Photonic devices depend critically on the dielectric materials from which they are made, with higher refractive indices and lower absorption losses enabling new functionalities and higher performance. However, these two material properties are intrinsically linked through the empirical Moss rule, which states that the refractive index of a dielectric decreases as its band gap energy increases. Materials that surpass this rule, termed super-Mossian dielectrics, combine large refractive indices with wide optical transparency and are therefore ideal candidates for advanced photonic applications. This Review surveys the expanding landscape of high-index dielectric and semiconductor materials, with a particular focus on those that surpass the Moss rule. We discuss how electronic band structures with a large joint density of states near the band edge give rise to super-Mossian behavior and how first-principles computational screening can accelerate their discovery. Finally, we establish how the refractive index sets the performance limits of nanoresonators, waveguides, and metasurfaces, highlighting super-Mossian dielectrics as a promising route toward the next performance leap in photonic technologies.
Dielectric and plasmonic materials make up almost all nanophotonic devices. The properties of these materials ultimately limit their functionality and performance. A simple connection between the optical properties of materials and the ultimate performance of devices that employ them can greatly aid design. In addition, such a relationship can significantly benefit material scientists in discovering and engineering better nanophotonic materials. Plasmonic materials have seen a systematic effort in this direction [1][2][3]. Plasmonic materials beyond noble metals were identified and evaluated for their performance in various device applications. Such comprehensive studies are lacking for dielectrics. With dielectric nanophotonics gaining prominence because of its smaller losses and ability to confine light to the nanoscale [4], the need to identify and evaluate various dielectric materials for their performance in nanophotonic devices is crucial [5]. This review presents a case for super-Mossian high-refractiveindex dielectrics, reviews recent efforts in this direction, and connects the performance limits of various nanophotonic devices to the refractive index of dielectrics. This work aims to guide material scientists in developing novel nanophotonic dielectrics and aid nanophotonic designers in choosing the right dielectric materials.
Dielectric materials with a high refractive index and low optical absorption are desirable for almost all nanophotonic applications. While a high refractive index enables a tighter confinement of light, low optical absorption guarantees high performance. Hence, materials with a high refractive index and low absorption are desired not only in linear optics, but also in non-linear optics. Many non-linear properties, such as second harmonic generation and the Pockels electro-optic effect, depend directly on the refractive index raised to an exponent of at least two [6]. Silicon is a serendipitous material choice that has paved the way for silicon nanophotonics [7][8][9]. Given the development of silicon-based nanoelectronic device fabrication, silicon is a promising dielectric platform for nanophotonics. However, having only a few materials in a designer’s library is a severe limitation. Hence, the question follows: Are there dielectric materials similar to or even better than silicon?
A quest for dielectrics with a high refractive index and low loss has intrigued researchers for decades. Early studies observed that the sub-bandgap refractive index of a semiconductor tends to decrease as its absorption edge or the direct band gap increases. In 1950, Moss quantified this empirical relationship as E g n 4 s = 95 eV, where E g is the fundamental band gap energy and n s is the long wavelength (sub-bandgap) refractive index [12]. This is commonly known as Moss’ rule. Figure 1 displays the refractive index versus band gap for a wide range of materials, including common semiconductors, along with Moss’ rule. While Moss’ rule captures the general inverse relation between band gap and refractive index, many materials exceed this prediction. We classify these as super-Mossian materials and define the Moss factor M as
such that M > 1 corresponds to super-Mossian behavior. Moss himself later noted that materials such as silicon, germanium, and diamond exhibit M ≈ 2 [13]. Subsequent theoretical work refined this understanding.
Finkenrath rigorously derived Moss’ rule for semiconductors with zincblende and diamond lattices [14,15]. while Penn proposed a simple model for isotropic dielectrics [16]. Several other models have since been developed to extend the applicability of these trends to differ- S1) and 280 are calculated using density functional theory (DFT) [10]. The experimental indices are shown as a function of the fundamental band gap energy, while the calculated indices are as a function of the direct band gap energy. The computed materials are categorized according to their anisotropy. For both experimental and computed materials, the component of the refractive index tensor with the highest value is shown. Frequency-dependent complex refractive indices for all computed materials are available in the CRYSP database [11].
The dashed lines show Moss relations with Moss factors of M = 3 and M = 5. Note the change in scales on the Eg and ns axes at 3.5 eV and 6, respectively.
ent materials and band gap ranges [17][18][19][20][21]. This long and evolving history has set the foundation for the ongoing search for new super-Mossian materials [5,[22][23][24].
This paper reviews advances in the recent decade in the pursuit of high-refractive-index semiconductors that surpass the Moss rule. In the following sections, we identify the physical origin of the super-Mossian behavior of semiconductors and review recent significant developments in the search for super-Mossian materials, considering both experimental and computational approaches. Then, we formulate figures of merit to assess t
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