We report the observation of field emission from InP nanocrystals epitaxially grown on an array of p-Si nanotips. We prove that field emission can be enhanced by covering the InP nanocrystals with graphene. The measurements are performed inside a scanning electron microscope chamber with a nano-controlled W-thread used as an anode. We analyze the field emission by Fowler-Nordheim theory and find that the field enhancement factor increases monotonically with the spacing between the anode and the cathode. We also show that InP/p-Si junction has a rectifying behavior, while graphene on InP creates an ohmic contact. Understanding the fundamentals of such nanojunctions is key for applications in nanoelectronics.