In this paper, we study the spectral efficiency (SE) and energy efficiency (EE) of wireless-powered full-duplex (FD) heterogeneous networks (HETNETs). In particular, we consider a two-tire HETNET with half duplex (HD) massive multiple-input multiple-output (MIMO) macrocell base stations (MBSs), FD small cell base stations (SBSs) and FD user equipments (UEs). UEs rely on energy harvesting (EH) from radio frequency signals to charge their batteries for communication with serving base stations. During the energy harvesting phase, UEs are associated to MBSs/SBSs based on the mean maximum received power (MMP) scheme. In the consecutive data transmission phase, each UE downloads packets from the same MBSs/SBSs, while uploads packets to the nearest SBSs using the harvested energy. We use tools from stochastic geometry to develop an analytical framework for the average UL power transfer and the UL and DL coverage probability analysis. We further investigate the EE of the proposed DUDe scheme to demonstrate the impact of different system parameters on the EE. Finally, we validate the analytical results through simulation and discuss the significance of the proposed DUDe user association to improve the average DL and UL SE in the wireless-powered FD HETNETs.