Graphene, a monolayer of carbon atoms, has gained prominence to augment existing chip-scale photonic and optoelectronic applications, especially for sensing in optical radiation, owing to its distinctive electrical properties and bandgap as well as its atomically thin profile. As a building block of photodetection, graphene has been co-integrated with mature silicon technology to realize the on-chip, high-performance photo-detecting platforms with broad spectral response from the deep-ultraviolet (UV) to the mid-infrared (MIR) regime. The recent state-of-the-art graphene-based photodetectors utilizing the combination of colloidal quantum dots (QDs) and graphene have been intensively studied, where QDs function as the absorber and the role of graphene is as a fast carrier recirculating channel. With such a configuration, an ultrahigh sensitivity can be achieved on account of the photogating mechanism; however, the response time is slow and limited to the millisecond-to-second range. To achieve balance between high sensitivity and fast response time, we have demonstrated a new photodetector that is based on graphene/two-dimensional heterostructures. The homogeneous thickness and the large contact of the heterostructure give rise to fast carrier transporting between the thin absorber layer and the graphene, leading to a fast response time. This thesis carefully investigates the optimization of fabrication as well as optoelectronic characterization of photodetectors based on graphene/semiconductor heterostructures field-effect transistors (GFETs). GFETs with different architectures were demonstrated and systematically studied under optical illumination ranging from deep-UV to MIR at varying optical powers. Noise behaviors have been studied under different device parameters such as device structure, area and gate-bias. Results show that the flicker noise of graphene-based devices can be explained by the McWhorter model in which the fluctuation of carrier numbers is the dominant process of noise in low frequencies; thus, it can be scaled down by reducing the number of introduced charged carriers with optimized fabrication. Besides, the impact of absorber on top of graphene and the bottom substrate has been comprehensively explored through various experimental techniques including current-voltage (IV), photo-response dynamics, and noise characterization measurements. With our configuration, the high sensitivity and fast response time of photodetectors can be obtained at the same time. In addition to this, the study of the bottom substrate with different doping levels suggests a concept of dual-photogating effect which is induced by the top absorbent material and the photoionization of the doped silicon substrate. In summary, this thesis showcases novel device architecture and fabrication procedures of GFETs photodetectors, optimizes device structure, quantifies the performance and evaluates the effect of various absorbent materials and substrate. It provides insight into the improvement of possible routes to achieve a broadband photo-detecting system with higher sensitivity, faster response time and lower noise level. / Doctor of Philosophy / The rapid expansion of networked devices and the development of the Internet of Things have given rise to an internet traffic and data explosion. Since conventional electrical interconnects are unable to rise to the occasion of the ever-growing demands of information technology and communication networking, next-generation alternative interconnects with higher performance and lower loss are attractive alternatives as the chip-scale optical interconnection. Among various optical interconnects, photodetectors play significant roles by converting optical input into electrical signal output. Sensing of light has a great impact in daily applications such as telecommunications, night vision, biomedical imaging and biochemical sensing. Graphene, belonging to the class of 2-dimensional materials, shows enormous potential as a building block of photodetection owing to its outstanding optical and electrical properties. One possible route to develop a sensitive and fast-operating on-chip photodetector is to integrate graphene into silicon photonics platforms since the latter has been widely studied and driven to maturity. In this thesis, graphene-based photodetectors with novel architectures have been fabricated, demonstrated and systematically investigated. Various measurements have been taken to quantify the performance of photodetectors in a wide detecting range from deep ultraviolet to mid-infrared.