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1
Isao H. Inoue Neeraj Kumar Ai Kitou
Enormous
electrostatic carrier doping of SrTiO3:
negative capacitance?
National Institute of Advanced Industrial Science & Technology (AIST) (Tsukuba, Japan)

isaocaius@gmail.com http://staff.aist.go.jp/i.inoue/
Isao H. Inoue, Invited Talk @ SPICE Workshop, Mainz, Germany 2 July 2015 5
insulator
metal
metal
Ideal capacitor
because

insulator
metal
metal
Non-idealcapacitorw/a“metal”electrode
"metal"
quantum capacitance
~ charge
compressibility

gate
insulator
G
non-metallic
substrate
NormalFETw/semi-conductorchannel
channelSD

gate
insulator
G
non-metallic
substrate
Fieldeffecttransistorw/a“metal”channel
channelSD
quantum capacitance
~ charge
compressibility

Isao H. Inoue, Invited Talk @ SPICE Workshop, Mainz, Germany 2 July 2015
InsulatingSrTiO3 singlecrystal

SrTiO3 isaninterestingmaterial

(a) (b)
EC
EV
µ/eVG =VFB
EC
EV
µ/e
(c)
EC
EV
µ/e
VG =VFB+VMI
□
V = Cins
□
nMI
ins
MI
φ = CSTO
□
□MI nMI
VMI ≡Vins + φMIMI
VG =VFB+V
V =ins
MI
VMI ≡V
SrTiO3metal
gate
insulator
VSTO
o
Vins
o
Vfb=Vins+VSTO
o o
SrTiO3metal gate
insulator
Sheet carrier density of SrTiO3
GateMetal
S D
SrTiO3
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
n
-6
-3
0
3
1/C
STO
(10
6
cm
2
/F)
6420
VG (V)
(ideally metallic channel)

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)
measured by
Hall effect
at 300K
10
11
10
12
n
-6
-3
0
3
1/C
STO
(10
6
cm
2
/F)
6420
VG (V)
Large deviation!!
GateMetal
S D
SrTiO3
12
Comparison to Hall effects

cannotbelargerthan ?
idealinsulator
noscreening
GateMetal
S D
SrTiO3

idealmetal idealinsulator
perfectscreening noscreening
GateMetal
S D
SrTiO3

perfectscreening noscreening
GateMetal
S D
SrTiO3
maximum!?

canbelargerthan
perfectscreening noscreeningexoticmetal?
negativecapacitance

Negativecapacitance!?
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)
measured by
Hall effect
at 300K
10
11
10
12
10
n(c
-6
-3
0
31/C
STO
(10
6
cm
2
/F)
6420
VG (V)

HfO2 / Parylene bilayer gate insulator
6nmParylene
20nmHfO2
Gatemetal
S D
SrTiO3 channel

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
18
HfO2 / Parylene bilayer gate insulator

SrTiO3
Al
HfO2
Au Ti
parylene
STEM-EDS mapping
19
No mixture of each layer

Capacitance of the gate insulator
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)
Cexp=CO+Area×C□
C□ = 0.47 µF cm-2
60
50
40
30
20
10
0
Cexp(pF)
100806040200
Area (10
-6
cm
2
)
Cexp(pF)
Area(10-6 cm-2)
100×100µm2
VG=1V T=300K
0
10
20
30
1/C(ω)(10
9
F
-1
)
10
2
10
3
10
4
10
5
10
6
ω/2π (Hz)
-90
-60
-30
0
θ(degree)
1/C(109F-1)
θ(deg)
100×100µm2
Ti (electrode)
Parylene-C (6nm)
HfO2 (20nm)
Au (electrode)
almostNOchangeinC
forelongatedVG application

FET characteristics
210
VD (V)
0.15
0.10
0.05
0
ID(µA)
1.6 V
VG =
1.7 V
1.5 V
10
13
10
14
VD = 1 V
T = 300 K
(a) (b)
(c) (d)
10
-14
10
-13
10
-12
10
-11
10
-10
10
-9
10
-8
10
-7
ID(A)
3210
VG (V)
0.02 V
0.1 V
0.5 V
VD =
6
5
m)
VD = 1 V
eff
ID(µA)
VD (V)
VG = 1.7V
VG = 1.6V
VG = 1.5V
Drastic modulation of the drain current
4µm
G
S D
210
VD (V)
0.15
0.10
0.05
0
ID(µA)
1.6 V
VG =
1.7 V
1.5 V
11
10
12
10
13
10
14
)
VD = 1 V
T = 300 K
(a) (b)
(c) (d)
10
-14
10
-13
10
-12
10
-11
10
-10
10
-9
10
-8
10
-7
ID(A)
3210
VG (V)
0.02 V
0.1 V
0.5 V
VD =
6
5
4
8
Ω-cm)
VD = 1 V
VG
= 0.5 V
DS
G
L
W
eff
VG (V)
ID(A)

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
Therefore
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.
Very small sub-threshold swing
S=170mV/dec is extremely small !
(~100mV/dec even for Si FET).
Small S means
very clean channel !!

1pA
1nA
1µA
ID
0
0
0.5
(µF/cm2)
2
subthreshold
region
metallic
region
exoticmetal
region
unchanged
Apossible scenario of gating SrTiO3

1pA
1nA
1µA
ID
0
0
0.5
(µF/cm2)
2
subthreshold
region
metallic
region
exoticmetal
region
unchanged

1pA
1nA
1µA
ID
0
0
0.5
(µF/cm2)
2
subthreshold
region
metallic
region
exoticmetal
region
unchanged
negative!
bigdeviation
canbeexplained?

Negative C in LaAlO3/SrTiO3
Negative C (negative charge
compressibility) is not a
strange phenomenon.
There have been many
reports in literature so far.
Even SrTiO3 shows it in the
LaAlO3/SrTiO3 interface.
g
proportional to f and is constant over a broad range of –0.05 V ≤ Vg ≤ 0.05
V. For Vg < –0.18 V, Iy/f displays a frequency dependence, which is
probably caused by effects of current leakage through the LAO layer. (C)
terface overscreens
0.37 V, again a f-d
current leakage th
5
8
7
A B
f
f
f
Fig. 4. The inverse of compressibility dm/dn determined from penetration
field measurements on (A) device 1 and (B) device 2. The electron density
at the interface is determined by integrating the C versus Vg curve at the
lowest frequency achieved. (C) The density n dependence of the lateral re-
sistivity of a differ
wafer. The device d
the frequency depe
S2) (16).
www.sciencemag.org SCIENCE VOL 332
Lu Li et al. Science 332, 825 (2011)
5
-100
0
30
0
0 1.5
0
10

What’s the origin of negative C?

Only for dilute carrier density
g
terface overscreens
0.37 V, again a f-d
current leakage th
5
8
7
A B
f
f
f
wafer. The device d
the frequency depe
S2) (16).
5
-100
0
30
0
0 1.5
0
10

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)
Our carrier density is too large?!
Our data
negative C case
g
terface overscreens
0.37 V, again a f-d
current leakage th
5
8
7
A B
f
f
f
wafer. The device d
the frequency depe
S2) (16).
5
-100
0
30
0
0 1.5
0
10
normal metal case

µ
Rigid band shift
ω
Correlation gap closure
D(ω)
µ
ω
ρ(ω)
spectral weight
transfer
quasi-particle spectra
~ DOS
Other mechanisms of negative C

µ
Rigid band shift
ω
D(ω)
Other mechanisms of negative C
Rashba splitting
µ
ω
ρ(ω)
spectral weight
transfer
quasi-particle spectra
~ DOS

Still our is too small !!
( is too large !! )

If wouldbetwo-ordersmaller

thatis, wouldbetwo-orderlarger

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)
Butthis istoolargetoenhancen□
is too small !!

Ordinary positive
is negligible
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)

Inhomogeneous channel ?
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)

Large enhancement is
due to inhomogeneity!
Inhomogeneity enhances n□
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)

39
Negative C is necessary
but not enough!
We need
negative C + positive C inhomogeneity
to explain
the enormously large n□

Evidence of the inhomogeneity

Summary
Very clean interface !!

-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
Hall effect measurements

···
Rα,1 Rα,N Rβ Rps···
Cα,1 Cα,N Cβ Cps···
Rα Rβ Rps
Cα Cβ Cps
60
40
20
0
1/Capacitance(10
9
F
-1
)
86420-2
log10(Frequency/Hz)
-90
-60
-30
0
Phase(degree)
raw data
totalfitting
1/Cβ(ω)
1/Cα(ω)
1/Cps(ω)
60
40
20
0
1/Capacitance(10
9
F
-1
)
86420-2
log10(Frequency/Hz)
-90
-60
-30
0
Phase(degree)
raw data
totalfitting
1/Cβ(ω)
1/Cα(ω)
1/Cps(ω)
(b) (d)
10
2
10
4
10
6
10
8
10
10
10
12
10
14
RHfO2(Ω)
1612840
layer number
(c)
Rα,j(Ω)
j (layer number)
(a)
1/C(ω)=−ωImZ(ω)
log10ω
∝tanh(log10ω)
1/C
1/RC
slope=1/(Clog10e)
log10e
log10(FrequencyHz-1) log10(FrequencyHz-1)
AC capacitance measurements

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