Capacitor, method of controlling the same, and transistor including the same
A capacitor comprises a first electrode, a second electrode provided on the first electrode, a ferroelectric film provided between the first electrode and the second electrode, and a dielectric film provided between the ferroelectric film and the second electrode, impedance of the ferroelectric film and impedance of the dielectric film are determined such that a control voltage applied between the first electrode and the second electrode is equal to a capacitance boosting operating voltage, and the capacitance boosting operating voltage is determined by the following equation: V MAX = ( 1 + ❘ "\[LeftBracketingBar]" Z 2 ❘ "\[RightBracketingBar]" ❘ "\[LeftBracketingBar]" Z 1 ❘ "\[RightBracketingBar]" ) t F E FM where V MAX is a capacitance boosting operating voltage, Z 1 is impedance of the ferroelectric film, Z 2 is impedance of the dielectric film, t F is a thickness of the ferroelectric film, and E FM is an electric field applied to the ferroelectric film having a maximum polarization.
1. An electronic device comprising:
a first electrode;
a second electrode on the first electrode;
a ferroelectric film between the first electrode and the second electrode, the ferroelectric film having a first impedance; and
a dielectric film between the ferroelectric film and the second electrode, the dielectric film having a second impedance,
wherein the ferroelectric film and the dielectric film are configured to have a capacitance boosting operating voltage substantially equal to a control voltage applied between the first electrode and the second electrode, and
wherein the capacitance boosting operating voltage is determined by the following equation:
V
MAX
=
(
1
+
❘
"\[LeftBracketingBar]"
Z
2
❘
"\[RightBracketingBar]"
❘
"\[LeftBracketingBar]"
Z
1
❘
"\[RightBracketingBar]"
)
t
F
E
FM
where V MAX is the capacitance boosting operating voltage, Z 1 is the first impedance, Z 2 is the second impedance, t F is a thickness of the ferroelectric film, and E FM is an electric field applied to the ferroelectric film having a maximum polarization change.
2. The electronic device of claim 1 , wherein
the first impedance (Z 1 ) is determined based on a conductance component (G 1 ) of the ferroelectric film and a capacitance component (C 1 ) of the ferroelectric film, and
the second impedance (Z 2 ) is determined based on a conductance component (G 2 ) of the dielectric film and a capacitance component (C 2 ) of the dielectric film.
3. The electronic device of claim 1 , wherein
an angular frequency of the control voltage is determined such that the control voltage is equal to the capacitance boosting operating voltage, and
the capacitance boosting operating voltage is determined by the following equation:
V
MAX
=
(
1
+
G
1
2
+
ω
C
1
2
G
2
2
+
ω
2
C
2
2
)
t
F
(
2
α
P
S
+
4
β
P
S
3
)
where
G
1
2
+
ω
2
C
1
2
G
2
2
+
ω
2
C
2
2
represents the
❘
"\[LeftBracketingBar]"
Z
2
❘
"\[RightBracketingBar]"
❘
"\[LeftBracketingBar]"
Z
1
❘
"\[RightBracketingBar]"
,
represents the E FM , G 1 is conductance of the ferroelectric film, C 1 is capacitance of the ferroelectric film, G 2 is conductance of the dielectric film, C 2 is capacitance of the dielectric film, ω is the angular frequency of the control voltage, Ps is polarization of the ferroelectric film when the electric field is applied to the ferroelectric film, α is a stability parameter, and β is a skewness parameter.
4. The electronic device of claim 1 , wherein the magnitude ratio
(
❘
"\[LeftBracketingBar]"
Z
2
❘
"\[RightBracketingBar]"
❘
"\[LeftBracketingBar]"
Z
1
❘
"\[RightBracketingBar]"
)
of the impedance of the dielectric film to the first impedance of the ferroelectric film is 0.01 or greater.
5. The electronic device of claim 1 , wherein current density of current flowing through the dielectric film and the ferroelectric film is 1 mA/cm 2 or less.
6. The electronic device of claim 1 , wherein spontaneous polarization of the ferroelectric film is 20 μC/cm 2 or more.
7. The electronic device of claim 1 , wherein a dielectric dissipation factor of the dielectric film is 0.1 or less.
8. The electronic device of claim 1 , wherein the ferroelectric film includes at least one of an oxide ferroelectric material, a polymer ferroelectric material, a fluoride ferroelectric material, and a ferroelectric semiconductor.
9. The electronic device of claim 8 , wherein the oxide ferroelectric material includes at least one of a perovskite ferroelectric material, a tungsten-bronze ferroelectric material, a bismuth layer-structured ferroelectric material, and a rare-earth ferroelectric material.
10. The electronic device of claim 1 , wherein the dielectric film has a high dielectric constant.
11. The electronic device of claim 1 , wherein the dielectric film is an oxide, and
the oxide includes at least one of Ca, Sr, Ba, Sc, Y, La, Ti, Hf, Zr, Nb, Ta, Ce, Pr, Nd, Gd, Dy, Yb, and Lu.
12. The electronic device of claim 1 , wherein the dielectric film has a thickness of 10 nanometers or less.
13. The electronic device of claim 1 , wherein
the first electrode includes a conductive material,
the second electrode includes a conductive material, and
the electronic device is a capacitor.
14. The electronic device of claim 1 , wherein
the first electrode includes a semiconductor substrate,
the second electrode includes a conductive material, and
the electronic device is a transistor.
15. The electronic device of claim 14 , wherein the electronic device is configured to perform as a metal-oxide-semiconductor capacitor during an ON operation of the transistor.
16. The electronic device of claim 14 , further comprising:
a source region, a drain region, and a channel region in the semiconductor substrate,
wherein the second electrode is a gate electrode.
17. The electronic device of claim 16 , wherein the channel region has an opposite conductivity type to the source region and the drain region.
18. The electronic device of claim 17 , wherein
the channel region as an n-type conductivity, and
the source region and the drain region have a p-type conductivity.
19. A method of controlling a capacitor comprising a first electrode, a second electrode on the first electrode, a ferroelectric film between the first electrode and the second electrode, and a dielectric film between the ferroelectric film and the second electrode, the method comprising:
controlling an impedance of the ferroelectric film and an impedance of the dielectric film such that a control voltage applied between the first electrode and the second electrode is substantially equal to a capacitance boosting operating voltage, wherein the capacitance boosting operating voltage is determined by the following equation:
V
MAX
=
(
1
+
❘
"\[LeftBracketingBar]"
Z
2
❘
"\[RightBracketingBar]"
❘
"\[LeftBracketingBar]"
Z
1
❘
"\[RightBracketingBar]"
)
t
F
E
FM
where V MAX is a capacitance boosting operating voltage, Z 1 is the impedance of the ferroelectric film, Z 2 is the impedance of the dielectric film, t F is a thickness of the ferroelectric film, and E FM is an electric field applied to the ferroelectric film having a maximum polarization change.
20. The method of claim 19 , wherein
the first impedance (Z 1 ) is determined based on a conductance component (G 1 ) of the ferroelectric film and a capacitance component (C 1 ) of the ferroelectric film, and
the second impedance (Z 2 ) is determined based on a conductance component (G 2 ) of the dielectric film and a capacitance component (C 2 ) of the dielectric film.
21. The method of claim 19 , further comprising:
controlling an angular frequency of the control voltage such that the control voltage is equal to the capacitance boosting operating voltage,
wherein the capacitance boosting operating voltage is determined by the following equation:
V
MAX
=
(
1
+
G
1
2
+
ω
C
1
2
G
2
2
+
ω
2
C
2
2
)
t
F
(
2
α
P
S
+
4
β
P
S
3
)
where
(
G
1
2
+
ω
2
C
1
2
G
2
2
+
ω
2
C
2
2
)
represents the
❘
"\[LeftBracketingBar]"
Z
2
❘
"\[LeftBracketingBar]"
❘
"\[LeftBracketingBar]"
Z
1
❘
"\[RightBracketingBar]"
,
represents the EFM, G 1 is conductance of the ferroelectric film, C 1 is capacitance of the ferroelectric film, G 2 is conductance of the dielectric film, C 2 is capacitance of the dielectric film, ω is the angular frequency of the control voltage, Ps is polarization of the ferroelectric film when the electric field E FM is applied to the ferroelectric film, α is a stability parameter, and β is a skewness parameter.
22. The method of claim 19 , wherein the magnitude ratio
(
❘
"\[LeftBracketingBar]"
Z
2
❘
"\[RightBracketingBar]"
❘
"\[LeftBracketingBar]"
Z
1
❘
"\[RightBracketingBar]"
)
of the impedance of the dielectric film to the first impedance of the ferroelectric film is 0.01 or greater.
23. The method of claim 19 , wherein when the control voltage is equal to the capacitance boosting operating voltage, a current density of current flowing through the dielectric film and the ferroelectric film is 1 mA/cm 2 or less.
24. The method of claim 19 , wherein spontaneous polarization of the ferroelectric film is 20 μC/cm 2 or more.
25. The method of claim 19 , wherein a dielectric dissipation factor of the dielectric film is 0.1 or less.