A UNIFIED MODEL OF THRESHOLD VOLTAGE, SUBTHRESHOLD SLOPE AND
INTERFACE COUPLING IN THIN FILM SO1 MOSFET'S
A. M. Ionescu1,2,S. Cristoloveanu', A. RusuZ,A. Chovet' and A. Hassein-Bey'
'LPCS, ENSERG, 23, Rue des Martyrs, BP 257,38016 Grenoble Cedex, France,
Fax: (33) 76 85 60 70, Phone: (33) 76 85 60 40
2University "POLITEHNICA"Bucharest, 3 13, Splaiul Independentei, 7000 Bucharest, Romania
Although powefil device simulators are being developed, analytical models are still essential for
depicting the underlying physical mechanisms. Recently, attention was paid to a "unified" approach able
to account for MOSFET continuous operation from weak to moderate and strong inversion [1,2].
In this paper, we propose an original model which applies not only to bulk Si and partially depleted
SO1 MOSFET's, but also to ultrathin SO1 transistors. For single-gate control (opposite interface in
accumulation or depletion), the drain current of a SOI-MOSFET, operated in the linear region, is
expressed as:
where q= aV,, I ay/, is the subthreshold swing and a/b = (WL) p CoxVDS.In strong inversion, the
bracket is dominated by the exponential term, whereas in weak inversion a first order expansion is used.
The transconductance is derived from eq. (1). By comparing with experimental results, the three basic
parameters (11, a and b) are extracted. Drawing log g,,, versus V,, allows determining 11 and a from the
slope and the intercept with the vertical axis, Fig. 1. The coefficient b is subsequently found from the
transconductance peak in strong inversion.
This model can be extended to include interface coupling effects in ultrathin film SO1 MOSFET's:
where the subscripts stand for front (1) and back (2) interfaces. Unified expressions of both the
transconductance (from weak to strong inversion) and subthreshold slope as functions of opposite gate
bias are simultaneously found. It is verified that well-known relationships [3,4,5] just represent limit
cases of our model.
It is worth noting that the model accounts analytically for the transition between moderate and strong
inversion. This offers a mathematical and physical support for defining the threshold voltage as the peak
position of the second derivative of the drain current. As pointed out by [6], such an extraction is very
useful in SO1 since the "extrapolated" V, suffers from interface coupling effects. Using eq. (l), a simple
and reliable expression is found for V,:
kT 1
V, = q-ln4
b
which is nothing but the gate-to-source voltage yielding ~ ~ $ Moreover,
2 .
it coincides with the
"classical" threshold voltage when approximating: I,
(ah)(V, - V,) for b eXp(qV,,/kT) >> 1 in eq.
J1). It will be shown that the derivative extraction method works even if a plateau occurs in g,,,(VGs)as
a consequence of interface coupling.
Experiments were conducted on n-channel MOSFET's fabricated on thin SIMOX film (80 to 150
nm). The thicknesses of the front and back oxides were 16.5 and 380 nm, respectively. Fig. 2 shows
drain current (in log and linear scales) and transconductance curves according to our analytical model,
for an ultrathin film SIMOX MOSFET. Reported in Fig. 3 are measured data that show very good
agreement with the model. Analytical transconductance calculations were also validated by direct
comparisons with 2D numerical simulations. The threshold voltage was extracted by various methods:
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(i) from the peak of the transconductance derivative (vertical bars in Fig. 4); (ii) fiom half-peak of the
transconductance (g,J2);
(iii) fiom eq. (3) and (iv) drain current extrapolation. Whlle conventional
methods may fail for strong interface coupling, it is found that derivative techmques yield reliable
results which well correspond to the physical definition of band bending of the interface.
In conclusion, a simple analytical model has been proposed which unifies the analysis of the various
regions of operation as well as the parameter extraction in SO1 MOSFET's.
REFERENCES
1. C. Park, C. Y. Lee, B. Moon, Y. Byun and M. Schur, IEEE Trans. El. Dev., 38 (1991), 399.
2. M. Schur, T. Fjeldly, T. Ytterdal and K. Lee, Solid State El., 35 (1992), 1795.
3. H. L h and J. Fossum, IEEE Trans El. Dev., 30 (1983), 1244.
4. B.Mazhari, S. Cristoloveanu, D.Ioannou and A. Caviglia, IEEE Trans. El. Dev., 38 (1991), 1289.
5 . D.Wouters, J. Colinge and H. Maes, IEEE Trans. El. Dev., 37 (1990), 2022.
6. A. Terao, D.Flandre, E. Lora-Tamayo and F. Van de Wiele, IEEE El. Dev. Lett., 12 (1991), 682.
<
10"
Y
a
I
10 -I0
1
1.5
2.5
2
3
VOl(V)
Fig. 1 Extraction of unified model parameters q, a
and b from the log and linear plots of versus VG,.
lo
-4
10
-6
Fig. 2 Simulated ID(VG)and g,,,(V,)
curves obtained by the
unified modeling.
/
I
12
I
r
v)
U
E
UI
U
10 -I1
10 - I 4
0
0.5
1
1.5
2
2.s
VG1 (V)
Fig. 3 Measured data corresponding to the simulation
given in Fig. 2.
Fig. 4 Threshold voltage extraction from the maximum of
the transconductance derivative.
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