Band Gap Modeling of Different Ternary and Quaternary Alumina Garnet Phases Y₃(Al_xGa_1–x)₅O₁₂ (YAGG) and Lu₃(Al_xGa_1–x)₅O₁₂ (LuAGG). A Semiempirical Approach

Abstract

A further generalization to quaternary oxide systems of the modeling equation of optical band gap values, based on the semiempirical correlation between the differences in the electronegativity of oxygen and the average cationic electronegativity, proposed some years ago, has been carried out by expanding the approach recently employed for ternary mixed oxides. The choice of oxide polymorphs and their influence on the fitting procedure of an experimental data set is evidenced by a detailed discussion of the fitting process of the literature's experimental band gap data pertaining two quaternary oxide systems of the garnet family, namely, Y 3 (Al x Ga 1−x ) 5 O 12 (YAGG) and Lu 3 (Al x Ga 1−x ) 5 O 12 (LuAGG), playing an important role in several engineering applications. The two investigated systems, moreover, span a quite large range of band gap energy values (from ∼5.5 to ∼7.5 eV), as a function of the Al/Ga ratio, allowing a rigorous test of the proposed modeling equation. Based on the wide existing literature on the presence of excitonic effects in the investigated systems some empirical correlations between an optical gap and a band gap in the presence of excitonic effects are suggested, too, which could provide some rationale to overcome the discrepancies frequently encountered in comparing band gap values reported in the literature for the same materials. The results of this work confirm the ability of this semiempirical approach in providing good agreement between experimental and theoretical band gap values also for very complex systems, where more sophisticated density functional theory-based methods face some difficulties in predicting the correct values.

Modeling of Optical Band-Gap Values of Mixed Oxides Having Spinel Structure AB2O4 (A = Mg, Zn and B = Al, Ga) by a Semiempirical Approach

“…However, we have to mention that for some partially inverted spinels of MgGa 2 O 4 (i = 0.44) and ZnGa 2 O 4 (i < 0.30), a quite good agreement between our bandgap estimate and the experimental band-gap values was observed. In many cases, our estimates of spinel band-gap values have shown a better agreement with respect to the 9 for quaternary alumina garnets, displayed a very good agreement with the fundamental band-gap values reported in the literature. Further experimental investigations aimed at explaining the observed discrepancies are welcome for reaching a deeper understanding of the influence of the preparation method on the solid-state properties of these technologically important materials.…”

“…By using the results of our recent study 9 on quaternary oxides as well as those reported above for the different polymorphs of ZnO and MgO, we will apply our semiempirical approach to the modeling of the following quaternary systems: (wz-ZnO, wz-MgO)//(α-Al x Ga 2−x )O 3 and (rs-ZnO, rs-MgO)//(β-Al x Ga 2−x ). With respect to the single spinel, for which we wrote the general formula…”

“…By using the results of our recent study on quaternary oxides as well as those reported above for the different polymorphs of ZnO and MgO, we will apply our semiempirical approach to the modeling of the following quaternary systems: (wz-ZnO, wz-MgO)//(α-Al x Ga 2– x )O 3 and (rs-ZnO, rs-MgO)//(β-Al x Ga 2– x ). With respect to the single spinel, for which we wrote the general formula (A 1– i B i ) T [A i B 2– i ] Oct. O 4 , where only two different cations A (usually representing the bivalent cation, Mg 2+ or Zn 2+ ) and B (usually indicating a trivalent cation, Al 3+ or Ga 3+ ) are present in different concentrations, on tetrahedral (T) and octahedral (Oct) sites, in the case of double spinels we are, generally, in the presence of three different cations so that, by following Ito et al, we can write the following general formula false( A 1 − i B j 1 B false( i − j false) 2 false) T false[ A i B false( 2 − x − j false) 1 B false( x − i + j false) 2 false] normalo ct . O 4 where A is the bivalent cation (Mg 2+ or Zn 2+ ) and B 1 and B 2 represent the trivalent cations, in our case, respectively, Al 3+ and Ga 3+ . j is the occupancy for B 1 in the 4-fold (or tetrahedral) coordinated site and i is the occupancy for A +2 in the 6-fold (or octahedral) coordinate site (or inversion parameter). …”

“…Numerous studies have been devoted to the fabrication and characterization of spinel oxides with general formula AB 2 O 4 covering a very wide range of band-gap values (1 eV < E g < 8 eV) as a function of the nature of the metallic cations A and B. Owing to their wide spectrum of electronic and physical properties, spinel oxides have been investigated as possible candidates in numerous engineering applications as electro-photocatalysis, electroluminescence, optoelectronics, photonics and spintronics, energy conversion and storage, and as materials for the fabrication of resistive random access memories (RRAM) for low energy consumption in data storage applications. − Lower band-gap values ( E g < 3.0 eV) have been reported for spinel oxides when the trivalent atom belongs to the transition d-metals, while highest band-gap values are, usually, reported for trivalent B atom belonging to the s,p-metal group (Al, Ga, In). Lower band-gap spinels have been largely investigated as possible photocatalysts and/or electrocatalysts in a photoassisted water-splitting reaction and for an electrochemical oxygen evolution/reduction reaction (OER/ORR). − High band-gap spinels ( E g > 3.0 eV) are of large interest for many relevant applications pertaining to the fields of electroluminescence, electronics, photonics, and energy conversion, including, possibly, future fusion energy devices. ,,, More specifically, ZnAl 2 O 4 and MgAl 2 O 4 spinel oxide systems are currently intensively investigated in the luminescence research area as possible phosphor candidates to substitute rare-earth-based alumina and gallia garnets, as well as catalytic support or active materials in photocatalytic processes. , On the other hand, MgAl 2 O 4 is also an interesting material for nuclear technologies as inert matrices for nuclear fuels or nuclear waste immobilization and as optical windows in fusion reactors and/or future fusion devices . ZnGa 2 O 4 has been investigated as photocatalytic material for the generation of molecular hydrogen, both under ultraviolet (UV) (250 nm) and under visible light (420 nm) as mixed spinel ZnFeGaO 4 .…”

“…In order to get the fundamental energy gap, E g,f , we need to add to E exc the electron–hole binding energy of the exciton . As suggested by Dorenbos, − for aluminum garnets, we can get a good estimate of the fundamental energy gap by using, as a first approximation, E exc and the relationship E normalg , normalf = E exc ( 1 + 0.008 E exc ) eV We have to say that the realm of validity of eq encompasses a class of materials wider than the aluminum garnets, while eq needs to be tested outside the range of materials investigated in ref . For these reasons, when the E exc term was accessible, we derived the E g,f value reported in Table by means of eq , while, in the absence of such information, we used eqs 6 and if the E g,opt value was known.…”