Theoretical and experimental investigation of the electronic properties of the wide band-gap transparent semiconductor ${\mathrm{MgGa}}_2{\mathrm{O}}_4$

We present an experimental and theoretical study of the electronic structure of the transparent conductive oxide semiconductor ${\mathrm{MgGa}}_2{\mathrm{O}}_4$. Its valence band and the core levels have been measured experimentally by angle-resolved photoemission spectroscopy and compared to theoretical ab initio density-functional calculations. The bands stem from oxygen orbitals and have a dispersion of about 0.6 eV and high effective masses, in agreement with the calculations. Angle-resolved measurements of the Ga 3d core levels indicate a sizable upward band bending, which in combination with an exact model potential yielded a quantitative estimate of the spatial extension of the depletion region, the effective Debye length in the material, and the extrinsic bulk carrier density.

Figure 1

(Left) Inverse spinel structure of ${\mathrm{MgGa}}_2{\mathrm{O}}_4$ with balls representing the different ions: (red) oxygen anions, (gray) tetragonal cations, and (violet) octahedral cations. Both these coordination sites are marked by the black lines. (Right) ${\mathrm{MgGa}}_2{\mathrm{O}}_4$ wafers prepared from a bulk crystal: insulating (top) and semiconducting (bottom).

Figure 2

Structure of ${\mathrm{MgGa}}_2{\mathrm{O}}_4$ in the fcc system with 14 atoms basis. Spheres colored in gray indicate the Ga atoms, in red the oxygen atoms, and in blue either Mg or Ga ions in the tetrahedral sites (see text).

Figure 3

$k_{\perp }$ dispersion represented by energy distribution curves stacked as a color map and overlapped to the ab initio band structure calculations, represented by the gray dotted lines. The horizontal red lines indicate the $\mathrm{\Gamma }$ and $X$ high-symmetry points of the Brillouin zone.

Figure 4

(a) ARPES maps at $h\nu =26\mathrm{eV}$ ($\mathrm{\Gamma }\text{−}X$ direction) and (b) $h\nu =39\mathrm{eV}$ ($X\text{−}W$ direction) overlapped to the theoretical band structure, shifted by $5.34\text{eV}$. The theoretical CBM energy is too low: the theoretically predicted gap is too small. (c) The full theoretical band structure plotted along the high symmetry directions of the fcc Brillouin zone, labeled by the high-symmetry points. (d) Orbital decomposition of the density of states of ${\mathrm{MgGa}}_2{\mathrm{O}}_4$.

Figure 5

Calculation of the band bending potential at semiconductor surfaces for different surface potentials $v_s$ and intrinsic potentials $u_b$, as indicated in the labels of the two panels.

Figure 6

Angle-resolved photoemission spectra of the Ga 3d core levels taken at the angles indicated in the label. A black vertical line indicates the peak maximum at normal emission (labeled $0^{\circ }$). A clear shift of the peak is observed when the photoelectrons are observed at grazing emission.

Figure 7

Temperature-dependent change of the (left) valence band at $h\nu =26\mathrm{eV}$ corresponding to the $\mathrm{\Gamma }$ point, averaged over $2^{\circ }$ about the normal emission direction; (right) 3d core levels and the valence band, averaged over $4^{\circ }$ at a photon energy $h\nu =39\mathrm{eV}$ corresponding to the $X$ point.

Figure 8

(Top) Examples of the valence band at the $\mathrm{\Gamma }$ point measured at different times: (red line) fresh surface right after the preparation, (green line) 3 h after the preparation, (blue line) 1 day after the preparation, and (black line) 3 days after the preparation. (Bottom) Examples of spectra taken at the beginning of the experiment to show the improvement of the surface quality upon sputtering and annealing. In the figure label, the sputtering parameters are indicated by $S(t,E)$, with $t$ indicating the sputtering time in minutes and $E$ indicating the ion energy in keV. Similarly, the annealing parameters are indicated by $A(t,T^{\prime })$, with $t$ giving the annealing time and $T^{\prime }$ the annealing temperature.

Figure 9

Temperature dependence of the photoemission spectra taken at normal emission under different illumination intensities (referenced to the mirror current) (left) at 300 K and (right) at 18 K. No shift in the spectra is visible, indicating no charge-up effects.

Figure 10

(Left) Experimental Laue diffraction image of ${\mathrm{MgGa}}_2{\mathrm{O}}_4$ done with an x-ray tube equipped with a Cu target. (Right) Theoretical calculation of the Laue diffraction pattern (see main text for details). Each diffraction spot is labeled with the Miller indices of the corresponding crystal planes and the radius of the circle is proportional to the theoretical intensity. The (800) diffraction spot is at the origin of the axes and the ($\overline{5}01$) point in the experimental figure (left) corresponds to the (1020) in the theoretical calculation (right). Similarly the ($\overline{3}10$) corresponds to the (1240) point.