Recent studies of n-type semiconductors have demonstrated spin-coherent transport over macroscopic distances, with spin-coherence times exceeding 100 ns; such materials are therefore potentially useful building blocks for spin-polarized electronics ('spintronics'). Spin injection into a semiconductor (a necessary step for spin electronics) has proved difficult; the only successful approach involves classical injection of spins from magnetic semiconductors. Other work has shown that optical excitation can provide a short (<500 ps) non-equilibrium burst of coherent spin transfer across a GaAs/ZnSe interface, but less than 10% of the total spin crosses into the ZnSe layer, leaving long-lived spins trapped in the GaAs layer (ref. 9). Here we report a 'persistent' spin-conduction mode in biased semiconductor heterostructures, in which the sourcing of coherent spin transfer lasts at least 1-2 orders of magnitude longer than in unbiased structures. We use time-resolved Kerr spectroscopy to distinguish several parallel channels of interlayer spin-coherent injection. The relative increase in spin-coherent injection is up to 500% in the biased structures, and up to 4,000% when p-n junctions are used to impose a built-in bias. These experiments reveal promising opportunities for multifunctional spin electronic devices (such as spin transistors that combine memory and logic functions), in which the amplitude and phase of the net spin current are controlled by either electrical or magnetic fields.