The growth and characterization of $In_{0.5}Ga_{0.5}As/In_{0.5}Al_{0.5}As$ narrow-gap inverted high electron mobility transistor structures, developed as a candidate material for spin-injection devices, are presented in this study. We have grown samples possessing surface $In_{0.5}Ga_{0.5}As$ channels of different thicknesses (30 nm and 60 nm) both with and without a thin 3 nm $In_{0.5}Ga_{0.5}As$ cap layer by using molecular beam epitaxy. We then investigated the in-plane transport properties as well as the Rashba spin-orbit coupling constant of the two-dimensional electron gas confined at the heterojunction interface.