COMPACT MODEL FOR LONGCHANNEL SYMMETRIC DOPED DG Antonio Cerdeira1, Oana Moldovan2, Benjamn Iiguez2

1
COMPACT MODEL FOR LONG-CHANNEL SYMMETRIC DOPED DG
Antonio Cerdeira1, Oana Moldovan2, Benjamín
Iñiguez2 and Magali Estrada1 1 Sección de
Electrónica del Estado Sólido, CINVESTAV, México
D.F., cerdeira_at_cinvestav.mx2 Departament
dEnginyeria Electrònica, Elèctrica i Automàtica,
Universitat Rovira i Virgili,Tarragona, Spain
TU Munchen
MOS-AK/ESSDERC/ESSCIRC Workshop
Sept. 14, 2007
INTRODUCTION The main problem for modeling fully
depleted DG devices is that the potential at the
surface and the potential at the middle of the
silicon layer are related and can not be treated
independently one from the other. In addition,
the electric field and gate voltage of the device
as function of these potentials are expressed by
transcendental equations that have no analytical
solution. In this paper we present for the first
time, an analytical continuous compact model for
the current-voltage characteristics, as well as
gate-source and gate-drain capacitance in long
channel symmetric DG MOSFETs which considers a
doped silicon layer and variable mobility. The
doping concentration of the silicon layer can
vary from 1014 cm-3 to 3x1018 cm-3 and gate
dielectric and silicon layer thickness, as well
as applied voltages can vary in the typically
used ranges. In order to validate the
expressions for modeling the potential and
difference of potentials in symmetric double-gate
structures these parameters were also calculated
using the numerical procedure proposed by
Mallikarjun and the currents were simulated in
ATLAS.
Normalized charge at drain in saturation
Saturation voltage
a) b) Fig 6 - Simulated and modeled
transconductance for Si layer doping
concentrations 1015 cm-3 and 1018 cm-3. A) VD
0.05 V B) VD 1 V.
Effective drain voltage
Drain voltage with variable mobility ID
where qs and qd are the normalized charges at
source and drain W- channel width L- channel
length
E1 6300 V/cm P1 0.19 ?o 1043 cm2/Vs for 1015
cm-3 E2 1.12x106 V/cm P2 1.45 1015
cm2/Vs for 1017 cm-3 793 cm2/Vs
for 1015 cm-3
Fig 7 - Simulated and modeled I-V characteristics
and their derivative around VD 0 V for Na 1017
cm-3 VG 1.5 and ts 20 nm.
and the surface electric field is defines
as
DG DEVICE STRUCTURE AND POTENTIALS
Threshold voltage is calculated by
where
Fig 3- Comparison between simulated and modeled
linear transfer characteristics for VD 0.05 V
and two Si layer doping concentrations 1015 cm-3
and 1018 cm-3.
Fig. 8 - Gate-source and gate-drain capacitances
at drain voltages equal to 0.05 V, 0.5 V and 1 V
from simulation (symbols) and modeled (lines). Si
layer doping concentrations is equal to 1016 cm-3
for constant mobility case equal 400 cm2/Vs.
Using the detailed numerical calculation it was
found that this magnitude can be expressed by
empirical analytical expressions in the analyzed
dimension and concentrations range.
CONCLUSIONS New compact analytical model for
long symmetric double-gate MOSFETs that for the
first time, considers a doped silicon layer in a
wide range of doping concentrations, between 1014
and 3x1018 cm-3, as well as variable mobility
with the medium surface electric field. The
charge carrier density is calculated using
analytical expressions obtained for modeling the
surface potential and the difference of
potentials at the surface and at the center of
the Si doped layer, without the need to solve any
transcendental equation or to introduce adjusting
parameters. The expressions for modeling the
current-voltage and capacitance-voltage were
validated using 2D ATLAS simulations. The
mobility parameters were extracted from the
obtained transfer characteristics. Modeled and
simulated transfer characteristics in the linear
and saturation regions, output characteristics
and gate-drain and gate-source capacitance-voltage
characteristics show an excellent agreement
between them in all the practical range of gate
and drain voltages, silicon layer doping
concentrations and equivalent gate dielectric and
Si layer thickness confirming the validity of the
proposed model. Because of its features, the
model can be used for long channel devices or
used as core model where the short channel
effects can be introduced further. It can be
easily implemented in circuit simulators.

Fig 4 - Simulated and modeled output
characteristics for VG 0.5, 1 and 1.5 V for a Si
layer doping concentration of 1015 cm-3 1017
cm-3 and 1018 cm-3.
Fig 2 - Modeled and numerically calculated
potential difference ?s-?o as function of gate
voltage for different Si layer concentrations and
three drain voltages 0, 0.5 and 1 V. tox 2.24
nm and ts 34 nm.
CHARGE AND CURRENT MODELS Based on the Unified
Charge Control Model (UCCM) following expressions
were calculated Normalized to Cox?t movil charge
concentration
Surface electric field
Fig. 5 - Comparison between simulated and modeled
transfer characteristics in saturation for VD 1
V and two Si layer doping concentrations 1015
cm-3 and 1018 cm-3.