High quality three-dimensional (3D) heterostructures were constructed by selective area (SA) molecular beam epitaxy (MBE) using a specially patterned GaAs (001) substrate to improve the efficiency of tarrier transport. MBE growth parameters such as substrate temperature, V/III ratio, growth ratio, group V sources (As2, As4) were varied to calibrate the selective area growth conditions and the 3D GaAs-AlGaAs heterostructures were fabricated into the ridge type and the V-groove type. Scanning micro-photoluminescence $({mu}-PL)$ measurements and the following analysis revealed that the gradually (adiabatically) coupled 1D-2DEG (electron gas) field effect transistor (FET) system was successfully realized. These 3D-heterostructures are expected to be useful for the realization of high-performance mesoscopic electronic devices and circuits since it makes it possible to form direct ohmic contact onto the (quasi) 1D electron channel.