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8/12/2019 Takagi Universal Mobility I 1994
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IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 41, NO. 12, DECEMBER 1994 2357
On the Universality of Inversion Layer
Mobility in Si MOSFET s: Part I-Effects
of Substrate Impurity ConcentrationShin-ichi Takagi, Member, IEEE, Akira Toriumi, Masao Iwase, and Hiroyuki Tango
Abstract-This paper reports the studies of the inversion layermobility in n- and p-channel Si MOSFET's with a wide rangeof substrate impurity concentrations to 10l8 cm- ). Thevalidity and limitations of the universal relationship between theinversion layer mobility and the effective normal field E,E)areexamined.
It is found that the universality of both the electron and holemobilities does hold up to l O I R cm -3. The dependences of
the universal curves are observed to differ betw een electrons and
holes, particularly at lower temperatures. This result means adifferent influence of surface ro ughness scattering on the electronand hole transports.
On substrates with higher impurity concentrations, the electron
and h ole mobilities significantly deviate from the universal curvesat lower surface carrier concentrations because of Coulombscattering by the substrate impurity. Also the deviation causedby the charge d centers at the Si/SiO2 interface is observed in themobility of MOSFET's degraded by Fowler-Nordheim electroninjection.
I. INTRODUCTION
HE inversion layer mobility in Si MOSFET's has beenT very important physical quantity as a parameter to
describe the drain current and a probe to study the electric
properties of a two-dimensional carrier system. Therefore,
much study [11 since the 1960's has revealed dominant scatter-
ing mechanisms determining the mobility. However, a compre-
hensive understanding of the inversion layer mobility, which
includes the quantitative description near room temperature,the effect of substrate impurity, the difference between the
electron mobility and the hole mobility and the effect of
surface orientation, is still insufficient.
On the other hand, it has already been reported that the
electron and hole mobilities in the inversion layer on a
(100) surface follow the universal curves at room temperature
independent of the substrate impurity concentration or the
substrate bias when plotted as a function of effective normal
fields, E,R [2]-[9]. E,ff is defined by the following equations.
where y is the elementary charge, S ~ s the permitivity of
s i , N d p l is the surface concentration of the depletion charge,
Manuscript received June 3, 1994. The review of this paper was arrangedby Associate Editor K. Tada.
S. Takagi is with the Solid State Electronics Laboratory, Stanford Univer-sity, Stanford, CA 94305 USA.
A. Toriumi, M. Iwase, and H. Tango are with the ULSI Research Labo-ratories, Research & Development Center, Toshiba Corporation, 1 KamukaiToshiba-cho, Saiwai-Ku, Kawasaki 210, Japan.
IEEE Log Number 9405895.
N, is the surface inversion carrier concentration. Here, 7 is
a key parameter in defining E,R and it has been reported
that, in order to provide the universal relationship, the value
of q should taken to be 1/2 for the electron mobility [2]
and 1/3 for the hole mobility [3]. This relationship has been
often utilized as a precise mobility model in device simulators
[lo]-[ 121. In spite of its usefulness, however, the origins of the
universality, the value of 7 and the effective field dependence
of the universal curves have not been fully clarified yet.
The aim of this paper (Part I) and the companion paper (Part
11) is to study the applicability and the physical meaning of
the universal relationship. While the Part I demonstrates thevalidity and the limitation of the universality of the electron
and hole mobilities on (100) surface experimentally, the Part
I1 examines the physical meanings of E,ff and 7 ,based on the
new experimental findings regarding the surface orientation
dependence.
In this paper we concentrate on the effect of substrate
impurity on the electron and hole mobilities. The motivations
to study the effect of substrate impurity are twofold. One is
to examine the validity of the universal relationship over a
wide range of substrate impurity concentration. The substrate
impurity concentration changes N d p l in (1) and the resultant
E,R, independent of N,. Therefore, the value of 7 that offers
the universal relationship can be determined experimentally
by comparing the mobilities on the different impurity con-centrations. However, the systematic study of the universality
over a wide range of substrate impurity concentrations has not
been done sufficiently. Such an extensive verification of the
universality allows us to characterize the E ff dependence of
the universal curve quantitatively. The second motivation is
to examine the influence of substrate impurity scattering. Al-
though Coulomb scattering by substrate impurity is considered
to degrade the mobility on higher impurity concentration sub-
strates, the quantitative characterization has been still lacking
in spite of the practical importance in the scaled MOSFET's.
From the above motivations, we investigate the electron and
hole mobilities with the substrate impurity concentrations of
1015 to 10 cm- 3 systematically in terms of the universal
relationship.
11. SAMPLE PREPARATION AND MEASUREMENTS
N-channel and p-channel MOSFET's used in this paper
were fabricated on (100) Si wafers. The substrate impurity
concentration was varied from to 10'' cmP3, using
0018-9383/94$04.00 994 IEEE
___~
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2358 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 41, NO. 12, DECEMBER 1994
boron or phosphorus ion implantation, followed by a long and
high temperature annealing (1 1 9 0 ° C 60 min). This annealing
allowed the impurity profile to be considerably flat to a 3 p m
depth from the Si surface. All the devices were of the surface
channel type. The gate oxide was grown to a thickness of 25
nm in dry oxygen at 900°C . The gate materials were n+ and
p+-poly Si for n- and p-channel MO SFET 's, respectively. The
channel length, L , and the channel width, W , f the measureddevices were 200 pm and 100 pm , respectively.
The effective mobility in the inversion layer, pLeff as
determined from the drain conductance gd in the linear region.
.9d was measured at the drain voltage, Vd of 50 or 10mV. The
surface carrier concentration, N ,? V , ) , was determined directly
through gate-channel capacitance Cgc ,), measurement [141,
[151.
1;
YNS V,) = .I_,C,c Vg)~~Vg. 3 )
The measurement frequency was selected to be as low as0.4-1.0 kHz in order to avoid the influence of the resistive
component of the channel [15].
The value of Eefiwas determined from ( l ) , (4), and ( 5 ) .
4)
Here, 4~ is the bulk Fermi energy, Nsub is the substrate
impurity concentration, k~ is the Boltzman constant, and n is
the intrinsic carrier concentration. Nsut, was determined from
the minimum capacitance in the high frequency (100 kHz)
C-V curves of the MOS diodes. We have confirmed, using
the process simulator (TO PAZ) [16 ], that the variation in the
impurity concentration within the depletion layer is less than
-around 30% for the doping of boron more than
The main issue regarding the universal relationship is to de-
termine the value of 77 in (1). This can be done experimentally
from the experimental mobilities with the different substrate
impurity concentrations. When the universal relationship holds
and the value of 11 is chosen appropriately, the mobility
should be described as the single universal curve against E,n,
independent of the substrate impurity concentration. If 77 is
incorrect, the mobilities with the different substrate impurity
concentrations are to have different values for a same E,tf
value, because 71 changes the weights of N , and NdPl .
c m P3 .
111. EXPERIMENTALESULTS
A . Unitiersal Relationship o Electron and Hole M obilities
Figs. I and 2 show the Eeff ependences of the electron
and hole mobilities in the inversion layer, respectively, at
300 K and 77 K. The parameter is the substrate acceptor
concentration, N.4, or the substrate donor concentration, N p .d in the measurement of gel was taken to be IO mV.
Here, the values of rI for the electron and hole mobilities
10' I I INA c i 3
m0 ELECTRON
-=
I I
1.010' 1
0.1
EFFECTIVE FIELD [ MV/cm 1
Fig. 1. Electron mobility in inversion layer at 300 K and 77 K versuseffective field E,=, as a parameter of substrate acceptor concentration, S I .
Here, Ec,fr s defined by E,n. = q . + . . V* /ES;ith of 1/2.
are taken to be 1/2 and 1/3, respectively. As seen in Fig.1, the electron mobilities at 300 K are represented by the
universal curve as a function of E,R in the range of 0.05 to 1.5
MV/cm independent of the substrate impurity concentrations
by choosing the value of 77 to be 1/2. Similarly, the hole
mobilities are also represented by the universal curve as a
function of E,ff in the range of 0.05 to MV/cm by choosing
the value of to be 1/3, as observed in Fig. 2 . These results
confirm us that universal relationships of the electron and hole
mobilities on (100) surface do hold up to the substrate impurity
concentration of 0ls cm-3. It is confirmed simultaneously
that the values of 71 for the electron and hole mobilities are 1/2
and 1/3, respectively, for a wide range of Eeff nd the substrate
impurity concentration. These values are in agreement with
those reported previously [ 2 ] , SI. Moreover, the electron andhole mobilities at 77 K also have the universality in high Eee,
which was defined by the same value of 17 as at 300 K.
It is, however, observed that the electron and hole mobili-
ties with higher substrate concentrations exhibit a significant
deviation from the universal curves near the threshold v oltage.
This issue will be discussed in Section 111-C in detail.
B . Effectitve Field Dependences o Universal
Curves for Electrons and Holes
We have obtained the universal curves that hold for the
impurity concentrations of 10l5 to 10 cm-3 for both the
electron and hole mobilities in Section 111-A. However, the
origin of the Ecff ependences have not been fully understood
yet. Especially, the E,ff dependence of the hole mobilityhas been studied little so far. In this section we study the
E,ff dependence of the universal curve with emphasis on the
difference between the electron mobility and the hole mobility.
From Fig. 1 , the characteristics of the E,ff dependence of
the electron mobility are summarized as follows. 1 ) At 300
K, the mobility is proportional to E at E,tf lower than0.5 MV/cm over a one order of magnitude Eeff ange. 2 ) At
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TAKAGI et al.: ON THE UNIVERSALITY OF MOBILITY: PART I 2359
I I I I
m
20I 1
0.1 1.0
EFFECTIVE FIELD [ MV/cm IFig. 2. Hole mobility in inversion layer at 300 K and 77 K versus effectivefield, E,n as a parameter of substrate donor concentration, ,Yo. ere, E e ~is defined by E p ~q . NCv,,,,1 7 , ) / E s , with T of 1/3.
........ Total Mobi l i t y
EFFECTIVE FIELD Ee ff
Fig. 3. Schematic diagram of E,E or AV, dependence of mobility ininversion layer by three dominant scattering mechanisms.
300 K, the mobility decreases steeply at E,R higher than 0.5
MV/cm. 3) At 77 K, the mobility is roughly proportional toE;: at high E,R.
In contrast, the E e ~ependence of the hole mobility in Fig.
2 as described below. 1 At 300 K, the E,R dependence does
not exhibit a single power law over any E e ~ange and is a
little stronger than E ’. 2 ) At 300 K, the change in a slope
at high Eeff s not so marked a s for the electron mobility. 3 ) A t
77 K, the hole mobility is nearly proportional to E: which
is rather weaker than that for the electron mobility.
In order to understand these E,R dependences quantita-
tively, it is necessary to characterize the universal curve in
terms of scattering mechanism. Fig. 3 shows a schematic dia-
gram of the l ? ~or N , ) dependences on the basis of a general
understanding of the inversion layer mobility. According to
this diagram, the universal curve can be divided into phonon
scattering term and surface roughness scattering term. If thisis true, the difference in the E,R dependence between the
electron mobility and the hole mobility can be ascribed to
surface roughness scattering, because the difference becomes
larger at high E,tf and/or at low temperature. In order to
examine this interpretation, the temperature dependences of
the electron and hole mobilities were measured.
5000 1 I i
: 000
5U I 000
22 500
>
-Ik
0200
ELECTRON
-..a
.. .....
.*
397K
447K
- . XPERIMENT
MODEL
100 L 1 I
0.1 1.0
EFFECTIVE FIELD [ MV/cm 1
Fig. 4. E,fl dependences of electron mobility in the inversion layer on 100)
surface in the range of 77 K to 447 K. Substrate acceptor concentration was3.9 x 1OI5 ~ 1 1 1 ~ ~ .ere, E,fi is defined with 1 of 1/2. Open circles showthe experimental data. The solid curves were calculated using 6H8).
0 . 1 1.0
EFFECTIVE FIELD [ MV/cm 1
Fig. 5. dependences of hole mobility in inversion layer on 100) surfacein the range of 30K to 447 K . Substrate acceptor concentration w as 5.2 x 1OI5
cm-’. Here, E,fi is defined with 11 of 1/3.Open circles show the experimentaldata. The solid curves were calculated using (6)-(8).
Figs. 4 and 5 show the E,R dependences of the electron
mobility with N A of 3.9 x 1015 cm-’ and the hole mobility
with N o of 7.8 x 1015 cm-’. Here, Vd in the measurement
of gd was taken to be 50 mV, because we focused on
higher N , region. The almost no temperature dependence
of the hole mobility in the range of 30-77 K means that
the mobility in this temperature region is limited only by
surface roughness scattering. It has been, therefore, confirmed
that the mobility limited by surface roughness scattering has
remarkably different Eeff dependences between electrons and
holes. With increasing temperature, on the other hand, the
E e ~ependences of both the electron and hole mobilities
approach roughly This fact shows that the mobility
limited by photon scattering follows the same power law for
both electrons and holes.
Based on the above findings, a calculation using a sim-
ple model was performed. The mobility limited by phonon
scattering, &,h, was determined by
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2360 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 41, NO. 12, DECEMBER I994
Here, the constant coefficient A was taken to be 2.0 x IO5
and 6.1 x lo4 for the electron and hole mobilities on (loo),
respectively, where p E e ~nd T should be in cm2/V.s,
V/cm, and Kelvins. The power of -0.3, was taken from
the results in Figs. 4 and 5 . The power of T , -1.75, was
determined from the temperature dependence of the electron
mobility at E,R of 0.2 MV/cm, where the contributions
of surface roughness scattering and Coulomb scattering areso small that the temperature dependence of only phonon
scattering can be determined.
The mobility limited by surface roughness scattering, ,uL,,,
was modeled separately for the electron and hole mobilities.
For the electron mobility
(7)
Here, the parameter, 7 , was determined to be 2.6 so that the
total mobility at 77K fitted the experimental data. T he constant
coefficient, B, was taken to be 4.5 x 10 . The reason why
y is slightly different from the power at 77 K, which was
roughly -2, is that phonon scattering still has an influence on
the electron mobility at 77 K . As for the hole mobility, on the
other hand, the experimental mobility at 30 K was used as psr.
It should be noted that, as seen in Fig. 5, psr or holes cannot
be represented by the single power law of E,R.
Using Matthiessen's rule, the total mobility, ptot, s de-
scribed by
8)
The solid line in Figs. 4 and 5 represent the calculated
results. A good agreement between the experimental and
calculated mobilities is obtained at moderate or high E,R,
where Coulomb scattering is negligible. This fact confirms us
that the difference in the E e ~ependence between the electron
mobility and the hole mobility is attributed to the difference
in the E,tf dependence of pYr. lso, the deviation of the hole
mobility at 300 K from E e 2 s understood by considering
that surface roughness scattering affects the hole mobility overa wider E,R range even at 300 K.
p5r= B .E,;
l d Fpl; + P,l'
C. Deviation j i n m the Universal Curves
As already seen in Figs. 1 and 2, the electron and hole
mobilities deviate from the universal cures near the threshold
voltage even at 300K. Moreover, this deviation becomes larger
as the substrate impurity concentration increases. These facts
suggest that the mobility is considerably affected by Coulomb
scattering associated with substrate impurity. It has been
pointed out [17]-[191, on the other hand, that the application
of a finite drain voltage can lead to a decrease in carrier
concentration near the drain and a resulting lower p e ~t low
N,. In order to minimize this error, d was selected to be as
low as 10mV for an accurate characterization of the mobilityat low N , .
The behavior of the mobility component corresponding to
the deviation, i~,o,~olnt,,was studied quantitatively using (9), in
order to examine whether the deviation is caused by substrate
impurity scattering.
10 I
I O i 1I
I O i i I O i 2
Ns [ cm-2 1
Fig. 6. Electron mobility compo nent determined from dev iation from univer-
sal curve, p , , , , , lorr, l , , versus surfac e carrier concentration,S as a parameter
of substrate acceptor concentratio n, \ ~ x { ,.r,,,l<,,,Ll,was calculated from 9).
104
L
300 K
NS= 2x10
\
; oi 016 1017 10'8
NA,ND bm31
Fig. 7. Dependences of pr,,ul~l,,,l, or electrons and holes in inversionlayer at 300 K on substrate acceptor concentration, -V~nd substrate donor
concentration, S n espectively. Here .\ , is 2 x 10 cm- .
Here, jLcoulomb was determined as a function of N , , becausethe Coulomb scattering rate should be characterized as func-
tion of N,, which is directly related to the screening effect
and the electron energy [20].
Fig. 6 shows the N , dependence of pcoulomb for the electron
mobility at 300 K as a parameter of N q . It is seen that
p co l o rn ~ncreases in proportion to N: , independent of
Moreover, p,,,,lomt, is found to decrease with an increase
in N.4. Fig. 7 shows the substrate impurity concentration
dependences of p,,,lomb of the electron and hole mobilities
at N , of 2 x 10l1 cm-2. At 300 K, the deviation from the
universal curves is distinctly o bserved in the substrate impurity
concentration higher than 7.2 x 1016 cm- 3 for the electron
mobility and higher than 1.6x 10 l6 cm-3 for the hole mobility.
The inversely linear relationship between /L,o,lomh and thesubstrate impurity concentrations confirms that the substrate
impurity is the main Coulomb scattering center.
With substrate impurity concentrations lower than 5 x
10" cm P3 , however, other Coulomb scattering centers are
responsible. Fig. 8 shows p,-o,lomb of the electron mobility at77 K at N, = 2 , 5 a nd 10 x 10 cm-'. Here, pcoulomb was
determined by subtracting the contribution of p p h estimated
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TAKAGI et al.: ON THE UNIVERSALITY OF MOBILITY: PART I 2361
7.2 x 1016cm-3 has the weaker N A dependence. It is known - O
[l], [20] that there are three types of Coulomb scatteringcenters that can affect the inversion layer mobility; substrate
8impurities, interface state charges and charges trapped in SiO2.
5 .
for bcoulomb with N A lower than 7.2 x 1016 cmP3. In - 0 ' -
is also considered to come from the change in the type of the
\
Thus interface state charges or trapped charges are responsible
addition, it is found that the N dependence of pcoulomb in
this N A region becomes weaker. This weaker N , dependence
dominant scattering centers. The Coulomb interaction between
- 2 .9
2
10'
10 I I I I
- .A.\ N 300 K
E L E C T R O N
j;
*.k.
N I N J E C T I O N
~ ~ . ~ x ~ o " c m - '
I .
:
NS [cm-*]
l x l o 2
2 X 1 0 1 1
I 5x10"
E L E C T R O N
\ x 10"
N A = ~ . ~ x ~ ~ ~ c ~ T I -m.1
E F F E C T I V E F I E L D E e f f C M V / c m 3
a deviation from the universal curve can be examined by
studying the mobility of MOSFET's degraded by carrier
injection, because carrier injection into Si02 is known to
generate interface charges [211. Therefore, the inversion layer
mobility after Fowler-Nordheim (FN) tunneling injection into
Si0 2 was studied. Electrons were injected into S io s from the
inversion layer in n-channel MOSFET's. The injection current
was maintained at a constant value (1 in j = 2.65x loP4A/cm2.
Fig. 9 shows the E,R dependence of the electron mobility
before and after FN tunneling injection as a parameter of the
number of injected electrons per unit area, Ninj. After the
injection the deviation from the initial curve is clearly observed
and becomes larger at lower E,R (thus lower N , ) , similar to
the mobility on higher impurity concentration substrates. Also,the deviation becomes larger with an increase in Ninj. Fig. 10
shows the relationship between pCoulomb at N , of 2 x 10l1
cmP 2and the threshold voltage shift, A&, estimated from C -
V curves. The number of interface charged centers per unit
area, Nint, s also shown in the horizontal axis. Here, Nlnt
was calculated from AV,, under the assumption that all the
generated charges are located at the interface. bcoulomb is
found to be inversely proportional to Nint. It is confirmed
from this result that the mobility degradation is caused by the
generated interface charges.
IV. CONCLUSION
This paper has reported the studies of the inversion layer
mobility in n- and p-channel MOSFET's over a wide range
of substrate impurity concentrations from the viewpoint of a
universal relationship against the effective field, E,R. Uni-
versality has been found to be maintained up to a substrate
impurity concentration of 10'' c m p3 .
It has also been found that the E e ~ependence of theuniversal curves can be explained over a wide temperature
range by the combination of phonon scattering and surface
roughness scattering. While phonon scattering provides the
same E,R dependence between the electron mobility and the
hole mobility, a difference in the E,E dependences of the
mobility limited by surface roughness scattering has been ob-
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2362 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 41, NO. 12, DECEMBER 1994
served. It has been concluded that surface roughness scattering
affects the electron and hole transports differently.
On the other hand, a significant lowering from the universal
curve, which is attributable to substrate impurity scattering, has
been observed even at 300 K for the substrate impurity con-
centrations higher than 7 . 2 x and 1 .6 x c m P3
for the electron mobility and the hole mobility, respectively.
The inversion layer mobility limited by substrate impurityscattering has been found to be in proportion to the N:’
for both electrons and holes. It has also been experimentally
confirmed in stressed MOSFET’s that a marked deviation from
the universal curve can be ascribed to Coulomb scattering
associated with the generated interface charges.
Shin-ichi Takagi (M‘93) was bom in Tokyo, Japan,on August 25, 1959. He received the B.S., M S , nd
Ph.D. degrees in electronic5 engineenng from theUniversity of Tokyo, Tokyo, Japan, in 1982, 1984,and 1987, respectively
He joined the Toshiha Research and DevelopmentCenter, Kawasaki, Japan, in 1987, where he hasbeen engaged in research on the device physicsof Si MOSFET’s. including the carrier transport ininversion layer, the impact ionization phenom ena,
the hot came r degradation and the electnc propertiesof Si/SiOz interface. He is currently d Visiting Scholar at Stanford University,Stanford, CA, where he ir working on the Si/SiGe heterostructure devicesDr. akagi is a member of the IEEE Electron Device Society and the Japan
Society of Applied Phyws
ACKNOWLEDGMENT
The authors wish to thank K. Nishinohara and N. Shigyo for
their valuable comments concerning the measurement method.
They would like to acknowledge N. Konishi’s contribution of
performing the process simulation. They are also grateful to
M. Yoshimi, K. Natori, and T. Wada for their encouragement
throughout this work. They are indebted to F. Umibe for
reviewing the original manuscript and suggesting revisions inits English.
Akira Toriumi received the B S. degree in physicsand the M.S. and Ph D. degrees in applied physicsfrom the University of Tokyo, Tokyo, Japan, in1978, 1980, and 1983, respectively.
He Joined the Toshiba Research and DevelopmentCenter, Kawasaki, Japan, in 1983, where he hasbeen engaged in research on the MOSFET devicephysics. Dunng 1988-1990 he was a Visiting Sci-entist at the Massachusetts Institute of Technology,where he studied the physics of quantum effectdevices. He is currently working on the physics and
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. -
technology o f 0.1 irm CM OS, thin Si02 reliability, a nd th e quantum effectsof very small silicon devices.
Dr. Toriumi is a member of the Physical Society of Japan, the Japan Societyof Applied Physics. and the American Physical Society.
Masao Iwase was born in Aom on, Japan, in 1963.He joined the Toshiba Research and D evelopment
Center, Kawasaki, Japan, in 1 982, where he hasbeen engaged in the development o f beam Iithog-
raphy and submicrometer CMOS technology. Heis currently in the Process Rewearch Department atToshiba ULSI Research Laboratones.
Mr. Iwase is a member of the Japan Society ofApplied Physics.
Hiroyuki Tango was born in Saitama Prefecture,Japan, on February IO, 1942 He received the B Sdegree in electncal communication engineering andthe M S and Ph.D. degrees in electronics engineer-ing, all from Tohoku University, Send ai. Japan. in
*i-
L” ’ 1965, 1967, and 1970In 1970, He joined the Toshiba Research and
Development Center. Kawasaki, Japan, where hestudied MOS device physics, MOS on bulk, andMOS on SOS integrated-circuit technology. From
1979 to 1983 he researched SOS LSI technoloevas the Head o f an SOS technology group at Toshiba. From 1 984 to I 9i khe supervised the research and development of MOS device physics, devicesimulation, MOS-LSI process. and MOS devices of SO1 technology. Since
1988 he has supervised the R&D of DRAM, EEPR OM, and CCD devices.Dr. Tango is a member of the Japan Society of Applied Physics and the
Institute of Electronics, Information, and Communication Engineers.