In recent decades, GaN-based technology has not only revolutionized solid-state lighting and optoelectronics but has also emerged as a key enabler of a more sustainable future, driving the development of high-efficiency radio-frequency and high-power electronic devices (Amano et al., 2018). Achieving this potential relies on the advancement of high-power transistors capable of switching large currents at high frequencies and across wide bandwidths. In this context, AlGaN/GaN high-electron-mobility transistors (HEMTs) have proven particularly promising, with commercially available devices already meeting these demanding performance requirements (Quay et al., 2017; Ture et al., 2019; Cwiklinski et al., 2019; 2020; Meneghini et al., 2021; Roccaforte et al., 2018; Krause et al., 2023).

In AlGaN/GaN HEMTs, electrons accumulate at the interface between the GaN channel layer and the AlGaN barrier due to the different bandgap energies as well as the spontaneous and piezoelectric polarizations inherent to these wurtzite nitride layers (Ambacher et al., 1999; Ture et al., 2019; Cwiklinski et al., 2019; 2020; Thome et al., 2022; Fichtner et al., 2024). These electrons are confined close to the interface, forming a two-dimensional electron gas (2DEG) with very high electron mobilities. The higher the 2DEG density n s , the higher the current and output power of the HEMT. In conventional AlGaN/GaN HEMTs with an Al content of 25%–30%, n s up to approximately 1 0 13 cm − 2 is attained. Higher n s can be achieved in AlN/GaN HEMTs (Cwiklinski et al., 2019; Manz et al., 2021; Papamichail et al., 2024), but the barrier thickness is limited to ∼ 5 nm due to the significant lattice mismatch between AlN and GaN. As a result, AlN/GaN HEMTs are prone to short-channel effects, degraded device performance, shorter lifetimes, and reduced reliability (Storm et al., 2013; del Alamo and Lee, 2019).

One approach to improve the performance of GaN-based HEMTs is to use the novel nitride semiconductors AlScN and AlYN as barrier layers. These materials have large bandgaps and intrinsically high spontaneous polarization, which allows for an enhanced n s in the mid 1 0 13 cm⁻² range (Žukauskaité et al., 2012; Sedrine et al., 2013; Hardy et al., 2017; Kazior et al., 2019; Ambacher et al., 2021). For Sc and Y concentrations below 30% and 50%, respectively, these materials crystallize in wurtzite lattice. Furthermore, for compositions of ∼ 7 − 11 % their a lattice parameter matches that of GaN (Dinh et al., 2023; Nguyen et al., 2024; Streicher et al., 2024b) thus overcoming the critical thickness limitations of AlN and allows for the growth of unstrained, thicker barrier layers (Zhang et al., 2013).

AlScN/GaN and AlYN/GaN heterostucture grown by molecular beam epitaxy (MBE) exhibit characteristics superior to those of conventional low-Al content AlGaN/GaN heterostructures (Hardy et al., 2017; Frei et al., 2019; Elias et al., 2023; Wang et al., 2023a,c,b; Hasan et al., 2024) and demonstrated the viability of utilizing AlScN and AlYN as barrier layers in GaN-based HEMTs. However, MOCVD is the preferred growth technique in industry because of its higher throughput, lower cost, and faster growth processes. On the other hand, the growth of AlScN and AlYN by MOCVD is challenging due to the low vapor pressure of available Sc and Y precursors. A heated gas mixing system was recently demonstrated at Fraunhofer IAF, enabling MOCVD growth with precursors that have extremely low vapor pressures. This advancement facilitated the successful growth of the first AlScN (Leone et al., 2020) and AlYN (Leone et al., 2023) by MOCVD, as well as AlScN/GaN (Streicher et al., 2023a; Leone et al., 2020; Ligl et al., 2020; Manz et al., 2021; Streicher et al., 2023b; 2024a) and AlYN/GaN (Streicher et al., 2024b) heterostructures with the presence of a 2DEG.

Optimization and further improvement of AlScN/GaN and AlYN/GaN HEMTs require accurate assessment of 2DEG properties and scattering mechanisms. Traditionally, charge carrier mobility μ and density n can be obtained with electrical Hall measurements at variable temperatures. The effective mass parameter m * , however, can be directly determined using cyclotron resonance measurements only at very low temperatures (LT) (4–10 K). At higher temperatures this method becomes impractical due to significant broadening of the energy levels. Hence, a combination of mid-infrared and electrical Hall measurements (e.g., Perlin et al., 1996; Kasic et al., 2000; Feneberg et al., 2013) is typically used to estimate the effective mass indirectly. The development of the optical Hall effect (OHE)–which applies generalized spectroscopic ellipsometry at long wavelengths in the presence of magnetic fields–has enabled the determination of electron effective mass, its anisotropy from low to room temperature (and beyond), as well as carrier density and mobility, all without requiring additional electrical measurements (Schubert et al., 2016).

In this work we report a study of the temperature-dependent 2DEG properties in MOCVD grown AlScN/GaN and AlYN/GaN HEMT structures by using the contactless THz OHE.

Figure 2 shows the results of a series of three Al 1 − x Sc x N/GaN and Al 1 − x Y x N/GaN structures with Sc and Y content in the ranges x = 4.6 − 17.3 % and x = 3.3 − 8.2 %, respectively, grown on GaN/sapphire templates. The room temperature (RT) T = 295 K OHE results reveal high 2DEG densities of n s = 2 − 3 × 1 0 13 cm − 2 for all Sc contents and mobility parameters of μ = 640 − 700   c m 2 ( V . s ) − 1 . For the Al x Y 1 − x N/GaN HEMT structures the mobility was found to be higher μ = 730 − 1000   c m 2 ( V . s ) − 1 , but for a slightly lower 2DEG density in the range of n s = 1.2 − 2.2 × 1 0 13 cm − 2 . This is in line with theoretical calculations, which predict that AlScN and AlYN barriers should provide 2DEG densities higher than low-Al content AlGaN. Note also the trend of increasing 2DEG density with decreasing Sc and Y content, indicating that pure AlN barrier should indeed provide even higher density. For all samples on sapphire substrates, the 2DEG effective mass parameters at RT were determined to be in the range m * = 0.33 − 0.39 m 0 . These values are higher than the commonly accepted value of m * = 0.23 m 0 for bulk GaN (Armakavicius et al., 2024a). The larger 2DEG effective mass observed here aligns with previous findings for AlGaN/GaN HEMTs (Kühne et al., 2018; Knight et al., 2023; Armakavicius et al., 2024b; Hofmann et al., 2012; Armakavicius et al., 2016; Pashnev et al., 2020; Adamov et al., 2021; Pashnev et al., 2022), where m * > 0.23 m 0 was reported at room temperature.

For two of the HEMTs on sapphire, one AlScN/GaN and one AlYN/GaN, OHE measurements at T = 40 K were also obtained. The analysis of these measurements shows that the carrier density changed little as expected for 2DEG. However, the mobility and the effective mass change considerably. The mobility increased to μ = 1530   c m 2 ( V . s ) − 1 and μ = 4400   c m 2 ( V . s ) − 1 for AlScN/GaN and AlYN/GaN, respectively. The effective mass decreased to m * = 0.27 m 0 and m * = 0.23 m 0 for AlScN/GaN and AlYN/GaN, respectively.

To further study the dependence of the 2DEG parameters on temperature, two HEMT samples grown on 4H-SiC substrates with 7% Sc and 5% Y in the barrier layers were selected. Figure 3 shows the 2DEG density n s , mobility μ and effective mass parameter m * as a function of temperature extracted from the analysis of the THz OHE measurements. The AlScN/GaN heterostructure has approximately twice the 2DEG sheet density as compared to the AlYN/GaN (Figure 3a). A slight increase in 2DEG density with temperature is also observed in both samples, which is unexpected for a pure 2DEG system. Streicher et al. (2024a) reported a similar behavior in AlScN/GaN structures and attributed it to 2DEG electrons being trapped in shallow acceptor states, likely caused by carbon impurities in the GaN channel, or to the presence of a small number of bulk donors that freeze out at low temperatures. In addition, strain-induced variations in piezoelectric polarization with temperature could also potentially contribute to the observed increase in 2DEG density.

The mobility parameter exhibits a typical trend, increasing as temperature decreases before saturating below 100 K (Figure 3b). For all temperatures, the 2DEG mobility in AlYN/GaN remains higher than in AlScN/GaN, reaching μ = 3600   c m 2 ( V . s ) − 1 and μ = 2000   c m 2 ( V . s ) − 1 , respectively, at low temperatures. The temperature dependence of the mobility parameter was modeled by taking into account the contributions of different scattering mechanisms using the equations for Fang–Howard variational wave function described in Ref. Jena (2022). We considered temperature-dependent scattering mechanisms, including polar optical phonon (POP), acoustic deformation potential (DP), and piezoelectric (PZ) scattering, alongside temperature-independent scattering from background residual impurities (IMP) and interface roughness (IF). In our calculations, 2DEG density and effective mass, and background impurity concentration are set to their measured values, with interface scattering parameters, i.e., correlation length and roughness, being the only adjustable variables. Due to the strong correlation between these two parameters, the correlation length was fixed at 3.5 nm, while roughness was varied to achieve the best fit. Figure 4 shows the individual contributions and the total mobility calculated according to the Matthiesen rule. At low temperature, the dominating mechanism is the interface roughness scattering. The best fits indicate similar interface roughness for the two samples, ∼ 0.9 nm and ∼ 0.8 nm for the AlScN/GaN and AlYN/GaN heterostructures, respectively. At high temperatures, scattering from polar optical phonons dominates. All other scattering mechanisms make only small contribution. Therefore, at both low temperatures and room temperature, the higher 2DEG mobility in AlYN/GaN compared to AlScN/GaN is likely due to its lower 2DEG density.

Figures 2c, 3c show that at low temperatures (bellow T = 100 K) the effective mass parameter is close to the widely accepted value of m * = 0.23 m 0 for bulk GaN (Armakavicius et al., 2024a), being 0.20-23 m 0 for AlYN/GaN and 0.25-27 m 0 for AlScN/GaN. Figure 5 shows the relationship between 2DEG effective mass and 2DEG density in different AlScN/GaN and AlYN/GaN structures (also including the samples grown on sapphire) measured at low temperatures (20 K–40 K). There is a trend of increasing low-temperature effective mass with the density, suggesting that the observed variation might be driven by band nonparabolicity effects (Syed et al., 2003; Spencer et al., 2016). According to the model proposed by Syed et al. (2003) and assuming a band-edge effective mass of m * = 0.21 m 0 , the effective mass increase due to non-parabolicity effects should range from 27% to 66% for the 2DEG densities of n s = 0.9 − 2.6 × 1 0 13 cm − 2 determined for our samples (Figure 5). Our results indicate that the low-temperature effective mass is enhanced by approximately half the predicted value. Note that if the 2DEG density remains constant with temperature, the increase in effective mass due to non-parabolicity effects should exhibit only a very slight temperature dependence (1%–2%) following the variations of band gap energy. In contrast, Figure 3c shows a strong temperature-dependent increase in the effective mass parameter. Until T = 100 K it is nearly constant, but it gradually increases afterwards and at RT reaches m * = 0.30 m 0 for AlYN/GaN and m * = 0.35 m 0 for the AlScN/GaN. At 360 K it increases even further to 0.37 m 0 and 0.42 m 0 (Figure 3c), i.e., 70% and 80% increase with respect to low temperature. Such an increase of the effective mass parameter in other GaN-based heterostructures have previously been reported (Kühne et al., 2018; Knight et al., 2023; Armakavicius et al., 2024b; Hofmann et al., 2012; Pashnev et al., 2020), as well as in bulk GaN and in thick GaN epilayers (Armakavicius et al., 2024a). The fact that this behavior is observed in different GaN structures and barrier materials hints at a common mechanism at play. However, such a large increase of the effective mass parameter with temperature is not easy to explain with the conventional mechanisms typically invoked, e.g., conduction band non-parabolicity and polaronic effects. In addition to the 1%–2% increase resulting from band gap energy variations with temperature, non-parabolicity effects may also arise if the 2DEG density changes with temperature. Considering the observed increase in 2DEG density Figure 3a (i.e., assuming it is entirely due to the detraping of electrons from shallow acceptor states) and using the equations in Syed et al. (2003), we estimate an increase of 12% between T = 20 K and T = 360 K for the effective mass. Note that this increase also takes into account the GaN bandgap change with temperature (e.g., Zubrilov et al., 1995).

Another cause of effective mass increase could be associated with the polaronic effect. The quasiparticle polaron is used to describe the interaction (coupling) of free charge carriers with the lattice vibrations, phonons. The formation of polarons decreases the carriers mobility and increases their effective mass. As the phonon population increases with increasing temperature, the polaronic effect is expected to be enhanced at RT and higher. This process is responsible for the reduction of carrier mobility at high temperatures (Figure 4). In the case of 2DEG weakly interacting with phonons in the surrounding 3D media, the relation between the effective mass of the polaron m p * and the band-edge effective mass m * of the free electrons is often described with the equation: m p * = m * 1 + π 8 α + 0.1272348 α 2 , (1) where α is the Fröhlich coupling constant α = 0.49 in GaN. In this case, the polaronic effect should lead to ∼ 22 % increase in the effective mass independent of the temeperature. However, Equation 1 is a simplification and previous theoretical studies have shown that polaron effective mass should explicitly depend on the temperature in a rather complex way (e.g., Fedyanin and Rodriguez, 1982a,b; Smilga, 1991; Peeters and Devreese, 1982), but in general should increase up to temperatures of the order of few hundreds Kelvin. From the relations presented in these works, we estimate effective mass enhancement of up to ∼ 12 − 15 % at T = 360 K , which can only partially explain our results. These relations are valid for polarons in 3D. In 2D the coupling should be stronger, however this may be compensated by screening effects (Peeters and Devreese, 1987; Devreese and Peeters, 1987). Fedyanin and Rodriguez (1982a) also noted that the coupling constant α and other parameters in the Pakar-Fröhlich Hamiltonian, which is used to describe polarons, should also be temperature-dependent.

Armakavicius et al. (2024a) discussed the possibility that the free-electron behavior deviates from the classical Drude model. One set of models introduces the so-called memory functions (Götze and Wölfle, 1972; Zwanzig, 1961; Mori, 1965). In some implementations of this model, the effective mass parameter becomes a function of both frequency and temperature (Rukelj, 2020; Kumari and Singh, 2020; Kupčić, 2017), and could potentially explain our results. However, analytical expressions for semiconductors have not been developed, and quantitative evaluation of these models is currently not straightforward.

Recently, Korotyeyev et al. (2022) proposed that deviations from the classical Drude model–arising from thermally activated inelastic electron scattering processes–could qualitatively explain the increase in the effective mass parameter with temperature in AlGaN/GaN with grating couplers as reported by Pashnev et al. (2020). According to Korotyeyev et al. (2022), their model, which accounts for inelastic scattering, requires only an 18% enhancement of the effective mass at room temperature to fit the experimental data of Pashnev et al. (2020), in contrast to the ∼ 55 % enhancement needed when using the classical Drude model. Such deviations from the Drude model could also explain the observed increase in the 2DEG effective mass in ScAlN/GaN and YAlN/GaN, which exceeds the enhancement predicted by nonparabolicity and polaron effects alone (Figure 3c). As the temperature increases, the contribution from polar optical phonon (POP) scattering, an inelastic process, also becomes more significant (see Figure 4), further enhancing the deviation from Drude-like behavior.

Finally, it should be noted that some earlier works on thick GaN layers, have reported effective mass at room temperature m * ≃ 0.23 m 0 . All these estimates involve measurements in the mid-infrared (MIR) – a combination of MIR reflectivity or ellipsometry and electrical measurements (Perlin et al., 1996; Kasic et al., 2000; Feneberg et al., 2013) and MIR OHE (Armakavicius et al., 2024a) – which led to the suggestion of possible frequency and temperature dependent deviations from the classic Drude model by Armakavicius et al. (2024a). However, a possible explanation for these results could be the relatively high doping levels in these samples, with a carrier concentration exceeding 4 × 1 0 18 cm − 3 . As Feneberg et al. (2013) pointed out, at such high concentrations the polaronic effects should be significantly reduced by screening and that non-parabolicity effects should also be small. Consequently, the effective mass was estimated to be m * ≃ 0.23 m 0 .

Because the effective mass can be most easily directly measured through cyclotron resonance at low temperatures, the polaronic, non-parabolicity, and other effects on the effective mass parameters at high temperature are not well studied experimentally and thus the existing theoretical models have not been rigorously tested. The recent development of the OHE made it possible for the first time to directly access the effective mass parameter at temperatures above RT and evidence for the increase of the effective mass parameter with temperature in GaN based materials has began to emerge. We have discussed several possible mechanisms that could partially explain this. While we are currently not in a position to conclusively identify quantitatively the process (or a combination of processes) responsible for the strong dependence of the effective mass parameter on temperature, we hope that our findings will stimulate further theoretical and experimental investigations on this subject. It would also be interesting to perform similar studies on other materials that are not GaN-based.

The 2DEG density, mobility, and effective mass parameters in AlScN/GaN and AlYN/GaN HEMTs have been determined using THz optical Hall effect measurements over a temperature range of 20 K–360 K. At room temperature, the AlScN heterostructures exhibit a 2DEG sheet density n s = 2.0 − 2.7 × 1 0 13 cm − 2 and mobility μ = 640 − 790   c m 2 ( V . s ) − 1 . For the AlYN heterostructures, the RT values are n s = 1.2 − 2.2 × 1 0 13 cm − 2 and μ = 750 − 1050   c m 2 ( V . s ) − 1 . At low temperatures, the mobility increases, reaching μ = 4400   c m 2 ( V . s ) − 1 for AlYN/GaN and μ = 2000   c m 2 ( V . s ) − 1 for AlScN/GaN. In this regime, mobility is primarily limited by interface roughness scattering. At low temperatures (T = 20–130 K) the effective mass is determined to be in the range 0.20–0.27 m 0 . These values correlate with the 2DEG density and their variation is attributed to conduction band nonporabolicity effects. Above 130 K, the effective mass parameter in both AlScN/GaN and AlYN/GaN HEMTs increases strongly with temperature in agreement with previous results for AlGaN/GaN HEMTs. We suggest that the observed increase in effective mass may be explained by a combination of temperature-dependent polaronic and nonparabolicity effect. Other factors, such as potential deviations from the classical Drude model caused by inelastic scattering or frequency-dependent scattering, could also play an important role. Further theoretical and experimental studies are necessary to establish a comprehensive understanding of the underlying mechanisms.