This paper studies the performance of an energy efficient ID-based wake-up solution for Internet of Things (IoT) devices over cellular networks. When the IoT device has no data to transmit, it turns its main circuitry off and switches to sleep mode. The transition back to the active mode is only achieved upon receiving a radio frequency (RF) wake-up signal from the device's serving base station (BS) containing the device's ID. The device experiences a successful wake-up event when it receives enough power to activate an added wake-up module that decodes the received wake-up signal and triggers the main circuitry if the ID of the device is detected. Using tools from stochastic geometry, we define a new composite success wake-up probability metric that takes into consideration the joint effect of sufficient power reception for wake-up and sufficient signal to interference and noise ratio (SINR) for ID detection. The obtained results demonstrate the superiority of the proposed ID-based solution in maintaining efficient performance and low power consumption.