First-Principles Approach to Calculating Energy Level Alignment at Aqueous Semiconductor Interfaces

A first-principles approach is demonstrated for calculating the relationship between an aqueous semiconductor interface structure and energy level alignment. The physical interface structure is sampled using density functional theory based molecular dynamics, yielding the interface electrostatic dipole. The $\mathit{GW}$ approach from many-body perturbation theory is used to place the electronic band edge energies of the semiconductor relative to the occupied $1b_1$ energy level in water. The application to the specific cases of nonpolar ($10\overline{1}0$) facets of GaN and ZnO reveals a significant role for the structural motifs at the interface, including the degree of interface water dissociation and the dynamical fluctuations in the interface Zn-O and O-H bond orientations. These effects contribute up to 0.5 eV.

Figure 1

(a) Simplified model for energy level alignment based on separate semiconductor and water energies with respect to vacuum. (b) Schematic for energy level alignment including the potential step due to the physical interface structure. Valence band energy level offset ${\mathrm{\Delta }}_V$ breaks into three contributions in Eq. (1) and shown here. (c) Illustration of the separate calculation of each of those three terms for the specific case of energy level alignment at the $\mathrm{GaN}(10\overline{1}0)$-water interface. Center panel: Results of the full interface simulation. Top: Planar, running, and time (thermal) average of the electrostatic potential ($⟨V_H⟩$, black line) superposed over 50 individual, planar-averaged snapshots. Bottom: Time and space averaged core potentials superposed over individual values from the same snapshots. Left panel: Bulk GaN simulation showing $E_V$ for GaN from DFT and $\mathit{GW}$ superposed on the averaged electrostatic potential and the averaged core potentials. Right panel: Bulk water showing $E_{1b_1}$ superposed on the same averaged potentials. Final energy level alignment requires shifting left and right panels in energy relative to the center panel as illustrated by the arrows to get the final alignment as in (b). Either $V_H$ or, equivalently, the core potentials can be used for alignment.

Figure 2

GaN-water interface simulation. (a) Snapshot from the equilibrated portion of the MD simulation illustrating the unit cell. (b) Planar and time averaged density of water molecules (black solid line) and ${\mathrm{OH}}^{-}$ ions (black dashed line) as a function of distance between the GaN interfaces (vertical gray lines). (c) Average number of hydrogen bonds for water molecules (solid black line) and ${\mathrm{OH}}^{-}$ ions (black dashed line) (d) Calculated O-O pair distribution function from the bulk water simulation (gray line) and the GaN interface simulation (black line) together with experiment [26].

Figure 3

Valence band density of states (DOS) of bulk water, relative to the vacuum level, calculated using DFT (top) and $\mathit{GW}$ (bottom). Experimental PES spectra [6] shown (bottom) with intensity scaled to match theory near the $1b_1$ peak.

Figure 4

(a) Valence band edges, relative to vacuum, of GaN and ZnO for different surface and interface configurations ($S_{\mathrm{I}}-S_{\mathrm{IV}}$). Solid horizontal lines depict the $1b_1$ level of water relative to vacuum. For the full interface case, $S_{\mathrm{IV}}$, it is used with the calculated offset ${\mathrm{\Delta }}_V$ to place the semiconductor valence band relative to vacuum. Atomistic schematics with the qualitative induced surface dipole shown (green arrows) due to: (b) relaxation of the clean ZnO surface, (c) molecular, and (d) dissociative water adsorption, both on the ideal ZnO surface.