One-Dimensional Analysis of Subthreshold Characteristics of SOI-MOSFET Considering Quantum Mechanical Effects

We have been studying on subthreshold characteristics of SOl MOSFETs in terms of substrate bias dependence, using a 1-D Poisson equation on an SO1 multi-layer structure for estimating structural parameters of real devices[l]. Here, we consider quantum mechanical effects in the electron inversion layer of thin SOl MOSFETs, implementing a self-consistent solver of Poisson and Schr6dinger equations in a 1-D subthreshold simulator. From results of simulations, we have concluded that quantum mechanical effects need to be considered in analizing thin SOl devices.


INTRODUCTION
In SOI(Silicon-on-Insulator) devices, substrate bias has great influence on subthreshold characteristics of MOSFET's such as threshold voltage "Vth" and sub- threshold voltage swing "S".Those characteristics are also affected by the structural device parameters of SOI multi-layers [2][3] [4].On the other hand, it is well-known that in thin electron inversion layer or thin silicon layer of SO1 devices, 2-dimensional elec- tron quantization effects should be taken into account [5].
In this study, we have implemented a self-consist- ent solver of Poisson and Schr6dinger equations as a 1-D SO1 MOSFET subthreshold device simulator and estimated device parameters by fitting simulated results with measured Vth-VBs characteristics curves.

Quantum Mechanical Modeling
Figure shows a schematic cross section of an SOI MOSFET.We solve following quantum mechanical models in the 1-D SOI multi-layer structure.Poisson equation (eq. 1) and Schr6dinger equation (eq.2) are solved self-consistently by the iterative method [6].
2mk dx 2 -qV(x) di (x) (2)   k=l,h Here, k denotes the lower or higher subband ladder; l/h, and denotes the subband index./:(x) is the elec- tron wave function and Eikis the energy level for ith subband of ladder k. nv k is the valley degeneracies (nvh= 2,nvh 4).m (= 0.98m 0 m 0 is the free elec- tron mass) and mh(= 0.19m0) are longitudinal and k is formutransverse mass of an electron.Then, m d lated as follows: md mh, md h /mlm h.
Oxide SOl-Layer Buried-Ox.Drain Current Modeling Drain current, I d, is calculated as eq.5, which is com- posed of the diffusion current term.The drift current term is not taken into account because the major con- duction mechanism is the carrier diffusion in subthreshold region.
kT ns na Id qWlu (5) q L Here, n d and n are channel carrier densities near source and drain, which are obtained by the 1-D simu- lation.We took into account thermal, ionized impurity and surface scattering effects for mobility, bt.

Comparison of Classical and Quantum-Mechanical Results
Figure 2 shows distributions of electric potential and electron concentration in the SOI layer for both classical and quantum mechanical simulations.It is notable that the classical simulation gives the maxi- mum of electron concentration at the front gate-oxide interface, while the quantum mechanical result shows zero at the interface.Figure 2 also shows a slight dif- ference in the electric potential distributions.Drain currents are 1.95 x 10-7[A] for the classical simula- tion and 1.54 10-VIAl for the quantum mechanical simulation, for the device of L=W--100gm.

DEVICE PARAMETER ESTIMATION
We measured Vth-VBs characteristics of SO1 MOS- FETs (Vth@Id=lOnA/L=W=lOOgm).Then, we fitted the simulated curves with measured data, tuning device parameters such as channel dopant concentra- tion, N A, gate oxide thickness, .Tfo x, SOl layer thick- ness, Tsol, and buried oxide thickness, Tbox.
Curve fitting procedure was carried out by the steepest descent method, evaluating a mean-square error of measured and simulated threshold voltages under various substrate bias conditions.
Figure 3 shows the best fitted curves along with measured data.The device parameters estimated from the curves are shown in Table I, with designed device parameters of real devices.The quantum mechanical model gives better results than the classical model in terms of extracted device parameters.

CONCLUSION
A device simulator for 1-D SOI MOSFET subthresh- old characteristics with a self-consistent Poisson and Schr6dinger equations solver was presented.Using the simulator, SOI device parameters were estimated by a curve fitting method for Vth-V,s characteristics.
From the results, it was concluded that the quantum mechanical effects should be considered in thin SOI devices to obtain a better agreement with experimental data.
FIGURE1-D device simulation of SO1 MOSFET with front/back bias conditions