Atomic networks as highways for holes in oxygen-deficient amorphous oxides

TL;DR

The paper addresses the origin of high hole mobility in oxygen-deficient amorphous TeO$_x$ and reconciles experimental observations with atomistic physics. It combines machine-learning-accelerated ab initio molecular dynamics with hybrid-functional defect calculations to show that substantial oxygen loss drives phase segregation into interpenetrating $a$-Te and $a$-TeO$_2$ networks, enabling percolative Te $5p$ hole pathways. Holes are favored by Te vacancies or contact-induced injection, while Se doping extends the conductive Te network and lowers the hole mobility edge $ riangle E_h$, achieving mobilities up to $15\, ext{cm}^2 ext{V}^{-1} ext{s}^{-1}$; similar behavior is found in amorphous SeO$_x$, suggesting a general design approach for high-mobility p-type amorphous oxides. These results reveal a tunable mobility-bandgap trade-off and offer a broadly applicable strategy for boosting p-type transport in disordered oxides.

Abstract

Oxygen-deficient amorphous tellurium oxides ($a$-TeO$_x$) have recently challenged the intrinsic hole mobility limits of amorphous oxides, with thin-film transistors reaching mobilities up to 15 cm$^{2}$V$^{-1}$s$^{-1}$ upon Se doping. However, the atomistic origins of this behavior, and its seeming contradiction with established semiconductor physics, have remained unresolved. Here, we combine machine-learning-accelerated ab initio molecular dynamics with hybrid-functional defect calculations to establish a new microscopic picture. We show that substantial oxygen loss drives spontaneous segregation into interpenetrating $a$-Te and $a$-TeO$_2$ domains, rather than forming dispersed oxygen vacancies. The diffuse Te-$5p$ states from the $a$-Te network supply percolative pathways for holes, so mobility rises monotonically with oxygen deficiency, enabling mobilities that exceed current records. Doped Se incorporates into the $a$-Te domain, enhancing the connectivity of conductive pathways, thereby increasing hole mobility. Similar behavior in amorphous SeO$_x$ suggests domain percolation as a general route to high-mobility p-type transport in amorphous oxides.

Figures (12)

• Figure 1: Atomic structures and oxygen-vacancy energetics in crystalline and amorphous TeO2. (a) Reference crystalline phases: trigonal tellurium ($c$-Te) and the polymorphs $\alpha$-, $\beta$- and $\gamma$-TeO2. Te atoms are displayed in blue, O atoms in red. (b) Amorphous counterparts obtained by melt-and-quench molecular-dynamics simulations for elemental Te ($a$-Te) and TeO2 ($a$-TeO2). (c) Schematic of the melt-and-quench protocol used to generate the amorphous structures from random initial configurations. (d,e) Formation energies of oxygen vacancies ($V_{\ce{O}}$) in (d) $\alpha$-TeO2 and (e) $a$-TeO2 as a function of the Fermi level (referenced to the VBM) ranging from zero up to the conduction-band minimum. Typical three charge states, $q=0$ (solid line), $+1$ (dotted) and $+2$ (dashed), in O-rich conditions are considered. The relaxed defect geometries are also depicted, where the vacancies are indicated by cubes, with the associated charge-density isosurfaces (in yellow) of the donor states at $q=0$. The isosurfaces are set to 10% of the maximum value each.
• Figure 2: Pair correlation functions and distributions of tellurium coordination numbers. (a--c) Pair correlation functions, $g(r)$, of (a) $a$-TeO2, (b) $a$-Te, and (c) $a$-TeO_1.2; Radial atomic distributions of Te--O, O--O, and Te--Te pairs for the amorphous samples are displayed in solid lines; those for crystalline $\alpha$-TeO2 (paratellurite) and Te (trigonal) are shown in dashed lines. The peaks are labeled and assigned to atomic pairs of the structural fragments shown in the insets. The curves are shifted vertically for clarity. (d--f) Histograms of tellurium effective coordination number, ECN$^{\ce{Te}}$, in number of nearest neighbors (NNN). The insets show fragments of the amorphous structures with corresponding ECN$^{\ce{Te}}$.
• Figure 3: Structural and thermodynamic signatures of Te segregation in oxygen-deficient amorphous tellurium oxides. (a) Distribution of effective charges defined from the Bader analysis for $a$-TeO$_{1.2}$ reveals three distinct populations of tellurium: neutral Te$^{0}$ (34%), partially oxidized Te$^{\delta+}$ (8%), and fully oxidized Te$^{4+}$ (58%). Refer to the main text and Methods for further details on the classification criteria. (b) Structural snapshots of amorphous TeO$_x$ for $x = 1.6$, $1.2$, $0.8$, and $0.4$ reveal the progressive formation of $a$-Te domains (orange) as oxygen content decreases. (c) Fraction of Te$^0$ extracted from Bader charge analysis compared to the ideal segregation model based on the composition (O:Te atomic ratio). (d) Formation energy convex hull for the Te-O binary system. Navy circles represent known crystalline phases on the convex hull, while blue crosses correspond to the simulated amorphous compositions. The elevated energy of a hypothetical hexagonal TeO structure (red circle), sourced from the Materials Project Database Jain_011002_2013, illustrates the thermodynamic driving force for a-Te segregation in oxygen-deficient TeO$_x$.
• Figure 4: Electronic properties of oxygen-deficient amorphous TeO_x. (a) Schematic of hole conduction in an amorphous semiconductor. Spatial distribution of wavefunctions is depicted as orange clouds, while green arrows represent hole transport paths. The hole mobility-edge offset, defined as the energy difference between the VBM and the mobility edge (${\Delta}E_h = |E_\mathrm{VBM} - E_c|$), represents the energetic barrier for accessing delocalized states and serves as an indicator of the potential for band-like hole transport. (b) Projected density of states (DOS) and inverse participation ratio (IPR, blue bars) for $a$-TeO$_{1.2}$, exhibiting localized states originated from Te$^0$-rich regions nearby the band edges. (c) Spatial distribution of Te$^0$ atoms (orange) within the TeO$_x$ matrix (grey), illustrating the charge localization associated with the upper portion of the valence band. The isosurface corresponds to the states within 0.5 below the valence band maximum (VBM), plotted at an isovalue of 5% of the maximum charge density. (d) Evolution of the electronic structure across the $a$-TeO_x series ($x$ = 2.0 to 0.4), with increasing oxygen deficiency. The DOS curves are aligned using the Te^4+ 3$d$ core-level peak as a common energy reference, with the zero-energy level set to match the VBM of $a$-TeO2. The grayscale color intensity reflects the degree of electronic localization within each energy interval, as indicated by the scale bar. (e) Hole mobility-edge offset, ${\Delta}E_h$, versus band gap for different compositions, showing a strong correlation between oxygen deficiency and enhanced hole accessibility to extended states, with shaded ellipses indicating statistical variability across simulation samples.
• Figure 5: Electronic properties and atomic models of amorphous Se-alloyed TeO$_{1.2}$ and SeO$_x$. (a) Schematic comparison between the original (adapted from Liu et. al.Liu_798_2024) and our proposed atomic models for Se-alloyed amorphous TeO$_x$. (b,d) Projected DOS and energy-resolved IPR of (b) Se-alloyed $a$-TeO$_{1.2}$ (Se$_{0.33}$TeO$_{1.2}$) and (d) $a$-SeO. (c,e) Spatial distribution of the upper valence band in (c) Se-alloyed TeO$_{1.2}$, showing the localization within the neutral Te$^0$ (orange) and Se (green) subnetwork, and in (e) $a$-SeO, highlighting the contribution from neutral Se atoms (green) within the oxidized matrix (grey). The isosurfaces in (c) and (e) are rendered using the same criteria as in Figure \ref{['fig:teox_dos']}c.