Tuning mid-infrared polarization sensitive reflectivity in GaN/AlGaN heterostructures

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Introduction
The study of the optical response of polar materials, in the infrared range, recently attracted a large amount of interest due to the presence of the so-called Reststrahlen band.In this frequency band, between longitudinal and transverse optical phonon frequencies, the electric permittivity is negative making it possible the excitation of surface waves.Combining different polar materials, it is possible to excite leaky coupling modes called Berreman modes [1] without the need for gratings or prism coupling mechanisms.We report the possibility of tuning and controlling a Berreman mode through AlN/GaN-type heterostructures on Sapphire substrate by analysing their polarizationdependent reflection spectra at an angle of incidence of 15°.The experimental results have been compared to theoretical predictions based on the implementation of a transfer matrix method for anisotropic layers [2].Good agreement between experimental and theoretical measurements was found through the introduction of a two-dimensional electron gas layer at the interface between AlGaN and GaN layers.We modeled the free electron high-frequency conductivity via Drude's model.

Experimental and Theoretical methods
A Bruker INVENIO-R FTIR spectrometer operating in 64-scan mode per measurement was used to study the reflectance spectrum at a fixed angle (15°) and varying the polarization angle of the incident field.Experimental measurements, shown in Figure 1 (a), reveal an absorption peak at phonon TO at about 650 cm -1 .This minimum is related to the presence of the AlN layer and its thickness but does not depend on polarization, as also shown in Figure 1 (a).The spectrum reports a second reflectance minimum close to the LO phonon (736 cm -1 ) dependent on GaN thickness.In this region the real part of the dielectric permittivity cross the zero value.An incidence angle of 15° is large enough to produce evanescent waves in the GaN layer and leaky surface modes at the GaN/Sapphire interface (Berreman mode).The experimental measurements qualitatively agree with the theoretical ones shown in Figure 1(b).However, the theoretical model shows higher contrast and lower reflection values.This difference is partially attenuated by including the effects of a thin two-dimensional electron gas layer (2DEG) formed at the AlGaN/GaN interface [3].
The characteristic parameters of the free electron gas were taken from literature [3] and compared with those declared during the crystal manufacturing process.In this case, the complex permittivity of the 2DEG is formed by a real background term given by the sum of the side layers and the conductive term related to the free electrons' mobility [4].Figure 2 finally shows the calculated rflection spectrum obtained by including the contribution of 2DEG at the two AlGaN/GaN interfaces.

Conclusions
The optical properties of GaN/AlGaN heterostructures on sapphire substrates in the mid infrared range have been investigated.The contribution of the 2D free electron gas at GaN/AlGaN interface has been modeled to evaluate how it affects the excitation of the Berreman mode at Sapphire interface.According to our model we expect this effect to become stronger in multilayer structures and to play a relevant role in the design of GaN-based optoelectronic devices operating in the mid IR.

Fig. 1 .
Fig. 1.(a) Experimental reflectance spectrum and related layer structure.(b) Simulated structure with transfer matrix model and related layer structure.Both are intended for 15° incidence angle and input polarization angles as reported in the legend ( 0° stand for s , 90° stands for p pol). /doi.org/10.1051/epjconf/202328714002

Fig. 2 .
Fig. 2. Simulated reflectance spectrum considering the 2DEG contribution in the transfer matrix model and the relative layer structure.