Commercially available inorganic white light emitting diodes (LEDs) are essentially based on the combination of a blue InGaN based LED chip covered by a long wavelength emitting (yellow, red) phosphor. We propose to avoid this step of phosphor deposition by taking advantage of the fact that yellow to red emission can be achieved using InGaN alloys. By stacking an InGaN/GaN multiple quantum well (QW) emitting in the yellow, acting as a light converter, and a short wavelength blue-violet pump LED grown on top, white light emission can be obtained. Furthermore, if we extend the emission spectrum of the light converter into the red, a warm white light color is demonstrated when a pump LED is grown on top. However, the high In content InGaN QWs of the light converter have a low thermal stability and the QW efficiency tends to degrade during the growth of the pump LED. Three different solutions are explored to avoid the thermal degradation of the light converter. The monolithic LED structures were grown by molecular beam epitaxy (MBE), by a combination of both MBE and metal-organic chemical vapor phase epitaxy (MOCVD), or by a low temperature full-MOCVD process. The best results are obtained using a complete MOCVD growth process. The structure and the MOCVD growth conditions are specifically adapted in order to avoid the thermal degradation of the large In composition InGaN QWs emitting at long wavelength during the growth of the subsequent layers.