The detailed performance analysis of Core Shell Gate All Around junctionless field effect transistor along with CMOS inverter as an application with quantum models is presented in this paper for the first time. To appreciate the performance of the device and the application even at smaller channel length, the comparison with classical models is also presented. The OFF current was calculated as 3.6810-16A on incorporating the quantum models. The subthreshold swing (SS) and Drain induced barrier lowering (DIBL) are found to be near ideal values. The SS and DIBL was calculated as 62.82mV/dec and 33.4mV/V. The DIBL was found to be lesser by 52.82% with quantum model than classical model. The performance obtained using quantum models are better than the classical models in terms of different parameters such as OFF current, ON current, SS, DIBL, threshold voltage, transconductance. Further, the performance of the CMOS inverter with quantum models by considering the n-type and p-type Core Shell Gate All Around junctionless field effect transistor is also presented . The OFF current of p-type and n-type was matched before designing the application. A sharp transfer characteristics of the CMOS inverter is obtained. The performance was also studied by calculating the drain current from each of p-type and n-type and found to be more than 110-7A and SNM (Static Noise Margin) was calculated as 267mV. The transient response of CMOS inverter exhibits the potential of CMOS inverter using the proposed device even at smaller channel lengths.