چكيده به لاتين
Mathematics is a tool that can be used to describe physical phenomena, describe a fabricated device and investigate measurement results. In this thesis, some of the less studied research topics are investigated and a new description of CMOS image sensors and pinned photodiodes are introduced by proposing novel mathematical models. In this thesis, a thorough investigation of prior studies is performed and it is concluded that two of the less studied subjects in modeling of CMOS image sensors are pinned photodiode capacitance and pinned photodiode's pinning process. In order to model PPD capacitance, inner region is proposed as a series capacitance to pn junction capacitances. By incorporating the series capacitance, the calculation of total capacitance vs. PPD potential is performed more accurately compared to previous models. In order to evaluate the model, a comparison is presented with an experimental result. To develop the pinning process model, the definition of inner region with variable boundaries is incorporated. The proposed model is a system of equations with 5 different equations and 5 unknown parameters. In the calculations of the model which is performed using MATLAB and published alongside the paper, it is possible to calculate dimensions or dopant concentrations or electron population as unknown parameters. It should be mentioned that the proposed model is the first published model that is capable of calculating PPD pinning characteristic, PPD electron population as a function of PPD potential. The evaluation of the model is performed by comparing with two experimental PPD pinning characteristics. The third model which can also be used to calculate the PPD characteristic, is a more general model which is capable of calculating the PPD characteristics for 3-D PPDs such as non-rectangular PPDs or PPDs with dimensions smaller than or comparable to 1 µm. The model benefits from the calculations of PPD SCR electron population and also the calculation of PPD inner region SCR. The evaluations are performed by comparing the results with two experimentally obtained PPD pinning characteristics. It is shown that the model is more accurate compared to the previous model. Moreover, the design process of CMOS image sensors is investigated and a list of necessary rules to design a CMOS image sensor is introduced. In the end, the design process and optimization of two novel CMOS image sensors are described. In the first device, a CDTI is used as a shared vertical transfer gate which is capable of complete vertical charge transfer despite the fact that a large parasitic capacitance exists between the transfer gate and the buried PPD. The evaluations are performed by using mathematics and carefully investigating the device outputs. The second device is designed to achieve a faster charge transfer by only changing one mask in the fabrication process. The idea resulted in 30% reduction in charge transfer time. The evaluation of the device simulations are performed by comparing the simulation with experimental results. Finally, the device performance is evaluated by using mathematics.
