Unveiling the complex electronic structure of amorphous metal oxides

Abstract

Amorphous materials represent a large and important emerging area of material’s science. Amorphous oxides are key technological oxides in applications such as a gate dielectric in Complementary metal-oxide semiconductor devices and in Silicon-Oxide-Nitride-Oxide-Silicon and TANOS (TaN-Al₂O₃-Si₃N₄-SiO₂-Silicon) flash memories. These technologies are required for the high packing density of today’s integrated circuits. Therefore the investigation of defect states in these structures is crucial. In this work we present X-ray synchrotron measurements, with an energy resolution which is about 5–10 times higher than is attainable with standard spectrometers, of amorphous alumina. We demonstrate that our experimental results are in agreement with calculated spectra of amorphous alumina which we have generated by stochastic quenching. This first principles method, which we have recently developed, is found to be superior to molecular dynamics in simulating the rapid gas to solid transition that takes place as this material is deposited for thin film applications. We detect and analyze in detail states in the band gap that originate from oxygen pairs. Similar states were previously found in amorphous alumina by other spectroscopic methods and were assigned to oxygen vacancies claimed to act mutually as electron and hole traps. The oxygen pairs which we probe in this work act as hole traps only and will influence the information retention in electronic devices. In amorphous silica oxygen pairs have already been found, thus they may be a feature which is characteristic also of other amorphous metal oxides.

Despite early attempts to describe the fundamental electronic properties of noncrystalline semiconductors (1–5), experimental and theoretical knowledge of localized states in the gap of amorphous semiconductors and insulators is still limited. General features of the electronic structure of amorphous semiconductors are quite well known, such as the broad distribution of coordinations and the lack of long range order that induces valence and conduction band tails in the band gap (6). However, the origin of these states is less explored experimentally (7, 8) and theoretical investigations are mainly limited to the crystalline polymorphs (9–11). Amorphous Alumina (am-Al₂O₃) is currently one of the key technological amorphous materials, where one promising application of am-Al₂O₃ is as a high-k dielectric in transistors (12). The use of am-Al₂O₃ in TANOS (TaN-Al₂O₃-Si₃N₄-SiO₂-Silicon) flash memories, which are currently investigated for gigabite and terabite scale flash memories, puts even higher demands on alumina as a current-blocking high-k dielectric.

From optical absorption and photoluminescence, states related to F-centers (9, 10) and impurities have been identified in the band gap of am-Al₂O₃ down to 3.18 and 3.25 eV relative to the valence band edge (13, 14). In another study, electron–beam induced states in the am-Al₂O₃ gap have been observed to be reversible but they were not characterized in detail (15). In the closely related system, am-SiO₂, charged and neutral oxygen vacancies as well as bound oxygen–oxygen atoms (peroxy radicals) have been found (16–18). Although the performance of am-Al₂O₃ depends largely on the presence of coordination-related defects in the optical gap, there are no detailed studies of its electronic structure. Certainly, the lack of crystalline order and the fact that am-Al₂O₃ is found with a wide range of densities, complicates any study of the electronic structure. In fact, the density of am-Al₂O₃ varies within an extremely large range, from 2.1 to 3.6 g/cm³ (19, 20). The greatly varying density of am-Al₂O₃ may well have been the major cause of the past debate on the coordination of oxygen around aluminum (21–25). In recent works, most authors find a mean coordination between 4 and 5 (26–29). In this article we bring attention to the electronic structure of am-Al₂O₃, which has not yet been investigated in any theoretical study. We synthesize an am-Al₂O₃ structure by means of Physical Vapor Deposition (PVD) and measure the defect states in the band gap with Near Edge X-ray Absorption Fine Structure (NEXAFS) and Resonant Inelastic Scattering (RIXS). Details of these techniques can be found in the Methods section. We analyze the origin of these states by two first principles methods; molecular dynamics (MD) and stochastic quenching (SQ). We show that the structure which best describes the NEXAFS contains trapped O-O pairs. These pairs have previously not been identified in am-Al₂O₃ and may be a feature which is generic also of other amorphous metal oxides.

Results and Discussion

In the NEXAFS spectra of am-Al₂O₃, Fig. 1, we find a double peaked structure with two peaks at 538.8 eV and 535 eV. Below this edge, a number of small additional features are observed: a peak at 530.3 eV, a shoulder at 528.4 eV, and another peak at 525.0 eV. Comparing with the NEXAFS spectrum of crystalline alumina, we can verify that all the small features below the oxygen absorption edge are originating from its amorphous character.

Fig. 1.

The oxygen K-edge NEXAFS of am-(black dots) and crystalline (green dots) Al₂O₃. Inset: An experimental EELS spectrum from Perevalov et al. (9, 10) of amorphous Al₂O₃.

In Fig. 2 we show the detailed features below the conduction band (CB) of the measured NEXAFS spectrum of am-Al₂O₃ along with the sum of all calculated oxygen p-projected partial DOS (pDOS), with a core hole on each oxygen, for the MD and SQ-generated structures. We observe that the experimental CB edge is shifted down by ≈2.5 eV in energy as one goes from crystalline to am-Al₂O₃. We found that the relative shift to lower energies is captured by both SQ and MD methods. The calculated band gaps of α-Al₂O₃ and the SQ- and MD-generated amorphous structures were 6.2, 2.5, and 3.0 eV respectively. We would like to point out that one cannot rely on any absolute value of the band gap from theory, due to the severe underestimation of the band gap by Density Functional Theory. For a closer look at the most prominent of these small features observed in NEXAFS, the peak at 530.3 eV, we recorded a RIXS spectrum at this very excitation energy, seen in Fig. 3. As a reference, a spectrum of gaseous O₂ was recorded at the same excitation energy (30). The RIXS spectrum of am-Al₂O₃ shows a clear resemblance to the O₂ spectrum; however, we observe an additional broad emission feature between -6 and -4 eV energy loss and a small hump at -2 eV loss, which are not present in the O₂-spectrum. By comparing the two spectra we conclude that quasi-free oxygen molecules, prevailing in the sample, are excited at 530.3 eV excitation energy. We believe that these molecules primarily are produced in the decomposition processes induced by the primary photons. The slight difference between the vibrational progressions in the gas-phase and am-Al₂O₃ spectra indicates weak interaction between the molecules and the solid. Intensity at larger energy-losses indicates that oxygen atoms in the solid are also excited at 530.3 eV. We attribute the oxygen atoms in the amorphous solid to precursors which form O₂ molecules at photon exposure.

Fig. 2.

The oxygen K-edge NEXAFS of am-(black dots) and crystalline (green dots) Al₂O₃. The sum of all oxygen 2p pDOS of the structures generated from SQ and from MD are denoted by black squares and green crosses. Details of the two methods can be found in the Methods section. The Z + 1 approximation was applied to all oxygen pDOS. The calculated CBs have been aligned to the experimental CB of am-Al₂O₃. We applied Gaussian smearing of 0.3 eV to both calculated datasets. The dashed line denotes the Fermi energy of the calculated spectra.

Fig. 3.

RIXS spectrum of the am-Al₂O₃ excited at 530.3 eV, along with the RIXS spectrum of the free O₂ molecule, excited at the same energy.

In search of plausible O-O configurations which could give rise to the intensity peak seen at 525 and 530.3 eV in the NEXAFS spectrum we studied the partial radial distribution function, g(r), for the MD- and SQ-generated structures. We find that the g(r) of the SQ-generated structure contains a small additional peak, not present in the g(r) of the MD-generated structure, which corresponds to O-O bonds of about 1.5 Å length. Out of 10 SQ structures generated from different random inputs, oxygens bound together are present at a concentration of 3–8%. On the other hand, there is not one single bound oxygen pair in 10 MD-generated structures.

In Fig. 4 A and B, the pDOS of two bound oxygen atoms without core holes are displayed. First we note that the oxygen pairs are nonmagnetic, with the π_g filled due to the interaction with Al from the Al₂O₃ matrix. One of these oxygens, O_I is bound to 2 Al atoms, whereas the other oxygen, O_II is bound to only one Al and introduces a small cavity in the structure. Furthermore, O_I attracts somewhat more electron density than O_II. Our found O-O bond length is in between that of the so-called split O-interstitial (31) (1.44 Å) and that of adsorbed atomic oxygen on the (0001)α-Al₂O₃ surface (1.55 Å) (32). Both oxygens display localized states at the top and bottom of the valence band (VB). These states closely resemble the states of a split O-interstitial in α-Al₂O₃ s- and p-orbital is bound to a lattice oxygen, which is denoted as a peroxide ion (31). In between these states, there is a broad band due to Al-O s and p overlap. The states at the bottom of the VB are of σ_g-character, whereas the states at the top of the VB display π_g-character. States at the top of the VB have also been reported for the split O-interstitial in α-Al₂O₃ (31) and were in a recent experimental study suggested to originate in coordination imperfection (7). The high energy occupied states are however not purely π_g-like, but contain some contribution from all three p-orbitals of different angular momentum projection. As a core hole is created on a quasi-molecular oxygen, the π_g-like states split from the VB and localize at the Fermi level (as is seen in Fig. 2). The localization is an effect of decreased screening from the core, increasing the Coulomb interaction between the positive core and the valence electrons. At the bottom of the conduction band, more localized states are present. These states are mainly of σ_u-character and we expect that they give rise to the peak at 530.3 eV in Fig. 2, as electrons are excited from deep lying σ_g states.

Fig. 4.

The orbital momentum projected and total pDOS of the two oxygens in a quasi-molecule with a bond length of 1.47 Å, O_I (A), O_II (B).

In Fig. 5 we compare our calculated partial density of states without core hole to Ultraviolet Photoemission Spectroscopy (UPS)-data (10). We find that the O 2p of am-Al₂O₃, generated from SQ and MD agree considerably better in shape and position with the UPS spectrum than the O 2p of the crystalline phase, although the peaks in the UPS spectrum below the upper VB are less intense in our calculated spectrum. Furtermore, the MD-generated structure lacks the small features seen at the top and bottom of the O 2p VB of the SQ-generated structure.

Fig. 5.

UPS data from Perevalov et al. (9, 10) along with the calculated occupied O 2p pDOS of amorphous alumina, generated by SQ and MD and with α-Al₂O₃.

We calculated the average total energy of 10 SQ-structures and 10 MD-quenches and found that the SQ average total energy was 0.4 ± 0.05 eV/atom higher than the corresponding energy of the ground state α-phase. The average energy of the MD-generated structures was 0.2 ± 0.01 eV/atom higher than that of α-Al₂O₃. This result and our analysis of the electronic structure imply that the SQ-method captures the high energy amorphous structures that are formed during physical vapor deposition, whereas MD tends to get trapped in low energy minima that correspond to more stable amorphous, or even quasi-crystalline structures. The total energy per atom as a function of the number of peroxide ions per cell for 10 different stochastic guesses is displayed in Fig. 6. From the fit to these data we find that the approximate energy required to form one peroxide ion is 2.6 eV. This energy is of the same order of magnitude as the energy required to form a split interstitial (open-shell triplet) in alpha-Al₂O₃ of 4.00 (5.38) eV/atom (31). The extrapolated intercept, -7.31 eV/atom, at zero concentration of peroxide ions, is close to the MD average energy of -7.35 eV/atom. Within the error bars there is no discrepancy between the MD average and the SQ intercept, implying that the difference in average energy between the MD and SQ structures is purely due to that the latter contains peroxide ions.

Fig. 6.

The linear fit between the number of peroxy ions and total energy of our 10 different SQ-generated structures, where the ± values indicate the 95% confidence interval of the parameter estimates. The average total energy per atom of the 10 MD structures is shown for reference and the bars indicates 95% confidence intervals for the SQ and MD intercept respectively.

The peak at 530.3 eV in the NEXAFS spectrum seems to find its explanation in the σ_u-like state of the peroxy ions which are exclusive to the structures generated by the SQ method. Instead, the peak at 525 eV is not trivial to explain. States just above the VB were previously found by high-resolution electron energy loss spectroscopy in am-Al₂O₃ and were attributed to coordination imperfection (8). In our calculated electronic spectrum (Fig. 2), the π_g-states are located just at the Fermi energy. However, we cannot exclude that the position of the π_g-states is an artifact of the core-hole approximation which we applied. We therefore investigated other possible mechanisms in which the π_g-like states may turn partially occupied. To study the trapping of electrons/holes by the peroxy defects, we added or removed one electron per peroxy ion. The charge localization energy of the electron and hole can be estimated as the difference between the perfect and defect electron affinities and ionization energies. We used the energy of the MD-generated structure with one electron removed or added as the energy of the perfect structure. The approximation is reasonable, because the MD-generated structure contains no peroxy ions. The charge localization energy can then be calculated as (38), for electrons and as for holes. We find that the energy required to trap one electron at the peroxy ion site is 0.57 eV/peroxy ion. Instead the trapping of a hole is energetically favorable with an energy gain of 1.35 eV/peroxy ion. The negatively charged quasi-molecule is nonmagnetic, whereas the capturing of a hole gives rise to a magnetic moment of 1.15 μBohr. If electron traps are available the π_g-states turn partially occupied and could give rise to the state at 525 eV at the Oxygen K-edge. Other structural defects may act as electron traps, compensating for the charged peroxy ions. We would like to point out that the states at the CB of am-Al₂O₃ were ascribed to oxygen vacancies by Perevalov et al. (10). We calculated the electronic structure of am-Al₂O₃, generated from the SQ method, with one oxygen vacancy and found that the removal of one oxygen out of 120, shifts the Fermi energy to the CB and could not give rise to the NEXAFS that we present in this work.

The effect of synchrotron radiation on the defect structure of am-Al₂O₃ was studied by irradiating the sample for 18 h (Fig. 7). The irradiated spot was then analyzed by X-Ray diffraction (XRD), where it was verified that the structure was still amorphous. After irradiation, the peaks in the band gap diminish and the conduction band increases in height which suggests that healing of the defect states and a subsequent amorphous-amorphous structural transition takes place. The sample surface also cracks, indicating leakage of O₂ and a densification of the sample. A possible mechanism for this structural transformation is that as the beam hits the sample, electrons are delocalized from the π_g bonds of the peroxy ion. This delocalization of electronic charge weakens the ionic bond between neighboring Al and the peroxy ion. At the same time the O-O quasi-molecular bonds are strengthened due to the decrease in population of the antibonding π_g states. The relatively long life time of the defect states, implies that they cannot originate in loosely bound surface oxygen molecules, but rather in oxygen pairs trapped in the bulk of the solid.

Fig. 7.

The NEXAFS oxygen K-edge on a fresh spot (red line) of am-Al₂O₃ and after 18 h of irradiation (dashed black line).

Methods

Experimental Details.

Thin films of aluminum oxide were prepared by reactive direct current magnetron sputtering in a versatile deposition system based on a Balzers UTT 400 unit. Sputtering took place from a 5 cm diameter Al (99.99%) target in a plasma of Ar + O₂ at a pressure of 15 mTorr and a discharge power of 300 W (power density 26 W/cm²). The O₂/Ar gas flow ratio was set to 4/60. Film thickness and refractive index were determined from interference oscillations in optical transmittance spectra recorded by a Perkin-Elmer Lambda 900 spectrophotometer in the wavelength range from 350 to 2,500 nm. For the present investigations we used samples with thicknesses between 650 nm and 1,240 nm. The refractive index of our films was between 1.35 and 1.40. The density was then estimated from the refractive index by a modification of the Clausius-Mosotti relation (33) to be about 2.35 g/cm³, a low value in the range of densities reported in the literature for amorphous alumina (2.1–3.6 g/cm³) (19, 20). A Hitachi S-4300 FEG-SEM, with a lateral resolution of 1.5 nm was used for scanning electron microscope imaging of cross sections of the coated substrate. The cross sections show a homogenous structure so that if pores exist, they must be smaller than the resolution of the image (about 20 nm). The films were studied by XRD using a Siemens D5000 diffractometer operating with radiation of a wavelength of 1.54 Å. No peaks were observed in the diffraction pattern, reassuring us that the films were amorphous. A Bruker D8 diffractometer, equipped with a Eulerian cradle was used to probe crystalline phases, possibly formed after irradiation. To make measurements possible on small areas, the X-ray beam was focused to a diameter of 0.05 mm. The measuring point was carefully selected by using a camera and a laser point, which is aligned with the X-ray beam. The data was collected by a Hi-star GADDS detector.

NEXAFS and RIXS measurements were performed at the ADRESS beamline (34, 35) of the swiss light source, Switzerland and Politecno di Milano, Italy. Here, both angle of incidence and angle of emission were 45°. The energy scale was calibrated using O₂ emission of air at atmospheric pressure as a reference. The effect of X-ray irradiation of the samples was measured at beamline I511-3 at MAX-lab, Lund, Sweden using a multichannel plate detector in fluorescence yield. The measurement geometry was normal incidence of the photon beam and the detector was positioned at an angle of 45° relative to the direction of propagation of the incident beam in the plane of the incident polarization.

Computational Methods.

The structure of amorphous Al₂O₃ was determined by using the Vienna Ab inito Simulation Package (VASP), within the projector augmented wave method (36) with the Gradient Generalized Approximation-PW91 functional (37), including the valence states 3s²3p¹ for Al, 2s²2p⁴ for O, and 2s²2p⁵ for F which we used in the Z + 1 calculations. We used an energy cutoff of 520 eV for the relaxations of the 200 atom systems but used 750 eV for the calculation of the electronic structure. We included only the Γ-point in the sampling of the Brillouin Zone, and verified that increasing the number of k-points did not change the total energy of the system by any significant amount. For the properties of crystalline α-Al₂O₃, we used a rhombohedral unit cell of 10 atoms, a 6 × 6 × 6 k-points Monkhorst-Pack mesh and an energy cutoff of 750 eV.

In a PVD process, the amorphous solid is formed directly from gas phase, constituting a gas-solid transition during a relatively short time. In general, the synthesis of amorphous oxides by PVD produces thin coatings with a density lower than that of the bulk solid produced from rapid cooling of the liquid. As we were to describe this transition from theory, our concern was that standard MD may not provide the correct structure, because it involves a step where the system is equilibrated in the liquid state at some temperature and is then cooled down as to simulate the liquid-solid transition. We instead described the solidification process without passing through the liquid phase by an alternative method to MD, the SQ method (39). The SQ method has previously been shown to accurately describe the potential energy landscape of metallic liquids as well as oxides (40–44). Here, the positions of the Al and O atoms were drawn from a random uniform distribution confined to the dimensions of the simulation box, at an Al∶O ratio of 2∶3 into a cubic unit cell. The system energy was then minimized in VASP with a nonlinear conjugate gradient method, keeping the cell geometry fixed, only allowing the atom positions to be optimized, without using any symmetry constraint (this is essentially the method used in ref. 41). We repeated this procedure for different densities so as to find a local energy minimum of this nonequilibrium system as a function of volume. We quenched from 10 different random configurations to investigate the reliability of this method for these specific systems.

The MD calculations were performed within VASP, starting from an initial stochastic configuration. The MD was equilibrated in the liquid state using a thermostat set at 3,000 K for 2 ps. After equilibration we continued the simulation for 2 ps with 1 fs time steps at constant total energy as a microcanonial ensemble. We then selected snapshots from this MD trajectory and quenched directly down to 0 K, to simulate the quick cooling of the PVD process. For reference, the melting temperature of am-Al₂O₃ is 2327 K.

We applied the Z + 1 approximation (45) to model the core hole created in the absorption process. We make use of the final state rule, which says that accurate emission and absorption spectra can be calculated from the final states of the X-ray processes (46). The calculated final states correspond to the neutral ground state for the emission and excited state with a core hole for the absorption. The theoretical simulation of the core hole can be achieved by using an explicit core hole, for instance by generating an atomic pseudopotential with one core electron missing, or by replacing the regarded atom by the next heavier element in the periodic table and removing one electron from this system, the Z + 1 approximation. The latter has been applied to calculate NEXAFS in this article. The limitations of this approximation will mainly be the treatment of the core electrons within the Projector Augmented Wave Method (47) including the frozen core approximation (48). The Z + 1 approximation has in earlier works been successfully applied to both molecules and solids (49, 50), and has also been applied to the α-Al₂O₃ system, and was found to improve coherence between calculated and experimental Electron-Energy-Loss Spectroscopy (EELS) spectra for the K-edge (51). We included a core hole for each oxygen and calculated its electronic structure in order to simulate the O(1s) NEXAFS.

Conclusions

We have stabilized a metastable amorphous phase of Al₂O₃ which exhibits empty states in the band gap by means of physical vapor deposition. By generating a series of amorphous structures with the SQ method we show rigid proof that the structure which describes the measured NEXAFS best contains trapped O-O pairs. These peroxide ions act as hole traps and influence the information retention in electronic devices such as CMOS devices or SONOS and TANOS flash memories. Our results indicate that the origin of defect states in the band gap is different to what was suggested in earlier works where they were instead ascribed to oxygen vacancies. Our analysis of the energetics and electronic structure imply that the SQ avoids trapping in quasi-crystalline energy valleys and reproduces both the Al-O coordination of am-Al₂O₃ and captures exotic features such as peroxide ions, not previously evidenced in am-Al₂O₃. This method may be applied to a wide range of amorphous metal oxides to determine structural and electronic properties of thin films deposited from gas phase.

Appendix

From the radial distribution function, g(r), of both SQ and MD-generated structures we find a mean Al-O coordination of 4.5 and a mean O-Al coordination of 3, which is in good agreement with the experimental results of ref. 26–29 (Fig. 8). The peak at 1.5 Å in the SQ g(r) corresponds to O-O bonds, is not present in the g(r) of the MD-generated structure. We furthermore calculated the X-ray structure factor, Fig. 9, for the SQ- and MD-generated structures and compared with the calculated structure factor by Vashishta et al. (28) and the experimental X-ray structure factor from Ansell et al. (22). The SQ structure factor better matches the data from Ansell et al. (22) and also displays more features below 2 Å than the MD-generated structure. These features most likely reflect the oxygen-oxygen bonds which are unique of the SQ-generated structure. Ansell et al. found that structure factors measured at a lower density contained more diverse features in this specific regime, than structures with a higher density, again strongly suggests that the SQ method is better capable than MD of describing the structure of low density amorphous Al₂O₃ deposited from gas phase.

Fig. 8.

Total radial distribution function of the SQ- and MD-generated structures, compared with (22) and (21).

Fig. 9.

Calculated [this work and by Vashishta et al. (28)] and measured (21) X-ray structure factors for am-Al₂O₃.