Study of the quantization effects in MOS inversion layer using a improved approach

Abstract

With the scaling down of MOSFET feature size, quantum mechanical (QM) effects on these devices are becoming important. It is found that, due to quantization, carriers move a distance away from the Si/ Si02 interface, which increases the effective gate oxide thickness and thereby affects the effective gate capacitance, inversion charge density, threshold voltage etc. Hence, an accurate modeling for such devices must be made to include these QM effects, which require calculation of eigenenergies and wavefunctions from Schr6dinger's equation. Conventionally this calculation is done using a boundary condition, referred to as conventional or zero boundary condition, that assumes that wavefunctions vanish at the interface i.e. there is no wavefunction penetration inside the oxide region. Actually, the validity of zero boundary condition is not justified for the deep submicron (~ 3011 gate oxide thickness) devices, as the error made is comparable to device dimensions. In such cases, for a more accurate modeling, the wavefunction penetration in the oxide should be taken into account. This work calculates gate capacitances of deep submicron MOSFETs by considering wavefunction penetration in the oxide using a new asymptotic boundary condition. In this work, using both conventional and asymptotic boundary conditions, shift of DC charge centroid and gate capacitance are calculated. To reduce the computational complexity in QM calculations, a recently developed Green's function formalism along with transmission line analogy is employed. A comparison of the calculated results show that the results are dependent on the choice of boundary conditions. It is also seen that the choice of appropriate boundary condition becomes more important as the devices are scaled down with reduced oxide thickness and increased surface electric field.