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All-quantum simulation of an ultra-small SOI MOSFET
V. Vyurkov1 , I. Semenikhin1, V. Lukichev1, A. Burenkov2 , and A. Orlikovsky1
1. Institute of Physics and Technology, Russian Academy of Sciences, Moscow, Russia, E-mail address:
[email protected] 2. Fraunhofer Institute of Integrated Systems and Device Technology, Schottkystrasse 10,
91058 Erlangen, Germany, [email protected]
The continuing progress in silicon VLSI technology challenges the transition to silicon-on-insulator (SOI)
wafers. Just these structures definitely suppress short channel effects which substantially impair the bulk
MOSFET performance. The ultra-thin (1-5nm) fully depleted silicon will be a structure to take an ultimate
advantage of SOI wafers and to provide an advancement of silicon technology to the extreme channel length
of about 5-10nm. The quantum simulation of such small devices becomes challenging [1, 2]. The allquantum simulation program we present in this communication is based on Landauer-Buttiker approach to
calculate current. The necessary transmission coefficients are acquired from the self-consistent solution of
Schrödinger equation. The latter is stabilized with the help of expanding the wave function over the modes of
transversal quantization in the transistor channel. The program also contains a domain for one-dimensional
classical ballistics intended for calculation of the initial state for subsequent all-quantum simulation. This is a
significant point of our approach as the straightforward procedure of the self-consistent solution of
Schrödinger equation from the very beginning is diverging or, at least, extremely time-consuming. At
present, the main goal of all-quantum simulation is to clarify the impact of interference on charged impurities
and quantum reflection from self-consistent potential on I-V curve reproducibility for different randomly
doped transistors in a circuit. The extreme technology node tri-gate (wrapped channel) structure used in
simulation has a gate length 10nm, both spacers of 3nm, a fully depleted body thickness 2nm, a channel
width 10nm, an effective gate oxide thickness 1.5nm, and contact doping 1020 cm-3. 20 discrete impurities
were dispersed by the source and drain contacts to imitate
the same doping. The gate voltage was equal to zero.
2.0
The calculated drain current vs. drain voltage curves for a
CB
particular discrete impurity distribution are shown in Fig.
QB
1.5
QB
1. The upper curve (CB) corresponds to classical ballistic
simulation. The obtained potential relief was used to
1.0
calculate the quantum transmission coefficients and,
afterwards, to calculate the associated current depicted in
0.5
the lower curve (QB*). It explicitly manifests the impact of
quantum phenomena on carrier transport. Worth noting in
both cases the time-reversible equations were solved,
0.0
0.00
0.25
0.50
0.75
classical or quantum ones. However, the multiple
VDS (V)
interference between chaotically placed discrete impurities
turned out to be quite analogous to strong scattering.
Therefore, the current is approximately twice smaller.
Fig. 1. Drain current vs. drain voltage.
The slight rolloff at higher voltage can be referenced to backscattering caused by quantum mechanical
reflection from a steep potential profile inside the channel. After iterating Schrödinger equation solution with
Poisson equation solution to achieve self-consistency the I-V curve rises and approaches that for classical
ballistics. The curve QB is, in fact, the resultant curve of all-quantum simulation. The most important feature
we demonstrate is its smoothness in spite of beforehand apprehension. The next peculiarity we came across
is that the current spans within 10% for different discrete impurity realizations.
IDS (mA/m)
*
The research was supported by NIX Computer Company ([email protected]), grant #F793/8-05, and Russian
Basic Research Foundation, grants #06-07-89151-а and #06-01-00097-а.
1. M. J. Gilbert and D. K. Ferry, “Vorticity and Quantum Interference in Ultra-Small SOI MOSFETs”, IEEE
Tr. Nanotechnol., 4, pp. 355-359, 2005.
2. A. Orlikovsky, V. Vyurkov, V. Lukichev, I. Semenikhin, and A. Khomyakov, “All quantum simulation of
ultrathin SOI MOSFET”, In Nanoscaled Semiconductor-on-Insulator Structures and Devices. Kluwer
Academic Publishers, 2007, to be published.