It has been shown that whispering gallery modes can be used to obtain a combination of modal and geometrical quasi-phase-matching in second-harmonic generation. This could be achieved in isotropic, nonferroelectric, strongly dispersive and highly nonlinear materials such as III-V semiconductors. Unfortunately the poor overlap between the second-harmonic field and second order nonlinear polarization limits the conversion efficiency. In this paper we show that by engineering the refractive index it is possible to increase field overlap and to enhance effective second order nonlinear polarization of semiconductor microdisks.