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Magnetic Oxide Heterostructures: EuO on Cubic Oxides ... - JuSER

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5.2. Thermodynamic analysis of the EuO/Si interface 99<br />

EuSi 2<br />

0 500 1000 1500<br />

(a) Silicide formation during initialization of EuO growth: 1000<br />

2(H-Si) + Eu<br />

(g)<br />

EuSi 2 + H 2<br />

EuSi<br />

-2000<br />

2 + 3Eu + O 2 2EuO + 2Si + 2Eu (evap) 0 500 1000 1500 2000<br />

2Si + 2(H-Si) + 2Eu<br />

(g)<br />

2EuSi 2 + H 2<br />

500<br />

2Si + Eu 2EuSi 2<br />

0<br />

(b) Silicide dissolution during oxygen-rich EuO growth:<br />

EuSi 2 + Eu + 3/2O 2 EuO + Si + SiO 2<br />

-500<br />

EuSi 2 + Eu + 3/2O 2 Eu 2 O 3 + 2Si<br />

-1000<br />

1/2(EuSi 2 )+Eu+3/2O 2 1/2(Eu 3 O 4 +SiO 2 +Si)<br />

-1500<br />

(c) Silicide dissolution during EuO distillation growth:<br />

temperature (K)<br />

ΔG reaction (T) (kJ/mol)<br />

temperature (°C)<br />

EuO formation (for orientation)<br />

Figure 5.10.: Resulting Gibbs free energies of EuO/Si interface reactions involving EuSi 2 .<br />

needed. Such a calculation has been conducted by Rushchanskii (2012) and Ležaić (2011)<br />

using the harmonic approximation in density-functional perturbation theory (DFPT). 191,192<br />

The chemical environment when beginning EuO synthesis is an Eu-rich seed layer for epitaxial<br />

growth on top of the hydrogen-passivated silicon surface, H-Si (001). These conditions<br />

reveal possible silicide formation reactions, as assembled in Fig. 5.10a. Their resulting<br />

Gibbs free energy is ΔG300 ◦ K<br />

> 0 (purple and red circles), which renders the silicide formation<br />

on H-Si unlikely. However, we analyze three different hydrogen coverages of the Si<br />

surface, complete passivation (purple circle), half surface passivation (red circle), and in case<br />

no hydrogen covers the Si surface surface, the asymptotic case of Eu + Si alloying (orange<br />

circle). It is evident, that only the complete hydrogen passivation of Si shows a large positive<br />

G300 ◦ K 500 kJ/mol, while the results for fractional Si passivation follow G◦ 300 K<br />

0, which<br />

is the thermodynamic threshold to a silicide formation probability. If no H passivation is left,<br />

the simple alloying reaction is thermodynamically favored to proceed (G300 ◦ K<br />

= −84 kJ/mol).<br />

This underlines the importance of a complete hydrogen passivation of the Si (001) surface in<br />

order to prevent EuSi 2 formation.<br />

Proceeding with the next stage of EuO synthesis on top of silicon, we analyze the two complementary<br />

EuO growth regimes (I) and (III), oxygen-rich growth in Fig. 5.10b and Eu distillation<br />

growth in Fig. 5.10c. During these EuO growth modes, EuO binds most of the supplied<br />

Eu, and any excess Eu is re-evaporated by the high synthesis temperature around the Eu sublimation<br />

point. Thus, during EuO synthesis silicides are thermodynamically unlikely formed<br />

(remember Fig. 5.9), and consequently we consider the disappearance of residual EuSi 2 from<br />

the initial Eu-rich stage of EuO growth. During oxygen-rich EuO growth (regime I. Red and<br />

yellow solid lines, red diamond in Fig. 5.10), the disappearance of EuSi 2 is very probable.<br />

Among the resulting phases, the formation of Eu 3 O 4 and Eu 2 O 3 are thermodynamically favored,<br />

yet not desired. During Eu distillation growth (regime III. Blue solid line in Fig. 5.10),<br />

Phonons of bulk EuSi 2 were calculated using DFPT 193 within local-density approximation 194 as implemented<br />

in Quantum-Espresso code. 225 A6×6×6 k-point mesh was used for Brillouin-zone integration with a<br />

plane-wave kinetic energy cut-off of 30 Ha. For pseudopotential construction, the following valence-electron<br />

configurations were considered: 5s 2 5p 6 4f 7 6s 2 for Eu and 3s 2 3p 2 for Si. In the structural relaxation, the Hellman-<br />

Feynman forces were minimized to 2 × 10 −4 Ry/Bohr. The thermodynamic potentials H and S were derived from<br />

the phonon density of state which was calculated at a 30×30×30 mesh in the Brillouin-zone.

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