Analysis of Electron Penetration into the Insulator in Finite Quantum Wells for Nanosheet MOSFETs

In this paper, we analyze and quantitatively compare the electron density distribution along the sheet thickness of quantum wells formed in the finite and infinite potential barrier cases, assuming a nanosheet structure consisting of a 5 nm thick Si sheet and HfO2 insulator. The maximum electron density in the finite well case is about 33% larger than in the infinite well case, and the electronic areal density is about 52% larger than in the infinite well case. The electron penetration distance into the insulator is 0.160 nm, which correspond to effectively increasing the sheet thickness by 6% for a sheet thickness of 5 nm. Additionally, for a device with EOT of 0.5 nm, the penetration is accounted for about 5.7% of the insulator thickness. The penetration distance is 0.036 nm larger than that of the previous work of Barker et al. Also, the electronic areal density in insulator range is 1.4 times larger than that of the previous work. It is found that the previous method is underestimated the electron penetration into the insulator.