For decades, the field of cryogenic low noise amplification has been driven by specialized semiconductor technologies such as InP and GaAs HEMTs, which, when cooled to extremely low temperatures, can achieve noise levels as low as 2\,K across wide bandwidths. However, as quantum computing research and cryogenic electronics continue to advance, the demand for scalable and widely available semiconductor solutions has grown. CMOS technology, which dominates modern semiconductor manufacturing, has shown significant promise for cryogenic applications, particularly in the development of low noise amplifiers (LNAs) for quantum computing readout systems. This dissertation explores the potential of cryogenic CMOS for ultra-low-noise microwave amplification, focusing on the cryogenic noise model of MOSFETs. The work is structured into three main sections: 1. Cryogenic device characterization and modeling: A detailed study of MOSFET devices across seven different technology nodes, examining their dc and small-signal performance from room temperature down to cryogenic levels have been presented. A key focus is placed on extracting small-signal noise models and characterizing the shot noise suppression factor, also known as the Fano factor. Together, the Fano factor and small-signal model parameters provide a clear and thorough understanding of the transistor noise model. The study includes a detailed analysis of the Fano factor at room temperature across devices of varying gate lengths and bias conditions. 2. Cryogenic CMOS LNA Design: Utilizing the extracted cryogenic small-signal models and the assumption of a temperature-independent Fano factor, a cryogenic noise model is developed. This model serves as the foundation for designing LNAs optimized for cryogenic operation, thereby demonstrating the noise performance limits of cryo-CMOS LNAs. The amplifiers also function as test-vehicles to experimentally validate or refute the hypothesis that the Fano factor does not change with temperature. 3. Cryogenic Fano factor extraction: The cryogenic Fano factor has been extracted through noise measurements of the amplifiers from three different CMOS technology nodes. Notably, the Fano factor is indeed found to be temperature-independent at a fixed current density for a given gate length. This finding significantly simplifies the extraction of the cryogenic MOSFET noise model, streamlining the design process for cryo-CMOS LNAs.