Low bandgap, monolithic, multi-bandgap, optoelectronic devices (10), including PV converters, photodetectors, and LED's, have lattice-matched (LM), double-heterostructure (DH), low-bandgap GaInAs(P) subcells (22, 24) including those that are lattice-mismatched (LMM) to InP, grown on an InP substrate (26) by use of at least one graded lattice constant transition layer (20) of InAsP positioned somewhere between the InP substrate (26) and the LMM subcell(s) (22, 24). These devices are monofacial (10) or bifacial (80) and include monolithic, integrated, modules (MIMs) (190) with a plurality of voltage-matched subcell circuits (262, 264, 266, 270, 272) as well as other variations and embodiments.