Optical materials

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Light carries most of the world’s data, through optical fibers and lasers, and lights our screens and rooms. Behind these technologies are crystals that change light: non-linear optical (NLO) crystals such as LiNbO₃ and LiTaO₃ double its frequency and modulate it in telecommunication networks, birefringent crystals control its polarization, and semiconductors such as InGaN and the metal halides emit it. Our calculations, starting from the electronic structure of these materials, explain why one crystal interacts with light more strongly than another, and guide our experimental collaborators towards new ones, made of cheaper, more abundant and less toxic elements.

Computed birefringence and 2V angle of metal-free perovskites — **Figure 1:** Computed birefringence Δn and 2V angle of metal-free perovskites.⁴

Second-harmonic generation. A crystal that generates the second harmonic combines two photons of light into one of twice the frequency, as first observed in quartz in 1961.¹ Only crystals without a center of symmetry can do so,² and a useful one must also be transparent at the wavelengths involved, which is especially hard in the deep ultraviolet.³ Our first-principles calculations found NLO activity in metal-free perovskites ABX₃, in which an organic cation A and NH₄⁺ replace the metals, and showed that the dipole moment of the organic cation tunes the response: adding a polar cyanide group to it raises the second-harmonic generation markedly, making these materials candidates for the deep ultraviolet.⁴ With experimental colleagues, we have explained the strong response of hybrid germanium bromide perovskites, five times that of the standard potassium dihydrogen phosphate (KDP) in CH₃NH₃GeBr₃, by the displacement of Ge²⁺ along the [111] direction and the interaction of its lone pair of electrons with the polar organic cations,⁵ and our calculated responses of two-dimensional Dion–Jacobson germanium iodide perovskites agree with those measured, up to 0.53 times that of AgGaS₂.⁶

Birefringence. A birefringent crystal slows light polarized along one direction more than along another, which is how waveplates and polarizers work. We compute the birefringence Δn of candidate crystals and the angle 2V between their optic axes (Figure 1).⁴ Van der Waals crystals of ferrocene combine high birefringence (Δn = 0.149 at 636 nm) with little absorption, and grow directly into ultrathin true zero-order waveplates that need no cutting or polishing; our calculations suggest that they work from 550 nm to 20 µm.⁷

Photoluminescence spectra of (Pr3BzN)2SbCl5 from 80 to 460 K, as curves and as an intensity map — **Figure 2:** Photoluminescence of the antimony(III) chloride (Pr₃BzN)₂SbCl₅, with square-pyramidal [SbCl₅] units, excited at 405 nm, from 80 to 460 K: spectra (left) and intensity map, from blue (dimmest) to red (brightest).⁹

Light-emitting metal halides. Metal halides of bismuth and antimony are lead-free relatives of the halide perovskites used in solar cells and light-emitting devices. We have calculated the stability and band gaps of the bismuth trihalides BiX₃ in known and hypothetical structures, and the role of the lone pair of electrons on Bi(III).⁸ In hybrid antimony(III) chlorides, the geometry of the antimony sites decides how brightly they shine: square-pyramidal [SbCl₅] units emit light with a quantum yield near one, whereas [Sb₂Cl₈] dimers barely emit at all (Figure 2).⁹ In layered bimetallic halides that alternate antimony chloride pyramids with two-dimensional layers, our calculations follow the measured band gaps, and compression tunes the electronic structure, raising the light emission of one compound eleven-fold at 19 GPa.¹⁰

Nitride light-emitting diodes. Blue and green LEDs are built from In_xGa_1−xN quantum wells, which lose efficiency as their indium content rises. Combining electron energy-loss spectroscopy at sub-nanometer resolution with multiscale models, we have shown that a random alloy describes wells with about 18% indium, but not those with 24% or more, where composition fluctuates far more and localizes the charge carriers.¹¹ In GaN-on-silicon heterostructures, these fluctuations become nanoscale optical inhomogeneities within single wells, and our calculations of the alloys’ mixing energies show that relaxing the epitaxial strain stabilizes particular compositions, so that both strain and composition must be controlled for homogeneous, long-wavelength light emission.¹²

Relevant references

All our papers on optical materials (9) →