Millimeter-wave astronomy contains rich information from the cosmic microwave background to cold matter, like cosmic dust and molecular gas. It is one of the key wavelengths to understand star formation and the evolution of the universe. The IRAM 30-m telescope is one of the largest telescopes in the millimeter wavelength range. It fully covers from the 2 mm to 0.8 mm atmospheric windows. For continuum wave observation, the NIKA2 instrument is designed for the 2 mm and 1 mm windows, and has been producing scientific results since 2017. NIKA2 has angular resolutions of 17.5" for 2 mm wavelength and 10.9" for 1 mm wavelength with a 6.5' field-of-view. To cover the 80 mm focal plane, 4-inch kilo-pixel lumped-element kinetic-inductance detector (LEKID) arrays are installed. This thesis studies possible improvements of the LEKID design utilized in the NIKA2 instrument, in order to render the instrument even more powerful in the available frequency windows.In this thesis, we first introduce the scientific motivation in Chapter 1 and the principles of LEKID in Chapter 2. In Chapter 3, the optical response of the current NIKA2 1 mm array is simulated and compared to measurements. The simulation shows the Hilbert curve inductor design has a 100% absorption efficiency. The measurement matches the simulated frequency response. In Chapter 4, we made a small pixel design to improve on-telescope angular resolution. The measurements show that the resolution can be improved from 10.9" to 10.2" with the new design. In Chapter 5, we applied the capacitor trimming technique on a compact and quasi lumped-element pixel design. Before trimming only 71% resonators can be used in the limited bandwidth. After trimming a yield of 97% is achieved. In Chapter 6, We further extended this technique on a 4-inch kilo-pixel array design. The optical yield of 76% is achieved, limited by the readout system and fabrication yield, instead of by the trimming technique. In Chapter 7, we developed a new method to locate the positions of resonators by measuring the reflected phase. We discuss the potential to use this technique on a large format array.