Figure 10: The pillar diameter dependence of the square root of PL integrated intensity. The fitting results by the least-square method are shown with the dashed line. The embedded pillar shows the 6.4-times increase of the slope. PL intensity is proportional to the luminescence area under the constant QD areal density. Thus the square root of PL integration intensity depends linearly on the pillar diameter. PL intensity is proportional to excitation rate ( ), internal quantum efficiency, number of QDs, light extraction efficiency ( ), and pillar cross section. Therefore, assuming the identical internal quantum efficiency for both structures, the fitted slope is proportional to , which reveals -times enhancement of , that is, the photon extraction efficiency including that of the excitation efficiency. In the Nb embedded structure, 0.3  m shifts from the origin is observed. This suggests formation of optically inactive region about 0.15  m from the Nb surface.