Semiconductor device and dielectric film including a fluorite-type crystal
A semiconductor device according to an embodiment includes a first conductive layer, a second conductive layer, and a dielectric film provided between the first and the second conductive layers. The dielectric film including a fluorite-type crystal and a positive ion site includes Hf and/or Zr, and a negative ion site includes O. In the dielectric film, parameters a, b, c, p, x, y, z, u, v and w satisfy a predetermined relation. The axis length of the a-axis, b-axis and c-axis of the original unit cell is a, b, and c, respectively. An axis in a direction with no reversal symmetry is c-axis, a stacking direction of atomic planes of two kinds formed by negative ions disposed at different positions is a-axis, the remainder is b-axis. The parameters x, y, z, u, v and w are values represented using the parameter p.
1. A semiconductor device comprising:
a first conductive layer;
a second conductive layer; and
a dielectric film provided between the first conductive layer and the second conductive layer in cross-sectional view, the dielectric film including a fluorite-type crystal, wherein
a positive ion site of the fluorite-type crystal includes at least one of Hf (hafnium) and Zr (zirconium), and a negative ion site of the fluorite-type crystal includes O (oxygen), and
following formulae (1) to (13) are satisfied in the fluorite-type crystal, when, among three axes of an original unit cell of the crystal, an axis in a direction with no reversal symmetry is c-axis, a stacking direction of atomic planes of two kinds formed by negative ions disposed at different positions is a-axis, remainder is b-axis, axis length of the a-axis of the original unit cell is a, axis length of the b-axis thereof is b, axis length of the c-axis thereof is c, a parameter is p, and x, y, z, u, v and w are values represented using the parameter p
x= 0.0000077293× p×p− 0.00091484× p+ 0.50556 (1)
y= 0.0000089659× p×p− 0.00082246× p+ 0.52512 (2)
z=− 0.000012625× p×p− 0.00045149× p+ 0.50696 (3)
u=− 0.000042665× p×p+ 0.00097971× p+ 1.0028 (4)
v=− 0.00032701× p+ 0.96306 (5)
w=− 0.000042194× p×p+ 0.00068404× p+ 0.96543 (6)
−0.0074≦ x−a≦ 0.026 (7)
−0.0075≦ y−b≦ 0.026 (8)
−0.0056≦ z−c≦ 0.006 (9)
−0.063≦ u−c÷a≦ 0.0055 (10)
−0.031≦ v−a÷b≦ 0.0024 (11)
−0.077≦ w−c÷b≦ 0.006 (12)
1≦ p≦ 40 (13).
2. The device according to claim 1 , wherein
following relation is satisfied when an atomic concentration of Hf (hafnium) and an atomic concentration of O (oxygen) in the dielectric film are q and r, respectively
1.95≦ r÷q≦ 1.99.
3. The device according to claim 1 , wherein
following relation is satisfied when the dielectric film includes at least one element selected from a group consisting of Zr, Si, Y, Al, Sr, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, F, Cl, and N, a total atomic concentration of the element of the group included in the dielectric film is s, and an atomic concentration of Hf is q
0.01≦ s ÷( q+s )≦0.2.
4. The device according to claim 1 , wherein
following relation is satisfied when the dielectric film includes Hf (hafnium) and Zr (zirconium), and an atomic concentration of Hf (hafnium) and an atomic concentration of Zr are q and t, respectively
0.4≦ q ÷( q+t )≦0.6.
5. The device according to claim 1 , wherein
following relation is satisfied when the dielectric film includes Zr (zirconium), and an atomic concentration of Zr and an atomic concentration of O (oxygen) are t and r, respectively
1.95≦ r÷t≦ 2,4≦ p≦ 40.
6. The device according to claim 1 , wherein
maximum range of protrusions and recesses on an interface between the first conductive layer and the dielectric film or maximum range of protrusions and recesses on an interface between the second conductive layer and the dielectric film is 0.15 nm or more and 1.0 nm or less.
7. A dielectric film comprising a fluorite-type crystal, wherein
a positive ion site of the fluorite-type crystal includes at least one of Hf (hafnium) and Zr (zirconium), and a negative ion site of the fluorite-type crystal includes O (oxygen), and
following formulae (1) to (13) are satisfied in the fluorite-type crystal, when, among three axes of an original unit cell of the crystal, an axis in a direction with no reversal symmetry is c-axis, a stacking direction of atomic planes of two kinds formed by negative ions disposed at different positions is a-axis, remainder is b-axis, axis length of the a-axis of the original unit cell is a, axis length of the b-axis thereof is b, axis length of the c-axis thereof is c, a parameter is p, and x, y, z, u, v and w are values represented using the parameter p
x= 0.0000077293× p×p− 0.00091484× p+ 0.50556 (1)
y= 0.0000089659× p×p− 0.00082246× p+ 0.52512 (2)
z=− 0.000012625× p×p− 0.00045149× p+ 0.50696 (3)
u=− 0.000042665× p×p+ 0.00097971× p+ 1.0028 (4)
v=− 0.00032701× p+ 0.96306 (5)
w=− 0.000042194× p×p+ 0.00068404× p+ 0.96543 (6)
−0.0074≦ x−a≦ 0.026 (7)
−0.0075≦ y−b≦ 0.026 (8)
−0.0056≦ z−c≦ 0.006 (9)
−0.063≦ u−c÷a≦ 0.0055 (10)
−0.031≦ v−a÷b≦ 0.0024 (11)
−0.077≦ w−c÷b≦ 0.006 (12)
1≦ p≦ 40 (13).
8. The dielectric film according to claim 7 , wherein
following relation is satisfied when an atomic concentration of Hf (hafnium) and an atomic concentration of O (oxygen) in the dielectric film are q and r, respectively
1.95≦ r÷q≦ 1.99.
9. The dielectric film according to claim 7 , wherein
following relation is satisfied when the dielectric film includes at least one element selected from a group consisting of Zr, Si, Y, Al, Sr, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, F, Cl, and N, a total atomic concentration of the element of the group included in the dielectric film is s, and an atomic concentration of Hf is q
0.01≦ s ÷( q+s )≦0.2.
10. The dielectric film according to claim 7 , wherein
following relation is satisfied when the dielectric film includes Hf (hafnium) and Zr (zirconium), and an atomic concentration of Hf (hafnium) and an atomic concentration of Zr are q and t, respectively
0.4≦ q ÷( q+t )≦0.6.
11. The dielectric film according to claim 7 , wherein
following relation is satisfied when the dielectric film includes Zr (zirconium), and an atomic concentration of Zr and an atomic concentration of O (oxygen) are t and r, respectively
1.95≦ r÷t≦ 2,4≦ p≦ 40.
12. A semiconductor device comprising:
a semiconductor layer;
a conductive layer; and
a first dielectric film provided between the semiconductor layer and the conductive layer in cross-sectional view, the first dielectric film including a fluorite-type crystal, wherein
a positive ion site of the fluorite-type crystal includes at least one of Hf (hafnium) and Zr (zirconium), and a negative ion site of the fluorite-type crystal includes O (oxygen), and
following formulae (1) to (13) are satisfied in the fluorite-type crystal, when, among three axes of an original unit cell of the crystal, an axis in a direction with no reversal symmetry is c-axis, a stacking direction of atomic planes of two kinds formed by negative ions disposed at different positions is a-axis, remainder is b-axis, axis length of the a-axis of the original unit cell is a, axis length of the b-axis thereof is b, axis length of the c-axis thereof is c, a parameter is p, and x, y, z, u, v and w are values represented using the parameter p
x= 0.0000077293× p×p− 0.00091484× p+ 0.50556 (1)
y= 0.0000089659× p×p− 0.00082246× p+ 0.52512 (2)
z=− 0.000012625× p×p− 0.00045149× p+ 0.50696 (3)
u=− 0.000042665× p×p+ 0.00097971× p+ 1.0028 (4)
v=− 0.00032701× p+ 0.96306 (5)
w=− 0.000042194× p×p+ 0.00068404× p+ 0.96543 (6)
−0.0074≦ x−a≦ 0.026 (7)
−0.0075≦ y−b≦ 0.026 (8)
−0.0056≦ z−c≦ 0.006 (9)
−0.063≦ u−c÷a≦ 0.0055 (10)
−0.031≦ v−a÷b≦ 0.0024 (11)
−0.077≦ w−c÷b≦ 0.006 (12)
1≦ p≦ 40 (13).
13. The device according to claim 12 , further comprising:
a second dielectric film provided between the semiconductor layer and the first dielectric film.
14. The device according to claim 12 , further comprising:
a source region and a drain region provided at a surface of the semiconductor layer on both sides of the conductive layer.