A light-emitting device includes a light-emitting die and, at least partially surrounding the light-emitting die, a phosphor element comprising (i) a binder and (ii) disposed within the binder, one or more wavelength-conversion materials for absorbing at least a portion of light emitted from the light-emitting die and emitting converted light having a different wavelength. The phosphor element has an outer contour having (i) a curved region that defines only a portion of a hemisphere having a hemisphere radius, and (ii) a base opposite the curved region having a non-zero centroid z-offset within the hemisphere, a ratio of the centroid z-offset to the hemisphere radius having a value ranging from 0.3 to 0.8.