Electron effective mass is a fundamental material parameter defining the free charge carrier transport properties, but it is very challenging to be experimentally determined at high temperatures relevant to device operation. In this work, we obtain the electron effective mass parameters in a Si-doped GaN bulk substrate and epitaxial layers from terahertz (THz) and mid-infrared (MIR) optical Hall effect (OHE) measurements in the temperature range of 38-340 K. The OHE data are analyzed using the well-accepted Drude model to account for the free charge carrier contributions. A strong temperature dependence of the electron effective mass parameter in both bulk and epitaxial GaN with values ranging from (0.18 +/- 0.02) m(0) to (0.34 +/- 0.01) m(0) at a low temperature (38 K) and room temperature, respectively, is obtained from the THz OHE analysis. The observed effective mass enhancement with temperature is evaluated and discussed in view of conduction band nonparabolicity, polaron effect, strain, and deviations from the classical Drude behavior. On the other hand, the electron effective mass parameter determined by MIR OHE is found to be temperature independent with a value of (0.200 +/- 0.002) m(0). A possible explanation for the different findings from THz OHE and MIR OHE is proposed. (c) 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)

This PhD thesis presents experimental and theoretical studies of the thermal conductivity of wide and ultra-wide bandgap semiconductors including GaN, AlN, β-Ga₂O₃ binary compounds, and Al_xGa_1−xN, Sc_xAl_1−xN, Y_xAl_1−xN ternary alloys. Thermal conductivity measurements are conducted using the transient thermoreflectance (TTR) technique and the results are interpreted using analytical models based on the solution of the Boltzmann transport equation (BTE) within the relaxation time approximation (RTA). 

The study is motivated by the increasing research interest in these material systems due to their potential for the development of high-power (HP) and high-frequency (HF) electronic devices. Due to its wide bandgap, high electrical field, and high electronic saturation velocity, GaN is an excellent material for fast-switching HP electronic devices. Al_xGa_1−xN is considered a natural choice for next-generation HP electronic devices since by tuning the bandgap from 3.4 eV to 6 eV a significant increase of the critical electric field and thus the device breakdown voltage, can be achieved. Furthermore, both n- and p-type conductivity can be realized in AlGaN allowing flexible device design. β-Ga₂O₃ is also promising for HP electronics because of its ultra-wide bandgap (4.8 eV) and a very high Baliga’s figure of merit (FOM) exceeding by far that of GaN. Moreover, the mature growth techniques of bulk β-Ga₂O₃ can enable low-cost substrates with high crystal quality. Sc_xAl_1−xN and Y_xAl_1−xN have recently emerged as a new class of III-nitride semiconductors. Due to the large piezoelectric coefficients and spontaneous polarization in these alloys, a very large density of two-dimensional electron gas (2DEG) can be achieved at (Sc,Y)_xAl_1−xN/GaN heterostructures enabling high mobility transistors (HEMTs) with an enhanced HF performance as compared with the common Al_xGa_1−xN/GaN HEMTs. 

For any HP and HF device, the thermal conductivity of the constituent materials in the device structures is of crucial importance. Such devices operate at high currents, high voltages, and/or high frequencies, so a high Joule heat is generated in the device’s active region. This heat must be effectively dissipated in order to ensure high device performance and reliability. Therefore, understanding the materials’ thermal conductivity is essential for the device’s thermal management. 

We have investigated different bulk materials and epitaxial layers and have established the effects of dislocation density, doping, alloying, layer thickness, and crystal orientation on thermal conductivity. The results presented in this Ph.D. thesis give new insights into the thermal properties of wide and ultra-wide semiconductors and could be useful for the design, optimization, and thermal management of electronic devices based on these materials. 

The main research results presented in this Ph.D. thesis are summarized in six scientific papers. 

Paper I is focused on studying the thermal conductivity of high Al-content Al_xGa_1−xN and β-Ga2O₃ thin layers. For β-Ga₂O₃ layers the effect of Sn doping on their thermal conductivity is also studied. The experimental measurements are performed in a temperature range of 280-350 K. A modified Callaway’s model is employed for the interpretation of the results. Calculations of the thickness-dependent thermal conductivity reveal quite different transport mechanisms of the two materials. 

Paper II presents experimental results of the thermal conductivity of thick Al_xGa_1−xN layers. A detailed discussion of the phonon-alloy scattering which is the main mechanism limiting the thermal conductivity of Al_xGa_1−xN is presented. Analyzing the interplay between the phonon-alloy scattering and the phonon-boundary scattering the experimentally observed thickness dependence of the thermal conductivity is explained. 

Paper III is devoted to studying the role of defects on the thermal conductivity of Al_xGa_1−xN alloys with 0 ≤ x ≤ 1. The effect of dislocations, impurities, free carriers, and alloying have been separately studied and discussed. The thermal conductivity of samples with various concentrations of the defect is measured and the results are interpreted using a theoretical model based on the solution of the BTE equation within the RTA. 

Paper IV focuses on the thermal conductivity study of Sc_xAl_1−xN and Y_xAl_1−xN alloys. The experimental measurements are performed for layers having compositions in the range of 0 ≤ x ≤ 0.22. The effect of phonon-alloy scattering in these alloy materials is discussed and compared with other phonon scattering processes. The experimental results are interpreted within the frame of a modified Callaway’s model in combination with ab-initio calculation for phonon dispersions and mode Grüneisen parameters. 

Paper V investigates the thermal conductivity anisotropy of bulk GaN. The thermal conductivity along the c- and m-axis crystallographic directions of wurtzite GaN is measured in a temperature range of 80-400 K. Experimental observations are elaborated by an analysis of the anisotropy of the phonon group velocity, the Debye temperature and the mode Grüneisen parameters. 

Paper VI explores the effects of doping and free carriers on the thermal conductivity of bulk GaN and homoepitaxial layers and heteroepitaxial GaN layers via both experimental and theoretical approaches. The impurities considered include Si, O, Mg, and Fe. The experimental results are analyzed using a non-Debye RTA model in combination with ab-initio calculations of the phonon dispersion. 

The hot-wall metalorganic chemical vapor deposition (MOCVD) concept, previously shown to enable superior material quality and high performance devices based on wide bandgap semiconductors, such as Ga(Al)N and SiC, has been applied to the epitaxial growth of beta-Ga2O3. Epitaxial beta-Ga2O3 layers at high growth rates (above 1 mu m/h), at low reagent flows, and at reduced growth temperatures (740 degrees C) are demonstrated. A high crystalline quality epitaxial material on a c-plane sapphire substrate is attained as corroborated by a combination of x-ray diffraction, high-resolution scanning transmission electron microscopy, and spectroscopic ellipsometry measurements. The hot-wall MOCVD process is transferred to homoepitaxy, and single-crystalline homoepitaxial beta-Ga2O3 layers are demonstrated with a 201 rocking curve width of 118 arc sec, which is comparable to those of the edge-defined film-fed grown (201) beta-Ga2O3 substrates, indicative of similar dislocation densities for epilayers and substrates. Hence, hot-wall MOCVD is proposed as a prospective growth method to be further explored for the fabrication of beta-Ga2O3.

For the high-power (HP) electronic applications the existing Si-based devices have reached the performance limits governed by the material properties. Hence the device innovation itself is unable to enhance the overall performance. GaN, a semiconductor with wide bandgap, high critical breakdown field, and high electronic saturation velocity is regarded as an alternative of Si. The material properties of GaN make it very suitable for fast-switching HP electronic devices and contribute to the fast growing of GaN technology. The state-of-the-art GaN devices operating up to 650 V have recently become commercially available. Further goal is to reach higher breakdown voltage which can be done via device engineering and material growth optimization.

Al_xGa_1−xN is an ultrawide-bandgap (UWBG) semiconductor which is considered as a natural choice for next generation in the development of GaN-based HP electronic devices. This material attracts particular interest due to the possibility for bandgap tuning from 3.4 eV to 6 eV which allows nonlinear increase of avalanche breakdown field. Furthermore, both n- and p-type conductivity can be achieved on this material permitting variety of device design with reduced energy losses during operation. β−Ga₂O₃ is also a promising material for HP electronics because of its ultra-wide bandgap (4.8 eV) and a huge value of Baliga’s figure of merit (FOM) exceeding by far that of GaN. More interesting feature making this material attractive is the availability of low-cost natural substrates, and then the possibility to obtain high crystal quality of device structures.

For the HP electronic devices thermal conductivity is one of the key parameters determining the device’s performance. The initial studies have shown that the thermal conductivity of Al_xGa_1−xN and β−Ga₂O₃ is quite low comparing with that of GaN. This is one of the biggest challenges slowing the development of these materials for HP device applications. Nevertheless, Al_xGa_1−xN- and β−Ga₂O₃-based field-effect transistors and Schottky-barrier diodes have been demonstrated showing performances superior to that of GaN. To optimize and maintain good performance and reliability, heat generated in the device active regions has to be effectively dissipated. Therefore the thermal conductivity of the materials in the device structures needs to be systematically studied and accurately determined. This information is critically important for the thermal management of the devices.

Transient thermoreflectance (TTR) is a contactless nondestructive method for measuring of the thermal conductivity of materials. TTR, which is based on a pump-probe technique, has shown its potential in evaluation of the thermal conductivity in bulk crystals as well as in thin layers in hetero-epitaxial structures. The method requires an analysis of experimental data based on the fit of thermoreflectance transients with the solution of the one-dimensional heat transport equations by a least-square minimization of the fitting parameters. Such a procedure allows to extract not only the thermal conductivity of the constituent materials in the structures, but also the thermal boundary resistance at different hetero-interfaces.

The main research results of the graduate studies presented in this licentiate thesis are summarized in three scientific papers.

Paper I. In this paper thermal conductivity of β−Ga₂O₃ and high Al-content Al_xGa_1−xN thin layers was studied. For β−Ga₂O₃ the the effects of Sn doping and phonon-bondary scattering on the reduction of thermal conductivity were discussed. For the Al_xGa_1−xN we studied the effect of Al-Ga alloying which gives rise to phonon-alloy scattering. It was found that this scattering process accounts for low thermal conductivity of this material. Finally, a comparison for the thermal conductivity of the two materials was made.

Paper II. In this paper the effect of layer thickness on the thermal conductivity of Al_xGa_1−xN layers grown by HVPE were investigated. Due to Al alloying the thermal conductivity of this material is degraded and reduced by more than one order of magnitude. On top of that we also observed further reduction of thermal conductivity when the layer thickness goes thinner. The mechanism of this phenomenon has been revealed by studying the phonon transport properties in bulk crystal and thin layer.

Paper III. This study emphasizes the role of defects in GaN and Al_xGa_1−xN to the thermal conductivity of these materials. The dislocations, impurities, free carries, and random alloying have been separately studied and discussed. Thermal conductivity of samples containing these defects with various concentrations was measured and the results were interpreted by a theoretical model based on relaxation time approximation (RTA).

Thermal conductivity of AlxGa1-xN layers with 0 <= x <= 0.96 and variable thicknesses is systematically studied by combined thermoreflectance measurements and a modified Callaway model. We find a reduction in the thermal conductivity of AlxGa1-xN by more than one order of magnitude compared to that of GaN, which indicates a strong effect of phonon-alloy scattering. It is shown that the short-mean free path phonons are strongly scattered, which leads to a major contribution of the long-mean free path phonons to the thermal conductivity. In thin layers, the long-mean free path phonons become efficiently scattered by the boundaries, resulting in a further decrease in the thermal conductivity. Also, an asymmetry of thermal conductivity as a function of Al content is experimentally observed and attributed to the mass difference between Ga and Al host atoms.