At block 280 of FIG. 2, a first contact structure may be formed to connect the semiconductor structure 301, and second contact structures may be formed to connect the p-doped cladding semiconductor layers 302. Referring to FIGS. 7A and 7B, a first contact structure 601 may be formed through the second dielectric layer 402 and the hard mask layer 200 to connect the semiconductor structure 301, and second contact structures 602 may be formed through the second dielectric layer 402 to connect the p-doped cladding semiconductor layers 302. The first contact structure 601 and the second contact structures 602 may each include, for example, gold (Au), titanium (Ti), copper (Cu), silver (Ag), Aluminum (Al), tungsten (W), cobalt (Co), Chromium (Cr), molybdenum (Mo), zirconium (Zr), nickel (Ni), tantalum (Ta), platinum (Pt), or an alloy thereof. The formation of the first contact structure 601 and the second contact structures 602 may include a step of etching contact holes through the second dielectric layer 402 and hard mask layer 200 to expose the top surfaces of the semiconductor structure 301 and the p-doped cladding semiconductor layers, and followed by a step of filling these contact holes with conductive material. To form contact holes, a suitable reactive ion etching (RIE) method for etching dielectric layer and hard mask layer may be used to etch the second dielectric layer 402 and hard mask layer 200. A conductive material may be formed to fill the contact holes with various deposition processes include, but are not limited to: physical vapor deposition (PVD), chemical vapor deposition (CVD), atomic layer deposition (ALD), electrochemical deposition (ECD), electroplating, electroless plating and spin coating.