Electronic structure of rare-earth semiconducting ErN thin films determined with synchrotron radiation photoemission spectroscopy and first-principles analysis

Erbium nitride (ErN) is an emerging rocksalt rare-earth semiconducting pnictide and has attracted significant interest in recent years for its potential applications in thermoelectric energy conversion, spintronic devices, and for the Gifford-McMahon cryocoolers. Due to the Er intra-$4f$ electronic transition, Er-doped III-nitride semiconductors such as GaN, InGaN, etc. exhibit strong emission in the retina-safe and fiber optical communication wavelength window of 1.54 μm that is researched extensively for developing solid-state lasers, amplifiers, and light-emitting devices. However, due to ErN's propensity for oxidation in ambient, high-quality ErN thin film growth has been challenging and an in-depth understanding of its electronic structure remains unanswered. In this work, the valence band electronic structure of ErN thin films is measured with normal as well as with resonant synchrotron-radiation photoemission spectroscopy. Photoemission measurements show a valence band maximum and Fermi energy difference of ∼2.3 eV in ErN. First-principles density functional theory (DFT) calculations are performed not only to explain the valence band electronic structure but also to determine transport properties such as effective mass and deformation potentials. Strong localized Er-$4f$ states are observed ∼6–8 eV below the valence band maxima and the valence band edge is found to exhibit N-$2p$ character. Resonant photoemission data corroborates the DFT calculations. To accurately capture the electronic structure in modeling, beyond generalized gradient approximation (GGA) methods such as (a) Heyd-Scuseria-Ernzerhof hybrid functional and (b) GGA+U Hubbard correction schemes are utilized. Determination of the electronic structure of ErN marks significant progress in developing ErN-based electronic, optoelectronic, and thermoelectric devices.

Figure 1

XPS core-level spectra of ErN film corresponding to (a) Er-$4d$ (b) N-$1s$ (c) Al-$2p$ and (d) O-$1s$ peaks are presented. As the ErN film was capped with 2 nm AlN, XPS signal arise from both the AlN and ErN layers.

Figure 2

(a) Synchrotron-radiation photoemission spectra of ErN thin-films after significantly sputtering out the top 20 nm AlN capping layer that shows its valence band electronic states. (b) The valence band shows the $\mathrm{Er}\text{−}4f$ and $\mathrm{Er}\text{−}5d, \mathrm{N}\text{−}2p$ hybridized states well as the valence band edge. (c) The total and partial DOS of the N-2p, $\mathrm{Er}\text{−}4f$ and Er-$5d$ states was calculated using GGA and without U correction (d) The total and partial DOS of the $\mathrm{N}\text{−}2p$ Er-$5d$ and $\mathrm{Er}\text{−}4f$ states was calculated using GGA+U with $\mathrm{U}=7\mathrm{eV}$ for $\mathrm{Er}\text{−}4f$ states where $\mathrm{Er}\text{−}4f$ electrons are considered as valence electrons. The valence band edge and $\mathrm{Er}\text{−}4f$ states align well with the experimental photoemission spectra. (e) The total and partial DOS of the N-2p and Er-$5d$ states was calculated using GGA+U with $\mathrm{U}=6\mathrm{eV}$ for $\mathrm{Er}\text{−}5d$ states where $\mathrm{Er}\text{−}4f$ electrons are treated as core.

Figure 3

Resonant photoemission spectra of ErN thin film deposited on the Si substrate at various photon energy is presented. Well-separated and distinct two peaks at ∼5.5 eV (A) and ∼9 eV (B) are observed in the valence band.

Figure 4

(a) Electronic band structure of ErN calculated using HSE functional with various exact exchange (α) values. Bandgap increases with an increase in the α values. (b) Corresponding total DOS for $\alpha =0.20$. (c) Band structure of ErN calculated using GGA and GGA+U with a U parameter of 6 eV for the $\mathrm{Er}\text{−}5d$ states where $\mathrm{Er}\text{−}4f$ electrons are treated as core electrons. (d) Corresponding total and partial DOS for $\mathrm{U}=6\mathrm{eV}$ in $\mathrm{Er}\text{−}5d$ states.

Figure 5

Comparison of the ErN band structure calculated using GGA, GGA+U (with $\mathrm{U}=6\mathrm{eV}$ for $\mathrm{Er}\text{−}5d$ states), and HSE functional (with $\alpha =0.2$). Both the GGA+U and HSE, shift the $\mathrm{Er}-5d$ states to higher energy and open higher bandgap. The charge densities are shown on the right-hand side correspond to CBM + 100 meV (top) and VBM - 100 meV (bottom) for the GGA+U method with $\mathrm{U}=0\mathrm{eV}$. Blue and violet spheres correspond to Er and N, respectively. Charge densities look similar for the other two methods as well.