A light-emitting device (LED) is described which exhibits high extraction efficiency and an emission profile which is substantially more directional than from a Lambertian source. The device comprises a light generating layer disposed between first and second layers of semiconductor material, each having a different type of doping. An upper surface of the first layer has a tiling arrangement of inverted pyramidal or inverted frustro-pyramidal indentations in the semiconductor material filled by a material of different refractive index and which together comprise a photonic band structure. The indentations and their tiling arrangement are configured for efficient extraction of light from the device via the upper surface of the first layer and in a beam that is substantially more directional than from a Lambertian source. An enhanced device employs a reflector beneath the second layer to utilise the microcavity effect. A method for fabricating the device is also described which employs anisotropic wet etching to produce the inverted pyramidal or inverted frustro-pyramidal indentations.