Inexpensive tags powered by energy harvesting (EH) can realize green (energy-efficient) Internet of Things (IoT) networks. However, tags are vulnerable to energy insecurities, resulting in poor communication ranges, activation distances, and data rates. To overcome these challenges, we explore the use of a reconfigurable intelligent surface (RIS) for EH-based IoT networks. The RIS is deployed to enhance RF power at the tag, improving EH capabilities. We consider linear and non-linear EH models and analyze single-tag and multi-tag scenarios. For single-tag networks, the tag's maximum received power and the reader's signal-to-noise ratio with the optimized RIS phase-shifts are derived. Key metrics, such as received power, harvested power, achievable rate, outage probability, bit error rate, and diversity order, are also evaluated. The impact of RIS phase shift quantization errors is also studied. For the multi-tag case, an algorithm to compute the optimal RIS phase-shifts is developed. Numerical results and simulations demonstrate significant improvements compared to the benchmarks of no-RIS case and random RIS-phase design. For instance, our optimal design with a \num{200}-element RIS increases the activation distance by \qty{270}{\percent} and \qty{55}{\percent} compared to those benchmarks. In summary, RIS deployment improves the energy autonomy of tags while maintaining the basic tag design intact.
