Quantitative Analysis of Valence Photoemission Spectra and Quasiparticle Excitations at Chromophore-Semiconductor Interfaces

Investigating quasiparticle excitations of molecules on surfaces through photoemission spectroscopy forms a major part of nanotechnology research. Resolving spectral features at these interfaces requires a comprehensive theory of electron removal and addition processes in molecules and solids which captures the complex interplay of image charges, thermal effects, and configurational disorder. Here, we develop such a theory and calculate the quasiparticle energy-level alignment and the valence photoemission spectrum for the prototype biomimetic solar cell interface between anatase ${\mathrm{TiO}}_2$ and the N3 chromophore. By directly matching our calculated photoemission spectrum to experimental data, we clarify the atomistic origin of the chromophore peak at low binding energy. This case study sets a new standard in the interpretation of photoemission spectroscopy at complex chromophore-semiconductor interfaces.

Figure 1

Valence photoemission spectrum of the $\mathrm{N}3/{\mathrm{TiO}}_2(101)$ interface: measured PES spectrum of Ref. 8 [blue (gray) line] and our quasiparticle calculation using Eqs. (1, 2) (black line and light blue shaded area). Inset: comparison between the measured PES spectrum of Ref. 8 [blue (gray) line] and the KS density of states at the $\mathrm{N}3/{\mathrm{TiO}}_2$ interface (black line and gray shaded area). In the DFT KS calculation, there is no gap between occupied (shaded regions) and unoccupied (unshaded) states.

Figure 2

(a) Schematic representation of the calculation procedure corresponding to Eq. (1): the spectral functions of semiconductor and chromophore obtained from separate calculations are superimposed after calculating the HOMO-VBT offset ${\Delta }_{\mathrm{int}}$ through Eq. (2). (b) Atomistic model of a representative $\mathrm{N}3/{\mathrm{TiO}}_2(101)$ interface (model I2b of Ref. 34) and isodensity plot of the highest occupied KS state, i.e., the N3 HOMO. The isodensity is $0.03{\AA }^{-3}$, and the atom color code is: Ti (silver), O (red), C (cyan), N (blue), H (white), and Ru (pink).

Figure 3

(a) Bar chart indicating all the contributions to ${\Delta }_{\mathrm{int}}$ according to Eq. (2). The bar ${\Delta }_{\mathrm{int}}$ on the right-hand side is obtained by adding up all the other bars. (b) Atomistic model of the $\mathrm{N}3/{\mathrm{TiO}}_2$ interface (cf. Fig. 2) and isodensity plot of the image charge induced by the removal of one electron from N3. The isodensity is $\pm 0.0025{\AA }^{-3}$ (blue, red). The screening charge corresponds to 0.20 electrons and is concentrated on the O atoms of the ${\mathrm{TiO}}_2$ surface.

Figure 4

Distribution of the four highest-energy KS eigenvalues of the $\mathrm{N}3/{\mathrm{TiO}}_2$ interface model during a 6-ps molecular dynamics simulation at 300 K (histogram). The eigenvalues are recorded at 0.01 ps intervals and the bin width is 0.01 eV. The red (dark gray) line is a Gaussian fit to the distribution of HOMO eigenvalues. The black line is a fit to the eigenvalues distribution based on four Gaussians. Inset: time-evolution of the four highest-energy KS eigenvalues at 300 K. The red (dark gray) line corresponds to the N3 HOMO, the (light) gray lines correspond to the HOMO-1, HOMO-2, and HOMO-3 states.