Negative charge compressibility at the channel of SrTiO3 field-effect transistor

1
Isao H. Inoue
Negative charge compressibility
at the channel of
SrTiO3 field-effect transistor
National Institute of Advanced Industrial Science & Technology (AIST)
(Tsukuba, Japan)

2
N. Kumar et al., Scientific Reports 6, 25789 (2016)

Plan & Review.
Double-layer gate
insulator. Oxygen
isotope exchange.
FET device
fabrication.
Characterisation
down to 4K.
Nonequilibrium
Mott transition.
SX growth of SrTiO3,
SrTi18O3,(Sr,La)TiO3
etc., and
characterisation.
Marcelo J. Rozenberg＠U. Paris-Sud
Masaki Oshikawa＠ISSP, U. Tokyo
Theory
Strong E field
effect with
topology.
Crystal
Magneto-transport
measurement below
100mK.
Pablo Stoliar＠CIC nanoGUNE
Neuromorphic
SrTiO3-FET.
Neuromorphic device
fabrication.
Computer simulation of
filament formation of
MottFET
Amos Sharoni＠Bar-Ilan Univ.
SX growth of
vanadates for
neuromorphic
devices.
Device
Ultra Low T
Takashi Oka＠MPI, Dresden
Isao Inoue＠ESPRIT, AIST
Alejandro Schulman＠ESPRIT, AIST
Naoki Shirakawa＠FLEC, AIST
Yasuhide Tomioka＠ESPRIT, AIST
Shutaro Asanuma＠NRI&TIA, AIST
Thin film growth of
perovskite TMO for
Tunnelling RRAM.
Thin Film
Thin film growth of VO2
for Mott FET.
Hiroyuki Yamada＠ESPRIT, AIST
Keisuke Shibuya＠ESPRIT, AIST
Thin film growth of
perovskite Nickelates.
Device fab in TIA?
Present Collaborators

isaocaius@gmail.com http://staff.aist.go.jp/i.inoue/
Superstripes 2016 @ Ischia, Italy June 2016
4https://www.facebook.com/isao.phys
Our target: SrTiO3

SrTiO3 isaninterestingmaterial

Metal-InsulatorTransitioninSrTiO3
Our preliminary data:
MIT occurs at
the quantum resistance of h/e2.c.f. 3.5×1018cm-3 for Si
3.5×1017cm-3 for Ge
3.3 3.8 4.3 4.8 5.3
103
105
107
109
1011
1013
Vg = 1.8 V
Vg = 2 V
Vg = 2.7 V
Vg = 3 V
Vg = 3.3 V
Vg = 4.5 V
R(Ω/)
1000/T (K-1
)
h/e2

M. Janousch et al.,Adv. Mat. 19, 2232 (2007)
0.2 mol% Cr-doped
SrTiO3
By applying 0.1MV/cm  
for about 30 min
Pt
Pt
Vo are created, distributed in
the channel, and form a
metallic path.
VO creation by electric-field

HfO2/Parylene bilayer
Hybrid gate insulator
HfO2 (ε = 21.5)
+
Parylene-C (ε=2.7)
Isao Inoue and Hisashi Shima,
Japan Patent Number: 5522688, Date of Patent: 18th April, 2014

Superstripes 2016 @ Ischia, Italy June 2016 9https://www.facebook.com/isao.phys
6nmParylene
20nmHfO2
G
S D
SrTiO3 channel
4µm
S
D
V1 V2 V3
V4 V5 V6
G
4µm
G
S D
VD =
VD =
VD =
W
L
STEM+EDX
SEM
SEM
I. Inoue and H. Shima, Japan Patent No.5522688 (2014)
I. Inoue, Japan Patent Application No.2016-013743 (2016)
N. Kumar,A. Kito, I. H. Inoue, Sci. Rep. 6, 25789 (2016)
TEM
Parylene/HfO2/SrTiO3 FET

Drain current ID vs. gate voltage VG
log10(ID)
VG
Ideal FET
Vth
threshold voltage
sub-threshold region
accumulation region
G
S D
VG
ID

Much better than any SrTiO3-FET in literature
10
-5
10
-3
10
-1
10
1
µFE(cm
2
/Vs)
630
VG (V)
VD = 1V
VD = 0.1V
1050
n (10
13
cm
-2
)
200
100
0
σ(µS)
VD = 1V
µ=10.9cm2/Vs
Accumulation Region
—- sheet conductivity
of the channel
—- sheet carrier density
of the channel

Drain current ID vs. gate voltage VG
log10(ID)
VG
Ideal FET
One order
60mV
theoreticalminimum
Vth
threshold voltage
sub-threshold region
accumulation region
G
S D
VG
ID

Much better than any SrTiO3-FET in literature
10
-5
10
-3
10
-1
10
1
µFE(cm
2
/Vs)
630
VG (V)
VD = 1V
VD = 0.1V
1050
n (10
13
cm
-2
)
200
100
0
σ(µS)
VD = 1V
µ=10.9cm2/Vs
Accumulation Region
—- sheet conductivity
of the channel
10
-13
10
-12
10
-11
10
-10
10
-9
10
-8
10
-7
ID(A)
3210
VG (V)
S = 171 mV/dec
VD = 1 V
10
-14
10
-13
10
-12
10
-11
10
-10
10
-9
10
-8
10
-7
ID(A)
3210
VG (V)
VD = 0.5 V
0.1 V
0.02 V
Sub-threshold Region
—- sheet carrier density
of the channel
S=170mV/dec is extremely small !
(~100mV/dec even for Si FET).

Gate
Insulator
G
non-metallic
SrTiO3
channelSD
Capacitances of normal FET

5
Subthreshold swing
GateMetal4 µm
1.2 mV
10
-13
10
-12
10
-11
10
-10
10
-9
10
-8
210
9 µm
0.8 mV
10
-13
10
-12
10
-11
10
-10
10
-9
10
-8
10
-7
2 µm
1.1 mV
3210
20 µm
0.6 mV
VG (V)
ID(A)
ISD(A)
VG (V)
L = 2µm L = 4µm
L = 9µm L = 20µm
S = 189 mV/dec S = 172 mV/dec
S = 200 mV/decS = 200 mV/dec
1
transport
factor
body factor
Subthreshold swing of an insulator (and semiconductor)
…… only the thermally excited
carriers can contribute the
transport.
…… definition
…… φ is the surface potential
C□
…… because = (1/ +1/ )-1n□ VGCSTO
□
CSTO
□φ = / = (1+ / )-1n□ CSTO
□ C□ VG
This does not depend whether
SrTiO3 is metallic, semiconducting,
or insulating.
Small S means
very clean channel !!
What is the sub-threshold swing?
・・・subthreshold swing
60mV/decade
=170mV/dec !!

16
HfO2/Parylene/SrTiO3
cleaner interface
continuous and large
doping control

Hall effect measurement
@RT
10
11
10
12
10
13
10
14
10
15
n(cm
-2
)
-6
-3
0
3
1/C
STO
(10
6
cm
2
/F)
6420
VG (V)
10
11
10
12
10
n(c
-6
-3
0
3
1/C
STO
(10
6
cm
2
/F)
6420
VG (V)
Parylene + HfO2
vbvb
4µm
S
D
V1 V2 V3
V4 V5 V6
G
-0.1
0
0.1
-9 -6 -3 0 3 6 9
B ( T)
VG = 6.2 V
-2
0
2
Rxy(kΩ)
VG = 3.6 V
-1
0
1 VG = 4.4 V
-0.4
-0.2
0
0.2
0.4
Rxy(MΩ)
VG = 2 V
-0.04
0
0.04 VG = 2.7 V
-0.2
0
0.2
Rxy(kΩ)
-9 -6 -3 0 3 6 9
B ( T)
VG = 5.4 V
-1
0
1
VH(mV)
-9 -6 -3 0 3 6 9
B (T)
VG = 4.8 V
-5
-4
-3
-2
-1
ΔV(mV)
1.20.80.40
Time (hours)
-9
0
9
B(T)
VG = 4.8 V
(a) (b)
ΔV(mV)
B(T)
VH(mV)
VG=4.8V
T=300K
B (T)Time (hours)(c)
B(T) B(T)
Rxy(kΩ)Rxy(kΩ)Rxy(MΩ)
VG = 2.7 VVG = 2 V
VG = 4.4 V
VG = 6.2 VVG = 5.4 V
VG = 3.6 V
VG=4.8V
⊗B

Gate
Insulator
G
non-metallic
SrTiO3
channelSD
Carrier density of SrTiO3 channel
+

Total capacitance estimation
subthreshold swing
60mV/decade
=170mV/dec !!
10
-13
10
-12
10
-11
10
-10
10
-9
10
-8
10
-7
ID(A)
3210
VG (V)
S = 171 mV/dec
VD = 1 V
10
-14
10
-13
10
-12
10
-11
10
-10
10
-9
10
-8
10
-7
ID(A)
3210
VG (V)
VD = 0.5 V
0.1 V
0.02 V
19
measured by fabricating
a capacitor structure

10
11
10
12
10
13
10
14
10
15
n(cm
-2
)
-6
-3
0
3
1/C
STO
(10
6
cm
2
/F)
6420
VG (V)
10
11
10
12
10
n(c
-6
-3
0
3
1/C
STO
(10
6
cm
2
/F)
6420
VG (V)
Gate
source
SrTiO3
drain
Parylene + HfO2
Low VG region is well explained
n□ obtained
by Hall effect
@RT

10
11
10
12
10
13
10
14
10
15
n(cm
-2
)
-6
-3
0
3
1/C
STO
(10
6
cm
2
/F)
6420
VG (V)
10
11
10
12
10
n(c
-6
-3
0
3
1/C
STO
(10
6
cm
2
/F)
6420
VG (V)
Parylene + HfO2
Metal-Insulator transition occurs
n□ obtained
by Hall effect
@RT
3.3 3.8 4.3 4.8 5.3
103
105
107
109
1011
1013
Vg = 1.8 V
Vg = 2 V
Vg = 2.7 V
Vg = 3 V
Vg = 3.3 V
Vg = 4.5 V
R(Ω/)
1000/T (K-1
)
h/e2
MI transition at RT

G
SDchannel
Gate
Insulator
G
non-metallic
SrTiO3
channelSD
22Gate
Insulator
non-metallic
SrTiO3
Metallic channel appears !

10
11
10
12
10
13
10
14
10
15
n(cm
-2
)
-6
-3
0
3
1/C
STO
(10
6
cm
2
/F)
6420
VG (V)
10
11
10
12
10
n(c
-6
-3
0
3
1/C
STO
(10
6
cm
2
/F)
6420
VG (V)
Gate
source
SrTiO3
drain
Parylene + HfO2
n□ obtained
by Hall effect
@RT
Before the MI transition
MI transition at RT

After the MI transition
10
11
10
12
10
13
10
14
10
15
n(cm
-2
)
-6
-3
0
3
1/C
STO
(10
6
cm
2
/F)
6420
VG (V)
n□ obtained
by Hall effect
10
11
10
12
10
n(c
-6
-3
0
3
1/C
STO
(10
6
cm
2
/F)
6420
VG (V)
Gate
source
SrTiO3
drain
@RT
Parylene + HfO2
MI transition at RT But, for to be larger than
its value before the MI transition,
must be negative !!!

10
11
10
12
10
13
10
14
10
15
n(cm
-2
)
-6
-3
0
3
1/C
STO
(10
6
cm
2
/F)
6420
VG (V)
50
49
C(pF)
10.50
Time (Hours)
VG = 0 V
VG = 8 V
VAC = 0.1 V
f = 1 kHz
50
49
VG=8V
VG=0V
Vac=0.1V
1kHz
0 1Time (hours)
Cins
(pF)
a Rig
Co
ω
Ra
spectral
weight
transfer
spectral
weight
transfer
cb
10
11
10
13
10
15
n(cm
-2
)
6420
VG (V)
1pA
1nA
1µA
ISD
0
0
0.5
(µF/cm2)
2
subthreshold
region
metallic
region
exoticmetal
region
Superstripes 2016 @ Ischia, Italy June 2016 25
https://www.facebook.com/isao.phys
If changes like
this, enhancement
is explained well
If channel becomes
simply metallic
Change of capacitance @ MI transition
non-metal
metal

G
SDchannel
26Gate
Insulator
non-metallic
SrTiO3
Negative charge compressibility !?
Here
then, it must be

µ
Rigid band shift
ω
Correlation gap closure
D(ω)
µ
ω
ρ(ω)
spectral weight
transfer
quasi-particle spectra
~ DOS
27
Chemical potential decreases

µ
Rigid band shift
ω
D(ω)
Rashba splitting
µ
ω
ρ(ω)
spectral weight
transfer
quasi-particle spectra
~ DOS
Chemical potential decreases

29
N. Kumar et al., Scientific Reports 6, 25789 (2016)

30
HfO2/Parylene/SrTiO3
Negative capacitance
for metallic channel
Rashba effect?

Band splitting due to SOC?
ZHICHENG ZHONG, ANNA T ´OTH, AND KARSTEN HELD
FIG. 1. (Color online) Band structure of t2g orbitals in bulk
SrTiO3 calculated by (a) DFT and by (b) a TB model derived in
this Rapid Communication. In the absence of spin-orbit coupling,
yz, zx, and xy are degenerate at the point. SOC splits the
sixfold-degenerate orbitals into +
7 and +
8 states separated by
O = 29 meV.
(yz
term
Hb
0
Its
agr
dee
are
the
Zhichen Zhong et al.,
Phys. Rev. B 87, 161102(R) (2013)
RAPID COMMUNICATIONS
PHYSICAL REVIEW B 87, 161102(R) (2013)

Band splitting due to SOC?
Yanwu Xie et al.,
Solid State Commun. 197, 25 (2014)
make the intercept of SH between 0 and 1.
Fig. 4. (Color online) Schematic electronic orbits. (a) Fermi surface when the
q2DEG consists of one light (l) and one heavy (h) subband, showing the inner light
circle and the outer heavier star-shaped geometry. The dark and shaded MB1 and
the yellow dashed MB2 indicate two possible magnetic breakdown (MB) orbits. The
green dots indicate the MB tunneling paths. By symmetry there are 4 equivalent
2
2

VG = 4V, VD = 100 mV
B (T)
-10 100
0
-100
100
Rxy(Ω)Temperature dep. Hall effect
0 50 100 150 200 250 300
1012
10
13
10
14
1015
nhall
nins
n(cm-2
)
T (K)
n□(cm-2)
T (K)
3001000 200
1012
1013
1014
1015
n□, Hall
n□, geometric
"Negative Capacitance"
is seen down to 4K
4µm
S
D
V1 V2 V3
V4 V5 V6
G ⊗B

-10 100
0
-10
10
Rxy–RHB(Ω)
B (T)
Non-linear Hall effect
Non-linearity with no hysteresis.
Subtraction of linear term RHB.
Not caused by magnetisation
-10 -8 -6 -4 -2 0 2 4 6 8 10
-100
-80
-60
-40
-20
0
20
40
60
80
100
ρxy
(Ω)
H (T)
4K
Fit
Vd = 100 mV
Vg = 4V
B (T)
-10 100
0
-0.1
Rxy(kΩ)
0.1
Fit by a two-band model

A tale of two bands
Our results
30100 20
T (K)
1014
1011
nL
nH µL
100
30100 20
T (K)
0 5 10 15 20 25 30 35
1011
10
12
10
13
1014
n(cm-2
)
T (K)
n1
n2
0 5 10 15 20 25 30
100
1000
µ1
µ2
µ(cm2
/Vs)
T (K)
n□(cm-2)
1013
1012
µH
µ(cm2/Vs)
1000
µH nH
high mobility &
low density band
µL nL
low mobility &
high density band
J. S. Kim et al., PRB 82, 201407 (2010)
For LAO/STO system
1016
1013
1000
1
ZHICHENG ZHONG, ANNA T ´OTH, AND KARSTEN HELD
FIG. 1. (Color online) Band structure of t2g orbitals in bulk
SrTiO3 calculated by (a) DFT and by (b) a TB model derived in
this Rapid Communication. In the absence of spin-orbit coupling,
yz, zx, and xy are degenerate at the point. SOC splits the
sixfold-degenerate orbitals into +
7 and +
8 states separated by
O = 29 meV.
Along the -X(π,0,0) direction (here in units of 1/a with
a = 3.92 ˚A being the calculated lattice constant of STO), the
yz band has a small energy dispersion corresponding to a
???

M. Lee et al., PRL 107,
256601 (2011)
What is the origin of the Kondo effect?
Magnetic impurity??
Our data
100
R□(kΩ)
1.20
0.96
1.12
1.04
10
T (K)
R□(kΩ)
100
T (K)
3002000
1013
103
n□=9.8×1013 cm-2
Kondo effect appears !

M. Lee et al., PRL 107, 256601 (2011)
This Kondo effect is unusual
R□–R□,5K(Ω)
200
0
T (K)
10
increasing
carrier density
R□–R□,5K(Ω)
T (K)
10010
200
0
n□=9.4×1013 cm-2
n□=9.8×1013 cm-2
increasing
carrier density
Originated in two bands of itinerant and nearly localised? (orbital Kondo?)
VG n□ TK ➡ TK
Our preliminary data
Or, TK increase as n□ increases due to Rashba effect?
c.f., D. Mastrogiuseppe et al., PRB 90, 035426 (2014)

36isaocaius@gmail.com http://staff.aist.go.jp/i.inoue/
38
zzz
high-k/Parylene to
protect surface
Summary
Miniaturisation Limit
Use Metal-Insulator Transition
to overcome the scaling limit.
Extremely good
FETwith MIT
Negative Capacitance"Kondo"
effect
nonlinear
Hall effect
two bands

36isaocaius@gmail.com http://staff.aist.go.jp/i.inoue/
39
Ongoing/future researches
VO2
(111) SrTiO3
NiO
RNiO3
RMnO3
SrTi(18O,16O)3
etc
4µm
G
S D
HfO2/Parylene/SrTiO3 FET
Artificial synapse
& neuron utilising
2D MI transition.
4µm
S
D
V1 V2 V3
V4 V5 V6
G ⊗B
spin degree of freedom is no longer the spin itself but the
so-called chirality, which for a given band and wave vector
k characterizes the orientation of the eigenspinor, which we
label by + and −. The resulting Fermi surface is formed by
two circles (ellipses for the anisotropic bands) and shown in
Fig. 9. The peculiar spin structure will be important when we
consider the effect of a magnetic field parallel to the interface.
The anisotropic bands have each two minima at ka
0 =
±mhα/ 2
on the axis corresponding to the heavy mass. The
separated minima become a ring of radius ki
0 = mlα/ 2
in
the isotropic band. A schematic view of the resulting band
structure is given in Fig. 3.
We will see in the following how, due to the density-
dependent Rashba coupling, the band structure, and in par-
ticular its (local) minima ϵi,a
0 = αki,a
0 /2 are functions of the
electron density.
D. Field-dependent Rashba coupling
Concerning the dependence of the Rashba coupling on the
electric field, in the absence of compelling first-principles
calculations, we borrow its functional form from semicon-
ductor physics, while the appearing parameters are inferred
FIG. 3. (Color online) Schematic view of the STO band structure
formed by an isotropic Rashba band (grey) and two anisotropic bands
(orange and blue). The isotropic band has a ring of minima at ki
0 =
m∗
α/ 2
, while the anisotropic bands have each two minima at ka
0 =
±mhα/ 2
, where ka
0 is along the direction with the heavy mass mh.
19Multi-band due to Rashba effect
may explain the weird phenomena
of our SrTiO3 FET?
"Quantum phenomena"
1. Quantum oscillation of SrTiO3
2. Quantum Hall effect of SrTiO3
3. Quantum critical point (QCP) of
ferroelectricitsy of SrTi(18O,16O)3
4. Superconductivity of SrTiO3
and SrTi(18O,16O)3

Negative charge compressibility at the channel of SrTiO3 field-effect transistor

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