Light emitting diodes include a diode region comprising a gallium nitride-based n-type layer, an active region and a gallium nitride-based p-type layer. A substrate is provided on the gallium nitride-based n-type layer and optically matched to the diode region. The substrate has a first face remote from the gallium nitride-based n-type layer, a second face adjacent the gallium nitride-based n-type layer and a sidewall therebetween. At least a portion of the sidewall is beveled, so as to extend oblique to the first and second faces. A reflector may be provided on the gallium nitride-based p-type layer opposite the substrate. Moreover, the diode region may be wider than the second face of the substrate and may include a mesa remote from the first face that is narrower than the first face and the second face.