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In this review, the nonparabolicity of the light-hole and electron bands at the Γ-point in cubic diamond or zinc blende semiconductors is derived from Kane’s 8×8k→⋅p→ model in the large spin–orbit splitting approximation. Examples of several approximations are given with InSb as an example, and their accuracy is discussed. To determine the temperature dependence of the effective masses and the nonparabolicity parameters, the unrenormalized bandgap must be utilized. This includes only the redshift of the bandgap due to thermal expansion, not the renormalization due to deformation-potential electron-phonon coupling. As an application of this method, the chemical potential and the charge carrier concentration of intrinsic InSb are calculated from 50 to 800 K and compared with electrical and optical experiments. These results are also relevant for other semiconductors with small bandgaps as needed for mid-infrared detector applications. 

Most cubic semiconductors have threefold degenerate p-bonding valence bands and nondegenerate s-antibonding conduction bands. This allows strong interband transitions from the valence to the conduction bands. On the other hand, intervalence band transitions within p-bonding orbitals in conventional p-type semiconductors are forbidden at k=0 and, therefore, weak, but observable. In gapless semiconductors, however, the s-antibonding band moves down between the split-off hole band and the valence band maximum due to the Darwin shift. This band arrangement makes them three-dimensional topological insulators. It also allows strong interband transitions from the s-antibonding valence band to the p-bonding bands, which have been observed in α-tin with Fourier-transform infrared spectroscopic ellipsometry [Carrasco et al., Appl. Phys. Lett. 113, 232104 (2018)]. This manuscript presents a theoretical description of such transitions applicable to many gapless semiconductors. This model is based on k→⋅p→ theory, degenerate carrier statistics, the excitonic Sommerfeld enhancement, and screening of the transitions by many-body effects. The impact of nonparabolic bands is approximated within Kane’s 8×8k→⋅p→-model by adjustments of the effective masses. This achieves agreement with experiments. 

The temperature dependence of the complex dielectric function [Formula: see text] of bulk Ge near the direct bandgap was investigated with spectroscopic ellipsometry at temperatures between 10 and 710 K. Second derivatives of the dielectric function with respect to energy are obtained using a digital linear filter method. A model that incorporates excitonic effects using the Tanguy model for the Hulthén potential [C. Tanguy, Phys. Rev. B 60, 10660 (1999)] was used to fit the dielectric function and its second derivatives simultaneously. Using [Formula: see text] theory and literature values for effective masses, reasonable agreement with the experiment is obtained for [Formula: see text] up to room temperature using the direct bandgap and its broadening as the only adjustable parameters. 

Antenna coupled detectors break the intrinsic tradeoff between signal and noise by “collecting over a large area” and “detecting over a small area”. Most antenna coupled detectors in the infrared rely on a metal resonator structure. However, there are losses associated with metallic structures. We have demonstrated a novel long-wave infrared (LWIR) detector that combines a dielectric resonator antenna with an antimonide-based absorber. The detector consists of a 3D, subwavelength InAsSb absorber embedded in a resonant, cylindrical dielectric resonator antenna made of amorphous silicon. This architecture enables the antimonide detection element to shrink to deep subwavelength dimensions, thereby reducing its thermal noise. It is important to note that this concept only applies when (a) the detector noise is limited by bulk noise mechanisms with negligible surface leakage currents and (b) the dominant source of current in the device is due to dark current (such as diffusion) that scales with the volume of the detector. The dielectric resonator enhances the collection of photons with its resonant structure that couples incident radiation to the detector. We will present results on the absorption in structures with and without the dielectric resonator antenna. The signal to noise enhancement in the LWIR photodiodes integrated with the dielectric resonator antenna using radiometric characterization will be discussed.