In this paper, we study terahertz (THz) simultaneous wireless information and power transfer (SWIPT) for future micro-scale 6G Internet-of-Things (IoT) networks. Since Schottky diodes are not efficient for THz energy harvesting (EH), we propose resonant tunneling diodes (RTDs) for EH at the IoT receiver (RX). As the electrical properties of RTDs are different from those of Schottky diodes, we develop a novel closed-form EH model for RTD-based RXs. In particular, we model the dependency of the instantaneous RX output power on the instantaneous received power by a non-linear piecewise function, whose parameters are adjusted to fit circuit simulation results. Furthermore, since coherent information detection is challenging at THz frequencies, we employ unipolar amplitude shift keying (ASK) modulation at the transmitter (TX) and utilize the RTD-based EH circuit at the RX to extract both information and energy from the received signal. We formulate an optimization problem to maximize the mutual information between the TX and RX signals subject to constraints on the peak amplitude of the transmitted signal and the required average harvested power at the RX. Moreover, we determine a feasibility condition for the formulated problem and, for high and low required average harvested powers, we derive the achievable information rate numerically and in closed form, respectively. Our simulation results highlight a tradeoff between the information rate and the average harvested power. Finally, we show that this tradeoff is determined by the peak amplitude of the transmitted signal and the maximum instantaneous harvested power for low and high received signal powers, respectively.