Infrared Dielectric Function of Single Crystal Homoepitaxial AlN

AlN, an extreme ultra wide band gap semiconductor material with bandgap energy ~6.1eV exhibits remarkable thermal conductivity, ease of P and N type doping, high critical breakdown field and high BFOM. AlN also allows for the integration of other group III elements to form multi-element AlN related compound semiconductors. Key end uses of AlN are electrothermal codesign of power electronics, in RF transistors, and as a substrate for optoelectronics in the deep ultraviolet (UV) regime. In the infrared band, polar semiconductors like AlN have a reststrahlen band with high reflectivity bounded by longitudinal optical (LO) and transverse optical (TO) phonons resulting in a broad peak in the transmission/reflectance frequency plot. The optical index of a material is strongly dependent on carrier concentration, where free carriers form a plasma that couples to the LO phonons giving rise to a LO plasmon coupled (LOPC) mode. In this paper, the optical index and loss functions from infrared reflectance spectra for AlN were extracted by Kramers-Kronig (K-K) analysis. K-K analysis enables the determination of the real parts of a complex function's response over all frequencies, if the imaginary part is known and vice versa. The method proposed was validated on bulk 4H-SiC substrates which are polar, with similar density, lattice constant, and crystal structure to AlN, then applied to MOCVD grown homoepitaxial AlN film ( LO= 940cm^-1, TO= 820cm^-1). If a low doped layer is grown on a high doped substrate, the resulting index contrast is expected to cause Fabry-Perot oscillations from which non-destructive measurements of film thickness can be made. Employing substrates sourced from two vendors, just a little difference in crystallinity between the film and substrate in the MOCVD grown AlN films were observed, however an anomalously high index of ~4 in the mid-IR range was observed for the films, this is higher than the expected value of ~2, as well as additional features around ~1500 - 2000cm^-1 attributed to oxygen concentration, which is lower in the film compared to the bulk AlN. The low oxygen concentration leads to higher thermal conductivity and UV transparency. Despite the substantial index contrast of ~0.4 between the substrates and epitaxial layers, no Fabry-Perot oscillations were observed, it was expected that the interface between the homoepitaxial layers should result in an oscillatory reflectance/transmission signal which should enable the determination of the film's thickness. Fabry-Perot oscillations also enable the determination of material bandgap, film dielectric constant and loss analysis, defects, surface roughness etc. The indices found were consistent across the substrates irrespective of vendor. The anomalously high index indicated a higher dielectric constant, suggesting the excess index due to states within the bandgap. To account for observed discrepancies with theory, 5 lossy Lorentzian oscillators were added in the analysis. These oscillators are ascribed to AlN phonons accentuated due to sub-bandgap states arising from relaxation of momentum conservation by substitutional impurities. The results suggest the presence of large polarons in the insulating bulk AlN. This conflicts with theoretical predictions of small polaron states and illustrates an example of non-destructive characterization of doping in this ultra-wide bandgap semiconductor.