We use stochastic geometry to analyze the performance of an energy-efficient joint downlink/uplink (UL) radio-frequency (RF) 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 completely OFF and switches to a deep sleep mode. The transition back to the active mode is only achieved upon receiving enough power at the device's front end. After wake up, the device initiates regular UL communication with its serving base station (BS). The device experiences a successful wake-up event when the total received power includes a wake-up signal transmitted from its serving BS, and the UL signal-to-interference-and-noise ratio (SINR) is above a predefined threshold. On the other hand, the device experiences a false wake-up event when the wake up is due to received power from neighboring BSs excluding the serving BS. We derive lower and upper bounds for the success and false wake-up probabilities in addition to closed-form expression for the UL SINR coverage probability after successful wake up. We present performance results as a function of various key design parameters and highlight the effectiveness and tradeoffs of RF wake up for IoT devices.