A broadcast model in which the transmitter sends confidential and common messages to two receivers is considered. It is assumed that the common and confidential data is stored in buffers prior to transmission and the transmitter operates under constraints on buffer violation probability. Under such constraints, effective capacity formulation is employed to determine the throughput. Moreover, energy per bit is used as the energy efficiency metric and energy efficiency is studied in the low-SNR regime. In particular, minimum energy per bit required for the reliable communication of common and confidential messages is determined and wideband slope regions are identified. The impact of buffer constraints, correlation between channels and secrecy requirements on the energy efficiency is investigated.