(Color online) HfO2:SiO2 interface model construction: satisfy lattice matching and charge neutrality.
(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.
(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.
(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.
(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.
(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).
The calculated VBOs vs experimental Vfb. They are a monotonic relationship.
(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.
(Color online) The calculated VBOs vs dopant parent metal valence. This result is against the vacancy model.
(Color online) The calculated VBO vs the dopant work function.
(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.
(Color online) The calculated electrostatic potential vs dopant work function.
(Color online) Schematic dipole formation in amorphous materials due to the screening ability difference at the interface; (a) no dipole, (b) dipole builds up.
(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.
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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