Hot-wall MOCVD for advanced GaN HEMT structures and improved p-type doping

The transition to energy efficient smart grid and wireless communication with improved capacity requires the development and optimization of next generation semiconductor technologies and electronic device components. Indium nitride (InN), gallium nitride (GaN) and aluminum nitride (AlN) compounds and their alloys are direct bandgap semiconductors with bandgap energies ranging from 0.7 to 6.0 eV, facilitating their utilization in optoelectronics and photonics. The GaN-based blue light-emitting diodes (LEDs) have enabled efficient and energy saving lighting, for which the Nobel Prize in Physics 2014 was awarded. GaN and AlN have high critical electric fields, high saturation carrier velocities and high thermal conductivities, which make them promising candidates for replacing silicon (Si) in next-generation power devices. The polarization-induced two-dimensional electron gas (2DEG), formed at the interface of AlGaN and GaN has enabled GaN-based high electron mobility transistors (HEMTs). These devices are suitable for high-power (HP) switching, power amplification and high-frequency (HF) applications in the millimeter-wave range up to THz frequencies. As such, HEMTs are suitable for next-generation 5G and 6G communication systems, radars, satellites, and a plethora of other related applications. Despite the immense efforts in the field, several material related issues still hinder the full exploitation of the unique properties of GaN-based semiconductors in HF and HP electronic applications. These limitations and challenges are related among others to: i) poor efficiency of p-type doping in GaN, ii) lack of linearity in AlGaN/GaN HEMTs used in low-noise RF amplifiers and, iii) MOCVD growth related difficulties in achieving ultra-thin and high Al-content AlGaN barrier layers with compositionally sharp Al profiles in AlGaN/GaN HEMTs for HF applications. In this PhD thesis, we address the abovementioned issues by exploiting the hot-wall MOCVD combined with extensive material characterization. Main results can be grouped as follows: i) state-of-art p-GaN with room-temperature free-hole concentrations in the low 1018 cm−3 range and mobilities of ∼ 10 cm2/Vs has been developed via in-situ doping. A comprehensive understanding of the growth process and its limiting factors, as related to magnesium (Mg), hydrogen (H) and carbon (C) incorporation in GaN is established. Further improvement of p-type doping in as-grown GaN:Mg is achieved by using GaN/AlN/4H-SiC templates and/or by modifying the gas environment in the growth reactor through the introduction of high amounts of hydrogen (H2) in the process. Using advanced scanning transmission electron microscopy (STEM) in combination with electron energy loss spectroscopy (EELS) we have established an improved comprehensive model of the pyramidal inversion domain defects (PIDs) in relation to the ambient matrix. First experimental evidence that Mg is present at all interfaces between PID and matrix allows for more accurate evaluation of Mg segregated at the PID, necessary for understanding the main limiting factor for p-type conductivity in GaN

Si [12], as the integrated circuit manufacturing industry is built based on this substrate.
Achieving process compatibility on Si substrates, could bring III-nitride based devices mass production earlier to the market. Apart from the substrate cost and technology compatibility, the thermal conductivity is a crucial factor of substrate choice, especially for HP devices.
The thermal issues related to the epitaxial growth of III-nitrides are less prominent. Most of the epilayers growth is done by metal-organic chemical vapor deposition (MOCVD) and at a smaller extent by molecular beam epitaxy (MBE), with both techniques providing high quality III-nitride materials with tunable properties.
The efficient blue light-emitting diode (LED) invented by Akasaki, Amano and Nakamura (Nobel prize in Physics 2014) [13] sparked intensive research and advances in III-nitrides optoelectronics. This pivotal achievement was made possible thanks to several prior steps of solving fundamental problems in epitaxial growth of III-nitrides. The development of AlN nucleation layer for accommodating the lattice mismatch between GaN and the sapphire substrate, the use of GaN buffer layer for reducing the dislocation density in the active layers, and the achievement of p-type GaN by thermal annealing of magnesium (Mg)doped GaN, were fundamental contributions for the III-nitrides field and created pathways for more efficient utilization of III-nitrides unique properties. At the same time, the 5G mobile network which supports low latency and high data-rate communications and enables unparalleled applications for smart homes, autonomous vehicles, the Internet-of-Things (IoT), etc., significantly increases the demand for high-performance, low-cost, and small-dimension mm-wave components. The III-nitride based devices have already shown enormous potential in this field and hence, further development is required in order to meet the continuously evolving device requirements.
In this thesis, we dedicate our investigations on two topics: a) p-type GaN growth and optimization via in-situ Mg-doping and b) development of high-linearity and highfrequency aluminum gallium nitride (AlGaN)/GaN HEMT structures and optimization of their two-dimensional electron gas (2DEG) properties.
For the p-type GaN, we explore the potential benefits of the hot-wall MOCVD process on the realization of efficient p-GaN. Efficient p-type doping of GaN is very challenging and despite the dedicated efforts of the research community during the last almost three decades, there are still limitations at fundamental level. The free-hole concentration and mobility, and the resistivity in p-GaN layers are decisive factors for using the material in power devices, and thus, need to be optimized.
Concerning the AlGaN/GaN HEMTs, it is well known that variation of the Al-content in the barrier layer has direct effect on the 2DEG density and the mechanism behind this process is extensively studied. Here, we investigate the 2DEG properties using THz optical Hall effect (OHE), which in addition to charge carrier density and mobility provides information on effective mass parameters. The latter is not well understood and only scarcy investigated. SECTION 1.2. Properties of group-III nitride semiconductors 3 We aim to better understand the basic mechanism causing the degraded mobility for high Al-content ≥ 20% in the AlGaN barrier layer of AlGaN/GaN HEMT structures in order to provide basis for further device optimization. In addition, we explore the polarization doping in AlGaN/GaN HEMTs through compositional grading of the channel layer which is a promising route for improving device linearity, necessary for realization of low-noise RF amplifiers. We examine this technology by hot-wall MOCVD and demonstrate devices with reduced third-order intermodulation figure of merit (IM 3 ) compared to conventional non-graded HEMTs, providing evidence of improved linearity. Finally, the HEMTs used for high-frequency oriented applications require device down-scaling which implies use of ultra-thin and high-Al content AlGaN barrier layers for GaN-based devices. We explore the MOCVD of such HEMT structures with an in-depth structural investigation and correlation with their 2DEG properties.

Crystal structure and polarity of group-III nitrides
III-nitride materials are direct bandgap semiconductors which make them attractive for numerous optoelectronic device applications while, the high dielectric breakdown voltage allows them to be utilized in high power devices. Their bandgap ranges from 0.7 eV for InN to 3.4 eV for GaN, and to 6.0 eV for AlN. Their ternary or quaternary alloys, enable the bandgap tuning ( Fig. 1.1) within the whole range between 0.7 − 6.0 eV and consequently, spanning from infrared (IR) to deep-ultraviolet (UV) in optoelectronic and photonic devices [14,15].
Although III-nitride semiconductors can crystallize in rocksalt, zincblende or wurtzite structure, the thermodynamically stable phase is the hexagonal wurtzite, in which the IIInitride films usually grow. The former two, rocksalt and zincblende, are meta-stable phases.
The wurtzite crystal lattice consists of two hexagonal close packed (hcp) sub-lattices. One sublattice consists of group-III cations (aluminum (Al) 3+ , gallium (Ga) 3+ , indium (In) 3+ ) while the other consists of nitrogen anions (N 3− ). The two sub-lattices are inter-penetrating each other and in the ideal case, they are shifted by uc = 3 8 c along the [0001] direction (c-axis). u is the internal parameter of wurtzite structure and corresponds to the bond distance between the anion and the cation atoms divided by the lattice constant c. In the ideal wurtzite structure, the c/a ratio is equal to 1 √ u = 8 3 ≃ 1.633, with a and c being the lattice constants along the [1210] and [0001] directions respectively. As shown in Fig. 1 seen from this schematic, the GaN polarity is determined by the direction of tetrahedrons in the unit cell. When three of the bonds of a Ga atom in a tetrahedral are pointing towards the substrate, the material is then determined as Ga-polar. In the opposite case where the three bonds of the Ga atom are pointing at the growth direction, the material is defined as N-polar.
It should be noted that the surface termination atoms could be either Ga or N in both metalor nitrogen-polar GaN although, it is common to use the terms Ga-or N-terminated and Gaor N-face as sign of the GaN polarity.

Polarization fields in III-nitrides
The electronegativity difference between the nitrogen and the group-III atom in wurtzite III-nitrides results in small ionicity degree in the group-III -N covalent bond. Since the electronegativity of N is higher than that of group-III atoms, the electron cloud of the covalent bond is shifted closer to the N atom thus, creating an electric dipole. Despite that the electric dipoles in the ideal wurtzite III-nitrides would cancel-out within the tetrahedral building blocks, both in the in-plane and out-of-plane direction (c-axis), the non-ideality of the tetrahedrons' structure in wurtzite III-nitrides bonding angle α < β ⇔ (c/a) < √ 8/3 results in 6 CHAPTER 1. PART I not fully compensated electric dipoles along the c-axis. Thus, a polarization is present in the tetrahedrons pointing from the N atom to the group-III atom.
The accumulated macroscopic polarization field along the c-axis is called spontaneous polarization (P SP ) because it occurs at strain-free conditions. The ⃗ P SP direction points towards the substrate for metal-polar material and its magnitude increases from GaN to InN to AlN along with decreasing c 0 /a 0 as shown in Table 1 [19], c Ref. [20], d Ref. [21], e Ref. [22], f Ref. [2] are screened by the nearest neighbouring dipole charges with the opposite sign. Since the wurtzite lattice lacks inversion symmetry, there are remaining unscreened charges at the metal-and N-face (negative and positive respectively) of the crystal boundaries which are called polarization induced sheet charges. This explains why P SP is measured in charge per unit area (C/m 2 ) units.
Strain induced in the wurtzite crystal (e.g., in heteroepitaxial growth), may further deform the tetrahedrons. This implies formation of an additional polarization field along the c-axis of the crystal. If the in-plane lattice parameter (a) of the epilayer is smaller than the substrate lattice parameter, then the epilayer is under biaxial tensile strain and the bond angle α becomes even smaller. Consequently, the induced polarization field is parallel to the c-axis and points in the same direction as the P SP . On the contrary, when the in-plane lattice parameter of the epilayer is larger than the substrate lattice parameter, the epilayer is under compressive strain and the bond angle α becomes larger. As a result, the induced polarization field is anti-parallel to P SP . The additional polarization field described above is called piezoelectric polarization (P PE ) and can be calculated by Eq. 1.1 using the polarization related parameters in III-nitrides listed in Table 1.1. The total polarization in a III-nitride layer (i.e. the sum of P SP and P PE ) Eq. 1.2 is a very useful material property utilized for the 2DEG formation as will be discussed below. To give an indication of the magnitude of P SP and P PE in the SECTION 1.2. Properties of group-III nitride semiconductors 7 AlN/GaN system, the P SP corresponds to ∼ 60% of the total polarization field and the rest ∼ 40% originates from the P PE .
P PE = (ϵ xx + ϵ yy )e 31 + ϵ zz e 33 = 2ϵ xx e 31 + ϵ zz e 33 where ϵ xx = ϵ yy and ϵ zz are the in-plane and out-of-plane strain components respectively, e 31 and e 33 are the piezoelectric coefficients and C 13 and C 33 the elastic coefficients.
Polarization induced sheet charges appear on the crystal boundaries along the c-axis of the wurtzite crystal. For metal-polar material, negative sheet charge appears at the top side and positive sheet charge at the bottom side (towards substrate) of the crystal. When combining two layers of different III-nitride materials e.g. AlGaN on top of GaN, the polarization induced sheet charge at their interface will be the sum of the sheet charges at the two sides of the interface. In other words, the interface charge will be the sum of the positive sheet charge from the AlGaN bottom surface and the negative sheet charge from the GaN top surface. If the total charge density at the interface is positive (+σ), then free electrons will be accumulated in order to compensate the polarization induced positive charge +σ. Thus, a 2DEG is formed with a sheet electron density n s only if the conduction band of the formed triangular quantum well at the interface drops below the Fermi level (E F ) [23,24] as depicted schematically in Fig. 1.4.
The 2DEG is positioned at the lower AlGaN/GaN interface as shown in Fig. 1 [26][27][28][29] Based on the charge neutrality condition when no external electric field is applied, and taking into account that the layers in the HEMT structure are not doped, the source of the free electrons in the 2DEG is connected to donor-like surface states [30]. These donor-like states are possibly related to N-vacancies in the AlGaN barrier layer [31].
The 2DEG density is affected by several factors in an AlGaN/GaN heterostructure, like the Al-composition and the thickness of the barrier AlGaN layer and the addition of a GaN cap layer. Increasing the Al-composition in the AlGaN layer results in higher P SP and P PE and hence, increase in the 2DEG density. Additionally, a thicker AlGaN barrier will result in higher n S while, the opposite effect will be present with increasing the thickness of the GaN where: d cap GaN and d barrier AlGaN are the thicknesses of cap GaN and barrier AlGaN layers while, σ pol , q, ε r,AlGaN , ε 0 and qϕ B is the polarization-induced charge density, the elemental electron charge, the dielectric constant of the barrier layer, the vacuum permittivity and the surface barrier height, respectively. The maximum electron sheet charge in a heterostructure is also limited by the critical thickness of the barrier layer (d critical ). Below the critical thickness, the AlGaN barrier layer can grow pseudomorphically on the GaN buffer-channel layer but for thicknesses higher than d critical , the strained AlGaN undergoes plastic relaxation through formation of misfit dislocations and cracks [33][34][35][36]. An example of the calculated N s vs. d barrier in an AlGaN/GaN heterostructure where the Al x Ga 1−x N barrier is pseudomorphically grown on the GaN buffer is shown in Fig. 1.6. The role of the channel, barrier, and cap layers in the HEMT structure will be discussed in detail in section 1.3.5. The dotted lines are eye guides to the expected N s for the barrier thickness / Alcontent pairs of 8 nm/50%, 5 nm/70%, and 4.5 nm/100%. For the simulations, the 1D Poisson numerical solver of Snider [37] was used, while the critical thickness values for the barrier were calculated using the approximation d critical ∼ b a /(2 xx ) after Refs. [35,38].
Another important aspect related to the III-nitrides is the so-called polarization engineering. Three-dimensional doping can be realized without using doping impurities in the lattice, by controlling the polarization field in the material. Although the removal of ionized impurity scattering is advantageous for mobility, other scattering mechanisms e. g. alloy scattering are compromising the mobility. Similarly to the 2DEG formed at the AlGaN/GaN interface in order to screen the polarization dipole in the AlGaN layer, the bulk polarization-induced doping results from the polarization field discontinuity in the material. In this case, the polarization discontinuity is spread along the polarization field direction, inducing fixed charge in the material. In order to satisfy Poisson's equation and charge neutrality at the equilibrium conditions, the fixed charge attracts free carriers, forming in this way a three-dimensional doping. The polarity and the concentration profile of the polarization-induced fixed charge N pol D and consequently of the free charge, depend on the divergence of the polarization field which changes along the growth direction (Eq. 1.4) where P(z) is the polarization along the growth direction (z).
Considering an Al x Ga 1−x N/GaN hetero-interface as an example, a uniform profile of positive fixed charge will be formed in Al x Ga 1−x N for a linear grading of x, which results in a uniform distribution of the induced free electrons in the Al x Ga 1−x N -three-dimensional electron gas (3DEG) [39][40][41]. In a similar manner, p-type polarization doping resulting in a threedimensional hole gas (3DHG) [42] can be achieved in N-polar Al x Ga 1−x N/GaN heterostructures.
The 3DEG/3DHG formation in metal-/N-polar graded-AlGaN/GaN heterostructures is depicted in Fig. 1.7. Formation of the 3DEG is predicted to improve the small-and largesignal linearity in HEMTs [43,44], rendering a constant cut-off frequency f T and maximum oscillation frequency f max over a wider range of input power [45][46][47][48][49], which is necessary for the realization of low-noise RF amplifiers (LNAs).

2DEG / 3DEG properties
The 2DEG properties are affected by several factors. In general, high 2DEG mobility values can be achieved using GaN with low impurity concentrations and AlGaN/GaN interface with low roughness [50,51]. Nevertheless, the scattering mechanisms that affect mobility in AlGaN/GaN heterostructures must be taken into consideration for explaining the decrease in mobility and for tuning of the structure parameters according to the desired outcome. Briefly, these mechanisms include: scattering of the 2DEG by acoustic and optical phonons (the effect is prominent at room temperature), alloy disorder scattering (increases with the Al-content in the barrier), remote ionized and background impurities scattering and finally, scattering by dislocations. All these mechanisms, specifically for the AlGaN/GaN system are extensively discussed by Jena et al. in Ref. [51].

1.
The scattering by phonons is the main mechanism limiting the 2DEG mobility at room temperature in the range of ∼ 2000 − 2400 cm 2 V −1 s −1 . The effect becomes more pronounced for high 2DEG densities (10 13 cm −2 ).

2.
The alloy disorder scattering is present at the AlGaN/GaN interface and gets more pronounced at high 2DEG densities leading to a decrease in mobility. With increasing 2DEG density, the 2DEG wavefunction penetrates more into the barrier because it is shifted closer to the junction. Similarly, for low Al-composition barrier, the conduction band discontinuity is smaller leading to large penetration of the 2DEG wavefunction in the barrier. Again, the increased alloy scattering results in lower mobility. Introducing a very thin (∼ 1 nm) AlN interlayer between the GaN channel and the AlGaN barrier effectively diminishes the penetration of the 2DEG wavefunction in the AlGaN and effectively minimize the alloy scattering in the process [52,53]. Alternatively, the alloy scattering can be minimized by the use of AlN instead of AlGaN as a barrier layer. In this case, the mobility limiting factor will be the interface roughness scattering.
3. The AlGaN/GaN interface roughness is introducing another scattering mechanism for the 2DEG, although the mobility dependence on the interface roughness is scaling with a factor of L −6 where L is the thickness of the quantum well [54]. Nevertheless, the growth processes nowadays allow for the formation of atomically smooth interfaces rendering mobilities > 2200 cm 2

5.
Threading dislocations in wurtzite c-oriented III-nitride epitaxial layers are introduced along the c-axis, thus, intervening perpendicular to the 2DEG and affecting its transport properties. The dangling bonds created along a threading dislocation, introduce additional states in the energy gap and the dislocations act like carrier traps. On device level the dislocations present current leakage paths. For dislocation densities in the common 10 8 cm −2 range, the mobility of low density (low 10 12 cm −2 ) 2DEGs is affected more by this scattering mechanism. Higher dislocation densities severely affect the mobility.
In graded Al x Ga 1−x N layers, the 3DEG is mainly affected by the alloy scattering and optical phonon scattering mechanisms. At the lower end of Al compositions, the mobility is mainly limited by the optical phonon scattering while at higher Al compositions, the alloy scattering becomes the main mobility limiting factor. [41,57,58]

Point defects and impurities in group-III nitride materials
The low intrinsic carrier concentration in wide bandgap semiconductors, like GaN and AlN, turn them into insulators at room temperature. The carrier concentration of a semiconductor is affected by the effective density of states in the conduction and valence bands (N C and N V ), the semiconductor bandgap E g and the temperature: shallow donor characteristics (90-260 meV below the conduction band edge), while V Ga (a deep acceptor) is also abundant in GaN due to its low formation energy [59].
UID-GaN can easily be n-type due to oxygen (O) and Si impurities incorporation during MOCVD growth. O and Si are shallow donors in GaN. Although nitrogen vacancy (V N ) also causes n-type conductivity, the formation energy of this defect is rather high [60] under normal growth conditions, limiting its contribution to n-type conductivity in as-grown GaN.
On the contrary, Si is present during growth originating from the quartz tube chamber while, O mainly originates from water adsorbed on the chamber walls during the chamber exposure to the atmosphere for substrate loading. Thus, pumping the cell down to low 10 −5 mbar before growth is very important. Other sources of O are the carrier gases (N 2 and H 2 ) and the precursors (metal-organic and NH 3 ). In order to reduce the O, ultra-high purity metal-organic sources are used while the NH 3 and the carrier gases are purified before use. Carbon (C) is amphoteric in GaN since it belongs to group-IV between Ga (group-III) and N (group-V). It can therefore act as a shallow donor when is substitutional to Ga site (C Ga ), or as a deep acceptor when is substitutional to N site (C N ) [61]. Theoretical calculations show that substitution of N is preferential in n-type material [61][62][63] (see Fig. 1.8). The as-grown GaN epilayers with high C-levels are highly resistive, instead of having a p-type character.
The high resistivity could be attributed to self compensation effects between C N and C I or C Ga [62,64].

n− and p− doping in III-nitrides
Si, germanium (Ge) and selenium (Se) act as donors in GaN when substituting Ga (Si Ga , Ge Ga and Se Ga ). Although Si is a group-IV element and could potentially act either as donor or as acceptor, it is shown by theoretical calculations that preferentially substitutes Ga [69], creating a shallow donor level which lies ∼ 30 meV below the conduction band. Additionally, O is a donor when incorporated on the N site (O N ) with similarly shallow level at ∼ 33 meV [70]. Since all of the aforementioned donors have ionization energy ∼ 30 meV which is comparable to the thermal energy at room temperature, almost all of the incorporated dopant atoms are ionized at these conditions. In general, Si is the dopant of choice for n-type doping. O is not desired in the MOCVD process, while it is difficult for Ge and Se to incorporate in the GaN lattice because of their large size compared to Si. C has amphoteric character but results in highly resistive GaN as discussed before. The group-II atoms suitable for p-type doping in III-nitrides are beryllium (Be) and Mg with the latter being the only successful p-type dopant for GaN and AlGaN. Mg is the shallowest acceptor for GaN but its ionization energy is relatively high (∼ 170 − 200 meV) [71,72] while for AlN is ∼ 500 − 630 meV [73,74] (330 ± 80 meV in recent report [75]). Since this study relates to Mg doping in GaN, the issues and limitations related to the Mg doping in GaN are discussed in detail in section 1.2.6.

Solubility
The solubility of Mg dopant in GaN represents the ability (maximum concentration) of Mg atoms to be incorporated in the GaN lattice under thermodynamic equilibrium conditions. As the dopant atom replaces a matrix atom, the dopant solubility depends on the size difference and chemical similarity between the two types of atoms, the temperature, and the abundance of dopant and matrix atoms in the growth environment.
These differences in size and chemical similarity lead to substitution of dopants at the wrong lattice sites while, exceeding the solubility limit would lead to dopant atoms segregation or formation of other phases. In the hcp unit cell of GaN, the maximum number of Ga-(or N-) sites available for Mg substitution, is given by Eq. 1.6.
where n GaN is the number of atoms in the unit cell, V GaN is the volume of the unit cell and a and c are the strain-free lattice constants of GaN [21]. Therefore, there is a phase is the lowest [76]. It has been reported that the maximum Mg concentration in GaN before reaching the saturation limit is in the mid-10 19 cm −3 range [77].

High ionization energy
The ionization energy of a donor (or an acceptor) denotes the amount of energy needed to move an electron from the donor atom to the conduction band (or to move a hole from the acceptor atom to the valence band i.e. move an electron from the valence band to the acceptor atom). In case that the ionization energy is smaller than the thermal energy, kT, at room temperature (≈ 25 meV), the dopants are completely ionized. Otherwise, the dopants are electrically inactive even if they are incorporated at the right crystal lattice site. Considering the hydrogen atom approximation (which is valid for shallow "effective mass" acceptors) [78], the Mg ionization energy in GaN can be estimated by Eq. 1.7: and ε r is the dielectric constant of GaN (8.9). This means that only a very small amount of acceptors (∼ 1%) are electrically active at room temperature. In order to get 100% ionized acceptors, the

Surface segregation and pyramidal inversion domains (PIDs)
Mg atoms tend to accumulate at the GaN surface. In these areas, where the Mg forms ∼ 1 monolayer, the high concentration exceeds the solubility limit and the Mg atoms form defects in order to deplete the material excess, which causes polarity inversion [81][82][83]. In this case, hexagonal-based pyramids are formed because of the preferential GaN growth towards specific crystallographic directions which happens at high Mg concentrations [84]. When the Mg levels overcome the solubility limit, formation of one monolayer of Mg 3 N 2 occurs and it is believed that this is the reason causing the polarity inversion [77]. Theoretical calculations [85] and experimental observations [86][87][88][89] revealed that in PIDs, a single Mg layer is inserted between two polarity inverted GaN

Unintentional dopants and post-growth annealing
As already mentioned at the beginning of this section, unintentional doping is always present in MOCVD processes and it is related to the high growth pressure and to residual impurities in the chamber, as well as in the precursors and in the carrier gases.
Contributing elements to the unintentional impurities in the growth of p-type GaN are: Si, O, C and H. Although Si and O form shallow donors, their concentration can be limited in our hot-wall MOCVD process to ∼ 3 − 5 × 10 15 cm −3 , which is close to the SIMS detection limits for these elements (∼ 2 × 10 15 cm −3 ). The amphoteric role of C was also discussed at the beginning of this section while the compensating effects of C in p-GaN are discussed in detail in the literature [86,94]. Similarly to Si and O, C can be controlled by modification of the growth process parameters down to ∼ 5 × 10 15 cm −3 .
The last impurity element to be discussed, H, is abundant in the MOCVD process as a result of the carrier gas mixture which contains H 2 (and N 2 ) and the cracking of NH 3  Mg-doped GaN growth would be beneficial in suppressing the formation of native defects (V N ) and at the same time enhance the Mg incorporation [95,96]. The formation energy of H + is similar but lower than the formation energy of V + N . Consequently, the E F at equilibrium, which is located near the point that the formation energy of Mg − Ga equals the formation energy of V + N , is shifted at a higher energy level, where the formation energy of Mg − Ga is lower. As a result, Mg incorporation is enhanced. An investigation based on this concept was done and is presented in Paper II (Ref. [97]) of this thesis.
Since the incorporated Mg is almost entirely passivated by H, a post-growth thermal annealing treatment is required to release the H and render electrically active Mg acceptors. Post-growth rapid or regular thermal annealing at temperatures between 750 − 900 • C under N 2 atmosphere is usually performed in order to activate the Mg in p-GaN. There are studies suggesting that different annealing temperatures are suitable for different Mg concentrations in p-GaN [98]. According to Liu et al., the process of Mg related donors transferring to non-radiative recombination centers is dominating over Mg acceptor activation in heavily doped p-GaN as the annealing temperature increases.
In the current study, we annealed the samples at 900 • C under N 2 atmosphere for 10 minutes to activate the Mg acceptors.

MOCVD process fundamentals
During the MOCVD process, precursors in vapor phase undergo chemical reactions leading to solid material deposition on the substrate. metal-organic (MO) precursors (group-III element sources) and ammonia (NH 3 ) (group-V element source) are used for the growth of III-nitride semiconductor materials. External energy in the form of heat is necessary for the precursors pyrolysis and the release of atomic species for reaction. As gaseous precursors are used for the MOCVD, the process relies on surface chemical reactions. MOCVD is a process with high complexity because, it incorporates gas flow dynamics, chemistry and thermodynamics, with numerous parameters being involved in the process [100]. Nevertheless, a simple description of MOCVD could be given by the main general steps, as depicted in Fig. 1.11: 1. Precursors in gas phase are transported to the growth zone.

2.
Gas-phase reactions of the precursors at the hot zone. Formation of reactive intermediates and by-products.
3. Mass transport (diffusion) of precursors and reactants through the boundary layer to the substrate surface.

4.
Surface reactions and adsorption of reactants on the surface .

5.
Surface diffusion of atoms to the growth sites.
6. Nucleation and surface reactions resulting in growth of solid material.
7. Surface desorption and mass transport of by-products away from the growth zone.
8. Non-reacted precursors and growth by-products are pumped out to the exhaust.

Gas flow and growth pressure
The MOCVD process is mainly controlled by the mass transport from gas phase to the substrate, thus, it follows the gas flow dynamics. For achieving high uniformity of the growth rate and of the solid material composition over the whole substrate, the growth process should be performed under laminar gas flow conditions. In such case, the gases flow in a parallel layer above the substrate surface with no formation of turbulent gas flow patterns.
The flow regime in a viscous system can be described by the Reynolds number (Re) Eq. 1.8, Eq. 1.9, is then defined as the gas layer for which the gas velocity is lower than u 0 as depicted in Fig. 1.12. Since the reactants must diffuse through the boundary layer to reach the substrate, the boundary layer thickness is a very important factor determining the growth rate. In a thin boundary layer, the reactants can easily diffuse to the substrate but their concentration in the boundary layer is quickly depleted at the downstream end of the deposition region [101].
For a homogeneous layer growth, a relatively thick boundary layer is needed. Therefore, controlling the thickness of the boundary layer can be achieved by adjusting the gas velocity, which practically means to adjust either the total gas flow or the pressure. In our process we mainly adjust pressure as the process parameter.
The MOCVD of III-nitrides is favored by a relatively low growth pressure (50 − 100 mbar) in several ways. Besides adjusting the boundary layer thickness as already mentioned, low pressure reduces the possibility of turbulent flow patterns formation, thus, minimizing the molecules interaction in the gas phase, which in turn means less parasitic reactions. This effect becomes more prominent in the III-nitrides growth process for semiconductor quality material where the growth temperature is high and the pre-reactions at the gas phase occur with higher rates. Nevertheless, the process pressure should not be very low either, because it 22 CHAPTER 1. PART I enhances the unintentional incorporation of impurities (mainly C) [102] which is detrimental for semiconductor quality materials.

Growth temperature
As mentioned earlier, an external energy source is needed to activate the reaction process for the precursor molecules. Energy in the form of heat is supplied to the system by increasing the temperature. The growth rate in this case is affected by the substrate temperature and can be divided in three different regimes relating the growth temperature with the major factor limiting the growth rate: i)low temperature regime where the surface kinetics become important and the growth rate is reaction rate limited, ii) medium-to-high temperature regime where the growth rate is mass transport limited and iii) high temperature regime where the thermodynamics become important and the growth rate is limited by parasitic reactions and decomposition [103].

i) Low temperature regime -kinetics limited
The growth rate in the low temperature regime increases exponentially with temperature, because it is limited by the reaction kinetics. In this regime, the rates of several thermally activated processes, like the gas phase reactions, diffusion of adatoms at the surface and nucleation, are greatly affected by small temperature variations. In this case, the slowest reaction is limiting the growth rate because it has the higher activation energy.
Consequently, the growth rate becomes very sensitive to small changes in temperature leading to unstable and non-reproducible material growth. It should also be noted that unintentional impurities incorporation is more pronounced when the growth of III-nitrides is performed in this regime.
ii) Medium-to-high temperature regime -mass transport limited In the medium temperature regime the growth rate is not affected by the temperature but only by the mass transport to the substrate surface, in other words to the diffusion rate of reactants through the boundary layer. Since the growth rate is proportional to the reactants flux (Eq. 1.10) in the mass transport limited regime, we can alter the precursor concentration or the boundary layer thickness in order to change the growth rate.
where J is the flux of reactants, P g and P s are the partial pressures of the III-group element in the gas phase and at the substrate surface respectively, D is the diffusion coefficient of the group-III element in the carrier gas and R is the gas constant. Except from the increase of precursor concentration in the gas phase, the flux J can be increased by reducing the boundary layer thickness or by increasing the diffusivity D. The Therefore, in our growth process we opt for a pressure range that allows for uniform and low impurity level depositions and we adjust the growth rate by the amount of precursor material introduced in the gas phase. iii) High temperature regime -thermodynamics limited In the high temperature growth regime, the growth rate is significantly reduced due to thermodynamic limitations. The driving force of growth, the supersaturation is decreased leading to increased desorption rate from the substrate surface. Several other processes related to the high temperature such as parasitic reactions in the gas phase (reduction of available reactants) and material decomposition due to increased vapor pressure of the solid material, lead to decrease of the growth rate.

Supersaturation
The MOCVD growth process relies on the minimization of the Gibbs free energy (G) in order to restore the vapor-solid system in equilibrium state. Eventually, the minimization of G 24 CHAPTER 1. PART I becomes the driving force for growth [104].
Initially, the system consisting of molecules in the gas and solid phase is brought to nonequilibrium conditions when temperature and pressure are changed. Under these conditions, the difference in chemical potential ∆µ, between the vapor and solid phases i. e. supersaturation (σ) is created, and must be consumed towards solid material growth. Increasing the process temperature, drives the system further away from the equilibrium condition and consequently increases the driving force for growth.
Considering the GaN growth by MOCVD, the solid growth is limited by the amount of growth species that diffuse through the boundary layer and reach the substrate surface, since the process is performed in the mass transport growth regime.
Eq. 1.12 defines the Ga supersaturation, where P 0 Ga is the input partial pressure of Ga species and P Ga is the equilibrium vapor pressure of Ga above GaN at the growth temperature.
For the calculation of P Ga , we consider the simplified chemical reaction taking place at the growing interface as: The equilibrium constant for the reaction in Eq. 1.13 is given by: where α GaN is the activity of GaN, P H 2 is the partial pressure of H 2 and P NH 3 is the partial pressure of NH 3 . The equilibrium constant (Eq. 1.14) is a function of temperature as given by: For the determination of the partial pressures P H 2 and P NH 3 , we should consider the total pressure in the system during GaN growth: where the P IG refers to the partial pressure of the inert gas, in our case N 2 . Since N 2 does not take part in the growth (or etching) process it is removed from Eq. 1. 16. In addition, the SECTION 1.3. MOCVD growth of Mg-doped GaN and AlGaN/GaN HEMTs 25 molar fraction of the diluent gas that gets involved in the growth reaction is given by: where P 0 H 2 and P 0 N 2 are the input partial pressures of the carrier gases, H 2 and N 2 . Furthermore, the cracking efficiency of NH 3 should be taken into account, with an adjustable parameter b added in Eq. 1.18 to account for it.
The reduced total pressure for GaN growth at the growing surface can be written as: Taking into account the molar conservation between the input partial pressure and the equilibrium partial pressure of Ga and NH 3 and the Eq. 1.19, the P Ga can be calculated and consequently, the supersaturation σ.
The Ga supersaturation in the GaN MOCVD for this thesis is calculated following the above mentioned steps as in Mita et al. [104]. Ga supersaturation is an easy-to-handle parameter containing information about the growth parameters in practice, and can simplify the understanding on the highly complex process of MOCVD growth. Nevertheless, other parameters should be always taken into account (e.g. the dopant/Ga precursor molecules ratio) in order to describe and/or predict the MOCVD process outcome. The C levels for instance, in Mg-doped GaN show linear increase with Ga-supersaturation. This effect can be related to either the growth temperature variation, or the amount of MO precursors in gas phase.

Hot-wall MOCVD concept
Hot-wall MOCVD is a unique modification of MOCVD reactor. State-of-the-art SiC [105,106] and group-III nitride materials [55,107,108] were demonstrated by hot-wall MOCVD in recent years. Hot-wall MOCVD is capable of delivering material at industry-relevant growth rates while maintaining the superior material purity and structural quality. A simplified schematic of a horizontal gas flow hot-wall MOCVD system is shown in Fig. 1.14. In such system, the carrier gases and the precursors in gas phase are delivered to the system and transported to the hot zone where the substrate is located. In the high temperature environment, the precursors react to form epitaxial layers on the heated substrate. The by-products and exhaust gases are pumped out of the chamber and pass through a filtering system 26 CHAPTER 1. PART I (scrubber) to be neutralized before releasing environmental friendly gases to the atmosphere.
The pressure during growth is controlled and maintained by the pumping system. The main difference between a hot wall and a cold wall MOCVD system is the way that the substrate is heated. Fig. 1.15 shows a schematic representation of the hot zone of the hot-wall MOCVD reactor used in this work (VP508GFR, Aixtron). The system has a capacity of 1 × 4 or 1 × 3 or 3 × 2 wafers depending on the satellite used. Heat is provided by current induction in the graphite susceptor parts which form a pocket environment around the substrate. The induction currents are formed by a coil wrapped around the quartz tube chamber when is operated at RF. The system can easily reach temperatures over 1400 • C. All the graphite susceptor parts are coated with tantalum carbide (TaC) which protects the graphite against corrosion under the harsh environment of NH 3 and its decomposition products at high temperature [109].
The substrate sits on the satellite which is placed on the satellite carrier. The satellite rotates during the growth using a gas-foil-rotation (GFR) system. The substrate rotation is very important for achieving uniform layers because it compensates for the reactants' depletion in the linear growth profile. Rotation is also important for maintaining the uniform temperature distribution on the satellite and consequently on the substrate.
The whole susceptor construction is surrounded by graphite foam which is used as thermal insulator to maintain the susceptor temperature and protect the quartz tube from melting.
The susceptor temperature is continuously monitored and measured by a pyrometer. After the reaction in the hot zone, by-products and exhaust gases are pumped out of the chamber and pass through a particle filter and the scrubber system for neutralization before releasing 28 CHAPTER 1. PART I to the atmosphere. The scrubbing system consists of a burner and an acidic solution bath for NH 3 neutralization. A mechanical dry pump is used for regulating the process pressure which is in the range of 50 − 100 mbar. Background gases introduce impurities in the material which is detrimental for the electrical properties of semiconductors. Therefore, an additional turbo-molecular pump is used prior to growth process for reducing the background pressure in the chamber to low 10 −5 mbar.
In general, the hot-wall MOCVD concept used here provides several advantages compared to the commonly used cold wall MOCVD reactors where only the substrate is resistively heated. In the hot-wall reactor configuration the whole susceptor is heated creating a hot zone with much lower vertical and horizontal temperature gradients. Thus, the substrate bowing during growth and the related strain induced in the epilayers is minimized. The highly uniform temperature distribution also results in highly uniform epitaxial layers [108,110].
In addition, several examples of III-nitride materials with exceptional quality, relevant for application in high-power, high-linearity and high-frequency electronics [7,55,56,107,111,112] and quantum technology [113], as well as, development of high-quality N-polar III-nitride materials relevant for device applications [114][115][116] were developed in this hot-wall MOCVD reactor. The (-)/(+) sign in lattice mismatch denotes tensile/compressive strain in GaN epilayer.

Choice of substrate for III-N MOCVD epitaxy and nucleation layer
it renders the best quality epilayers in terms of dislocation density, because of the homoepitaxial growth. Additionally, GaN has high thermal conductivity, a crucial factor when designing devices for high power applications. AlN has even higher thermal conductivity compared to GaN and small lattice mismatch of ∼ 2.5% but the production of AlN substrates is still limited to 2-inch wafers with high cost. At the moment, the best alternative to combine high thermal conductivity and low lattice mismatch with GaN is SiC. Semi-insulating SiC substrates are available in large wafer size (8-inch) and although their cost is much higher than sapphire and Si, they are still cheaper than bulk GaN.
4H-SiC substrates were used for the development of p-GaN and HEMT structures growth process in this thesis. n-type 4H-SiC from Cree Inc. is used for GaN growth optimization and SI-4H-SiC from Norstel AB and SICC for Mg-doped GaN and HEMT structures development.
A high-temperature pre-treatment of the SiC substrates under H 2 environment is required to form a step-like surface morphology which promotes the step-flow growth of the III-nitride epilayers. After dicing, the chemical mechanical polished (CMP) SiC substrates are chemically cleaned for removing residual organic contaminants and particles. Before growth start of the epilayers, the high temperature pre-treatment is performed in order to remove any contaminants and the oxide formed on the SiC surface. During this process, the Si atoms are evaporated due to the high temperature and the C atoms react with the H 2 to form hydrocarbon gases, etching in this way the SiC surface [123]. If the evaporation rate of Si 30 CHAPTER 1. PART I atoms equals the C-to-hydrocarbon conversion rate, then a step-like surface morphology will be formed [124]. The step-flow etching is required to depress the defect formation on SiC surface upon preparation for epilayer growth [108].
A nucleation layer between SiC and GaN is required to accommodate the large lattice mismatch (∼ 3.5%) and to provide a 2-dimensional surface for GaN growth. Since AlN has ∼ 1% lattice mismatch with SiC, it serves as a useful transition layer reducing the mismatch hence, preparing the surface for GaN growth [125]. Direct growth of GaN on SiC results in non-continuous layers because of surface wetting problems [126,127]. AlN nucleation layer was grown in all the structures included in the thesis at a temperature of 1250 • C and V/III ratio ∼ 1260 with a growth rate of 0.33 − 0.36 µm/h. A thickness of ∼ 60 nm was enough for providing a good template for subsequent GaN growth.
All the structures in this thesis were grown on semi-insulating 4H-SiC substrates, following the in-situ substrate pre-treatment and the AlN nucleation layer growth steps as described above.

Epitaxy of Mg-doped GaN
The process of acquiring p-type GaN consists of two steps with important consideration to be taken into account: the epilayers growth conditions and the post-growth annealing conditions.
The AlN nucleation layer has high-density of threading dislocations, which originate from the strain relaxation in this layer when its thickness goes beyond the critical thickness.
The dislocations propagate in the subsequent GaN epilayer and their density reduces with increasing GaN thickness as moving away from the AlN/GaN interface. The density of edge-(a)-type or mixed-(a + c)type threading dislocations (TDs) is one order of magnitude higher than the screw-(c)-type TDs for GaN on SiC. In our study for p-type GaN growth, 1µm thick UID-GaN served as a buffer layer for the Mg-doped layer in the optimized structures.
The edge-and screw-type dislocation densities in these structures were ∼ 5 × 10 8 cm −2 and ∼ 2 × 10 7 cm −2 respectively. The buffer layer should be highly resistive to avoid current leakages.  130] atmosphere. Commonly, N 2 atmosphere is used for suppressing N dissociation from GaN at high temperatures (750 − 900 • C). In this study, we used both a conventional annealing method with annealing parameters 900 • C under N 2 atmosphere for 10 minutes, and RTA at 900 • C in order to activate the Mg acceptors. It should be mentioned that we observed p-type conductivity in the as-grown samples without the need to anneal which is a unique advantage of GaN:Mg growth by hot-wall MOCVD and the specific growth parameters used (Paper I and Paper II).

Epitaxy of AlGaN/GaN HEMTs
The growth process of HEMT structures consists of several different steps, each of them requires optimization in order to acquire the desired properties. The HEMT structures developed in this work can be split in three groups, according to their design and the target transport properties, with investigation on: A) the most basic AlGaN/GaN HEMT structure, Fig. 1.17 (a) and (b), B) graded AlGaN channel HEMT structures for high-linearity and low-noise RF applications, Fig. 1.17 (c), and C) high Al-content AlGaN/GaN HEMT structures for high-frequency applications Fig. 1.17 (d).
The transport properties of these type of structures are discussed in detail in section 1.2.3.
The role of all the layers above the AlN nucleation layer for each type of structure will be discussed here.

GaN buffer layer
The GaN buffer layer in a HEMT structure serves to provide atomically flat surface 32 CHAPTER 1. PART I of the channel region where the 2DEG is formed. Moreover, it reduces the threading dislocations density in order to minimize the current leakage paths (note that the threading dislocations intersect the 2DEG) while it also prevents the parallel conduction in the structure. For the latter, GaN buffer layers must be semi-insulating and this property can be achieved in various ways. As already mentioned, tuning of the growth conditions in MOCVD will render intrinsically semi-insulating GaN. Other ways to increase the resistivity of the GaN buffer layer is to intentionally dope it with acceptor impurities, most commonly C or Fe. C-doping may be realized by adjusting the growth conditions. As previously discussed, the residual C from the TMGa cracking can be incorporated in GaN if it is not transformed to CH4 gas. This process is highly related to the growth temperature and pressure as well as the flow of NH 3 . The available C for

AlN interlayer (carrier exclusion layer)
An AlN interlayer is grown between the channel and the AlGaN barrier layer. The reason for introducing this layer is to create an abrupt band discontinuity between the channel and the barrier, and to prevent the 2DEG wavefunction from penetrating the barrier layer. In this way, the alloy scattering is minimized as discussed in section 1.2.2 leading to higher mobility of the 2DEG. The thickness of the AlN interlayer is nominally ∼ 1.5 nm.
Samples from group-(A) were grown either with-or without AlN interlayer, for characterization of the transport properties by THz-OHE (Paper V). The AlN interlayer was shown to have no big effect on the mobility improvement in graded channel HEMTs (Paper IV) while for high Al-content barrier layers (x > 0.50), no AlN was formed, despite that it was nominally grown (Paper VI).

AlGaN barrier layer
The most important layer in a HEMT structure is the barrier layer because it defines the 2DEG properties which can be tuned by the Al-content and the thickness of the barrier. Higher Al-content in the AlGaN and larger barrier thickness lead to higher 2DEG density. Notably, all the barrier layers have to be grown pseudomorphically to GaN which can be verified by XRD reciprocal space map (RSM). Increasing the Al-content or/and the layer thickness could lead to plastic strain relaxation and cracking of the 34 CHAPTER 1. PART I layer. Additionally, local elastic relaxation would lead to reduced strain field in the barrier layer and reduction of the 2DEG density. For these reasons, the AlGaN barrier growth should be treated with special care. The Al-content can be adjusted by the TMAl precursor over the total amount of metal-organic precursor gas phase ratio: TMAl TMGa+TMAl but it is also sensitive to the growth temperature since higher temperatures facilitate Al incorporation, as well as to the growing surface. A combination of ultra-thin (sub-10 nm) and high Al-content (x > 0.50) AlGaN barrier layers, enables the rapid gate control and to maintain the high sheet electron density (see Fig. 1.6), respectively. The scaling down of the HEMT structure as such, allows for high-frequency operating devices [134][135][136][137].

GaN cap layer
The 2DEG transport properties are affected to a great extent by energy states in the near-surface area. As discussed before, the 2DEG density depends on the Al-content of the AlGaN barrier which directly affects the P PE . As the barrier layer is very thin (usually up to 30 nm), introducing a thin cap layer has a double role for the HEMT structure: a) to protect the barrier layer from oxidation and b) to prevent the strain relaxation of the barrier layer over time or due to thermal stress during the HEMT operation [138,139]. As a result, there is no deterioration of the AlGaN quality due to oxidation from the exposure to the environment. Additionally, the strain condition of the barrier layer is maintained, avoiding unwanted alteration in the P PE which would be detrimental for the 2DEG density. The cap layer may also increase the biaxial tensile stain in the barrier layer leading to additional increase of the 2DEG density. At a device level, the cap layer improves the electrical characteristics such as the breakdown voltage [138]. Furthermore, a cap layer on an AlGaN barrier could stabilize the surfacial composition of AlGaN by minimizing the peferential etching of Ga over Al atoms from this layer during the cooling down after growth process [140]. The most commonly used materials as HEMT cap layers are silicon nitride (Si 3 N 4 ) and GaN with thicknesses ranging from ∼ 2 to 10 nm [141][142][143]. All the samples included in the thesis had a 2 − 3 nm GaN cap layer, except of the samples without AlN interlayer from group-(A).
Overall, investigation of the simplest AlGaN/GaN HEMT structure consisting of AlGaN barrier on GaN buffer-channel layer grown on AlN/SiC templates ( Fig. 1.17 (a), enabled the

Optical Microscopy
Optical microscopy is an efficient technique for getting quick feedback about the surface morphology and overall material quality of the samples. Imaging the sample using an optical microscope can reveal significant film non-uniformity, microscopic defects and any other microscopic surface features. Differential interference contrast microscopy defects (e.g. pits, etched points, surface pyramids) that help for the tuning of the growth process parameters in order to maintain the desired quality of epitaxial layers. An example of optical microscopy images from GaN layers grown on SiC substrate is given in Fig. 1.18.    (1.20) and the ratio between them is expressed as the ellipsometric data outcome:

Spectroscopic ellipsometry
For the determination of the ellipsometric parameters Ψ and ∆, the dielectric function ε and the thickness of each of the layers should be taken into account and modelled properly. The best fitting parameter values will determine the Ψ and ∆.
In case of optically anisotropic samples, conversion between s-and the p-polarized light happens when the light is reflected from the sample. In this case, the previously described method of standard ellipsometry, determining Ψ and ∆ is not sufficient to fully describe the optical response of the sample. In this case, generalized ellipsometry approach should be used where the polarization state of light is represented by the Stokes vectors: (1.23) The Mueller matrix elements values are obtained by the ellipsometric measurement and contain all the information about the optical properties and thickness of the studied thin films. Using the appropriate model, one can fit the experimental data and acquire the optical 40 CHAPTER 1. PART I constants and the thickness of each layer in a multi-layered structure. For optically in-plane isotropic samples, the off-diagonal elements of the Mueller matrix are equal to zero so, the matrix gets a more simplified form. In such case, the standard ellipsometry is sufficient for characterization of the sample. All the samples included in the current thesis are characterized using Mueller matrix ellipsometry, despite being optically isotropic, since any deviation from this behavior could only be identified using Mueller matrix ellipsometry.

Optical Hall effect
The OHE is an ellipsometry-based method which can be used for determination of the free charge carrier concentration, mobility and effective mass in conductive materials. The OHE describes the optical birefringence of conductive materials in the IR and THz frequency range.
The optical birefringence occurs due to the motion of free charge carriers in the material under the influence of the Lorentz force, upon exposure of the sample to a magnetic field.
This phenomenon is observed when the off-diagonal elements of the dielectric function tensor of the material are augmented by the magnetic field, which results in conversion between s-and p-polarized light upon reflection or transmission. The dielectric function tensor of conductive materials at the IR and THz range, when they are exposed to an external magnetic field is written as: where ε ∞ is the magnetic field-independent high frequency permittivity tensor, χ L is the lattice electric susceptibility tensor, and χ FCC−MO is the magneto-optic free charge carrier electric susceptibility tensor. The magneto-optic electric susceptibility tensor, χ FCC−MO is given by: where e is the unit charge and τ is the scattering time. Since the magnitude of the conversion among s-and p-polarized light due to the OHE strongly depends on the free charge carrier sheet density and mobility parameters, for samples with low sheet carrier density and mobility, the sensitivity of the OHE measurement is limited. A modification of the measurement method by adding a backside cavity with a highly reflective backside surface, cavity-enhanced OHE, enhances the OHE in HEMT structures, as a result of the formation of Fabri-Pérot oscillations within the sample-cavity system [146,147]. Cavity-enhanced THz OHE [148,149] was employed for the 2DEG properties characterization in our samples. The measurements were carried out at RT under a magnetic field a field of ±0.6 T, 45 • angle of incidence and an air gap of ≈ 100 µm between the sample substrate and the surface of the magnet. All the OHE measurements were performed with the in-house built THz ellipsometer and OHE instrument at the Terahertz Materials Analysis Center (THeMAC) [150].

High-resolution X-ray Diffraction
High-resolution X-ray diffraction (HR-XRD) is commonly used for the characterization of the structural properties of epitaxial layers. It provides information on lattice parameters, alloy composition, strain, defect densities in the layers etc. Since HR-XRD is a non-destructive and fast characterization method, it is extensively employed for the evaluation of the structural quality in III-nitrides.
The wavelength of x-rays is comparable to the interplanar spacing in crystals (few Å) thus, allowing the characterization of their crystallographic structure. The incident x-rays radiation undergoes elastic scattering upon interaction with the core electrons of the atoms giving rise to diffraction effects. The result of the interference of the scattered x-rays from the sample is a diffraction pattern. A peak of intensity in the diffraction pattern corresponds to constructive interference from a set of (hkl) lattice planes when the Bragg's law condition is fulfilled: where n is the diffraction order, λ is the x-rays wavelength, θ is the angle of incidence and d is the interplanar spacing between two adjacent planes, as illustrated in Fig. 1.22. Considering the wurtzite hexagonal crystal structure, the interplanar distance equation results in: with i = −(h + k).

Lattice parameters
For the lattice constants determination, 2θ − ω scans of at least one symmetric and one asymmetric peak must be measured. θ is the angle between the incident and the diffracted beam while, ω = θ is the angle of incidence for the x-rays. Finite layer thickness and heterogeneous strain are the main factors causing broadening of the 2θ − ω peaks. Using Eq. 1.29 and Eq. 1.30 for the measured θ of the symmetric peak, e. g. 0002, the c lattice parameter can be determined. Repeating these steps for an asymmetric peak, e. g. 1015, and using the already determined c lattice parameter, one can estimate the a parameter.
For the HR-XRD structural characterization of the samples discussed in the current thesis, a PANalytical Empyrean diffractometer was used. At the incident x-ray beam, a hybrid monochromator consisting of a parabolic x-ray mirror and a two-bounce Ge(220) crystals provided x-rays with wavelength λ = 1.5406 Å (CuKα 1 radiation) while, on the detector side, a symmetric three-bounce Ge(220) analyzer placed in front of a solid state detector (PIXcel 3D ) used in 0D-mode, provided a 2θ resolution of ∼ 0.003 • (∼ 11 arcsec). For the Mg-doped GaN samples, the symmetric 0006 and asymmetric 1015 Bragg reflections were used to determine the c and a lattice parameters, respectively.
After the a and c lattice parameters determination, the in-plane and out-of-plane strain values xx and zz can be determined by Eq. 1.31, where α 0 and c 0 are the strain-free lattice parameters which can be obtained from the literature [21,151].
In the case of lattice parameters determination, a RSM of an asymmetric peak can be used instead of the single 2θ − ω scans, using Eq. 1.32: where Q x and Q z , the reciprocal lattice vectors in the in-plane and out-of-plane direction, respectively. A reciprocal space map consists of sequential 2θ − ω scans where the ω is varied by a small constant step for each scan. The measured data are then visualized using intensity contour plots. A lot of information can be extracted from the inensity, the position and the shape of the measured peak in a RSM, e. g. the lattice parameters, the crystalline quality, the alloy composition and the residual strain in the layer. RSM of the asymmetric 1015 and the symmetric 0004 peaks were measured for the Mg-doped GaN samples in order to identify effects related to the structural quality of the material after doping. The RSM of the asymmetric 1015 peak was extensively utilized for the average Al-content determination in the AlGaN/GaN structures (e. g. Fig. 1.23). Due to the limited thickness of the AlGaN barrier layers, the intensity was limited when using the symmetric three-bounce Ge(220) analyzer with open detector so, the analyzer was omitted and the detector was used in scanning line mode instead.

Dislocation density
The screw-and edge-type dislocation densities, N S and N E , were estimated by a commonly used method proposed by Srikant et al. [152,153]. In order to use this method it is necessary to determine the tilt, α S , and twist, α E , angles and use the values of the Burgers vectors along the cand a-axis, b c and b a , respectively.
The tilt angle, α S , can be determined from the slope of the Williamson-Hall plot (βsinθ/λ versus sinθ/λ) for the symmetric 0002, 0004, 0006 peaks of GaN [153]. Using α S and the magnitude of the Burgers vector along the c-axis (b c = 0.5185 nm) in Eq. 1.33, we estimate the screw-type dislocation density. For the estimation of edge dislocation density, the twist angle α E is obtained from the fitting of the plot of integral widths β of the rocking curves from the asymmetric 1011, 1012, 1013, 1014 1015, and 3032 peaks, versus the inclination angle X (the clockwise angle between the diffraction vector normal and the sample surface) [152]. The value for α S , obtained from the Williamson-Hall plot is used as input parameter to fit the data and obtain α E . The Burgers vector along the a-axis with a value of b a = 0.3189 nm is used for the estimation of N E .

Al composition in AlGaN
The Al-content (x) determination in Al x Ga 1−x N ternary alloys can be estimated from the lattice parameters of the respective layers [154]. The heteroepitaxial growth and the lattice mismatch between the GaN, AlGaN and AlN, result in large residual strain in the layers. Therefore, strain must be taken into account to avoid erroneous results. Under biaxial strain, ϵ xx = ϵ yy , the stress along the growth direction [0001], σ zz , is zero as the surface is free to expand or retract during growth or cooling down: and since the in-plane strain is ϵ xx = ϵ yy , the Eq. 1.34 can be rewritten as: where C 13 and C 33 are the elastic stiffness constants. For the measured lattice parameters, a(x) and c(x), the Eq. 1.35 is formed as: where α 0 (x), c 0 (x) and R B (x) are the relaxed lattice parameters and the biaxial relaxation coefficient, respectively, for AlGaN with Al-content x. C 13 (x) and C 33 (x) are the elastic stiffness constants of Al x Ga 1−x N.
According to Vegard's rule, it is assumed that there is a linear dependency of the lattice parameters and the elastic stiffness constants on the Al-content, from 0 to 100% for GaN and AlN respectively: Eq. 1.36 can then be re-written as Eq. 1.38 and the solution of this equation which lies in the range between 0 ≤ x ≤ 1 gives the Al-content of the alloy. After determination of the Al-content x, the relaxed lattice parameters α 0 (x), c 0 (x) and the strain can be determined by Eq. 1.37 and Eq. 1.31 respectively.

Mercury probe capacitance-voltage
Capacitance-Voltage (C-V) measurement is a non-destructive method for determining the net carrier concentration (donor or acceptor) in a semiconductor layer as a function of thickness.
The measurement requires the formation of two Schottky contacts which are realized by liquid mercury. The surface areas of the contacts differ a lot, with their diameters being 3 mm for the large and 0.7 mm for the small contact, respectively. The larger contact is set at forward bias and is considered as quasi-ohmic contact compared to the smaller Schottky contact. Thus, the free charge carriers below the Schottky contact can be depleted when the contact is reverse biased. In addition to the DC bias, a small sinusoidal AC voltage (∼ 100 mV) which is operating with frequency in the range of 100 Hz − 1 MHz is applied in order to change the width of the depletion layer. An LCR meter is measuring the depletion capacitance versus the bias voltage and from the measured data we can determine the net acceptor concentration (N A − N D ) in the semiconductor layer as a function of depth. The net doping concentration and the depletion depth are given by Eq. 1.39 and Eq. 1.40 respectively.

46
CHAPTER 1. PART I where q is the elementary charge, A is the Schottky contact area, C is the capacitance, x d is the depletion region depth and ε 0 and ε r is the vacuum permittivity and the dielectric constant of the semiconductor, respectively. The net doping concentration is estimated from the slope of the plotted C −2 − V curve using Eq. 1.39.
It should be noted that for relatively high Mg concentrations ∼ 10 19 cm −3 , the depletion layer becomes very thin and consequently the tunneling through this layer increases. The increased leakage current in the Schottky diode leads to erroneous capacitance data thus, the useful range for extracting the net acceptor concentration relies only on a narrow voltage range. can be estimated by the slope of the Eq. 1.42 plot for bias lower than the V p by assuming that the system resembles a parallel plate capacitor (Eq. 1.43).
In the equations above, q is the elementary charge, n or p is the carrier concentration, µ e or µ h is the mobility of either electrons or holes, t is the layer thickness and ρ is the resistivity.
The electrical properties of the samples studied in this thesis were characterized by Hall effect with either room temperature or temperature-dependent measurements. Ni/Au (5/250 nm) contacts were evaporated on the p-GaN and annealed at 450 • C in air in order to become ohmic, and the samples were measured in Van der Pauw configuration using a Linseis HCS 1 instrument.

Contactless measurements of electrical properties
Post where, P s is the absorbed power assuming no flux leakage phenomena, E T is the rms primary RF voltage, n is the number of primary turns on the ferrite core. σ, ρ and t is the semiconductor conductivity, resistivity and thickness respectively. By applying this method we can SECTION A single-carrier or multi-carrier model can be considered for determining the 2DEG transport properties either for a single type of carriers or a multi-carrier system. For the latter, the contribution of each carrier in the overall transport behavior is presented in terms of carrier density and mobility. Since the transport properties are extracted form fitting, defining as many parameters as possible to the algorithm will result in more accurate fitting outcome.
Therefore, the R s and the epilayer thickness are provided as input for the measurement. R s is measured by the contactless method described before while the thickness is measured by spectroscopic ellipsometry.

Poisson-Schrödinger simulations
The band diagram and the electron density in a HEMT structure can be given by the selfconsistent solutions of the Poisson and Schrödinger equations in one dimension. The electric CHAPTER 1. PART I potential and hence, the band bendings across the z-direction in the HEMT structure is given by the Poisson equation solution while the charge density distribution is given by the solution of the time-independent Schrödinger equation [158]. For the simulations in this thesis, the 1D Poisson numerical solver (version beta-8k) by Snider [37] was utilized. As input for the simulations, piece-wise linear approximations of the Al-profiles and relations for the x-dependent Al x Ga 1−x N properties [159][160][161][162][163][164][165][166]

Transmission electron microscopy
Transmission electron microscopy (TEM) is a powerful characterization technique which allows the visualization of the materials structure at the atomic level and in order to achieve such high resolution, the use of electrons is required. The basic setup of a TEM consists of the electron gun, electromagnetic lenses for beam control, beam apertures for coherency and imaging mode selection, and the detectors for imaging and spectroscopy. The electron gun emits electrons from the tip of a tungsten (W) wire by Schottky field-emission. A condenser system collects and focuses the beam on the electron optical axis. The electromagnetic objective lens focuses the image and together with the projection system the magnification is generated. The brightness and the electron dose are determined by the type of electron gun, the mode of the condenser system, and the apertures used. A very important aspect is that the electromagnetic lenses introduce electromagnetic abberation which must be minimized by abberation correctors (non-symmetrical lenses) in order to achieve atomically resolved imaging [167]. The sample must be transparent to electrons with thickness often less than instance, light elements which scatter electrons at smaller angles will give intensity contrast at the outer annulus of the the BF disk producing the annular bright-field image (ABF). In order to increase the compositional contrast and avoid the diffracted intensity, the collection angles should be increased (> 80 mrad) which gives the high angle annular dark-field (HAADF) imaging described by thermal diffuse Rutherford scattering. The intensity in HAADF image depends on sample density and thickness while the contrast is sensitive to the average atomic number-Z of the atoms in the atomic column [168,169]. A simplified schematic of a TEM setup is shown on Fig. 1.26.
The inelastic interaction of electrons with the sample enable the compositional analysis, with electron energy loss spectroscopy (EELS) and X-ray energy-dispersive spectroscopy (EDS) being the commonly used techniques [170]. The elemental composition and bonding information from the sample can be extracted by these techniques. For EELS, the energy loss of the primary electrons passing through the sample is measured and can be affected by several parameters like the sample thickness, the bonding states, and the elements present in the sample. On the other hand, in EDS, X-rays are generated from core electrons excitations during electron illumination of the sample. Since the emitted X-rays are characteristic for each element, the collected spectra allow for elemental identification (peaks appearance) and concentration

Summary of main results
One of the main foci of this thesis is the development of p-GaN growth by hot-wall MOCVD.
The goal is to achieve state-of-the-art Mg doping and activation in GaN in order to im- We have shown that the Mg concentration in the range ∼ 2.5 × 10 18 − 1.1 × 10 20 cm −3 scales linearly with the Mg-to-Ga precursor flux ratio but it is also affected to some extent by the Ga-supersaturation. [   We further focused our efforts on increasing the amount of non-passivated Mg acceptors in as-grown GaN:Mg below the threshold of PID formation by using high amounts of H 2 in the carrier gas mixture during growth. We have shown that using this approach one can increase by more than one order of magnitude the free hole concentration in as-grown GaN:Mg, e.g., from 7.6 × 10 15 to 8.6 × 10 16 cm −3 ) for material grown under 'regular' and high-H 2 growth environment, respectively (Paper II). The use of 1µm thick GaN buffer layer to reduce the dislocation density allows for further enhancement of free hole concentration in as- Reprinted from Ref. [97] which is an indication of a low channel/barrier interface roughness. The 2DEG density is found to increase with the Al-content, as expected, while the mobility is mostly decreasing for high Al content and the effective mass is generally higher compared to bulk GaN electron m eff for x < 0.42. The study revealed that the mobility decrease in HEMT structures with (0.13 < x < 0.42) is mainly driven by reduction of the 2DEG scattering time while the larger effective masses observed for x < 0.42 can be explained by the combined effects of electron wavefunction penetration into the AlGaN barrier, conduction band nonparabolicity and polaron enhancement (Paper V). These results presented a good basis for the next steps in realizing AlGaN/GaN HEMT structures with improved linearity and high-Al content AlGaN/GaN HEMTs needed for high-frequency applications.
In order to investigate the polarization doping in GaN for improved linearity AlGaN/GaN HEMTs, we explore the development of compositionally graded channel HEMTs in our hotwall MOCVD reactor. In Paper IV, we demonstrated different grading profiles (exponential, hybrid tanh-linear, and linear) of a 10-nm thick Al x Ga 1−x N channels from x = 0 to x = 0.1 in AlGaN/(Al)GaN HEMTs. We optimized the channel grading and the channel-to-barrier transition growth process through modification of the MOCVD process parameters and correlation with the resulting Al-profiles and interface sharpness, as determined from STEM combined with EDS. The channel properties (electron density, electron mobility, and sheet resistance) of the developed HEMT structures were then coupled with the electron density distribution obtained by Poisson-Schrödinger simulations. Our observations showed that Figure 1.30: Al content profiles across the graded channel and barrier layers obtained from EDS: cyan -S 1 (Exponential), black -S 2 (Hybrid linear-tanh) and red -S 3 (Linear). The inset shows a schematic of the graded channel HEMT structures. Reprinted from Ref. [56] the 2DEG/3DEG density, N s , in the samples with the different type of channel grading was similar, in the range of (8.1 − 10.5) × 10 12 cm −2 while, the incorporation of an AlN interlayer (high-Al content AlGaN) between the linearly graded channel and the barrier layer has only marginal effect on the 2DEG/3DEG properties (∼ 10% improvement in N S ) in contrast to conventional AlGaN/GaN HEMTs where significant improvement is observed (∼ 25% improvement both in N S and mobility). The alloy scattering is the main mobility-limiting mechanism in the optimized graded channel HEMT structure compared to the conventional one, 958 cm 2 /V.s and 2368 cm 2 /V.s, respectively. The N S is similarly high in both structures in the range of 9 × 10 12 cm −2 , owing to the similar thickness and Al-content of the barrier layer. More importantly, the transconductance g m of the graded channel HEMT is generally flatter over a wider range of gate bias with smaller g m and g m as compared to conventional AlGaN/GaN HEMTs, implying improved device linearity, a feature necessary for devices used in low-noise RF amplifiers. The first large signal measurements in Europe of a graded channel AlGaN/GaN HEMT has been carried out demonstrating improved linearity figure of merit IM 3 by 10 dB compared to conventional Fe-doped GaN buffer devices. These results are showing state-of-the-art performance and pave the way for novel highly linear GaN receivers.
We further explored the AlGaN/GaN heterostructure for high-frequency operation HEMTs. In this case, down-scaling of the device is required, implying a short gate length and a high gate length/gate-to-channel distance aspect ratio. In order to achieve that, we introduce ultra-thin and high Al-content AlGaN barrier layers in the conventional Al x Ga 1−x N/GaN  1.31). Additionally, the intended AlN interlayer between the GaN channel and the AlGaN barrier was not formed in any of the structures. The correlation of the measured 2DEG properties with simulations of the electron density distribution in combination with STEM imaging, shows that the severely altered from the intended design Al profiles (above ∼ 50%) has negative impact on the 2DEG properties. The extended penetration of the electron wavefunction into the barrier layer results in increased alloy scattering consequently limiting the 2DEG mobility. For example, for the intended AlN barrier structure the electron density is 8.8 × 10 12 cm −2 instead of the expected 2.9 × 10 13 cm −2 and the mobility value drops to 1268 cm 2 /V.s as compared to 1733 cm 2 /V.s for the HEMT structure with a box-like profile SECTION 1.6. Outlook 59 with x=0. 46. The observed deviations can be associated with the specifics of the MOCVD growth techniques and our results provide a good basis for further understanding of its potential limitations and optimization for implementation of AlGaN/GaN HEMT structures in high-frequency applications.

Outlook
It is exciting to see that despite the extensive research conducted in the area of III Nitride semiconductors over the last decades, there is still a lot of room for new topics exploration and improvement on ever-lasting issues. Further advances in the field are necessary to enable better exploitation of the unique properties if III-Nitrides. I thereby briefly give an outlook of how the results in this thesis may contribute to future developments in the field.
It is shown in this thesis that hot-wall MOCVD is capable for delivering p-type GaN-on-SiC with state-of-art free-hole concentration and mobility. From a technological aspect, the p-type GaN can be used as a gate material in normally-off HEMTs and a next step represents its implementation in the advanced HEMTs device concepts developed here. Additionally, based on the acquired knowledge of the effect of growth parameters variation on the material structural quality, the Mg-doping level and the incorporated impurities level, development of p-type GaN-on-GaN by adapting the growth conditions will provide material suitable for high-power devices such as p-n diodes. The reduction of dislocation densities upon homoepitaxial growth is expected to further improve material quality and consequently device reliability.
Taking advantage of the polarization doping in III-nitrides, it is possible to control the charge density distribution in the material without elemental doping. As such, HEMT structures with different types of compositional grading in the AlGaN channel layer were developed, proving the capabilities of MOCVD in this area. Very promising results were demonstrated on HEMTs with improved linearity, which is a necessary characteristic for devices intended for use in low-noise RF amplifiers. Further improvements under consideration are related to the correlation of device performance characteristics with respect to the channel thickness and type of grading, as well as the type of buffer layer used.
AlGaN/GaN HEMTs intended for high frequency operation, require aggressive device down-scaling which implies growth of ultra-thin and high-Al content barrier layers. Using MOCVD as the preferred method for large scale production for the development of such HEMT structures, poses limitations related to thickness, and most importantly, composition control in high-Al containing AlGaN layers grown on GaN. As shown in the thesis, Al 0.50 Ga 0.50 N layers can be grown with sharp box-like Al profile on GaN but, for higher Al-content the Al profile gets graded and the intended Al-content is not reached, which results in compromised 2DEG properties. In order to fully analyze the causal factors for this effect, a combination of extensive experimental work in combination with advanced character-60 CHAPTER 1. PART I ization techniques is required and it is worth exploring. New directions of implementing the proposed HEMTs device designs on different substrates such as AlN also present interest.

List of abbreviations
2DEG two-dimensional electron gas 2DHG two-dimensional hole gas 3DEG three-dimensional electron gas