Over the past few years, the size of semiconductor devices has been shrinking whereas the density of transistors has exponentially increased. Thus, thermal management has become a serious concern as device performance and reliability is greatly affected by heat. An understanding of thermal transport properties at device level along with predictive modelling can lead us to design of new systems and materials tailored according to the thermal conductivity. In our work we first review different models used to calculate thermal conductivity and examine their accuracy using the experimentally measured thermal conductivity for Si. Our results suggest that empirically calculated rates used in thermal conductivity calculations do not capture the scaling behavior for three phonon scattering mechanism properly. This directly affects the estimation of the thermal conductivity and therefore we need to capture them more accurately. Also, we observe that at low temperature the Callaway and the improved Callaway model show good agreement where boundary scattering is dominant, whereas at high temperature iterative and RTA models show good agreement where three-phonon scattering is dominant. Therefore, their lies a need for a model which can characterize K properly at low and high temperature. Second, we then calculate the three phonon scattering rates using first-principles and combine them into the Callaway model. Through our work we successfully build a hybrid model which can be used to describe thermal conductivity of Si for a temperature range of 10K to 425K which captures the thermal conductivity accurately. We also show that in case of Si the improved Callaway model and Callaway model both perform equally well.