Electronic structure of GaN and Ga investigated by soft x-ray spectroscopy and first-principles methods

The electronic structure and chemical bonding of wurtzite-GaN investigated by $\text{N}1s$ soft x-ray absorption spectroscopy and $\text{N}K$, $\text{Ga}{M}_1$, and $\text{Ga}{M}_{2,3}$ emission spectroscopy is compared to that of pure Ga. The measurements are interpreted by calculated spectra using first-principles density-functional theory (DFT) including dipole transition matrix elements and additional on-site Coulomb interaction $\left(\text{WC-GGA}+U\right)$. The $\text{Ga}4p\text{-N}2p$ and $\text{Ga}4s\text{-N}2p$ hybridization and chemical bond regions are identified at the top of the valence band between $-1.0$ and $-2.0$ and further down between $-5.5$ and $-6.5\text{eV}$, respectively. In addition, $\text{N}2s\text{-N}2p\text{-Ga}4s$ and $\text{N}2s\text{-N}2p\text{-Ga}3d$ hybridization regions occur at the bottom of the valence band between $-13$ and $-15\text{eV}$, and between $-17.0$ and $-18.0\text{eV}$, respectively. A bandlike satellite feature is also found around $-10\text{eV}$ in the $\text{Ga}{M}_1$ and $\text{Ga}{M}_{2,3}$ emission from GaN, but is absent in pure Ga and the calculated ground-state spectra. The difference between the identified spectroscopic features of GaN and Ga are discussed in relation to the various hybridization regions calculated within band-structure methods.

Figure 1

(Color online) XRD from the GaN (0001) thin film sample in comparison to pure Ga. The sharpness of the 0002 reflection is 60.3 arcseconds from rocking curve measurements which shows that the GaN coating is of very high epitaxial crystal quality.

Figure 2

(Color online) Top right: $\text{N}1s$ SXA-TFY spectra and left: resonant and nonresonant $\text{N}K$ SXE spectra of GaN. The SXA spectra were normalized by the step edge below and far above the $\text{N}1s$ absorption thresholds. All spectra are plotted on a photon energy scale (top) and a relative energy scale (bottom) with respect to the top of the valence band. The SXE spectra were resonantly excited at the $\text{N}1s$ absorption peak maximum at 402.8 eV and nonresonant far above the $\text{N}1s$ absorption threshold at 430.0 eV. The excitation energy (402.8 eV) of the resonant SXE spectrum is indicated by the vertical tick at the main peak in the SXA-TFY spectra and by the very weak elastic peak enlarged by a factor of 10. To account for the experimental bandgap, the calculated SXA-TFY spectra were shifted by $+1.84\text{eV}$. The calculated $\text{N}2p$ charge occupation of $w\text{-GaN}$ is 2.858e.

Figure 3

(Color online) Experimental and calculated $\text{Ga}{M}_1$ and $\text{Ga}{M}_{2,3}$ SXE spectra of GaN in comparison to pure Ga. The experimental $M_1$ and $M_{2,3}$ spectra were excited nonresonantly at 180 and 145 eV, respectively. For GaN, resonant spectra excited at the $3p_{3/2}$ (107.8 eV) and $3p_{1/2}$ (110.8 eV) edges are also shown. A common energy scale with respect to the top of the valence-band edge of GaN is indicated in the middle (vertical dotted line). The calculated $\text{Ga}4s$, $4p$, and $3d$ charge occupations of GaN: $4s$: 0.515e, $4p$: 0.474e, $3d$: 9.847e and for pure Ga $4s$: 0.693e, $4p$: 0.307e, $3d$: 9.766e. The area for the $M_2$ component was scaled down by the experimental branching ratio and added to the $M_3$ component. The calculated $\text{Ga}{M}_1$ spectrum of pure Ga was shifted by $+1.71\text{eV}$ corresponding to the calculated core-level shift between GaN and pure Ga.

Figure 4

(Color online) (a) Calculated ground-state band dispersions in GaN along the $\Gamma \to M\to K\to \Gamma \to A$ direction for $U=0\text{eV}$ (black solid lines) and $U=10\text{eV}$ (red/gray dashed lines). (b) Partial density of states as computed for the $U=10\text{eV}$ case by using the relaxed unit-cell geometry.