Optoelectronic excitations and photovoltaic effect in strongly correlated materials

Solar cells based on conventional semiconductors have low efficiency in converting solar energy into electricity because the excess energy beyond the gap of an incident solar photon is converted into heat by phonons. Here we show by ab initio methods that the presence of strong Coulomb interactions in strongly correlated insulators (SCIs) causes the highly photoexcited electron-hole pair to decay fast into multiple electron-hole pairs via impact ionization (II). We show that the II rate in the insulating $M_1$ phase of vanadium dioxide (chosen for this study as it is considered a prototypical SCI) is 2 orders of magnitude higher than in Si and much higher than the rate of hot electron-hole decay due to phonons. Our results indicate that a rather broad class of materials may be harnessed for an efficient solar-to-electrical energy conversion that has been not considered before.

Figure 1

Top: The standard process in conventional semiconductors is shown above (green bands). Bottom: The expected process in strongly correlated insulators is shown below (red bands). See text for explanation.

Figure 2

The imaginary dielectric constant for Si within PBE + scGW + BSE. The calculated results agree well with the experimental data in Ref. [29], and similar GW + BSE results have been published by others (see Rocca et al. [30] and references therein). We conclude that the implementation of the BSE method that we used produces correct results.

Figure 3

Estimated impact ionization rate (IIR) as a function of excitation energy in silicon. The electron- and hole-initiated biexcitons were both considered. Our results are compared to previous calculations by Govoni et al. and Kotani and van Schilfgaarde in Refs. [32] and [33], respectively. Kotani and van Schilfgaarde applied the same approximation in the self-energy that we do, though a different basis set was used. Areas in our calculation which are numerically inaccurate are shown in brown and labeled as “filtered points.” We also highlight (yellow) the energy regions in which biexcitons can be created by light in the solar spectrum.

Figure 4

(a) Schematic diagram of the bands of highly correlated electrons (vanadium $d$ orbitals) and conventional bands ($s,p$ orbitals). The origin is set in the middle of the fundamental band gap. $E_{\mathrm{g}}$ = 0.63 eV is the calculated fundamental direct gap of $M_1-{\mathrm{VO}}_2$. (b) The convergence of the first absorption peak by the BSE method as a function of the valence bandwidth ($E_w$ measured from the top of the valence band) included in the BSE calculation. (c, d) The experimental data taken from Ref. [35] for the reflectance of $M_1-{\mathrm{VO}}_2$ for polarization parallel (c) and perpendicular (d) directions is compared with the results of PBE + scGW + BSE calculation. The PBE + scGW spectra are given to show the exciton effects captured by the BSE method.

Figure 5

(a) The IIR of Si and $M_1-{\mathrm{VO}}_2$ within our method. Additionally, the regions of the solar spectrum and rate of decay into phonon modes [2] are outlined for clarity. Points where the decay rate of electrons to phonons has recently been calculated [1] are highlighted in blue. The band gaps for Si and ${\mathrm{VO}}_2$ are between the purple and black vertical lines with distance of approximately 1.2 and 0.6 eV, respectively. (b) ${\mathrm{VO}}_2$ density of states.

Figure 6

(a) The parallel to the $a$-axis imaginary part of the dielectric function as calculated for a 5 $\times 5$ $\times 5$ and a 7 $\times 7$ $\times 7$ $k$-point set where $n_v$ = 18 and $n_c$ = 8. (b) Convergence of ${\epsilon }_{2\left|\right|}$ with number of valence bands ($n_v$) using a fixed number of conduction bands ($n_c$) for the case of the full BSE calculation. All calculations here use HSE06 + ${\mathrm{G}}_0{\mathrm{W}}_0$ + BSE.