Fig. 1
Fig.
Fig. 3 2
Fig. 4
A NEGF study of the effect of surface roughness on CMOS nanotransistors
A. Martinez1, A. Svizhenko2, M. P. Anantram2, J. R. Barker1 and A. Asenov1
1
Device Modelling Group, Dept of Electronics & Electrical Engineering, University of Glasgow, Glasgow G12 8LT,
United Kingdom; Phone: +44 141 330 4792, Fax: +44 141 330 4907, Email: antonio@elec.gla.ac.uk
2
NASA Ames Research Center, MS:229-1, Moffet Field, California 94035-1000, USA
In the past the study of the quantum transport through narrow channels in nano CMOS transistors has been mainly
limited the so called mode space approach applying 1D NEGF formalism in the transport direction even when 2D and
3D device structures were considered. The influence of interface roughness between the gate oxide and the channel on
carrier transport increases, particularly in thin body double gate devices where the roughness is correlated to body
thickness fluctuations. When the body thickness of double gate transistors is in the order of a few nanometres the
current flow has a 2D character due to irregularity of both interfaces. Therefore, a careful treatment is required in order
to resolve the sub-nanometer scale features of the interface and their impact on the carrier transport. In this work, a new
discretisation scheme has been implemented in a quantum device simulator based on a 2D self-consistent nonequilibrium Green’s function (NEGF) [1] formalism. The discretisation is based on an integral (control volume)
formulation of the NEGF equations and Poisson equation around every mesh point.
In our simulations, the electron density can penetrate into the oxide in order to describe properly the quantum
mechanical boundary conditions when small interface irregularities occur. The adopted band model is isotropic but the
effective mass reproduces the real density of states for Si. The electron transport is assumed ballistic because of short
channel length.
Devices with different randomly generated interfaces have been simulated and a detailed study of the 2D current
densities has been carried out. The interfaces are randomly generated assuming an exponential autocorrelation function
with correlation length, =1.8 nm and digitised interatomic layer step height of 0.3 nm [2]. The grid at the interface is
designed to match the one interatomic layer interface steps. The double gate (DG) MOSFET structure considered in the
simulations has a channel length of 10 nm and a channel thickness of 2 nm. The oxide thickness is fixed to 1.6 nm.
The ID-VG characteristics at 300 K for 8 different devices with randomly generated surface roughness are shown in Fig.
1 for a drain voltage of 0.5 V. The current for the device without the surface roughness is also shown for a comparison.
The influence of the interface roughness on the current and the threshold voltage is significant but the sub-threshold
slope is only slightly affected. This is because the fluctuations in oxide thickness induced by the roughness are a small
perturbation compared to the total oxide thickness, which controls the electrostatics. The ID-VG characteristics with the
interface roughness but without electron penetration in the oxide have been also calculated. The currents obtained are
around 15 % smaller compared to the cases with electron penetration but the subthreshold slope is similar. It is possible
to correlate the exact features of the interface to the IV characteristic because with short channel lengths the random
features of the surface do not average out. The density of states along the device channel shows some small jumps due
to the body thickness fluctuation created by the interface.
Fig. 2 shows the 2D map of the vector current density in the channel for a random generated oxide interface. The
interaction between the random steps at the interfaces and the body thickness variations resulting in confinement
variations produce a meandering flux of the current. The current is flowing through an effective body thickness, which
is wider than the vertical cross section. This effect modifies the current as compared with a purely horizontal current
flow. The 2D profile of the horizontal current (y-direction) is plotted in Fig. 3. It shows the squeeze of the current (ydirection) when passing the narrower regions with stronger confinement.
[1] A. Svizhenko, M. P. Anantram, T. R Govindan and B. Siegel, J. App. Phys. 91, 2343 (2002)
[2] A. Asenov, S. Kaya and A. R. Brown, IEEE Trans. Electron Dev., Vol. 50, pp.1254-1260, 2003.
Figure 1: ID-VG characteristic for different
randomly generated interfaces.
Fig. 2 The 2D current density vector field
and the effective cross-section created as a
result of the interface roughness.
Fig. 3. 2D profile of the current in the
transport direction showing the non
homogeneity along the channel.