In a thermophotonic device used in an energy-harvesting configuration, a hot light-emitting diode (LED) is coupled to a photovoltaic (PV) cell by means of electroluminescent radiation in order to produce electrical power. Using fluctuational electrodynamics and the drift-diffusion equations, we optimise a device made of an AlGaAs PIN LED and a GaAs PIN PV cell with matched bandgaps. We find that the LED can work as an efficient heat pump only in the near field, where radiative heat transfer is increased by wave tunnelling. A key reason is that non-radiative recombination rates are reduced compared to radiative ones in this regime. At 10 nm gap distance and for 100 cm.s −1 effective surface recombination velocity, the power output can reach 2.2 W.cm −2 for a 600 K LED, which highlights the potential for low-grade energy harvesting.