Trusted identification is critical to secure IoT devices. However, the limited memory and computation power of low-end IoT devices prevent the direct usage of conventional identification systems. RF fingerprinting is a promising technique to identify low-end IoT devices since it only requires the RF signals that most IoT devices can produce for communication. However, most existing RF fingerprinting systems are data-dependent and/or not robust to impacts from wireless channels. To address the above problems, we propose to exploit the mathematical expression of the physical-layer process, regarded as a function $\mathbf{\mathcal{F}(\cdot)}$, for device identification. $\mathbf{\mathcal{F}(\cdot)}$ is not directly derivable, so we further propose a model to learn it and employ this function model as the device fingerprint in our system, namely $\mathcal{F}$ID. Our proposed function model characterizes the unique physical-layer process of a device that is independent of the transmitted data, and hence, our system $\mathcal{F}$ID is data-independent and thus resilient against signal replay attacks. Modeling and further separating channel effects from the function model makes $\mathcal{F}$ID channel-robust. We evaluate $\mathcal{F}$ID on thousands of random signal packets from $33$ different devices in different environments and scenarios, and the overall identification accuracy is over $99\%$.