Effective bands and band-like electron transport in amorphous solids

TL;DR

The paper addresses how electrons can retain band-like transport in amorphous solids lacking long-range order. It introduces a fully first-principles framework that treats the amorphous state as an ensemble of local environments, combining random-structure sampling with quasiparticle self-consistent GW (QSGW) calculations to obtain an effective average band structure and disorder-limited mobility. Demonstrated on amorphous $In_2O_3$, the approach yields a dispersive conduction band with $m^{*}\approx 0.2\,m_0$ and mobility around $13\,\text{cm}^2\!\!\mathrm{V}^{-1}\mathrm{s}^{-1}$, while identifying O–O defects as major scattering centers that localize states and broaden the CBM. The work explains band-like transport without long-range order via the direction-agnostic $In$-$5s$ conduction-band character, preserved polyhedral connectivity, and a low density of detrimental defects, and it provides a general, first-principles path to quantify disorder-limited transport in disordered materials.

Abstract

The localization of electrons caused by atomic disorder is a well-known phenomenon. However, what circumstances allow electrons to remain delocalized and retain band-like characteristics even when the crystal structure is completely absent, as found in certain amorphous solids, is less well understood. To probe this phenomenon, we developed a fully first-principles description of the electronic structure and charge transport in amorphous solids by combining a novel representation of the amorphous state with the state-of-the-art many-body (QSGW) electronic structure theory. Using amorphous In2O3 as an example, we demonstrate the accuracy of our approach in reproducing the band-like nature of the conduction electrons as well as their disorder-limited mobility. Our approach reveals the physical origins responsible for the electron delocalization and the survival of the band dispersions despite the absence of long-range order.

Figures (12)

• Figure 1: (a) In our work the structure of amorphous solids is represented as a composite of local environments. (b) Calculated XRD intensity and structure factor for a-In$_2$O$_3$ averaged over local environments agree well with the available experimental data. (c) Comparison of the calculated partial pair distribution functions $g(r)$ between crystalline and amorphous In$_2$O$_3$. (d) Calculated (QSGW) electronic density of states is shown against photoemission (UPS) measurements. (e) Calculated (QSGW) spectral functions as a function of electron energy at different k-points. (f) Spectral functions of the conduction band (red rectangle in (e)) shown as a heat map; the dispersion E(k) is clearly visible and the energy broadening is labeled. A heat map of the spherically averaged conduction band of crystalline In$_2$O$_3$ is also shown for comparison.
• Figure 2: (a) The spectral functions averaged over structures with no O-O bonds and a typical CBM charge density of one of those structures. (b) The spectral functions averaged over structures that contain O-O bonds and a typical charge density for one of those structures. (c) The calculated density of states averaged over structures with and without O-O bonds compared to the total DOS and experiment. (d) Heat maps of the spectral functions for the conduction bands when the structures are ensemble averaged weighted by the Boltzmann distribution at different effective temperatures. (e) The calculated mobility of different structures as a function of the effective temperature. The correspondence with the experimental deposition temperature is indicated.
• Figure S1: The spacegroup-resolved thermodynamic density of states for the 1500-structure random sample of 40-atom In2O3.
• Figure S2: Comparisons of the calculated q(S(q)-1) structure factor over the set of 1500 structures (black), 100 randomly chosen sets of 100 structures (grey), and the 100 randomly chosen structures used for QSGW electronic structure calculations (red).
• Figure S3: The PBE spectral functions of amorphous SiO$_2$ calculated over 3000 structures, showing a flat band and a dispersive band above the Fermi energy.