In one embodiment of an epitaxial LED device, a buffer layer (e.g. dielectric layer) between the current spreading layer and the substitute substrate includes a plurality of vias and has a refractive index that is below that of the current spreading layer. A reflective metal layer between the buffer layer and the substitute substrate is connected to the current spreading layer through the vias in the buffer layer. The buffer layer separates the current spreading layer from the reflective metal layer. In yet another embodiment, stress management is provided by causing or preserving stress, such as compressive stress, in the LED so that stress in the LED is reduced when it experiences thermal cycles. In one implementation of this embodiment, a layer is attached to the LED and reflective metal layer, and causes or preserves stress in the LED along one or more directions parallel to an interface between the LED epitaxial layers so that stress in the LED is reduced in said one or more directions when temperature of the structure is increased.