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Atomic mechanism of electric dipole formed at high-K: SiO2 interface
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Image of FIG. 1.
FIG. 1.

(Color online) HfO2:SiO2 interface model construction: satisfy lattice matching and charge neutrality.

Image of FIG. 2.
FIG. 2.

(Color online) As-constructed interfaces with dopants: (a) La, (b) Al, (c) Sr, (d) Ti, (e) Nb, (f) V, (g) P, (h) B, and (i) N. Symbols for elements are the same in the whole paper.

Image of FIG. 3.
FIG. 3.

(Color online) Energy comparison for La dopants: (a) two La’s and an O vacancy in the interface, (b) two La’s in bulk HfO2, (c) two separate La’s in bulk HfO2, (d) O vacancy away from the interface.

Image of FIG. 4.
FIG. 4.

(Color online) Relaxed structure with group dopants (a) La, (b) Al, (c) Sr, (d) Ti, (e) Nb, (f) V, (g) P, (h) B, and (i) N.

Image of FIG. 5.
FIG. 5.

(Color online) Relaxed structure with double sized supercell and half dopants: (a) P dopant, (b) B dopant, (c) Al dopant, (d) La dopan, t and (e) Nb dopant.

Image of FIG. 6.
FIG. 6.

(Color online) (a) Convergence test of calculated VBOs vs oxide thickness in the HfO2:SiO2 model, from 3 HfO2 layers to 5 HfO2 layers and to 4 SiO2 layers; (b) Convergence test of calculated VBOs for different dopants using double sized supercell and [1/2] dopant (for Al, La, and Nb).

Image of FIG. 7.
FIG. 7.

The calculated VBOs vs experimental Vfb. They are a monotonic relationship.

Image of FIG. 8.
FIG. 8.

(Color online) VBO caused by dopants in bulk HfO2, at the interface and in bulk SiO2. The Black line is the VBO of pure HfO2:SiO2.

Image of FIG. 9.
FIG. 9.

(Color online) The calculated VBOs vs dopant parent metal valence. This result is against the vacancy model.

Image of FIG. 10.
FIG. 10.

(Color online) The calculated VBO vs the dopant work function.

Image of FIG. 11.
FIG. 11.

(Color online) (a) Electrostatic potential plots across the HfO2:SiO2 interface. The black wavy line is plane-to-plane electrostatic potential, while the red line is the macroscopic potential obtained after smoothing. (b) Comparison of calculated electrostatic potential offsets and valence band offsets. The red line is linear fitting.

Image of FIG. 12.
FIG. 12.

(Color online) The calculated electrostatic potential vs dopant work function.

Image of FIG. 13.
FIG. 13.

(Color online) Schematic dipole formation in amorphous materials due to the screening ability difference at the interface; (a) no dipole, (b) dipole builds up.

Image of FIG. 14.
FIG. 14.

(Color online) Physics of the origin of interfacial dipole and VBO shifts: discontinuity in the elements’ electronegativity generates a dipole both at the interface side and at the high-K materials side, while the dipole at the high-K side will be screened, so a net dipole builds up; using an interfacial dopant element with different electronegativity will change the magnitude of the net dipole and therefore shifts the VBO.


Generic image for table
Table I.

Formation energy per interface comparison for various substitutions of La, Al, Sr, Nb, and N dopants. Configurations (a), (b), (c), and (d) are identical to those in Fig. 3 (unit eV).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Atomic mechanism of electric dipole formed at high-K: SiO2 interface