Lattice-matched GaInAs p-i-n diodes of different i-region thicknesses have been MBE grown on n-type InP (100) and (111) crystallographic orientation substrates. It has been found that terahertz emission from such structures when illuminated with femtosecond laser pulses can be more efficient than that from the known to date best surface terahertz emitter (111) p-InAs. The explanation of the terahertz generation mechanism from p-i-n diodes is based on ultrafast photocurrent effects. Anisotropic transient photocurrents causing the 3ϕ azimuthal angle dependence are observed in the sample on (111) substrate. These p-i-n structures allow covering a technologically important 1.55 μm range and may provide controllability and compactness of a THzTDS system when biased with an external voltage source.