In this work we study the secrecy energy efficiency (SEE) maximization problem for a multi-carrier and multiple-input-multiple-output (MIMO) multiple eavesdroppers communication system. By utilizing the full-duplex (FD) operation, the system is simultaneously capable of bidirectional communication and jamming to the potential eavesdroppers. In particular, we opportunistically utilize different communication and jamming channel conditions at different subcarriers, raised due to multipath fading or large bandwidth, in order to improve the SEE. Due to the non-convex and non-smooth nature of the resulting optimization problem, we propose an iterative solution with a guaranteed convergence to a stationary point based on the successive inner approximation and Dinkelbach's algorithm. The numerical evaluations show a considerable improvement of the system SEE under the condition that the self-interference of the FD transceivers can be efficiently mitigated.