1. Introduction

Surface phonon polariton (SPP) is an elementary excitation resulting from the coupling of an infrared (IR) photon (with transverse magnetic mode) with a transverse-optic (TO) phonon in polar crystals. Typically, the frequency of this surface mode falls in the mid-IR region. It is distinguished from bulk phonon polariton (BPP) modes by the fact that it can only propagates along the interface between two different media. The propagation mode of the SPP mode is along a direction perpendicular to the surface normal and its amplitude is attenuated exponentially from surface to bulk. Other unique characteristics of the SPP are that it can propagate through the forbidden band of the BPP modes (i.e., interval between the TO and longitudinal-optic (LO) phonon frequencies) and results in the surface-enhanced IR absorption.

Recently, the SPP properties have attracted both academic and technological extensive research again. This is due to the SPP having been shown to provide application for some photonic devices [1–4] as well as near-field microscopy [5,6]. For instance, a reflection-type sensor in the mid-IR region based on resonant excitation of SPP was demonstrated by Balin et al. (2009) [1].

At present, the SPP properties of III-nitride binary and ternary semiconductors have been extensively investigated [7–18]. While for III-nitride quaternary alloy, only the theoretical results for bulk InAlGaN crystal are reported [19]. Since bulk InAlGaN (as well as other III-nitrides) semiconductors are still not available, researchers have no choice but to grow nitrides heteroepitaxially. Therefore, the SPP characteristics in InAlGaN heterostructure system still remain unclear or unexplored.

The SPP in the InAlGaN quaternary semiconductors are investigated experimentally and theoretically in order to contribute to the understanding of the fundamental properties of this material. We investigate the In_0.04Al_0.06Ga_0.90N quaternary alloy because it is lattice matched to GaN and has potential for use in GaN-based optoelectronic devices [20]. Through this study, new applications based on the SPP properties are likely to emerge in the future.

2. Experimental details

Molecular beam epitaxy growth InAlGaN wafer from SVT Associates Inc., USA, was used in this study. Unintentionally doped wurtzite (α-) structure In_xAl_yGa_0.90N epilayer with In composition, x = 0.04 and Al composition, y = 0.06 was grown on an AlN buffer layer on sapphire (Al₂O₃) substrate. The thickness of the In_0.04Al_0.06Ga_0.90N epilayer and the AlN buffer layer as measured by Filmetrics F20 is about 110 and 20 nm, respectively. The full width at half maximum of the X-ray diffraction rocking curve of (0002) plane of In_0.04Al_0.06Ga_0.90N epilayer measured in the omega scan mode is about 16 arcmin.

Room temperature IR attenuated total reflection (ATR) measurement was carried out using a Fourier transform IR spectrometer (Spectrum GX FTIR, Perkin-Elmer) together with an optional ATR with germanium (Ge) single reflection plate (MIRacle, PIKE Technologies). The measurement was taken under p-polarized light by means of a wire grid thallium iodide bromide IR polarizer. Since the total alloying compositions for In and Al is only 0.1, the SPP features of this gallium-rich quaternary alloy should be close to GaN binary compound, i.e., within 600 – 1000 cm⁻¹ [13]. For this reason, the ATR spectrum was recorded from 600 to 1000 cm⁻¹ with spectral resolution of 4 cm⁻¹.

3. Theory

The surface polariton (SP) dispersion curve and theoretical ATR spectrum are simulated using the standard matrix formulation by taking into account the films and substrate anisotropy. For the SPs dispersion curve, the simulation is based on four layers model, i.e., vacuum, AlInGaN film, AlN film, and Al₂O₃ substrate. While that for ATR spectrum, five layers model is used, i.e., prism, vacuum, AlInGaN film, AlN film, and Al₂O₃ substrate. More details about the standard matrix formulation method can be found in Ref [21].

Let assume that the optic axis c of the crystal parallel to the surface normal (c _axis || z) and perpendicular to the propagation direction of the SP (c _axis ⊥ x). For unixial crystal, two independent sets of dielectric tensors are required to describe its dielectric function. Commonly, the expression for these two sets of dielectric functions can be expressed by [21]:

It should be pointed out here that the dielectric functions given in Eq. (1) can be used to describe the behavior of the zone centre phonons modes of binary semiconductors. For ternary alloys, the dielectric constants as a function of alloy composition x can be linearly interpolated from its constituents [22]. While for the quaternary alloys, general expression for the dielectric functions has not been found. However, in a manner analogous to the energy band gap of the In_xAl_yGa_{1- x - y}N quaternary alloy [23], the ε _||(⊥)(w) of this quaternary alloy can be interpolated from the dielectric functions of its ternary alloys. Therefore, the resulting dielectric functions of the In_xAl_yGa_{1- x - y}N can be written as:

In this work, the parameters used to model the SP dispersion curve and the theoretical ATR spectrum are obtained from the best fit of experimental IR reflectance spectrum of the studied structure with the theoretical spectrum (not shown here). More details about the results of the IR reflectance study of the In_0.04Al_0.06Ga_0.90N/AlN/Al₂O₃ heterostructure can be found in Ref [24]. Note that the values of ε _{∞, ||(⊥)} used in all the modeling are obtained from Refs [25–28].

4. Results and discussion

Figure 1 shows the room temperature p-polarized IR ATR spectrum for the In_0.04Al_0.06Ga_0.90N/AlN/Al₂O₃ heterostructure. From Fig. 1, it is found that the ATR spectrum exhibits four prominent absorption dips at 630, 671, 739, and 798 cm⁻¹, as well as a weak and broad absorption dip centered at 891 cm⁻¹. Generally, the appearances of these features are the results of the resonance at frequency where the wave vectors of the incident radiation and the surface (interface) polaritons are matched. In other words, these observed features are actually correspond to the crossing of the surface polariton (SP) dispersion curves with the light waves [k_p(w)] in the ATR prism [21].

 

Fig. 1 Room temperature p-polarized IR ATR spectrum of α-In_0.04Al_0.06Ga_0.90N/AlN/Al₂O₃ heterostructure.

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In general, the observations are in good agreement with the theoretical ATR spectrum, as shown in Fig. 2(f) and will be discussed soon. However, a striking difference between both spectra is the presence of a weak and broad absorption dip centered at 615 cm⁻¹ in the theoretical spectrum, which is absent in the experimental spectrum. It is believed that the discrepancy is, in part, a consequence of the fact that the intensity of this feature is too low. Therefore, it might be masked by the background noise. Overall, the average discrepancy between the experimental and theoretical results is less than 1%. Possible origins for these discrepancies are the interface roughness and sample quality, in particular the carrier concentrations, which we did not take into account in our modeling.

 

Fig. 2 Theoretical SP dispersion curves (a) air-In_0.04Al_0.06Ga_0.90N, (b) air-AlN, (c) air-Al₂O₃, (d) air-In_0.04Al_0.06Ga_0.90N/Al₂O₃, (e) air-AlN/Al₂O₃, (f) air-In_0.04Al_0.06Ga_0.90N/AlN/Al₂O₃ structures together with the theoretical ATR spectra. For the ATR spectra, the prism material is the Ge crystal. The vacuum light wave and the light wave in ATR crystal (k_p) are indicated by dash and dash-dot-dot lines, respectively. The intersections of the k_p line and the branches of the SP dispersion curve correspond to the SPP and interface modes. The crossing points marked by “*” correspond to the virtual SPP mode.

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For ease of identification of the origin of the absorption dips in the measured ATR spectrum, the SP dispersion curves based on anisotropy model for (a) air-InAlGaN, (b) air-AlN, (c) air-Al₂O₃, (d) air-InAlGaN-Al₂O₃, (e) air-AlN-Al₂O₃, and (f) air-InAlGaN-AlN-Al₂O₃ are included, as shown in Fig. 2. In order to resolve all the surface modes, all the SP dispersion curves are modeled in the lossless limit (i.e., γ = 0). In Fig. 2, the positions labeled are the intersections of the SP dispersion curves with the k_p lines and are correspond to the SPP or the other interface mode. Also shown in Fig. 2 are the associated theoretical ATR spectra for each mentioned structures. From Fig. 2, it is worth noting that the position for some absorption dips in the ATR spectra are not coincide with the points where the k_p line crosses the SP dispersion curves. This is mainly because the calculation of the SP dispersion curves does not account for the coupling effect of the ATR prism and the finite thickness of air gap. Nevertheless, the SP dispersion curves are very important for identifying the origin of the detected features.

We consider first the SP dispersion curve of the air-InAlGaN. As can be seen from Fig. 2(a), there are four intersection points with the k_p line. However, only the crossing points located on the first three branches (we refer to the branch starting at the lowest frequency as the first, and so on) are assigned to real SPP modes, while that with the fourth branch is associated to the virtual SPP mode. The fourth branch will disappear in two or more interface structures because this branch is not the solution for the SP dispersion curves of those structures, as evidence from Figs. 2(d) to 2(e).

For air-InAlGaN-Al₂O₃ structure [Fig. 2(d)], the SP dispersion curves become more complicated. Totally, there are six branches and six intersection points with the k_p line. In this case, the first, third and fourth branches (crossing points) are originated from the InAlGaN layer [Fig. 2(a)], while the second and sixth branches are originated from the Al₂O₃ substrate [Fig. 2(c)]. The fifth branch is believed to be arisen from the InAlGaN/Al₂O₃ interface and its spectral strength is very weak as compared to other branches. For this reason, feature due to this mode is not present in the calculated spectrum. From Fig. 2(d), one can see that the SPP modes of the InAlGaN (except the mode located at the first branch) are shifted towards higher frequency as compared to that in Fig. 2(a). In fact, the position of the SPP mode is film thickness dependent and blue shifted as the film become thinner [7]. The odd behavior of the first InAlGaN SPP mode is not understood at present.

For air-InAlGaN-AlN-Al₂O₃ structure [Fig. 2(f)], the SP dispersion curves have eight branches and eight intersection points with the k_p line. The additional branches due to the inclusion of AlN layer are the fourth and the eighth branches [Fig. 2(b)]. The origins of these branches are the AlN SPP and the AlN/Al₂O₃ interface modes, respectively. Nevertheless, features due to these modes cannot be clearly seen in the calculated ATR spectrum. Indeed, the AlN layer is too thin to make any significant difference, as clearly demonstrated in Figs. 2(c) and 2(e).

Based on the above discussion, the origin of the prominent dips observed in Fig. 1 can be summarized as follows: The absorption dips of 623 and 798 cm⁻¹ are arisen from Al₂O₃ substrate, i.e., the Al₂O₃ SPP and InAlGaN/Al₂O₃ interface modes, respectively. While the absorption dips of 671 and 739 cm⁻¹ are associated with the α-In_0.04Al_0.06Ga_0.90N SPP modes. Finally, the feature centered at 891 cm⁻¹ is believed to be stemmed from the Al₂O₃ substrate, i.e., weak coupling between the evanescent wave with the BPP mode (LO mode) of the Al₂O₃ substrate.

5. Conclusion

SPP characteristics of α-In_0.04Al_0.06Ga_0.90N/AlN/Al₂O₃ heterostructure have been investigated experimentally and theoretically. The agreement between the experimental results and the theory predictions are good.