array period of $1.7\mathrm{\mu }\mathrm{m}$ and pattern depth of $0.4\mathrm{\mu }\mathrm{m}$ and a particular random pattern with a feature width of $0.85\mathrm{\mu }\mathrm{m}$ and depth of $0.4\mathrm{\mu }\mathrm{m}$ . The enhancement is believed to be due to mitigation of both total internal reflection and Fresnel reflection phenomena at the semiconductor–air interface.