Hardware accelerators provide significant speedup and improve energy efficiency for several demanding deep neural network (DNN) applications. DNNs have several hidden layers that perform concurrent matrix-vector multiplications (MVMs) between the network weights and input features. As MVMs are critical to the performance of DNNs, previous research has optimized the performance and energy efficiency of MVMs at both the architecture and algorithm levels. In this paper, we propose to use emerging silicon photonics technology to improve parallelism, speed and overall efficiency with the goal of providing real-time inference and fast training of neural nets. We use microring resonators (MRRs) and Mach-Zehnder interferometers (MZIs) to design two versions (all-optical and partial-optical) of hybrid matrix multiplications for DNNs. Our results indicate that our partial optical design gave the best performance in both energy efficiency and latency, with a reduction of 33.1% for energy-delay product (EDP) with conservative estimates and a 76.4% reduction for EDP with aggressive estimates.