vth definition
TRANSCRIPT
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SIiVIULATION OF SEiVIICONDUCTOR DEVICES AND PROCESSES Vol.
6
Edited
by H. Ryssel P.
Pichler September
1995
A M ethod for Extra cting th e Threshold Voltage
of M O SF E T s Based on Current Components
K. AOYAMA
NTT LSI Laboratories,
3-1, Morinosato Wakamiya, Atsugi-shi, Kanagawa Pref., 243-01 JAPAN
Abstract
A new method for extracting the threshold voltage of MOSFETs is presented.
The threshold voltage is the gate voltage at which the second difference of the
logarithm of the drain current takes a minimum value. The method is applied to
a 0.6-pm NMOSFET. The threshold voltage characteristics are compared with
ones measured with previous methods and it is shown that the proposed method
overcomes previous problems. The threshold voltage is extracted based on a
physical background verified with 2D device simulation and shows a transition
voltage at which drift and diffusion components in the drain current are equal.
1. Introduction
A serious problem is that threshold voltage definitions in measurements differ from
the one in compact MOSFET models. The threshold voltage in compact models is
defined as the gate voltage at which the surface potential 4 f the channel reaches
the double Fermi potential in the bulk 2d f. This definition is very popular but has the
disadvantages tha t the position where 4 2dj in the channel is not clear and it is
difficult to measure
4
in MOSFETs. On the other hand, threshold voltages in mea-
surements are extracted by the constant current CC) , the linear extrapolation LE)
and the transconductance change TC ) methods [ I], [2]. With
C C
the difficulties are
measuring the effective channel length and width and defining
a.
constant value of the
drain current. LE should be applied only in the low drain voltage region. In the high
drain voltage region, however, the square root of current extrapolation SRE) should
be applied. With extrapolation methods such as LE and SRE, th e continuity in all
operation voltages is lost. The threshold voltage characteristics with T C are strange
for drain voltage changes, as shown in Fig. 1. A threshold voltage definition th at
overcomes the above disadvantages is needed. This paper presents a new method for
extracting the threshold voltage: the second difference of the logarithm of the drain
current minimum SDLM).
2.
Method
The diffusion component and the drift component can be respectively approximated
by an exponential function and a polynomial expression, as shown in Fig. 2. The
first difference of the logarithm of the drain current almost stays constant when
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K. Aoyam a: Method for Extra cting the Threshold Voltage of MO SFET s
119
th e diffusion comp onent is domin ant and grad ually app ro acl~ es ero when th e drift
comp onent is dom inant, as shown in Fig. 3 (a) . Fig.
3
( b ) s.hows the second difference
takes a minim um value at th e unique transition voltage in an N M OS FE T. In this work,
this voltage is defined as the thresh old voltage. Th is threshold voltage is shown in
Fig. 1 for various drain voltages com pared to ones extrac ted w ith previous meth ods .
Th e characteristics are reasonable even for drain voltage changes.
3 Verification
With a view to certify that the dominant component in the drain current changes
from diffusion to drift at the threshold voltage extracted with the above method, the
rate of each comp onent was calculated by 2D device simulation. In the sim ulation , an
NM OSFET wi th L 1.Opm was used w ith Vd, 3.OV an d sb OV. As a result, the
min imu m value is calculated with this meth od a s shown in Fig.
4
like in measu rem ents
and the po tent ia l dis tr ibutions a t the interfaceof Si and SiOz obta ined are those shown
in Fig. 5. T he drift comp onent and diffusion conlponent [id s(d ij/)] re
where is th e electron mobility,
n
is th e electron density, is th e cond uction band
potent ia l ,
4
[, is the relative potential an d
[
is the electron q uasi-Fermi potential.
At each position at the interface, the rates of drift and diffusion compete with the
rates of (d$ /dx) and
[-d(
,)/dx]. Fig.
6
shows the distribu tion of the r ate of
current com ponents throu gh t he channel. T he average rate of th e drift compo nent in
th e channel region is
where x, and xd ar e the source edge an d th e drain edge and
L
is t h e channel length.
Fig.
7
shows the rate of the drift component in the channel increases as the gate
voltage increases. At
V
0.215V, drift equals diffusion. The refore , the threshold
voltage defined with this m ethod shows th e unique gate voltage th at is the trans ition
voltage in the dom inant com ponent in th e dra in current .
4.
Summary
A method for extracting the threshold voltage with the second difference of the loga-
rithm of the drain current was proposed and verified from the physical point of view
using 2D device sim ulation. Th e ex trac ted threshold voltage has the following fea-
tures: It is extrac ted from only th e drain current without both th e effective channel
leng th and w idth and has a physical meaning. It shows th e ga te voltage a t which
drift and diffusion in the drain current are equal each other. These features may be
useful for unifying the threshold voltage in compact models and in measurement.
References
[ I ] M.
J.
Deen and
Z. X.
Yan, A new meth od for measuring t h e threshold v oltage of
small-geometry M OS FET s from subthreshold conduct ion , Sol id-Sta te Electron-
ics, vol. 33, no. 5, pp. 503-511, 1990.
[2]
H. S.
Wong,
M. H.
White ,
T. J.
Krutsick and
R.
V. Bo oth , Mo deling of transco n-
ductance degradation and extraction of threshold voltage in thin oxide MOS-
FETs , Solid-State Electronics, vol. 30, no. 9, pp. 953-968, 1987.
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12
K.
Aoyama: A Method for Extracting the Threshold Voltage of
MOSFETs
NMOSF T
Lp=Odpm Wpe l l OW V s W V
transition polynomial
- voltage expression
diffusion
exponential
. . . . . .
. . . . .
function
I I
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
gate voltage: Vgs
drain voltage: Vds V)
Fig. 2. The idea of extracting the
Fig.
1.
Comparison of the threshold voltages
threshold voltage in this work.
extracted with previous methods and SDLM
for various drain voltages using the measured
drain current in the NMOSFET.
12
g-10
-
-
V
N
f 8 8-20
>
V
z
A
V
4
M
30
-
-
0
-40
0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.4 0.6 0.8 1.0 1.2
gate voltage: Vgs V)
gate voltage: Vgs V)
a) b)
Fig. 3. Results for this method when applied to a submicron NMOSFET for the
various substrate voltages. a) The first difference-of he drain current.
b)
The
second difference of the drain current.
16
--
0
il
M
-
0
V
-20
f 8
6 -40
V
-
. 4
3
60
8 ;
4
-80
0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0
gate voltage: Vgs V)
gate voltage: Vgs V)
a) b)
Fig. 4. The derivatives of the drain current calculated from 2D device simulation.
a) The first difference of the drain current. b) The second difference of the drain current.
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K.
Aoyarna: A Method for E xtracting the Threshold Voltage of MOSFET s 12
1
. . . . . .
. . . . .
. . . . .
. . . . .
. . .
j j
4.0
ativd pot edti al.... '..... hk
onduct~on and potential
4.5
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
distance: x pm )
Fig. 5. The conduction band potential and the relative
potential distribution at the interface at Vds=3.0V and
Vgs=02V using 2D device simulation results. The device
structure used in the simulation is also shown.
1.3 1.4 1.5 1.6 1.7 1.8 1.9
distance: x pm)
Fig.
6 The rate of the two drain current
components in the channel calculated
using the conduction band potential and
the relative potential at the interface of Si
and S i0 2 .
Vth
extracted with S LM method
0.15 0.20 0.25 0.30 0.35
gate voltage: Vgs V)
Fig.
7
The RATE of the drift current
component at the interface for various
gate voltages. At Vgs=0.215V, the drift
component is equal to the diffusion
component.