Chapter 1: Introduction

Narita, T. and Kachi, T. (2020), “Introduction,” in Narita, T. and Kachi, T. (eds.), Characterization of Defects and Deep Levels for GaN Power Devices, Melville, New York: AIP Publishing, pp. 1-1–1-24

For some time now, the term “defect,” when applied to gallium nitride (GaN), has usually denoted a threading dislocation. This has been the case because GaN crystals were grown on substrates made of other materials (such as sapphire) in early research, and these materials had large lattice mismatches and significantly different thermal expansion coefficients compared to GaN. The development of low temperature aluminum nitride (LT-AlN) buffer layers by Amano et al.¹  later permitted the epitaxial growth of GaN and drastically reduced the threading dislocation density in GaN films. The subsequent development of Mg-doped GaN exhibiting p-type conduction based on hydrogen removal^2–4  and advances in technology for the epitaxial growth of InGaN alloys^5–8  paved the way for the fabrication of light emitting devices providing blue or violet light. However, even after the breakthrough associated with the fabrication of LT-AlN buffer layers, the threading dislocation densities in GaN remained in the range of 10⁸–10¹⁰ cm⁻².⁹  This areal density of dislocations did not sensitively affect the lifetimes of InGaN-based light emitting diodes (LEDs) but limited the lifetimes of laser diodes (LDs). Thus, there followed a prolonged period of time during which research was devoted to reducing threading dislocations in GaN. The application of the epitaxial lateral overgrowth (ELO or ELOG) technique using a SiO₂ mask was found to reduce the threading dislocation density in the overgrowth region to as low as 10⁸ cm⁻²,^10–13  which contributed to increases in the lifetime of LDs.^12 ,13  In addition, in the early 2000s, trials to control the propagation of dislocations using facets via the facet-initiated epitaxial lateral overgrowth (FIELO)¹⁴  or facet-controlled epitaxial lateral overgrowth (FACELO)^15 ,16  methods produced reductions in the densities of threading dislocations to below 10⁷ cm⁻². Karpov and Makarov demonstrated on a theoretical basis that a dislocation density as low as 10⁷ cm⁻² can saturate non-radiative recombination channels, resulting in high internal quantum efficiency in a light emitting device.¹⁷  This scenario is significantly different from the case of other group III–V materials that are sensitive to the threading dislocation density. Thus, efforts to reduce threading dislocation densities in InGaN-based LEDs had fortunately achieved a major milestone. In previous research, the full-width at half-maximum (FWHM) values obtained from x-ray rocking curves were used as indicators of crystal quality, while the propagation of threading dislocations was sometimes evaluated using transmission electron microscopy (TEM).^11 ,16  Etch pit measurements were also employed to estimate threading dislocation densities in epitaxial layers with threading dislocation densities below 10⁷ cm⁻².¹⁴ 

In addition to extended defects such as threading dislocations, point defects that generate deep levels in the bandgap of GaN have also been studied for some time now. The application of deep-level transient spectroscopy (DLTS) to the analysis of defects in GaN was first reported by Hacke et al. in 1994,¹⁸  and the origins of these defects have been examined based on comparing experimental data with calculated energy levels.¹⁹  Subsequent research primarily focused on distinguishing deep levels resulting from various defects, including vacancies, impurities, and threading dislocations.²⁰  Since GaN has various photoluminescence (PL) bands related to point defects involving impurities, the luminescence properties of this material have been investigated as indicators of deep levels.^21–26  Point defects have also been assessed with regard to their role in degrading the threshold current density of InGaN-based LDs with low threading dislocation densities.^27 ,28  In the case of lateral electron devices based on a two-dimensional electron gas (2DEG), such as high electron mobility transistors (HEMTs), point defects are thought to increase the dynamic on-state resistance during operation, called current collapse.^29–31  A lateral HEMT device often requires high resistivity in the buffer layer to suppress the leakage current between the source and the drain electrodes under a high drain bias, where carbon (C)^32 ,33  or iron (Fe) doping^34–37  was used to trap electrons into the deep levels. Thus, the study of deep levels has become increasingly important as a means of clarifying the degradation mechanism during the operation of such devices.

A vertical GaN power device potentially useful in applications requiring power switching in conjunction with a high blocking voltage and high current capacity [such as in an electric vehicle (EV)]³⁸  was first demonstrated by U. K. Mishra's group at University of California Santa Barbara. This device comprised a current aperture vertical electron transistor (CAVET). The first demonstration of this technology employed a quasi-vertical structure based on heteroepitaxial growth on a sapphire substrate.^39–41  Later, in 2007, fully vertical devices on freestanding GaN substrates were reported and showed good pinch-off characteristics,^42–44  but lower breakdown voltages than expected.⁴⁴  Owing to improvements in GaN substrates, epitaxial growth technology and fabrication processes, vertical p-n diodes exhibiting blocking voltages greater than 1 kV were first demonstrated in 2011,^45–48  followed by a report of a CAVET with a blocking voltage over 1 kV in 2014.⁴⁹ 

The authors believe that a GaN-based vertical power switching device will be more sensitive to both threading dislocations and point defects compared to optical or lateral electric devices for the following reasons.

1. The high current capacity of vertical GaN power devices necessitates a large active area in excess of 1 mm², which can contain 10⁴ threading dislocations as described above even when using a freestanding GaN substrate with a threading dislocation density of approximately 10⁶ cm⁻². In addition, an electric field is applied along with threading dislocations in a vertical device, which can produce the leakage pass through the junction. This is a different from a lateral device in which the electric field is perpendicular to the threading dislocations that are not across the active region between source and drain electrodes.

2. In the case of a high blocking voltage, the doping concentration in an n-type drift layer will be much lower than that in the active layer of an LED or LD. As an example, an effective donor concentration of (1–2) × 10¹⁶ cm³ is needed to obtain a 1 kV blocking voltage, as described in Sec. 1.2.1. The point defects concentration is not negligible compared with a carrier concentration, leading to the significant carrier compensation.

3. The processes used to fabricate power field-effect transistors (FETs), such as dry etching and ion implantation, tend to damage the device. Therefore, both extended and point defects can be introduced during processing and can subsequently affect the device performance.

Vertical GaN power devices have associated reliability issues, such as degradation during operation, and so it is important to understand the structural and electrical properties of defects. Advanced techniques for visually characterizing defects on the wafer scale are also required for devices having large active areas. For these reasons, the present text is organized around a discussion of point and extended defects as they relate to power device applications and introduces various advanced methods of defect characterization.

Many reports have summarized the physical properties of GaN, although the values provided for these properties sometimes differ. This variation is attributed to the use of specimens having high dislocation densities or elevated levels of residual impurities, or to the use of calculated rather than empirical values. Regardless, such variations can prevent precise evaluations of defect characteristics or limit the direct comparison of device performance between different studies. In this section, we reconsider the material properties reported for GaN on the basis of prior high quality experimental work.

Table 1.1 presents a summary of the physical properties of GaN. The wurtzite structure is the most stable for this compound, and the lattice parameters in this structure can be affected by the free electron concentration, the dopant, and the strain to which the crystal is subjected.⁵⁰  The degree of strain is most likely responsible for fluctuations in the physical properties of GaN because the seed crystals of experimental specimens are typically generated using heteroepitaxy on the other substrates. Darakchieva et al. precisely measured the lattice parameters of a strain-free GaN layer with a thickness of 2 mm and a threading dislocation density below 10⁻⁶ cm⁻² grown by hydride vapor phase epitaxy (HVPE) and obtained values of 3.18926 ± 0.0004 and 5.18523 ± 0.0002 Å for the a- and c-axes at room temperature (RT).^51 ,52  These values are almost equal to the means of the values reported for HVPE-grown thick GaN samples (a = 3.1890–3.1894 Å and c = 5.1849–5.1854 Å) based on the associated measurement errors.⁵¹  The sample examined by Darakchieva et al. exhibited a free electron concentration below 10¹⁷ cm⁻³; therefore, fluctuations in the lattice parameters as a result of residual donor impurities were negligible.⁵²  The lattice parameters reported by Darakchieva et al. are believed to be the most accurate since these values are in good agreement with those determined for a bulk GaN crystal grown using a basic ammonothermal method.^53 ,54 

In the case of a strained material, the extent of elastic deformation must be considered, and the ratio of the strains along the c- and a-axes follows the relationship $−2ν/(1−ν)$⁠, where ν is Poisson's ratio. The elastic stiffness constants, C_ij, for such materials are typically determined by Brillouin scattering^55–58  or x-ray diffraction (XRD),^59–62  and values for ν between 0.114 and 0.183^55–62  have been reported for hexagonal structures based on the relationship $−2ν/(1−ν)=(C12C33−C132)/(C11C33−C132)$⁠. Thermal expansion is also an important factor associated with heteroepitaxial growth. The thermal expansion coefficient of a material is affected by temperature, and this effect is often characterized based on the Debye temperature, Θ_D, or Einstein temperature, Θ_E. In the authors’ opinion, the reports of Reeber and Wang⁶³  and Roder et al.⁶⁴  are useful in this regard, because these studies established thermal expansion coefficients over a wide temperature range and are quite consistent with one another.

For GaN with a wurtzite structure, the valence band is split into A, B, and C subbands near the Γ point. The bandgap energy, E_g(T), is determined by the sum of the transition energy of the free-A-exciton and the binding energy. The transition energy, in turn, is significantly affected by the biaxial strain originating from heteroepitaxy.^65 ,66  Based on averaging various experimental values, Vurgaftman et al. obtained a transition energy of 3.484 eV and binding energy of 0.023 eV for the free-A-exciton, which equate to a bandgap energy of 3.507 eV at 0 K.⁶⁷  However, Shikanai et al. suggested that the strain-free value for the free-A-exciton is 3.478 eV,⁶⁶  which agrees with the PL data obtained from a strain-free HVPE-grown GaN specimen reported by Monemar et al.⁶⁸  Monemar determined a free-A-exciton binding energy of 0.025 eV based on the survival of the exciton peak in a PL spectrum at RT,⁶⁸  which is consistent with the study by Rodina et al.⁶⁹  Therefore, the authors recommend a value of E_g(0 K) = 3.503 eV, as shown in Table 1.1. In other work, the empirical relationship developed by Varshni⁷⁰  and the average of reported values were used by Vurgaftman et al. to calculate temperature coefficients of α = 0.909 meV/K and β = 830 K,⁶⁷  as indicated in the equation provided in Table 1.1, giving E_g (300 K) = 3.431 eV.

GaN with a wurtzite structure has an anisotropic static relative permittivity (that is, dielectric constant) $εS$⁠.⁷¹  The relative permittivity values parallel and perpendicular to the c-axis (⁠$εS||$ and $εS⊥$⁠) are reported to be within the ranges of 9.8–10.6^72–75  and 8.9–9.5,^61,72,73,75  respectively, which correspond to the results of first-principles calculations (⁠$εS||=10.34$ and $εS⊥=9.25$⁠).⁷¹  Based on this, the authors have used $εS||=10.4$⁷²  in recent studies to estimate the breakdown electric field in the vertical direction.^76 ,77  The high frequency relative permittivity of GaN, $ε∞$⁠, is also used for the analysis of Hall-effect mobility in this material, and experimentally derived $ε∞$ values have been reported to be within the range of 5.14–5.35,^{61 ,72 ,73 ,78}  with the exception of a result of $ε∞=4.5$ published by Logothetidis et al.⁷⁹  Yu et al. reported a relatively small difference between $ε∞||=5.31$ and $ε∞⊥=5.14$⁠,⁷⁸  although this anisotropy is ignored in Table 1.1. Look et al. obtained a value of $ϵ∞−1−ϵS−1=0.113$ based on a fitting analysis in association with a study of the Hall-effect mobility of electrons,⁸⁰  which gives a smaller $ε∞$ value of 4.44–4.58 for $εS⊥=8.9−9.5$⁠.

The effective electron or hole mass is an important parameter used to analyze transport property or to estimate the electron or hole capture cross section of a deep level. The experimentally determined values for the effective electron mass, m_e, have been within the range of 0.20–0.237m₀,^72 ,81–85  where m₀ is the static electron mass, although the value of 0.22m₀⁸²  in Table 1.1 appears to be most widely used. In fact, the temperature-dependent electron mobility values determined via Hall-effect measurements can be accurately reproduced using m_e = 0.22m₀.^86–89  Strictly speaking, there is a degree of anisotropy associated with this variable as well, although Perlin et al. noted that the difference between the parallel $(me||)$ and perpendicular $(me⊥)$ components must be minimal based on a lack measurable anisotropy in plasma frequency data.⁸²  Kasic et al. also suggested a small degree of anisotropy with values of $me||=(0.228±0.008)m0$ and $me⊥=(0.237±0.006)m0$ based on analyses by infrared spectroscopic ellipsometry (IRSE).⁸⁵  On this basis, anisotropy of this variable is neglected in Table 1.1.

The effective hole mass is more complicated because of the split of the A-, B-, and C-valence subbands and anisotropy effects. Consequently, the effective hole mass in GaN is usually derived via the calculation of an electronic energy band structure, while direct estimations based on experiments remain limited. Using first-principles calculations with a local density functional theory (DFT) approach, Suzuki et al. predicted significant anisotropy of the valence band near the Γ-point⁹⁰  and this was supported by more recent calculations^91 ,92  using the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional approach.^93 ,94  The majority of experimental trials have determined an isotopically averaged value, $mh,A$⁠, for the effective hole mass of the A-valence subband.^85 ,95–97  In addition, the effective hole mass determined based on PL data is associated with a hole-polaron effective mass⁹⁵  and so requires a correction of approximately 13%.^69 ,95  Average $mh,A$ values reported to date based on the polaron correction have varied widely, within the range of 0.52–2.2m₀.^85 ,96 ,97  Rodina et al. experimentally separated the parallel (⁠$mh,A||$⁠, $mh,B||,andmh,C||$⁠) and perpendicular (⁠$mh,A⊥$⁠, $mh,B⊥,andmh,C⊥$⁠) components of this variable⁶⁹  and obtained values relatively close to those predicted by HSE calculations, as summarized in Table 1.2.^91 ,92  The authors compared the results of calculations using various effective mass values with experimental temperature-dependent Hall-effect mobility data for a p-type GaN layer grown on a freestanding GaN substrate and obtained the best fit using $mh,A=1.7m0$⁠, assuming a Hall scattering factor of unity.⁹⁸  Based on this, it appears that the average m_hh value is likely within the range of 1–2.2m₀, although some uncertainty remains. In any case, it is more important to indicate which effective mass value is used in a study than to select any particular value.

The transport property of an electron device is characterized by the carrier mobility. At RT, electron mobility is primarily determined by phonon and ionized impurity scattering. At the low limit of the ionized impurity concentration, N_I, we can define a value referred to as the intrinsic electron mobility, $μe⊥$⁠. Figure 1.1 plots the electron mobility at RT in the c-plane as a function of N_d at RT, using N_d values obtained by fitting the temperature-dependent electron concentrations based on the charge neutrality condition.^87–89 ,99  These data were obtained from an n-type GaN layer with a threading dislocation density of at most 3 × 10⁷ cm⁻², such that the effect of the dislocation scattering was minimal.⁸⁸  Here, the solid line indicates the calculated electron mobilities at 300 K based on impurity and phonon scattering with N_a/N_d = 0.2 and without consideration of electron compensation, using m_e = 0.22m₀,⁸²  $εS⊥=9.5$⁷² , and $ε∞⊥=5.14$⁠.^61 ,78  The experimental values are seen to be positioned almost along this calculated line. These data demonstrate that the Hall-effect mobility approaches approximately 1300 cm² V⁻¹ s⁻¹ at the low limit of N_d, which indicates the intrinsic lateral mobility, $μe⊥$⁠, at 300 K assuming a Hall scattering factor of unity. The vertical mobility along with c-axis remains unclear. Based on the anisotropic components determined for m_e, $εS$⁠, and $ε∞$⁠,^72 ,78 ,85  $μe||$ could be 6% greater than $μe⊥$⁠. Kizilyalli et al. determined a vertical mobility of 1750 cm² V⁻¹ s⁻¹ at 298 K for a p-n diode with a 40-µm-thick drift layer, assuming a lack of conductivity modulation.¹⁰⁰  Because this value possibly includes the effect of extrinsic photon recycling,¹⁰¹  further experimental analyses of $μe||$ values are required. The intrinsic in-plane hole mobility, $μh⊥$⁠, was estimated to be 31 cm² V⁻¹ s⁻¹ at 300 K by Horita et al.,¹⁰²  while the vertical mobility of holes is presently unknown.

A power device is usually operated above RT, such that polar-optical-phonon scattering significantly limits the carrier mobility. Under these conditions, the mobility component due to polar-optical-phonon scattering is characterized by the longitudinal optical (LO) phonon energy, $Epop$⁠, as well as the Debye temperature $(TLO=Epop/kB)$⁠. The value of $Epop$ can be determined based on the energy spacing among LO phonon replicas for the exciton lines or the donor-acceptor pair (DAP) bands in a PL spectrum, and values of $Epop=91−92meV$ have been reported.^{26 ,68 ,72 ,95}  According to Xu et al., the variation of 1 meV among these data can likely be attributed to differences in the experimental temperatures.¹⁰³  Based on this, the authors recommend using $Epop=92meV$ as well as $TLO=1068K$ as the low temperature limit.¹⁰³ 

The electron saturation velocity, $νsat$⁠, is one indicator of the switching performance of a high frequency device, and the relationship $νsat≈Epop/mem0$ gives the expected value of 2.7 × 10⁷ cm/s when using the physical parameters in Table 1.1. Liberis et al. experimentally determined a value of ν_sat = 2.8 × 10⁷ cm/s at 290 kV/cm for a Si-doped n-type GaN layer.¹⁰⁴  However, the drift velocity is likely reduced by a factor of 1.5–2 as a result of the hot phonon effect in the 2DEG channel formed in an AlGaN/GaN heterostructure.^104–106  In Table 1.1, ν_sat = 2.8 × 10⁷ cm/s is provided as the most suitable value for bulk GaN.

The critical electric field E_crit is the most important value in terms of determining the breakdown voltage of a power device and is sometimes presented as an intrinsic value. However, the true physical values related to this parameter are the impact ionization coefficients for electrons and holes (α_n and α_p), both of which are greatly affected by the application of an electric field. The effect of an electric field on these coefficients can generally be expressed by Chynoweth's equation $α=aexp(−b/E)$⁠,¹⁰⁷  and Table 1.3 summarizes the reported values for the electric field dependence of each of α_n and α_p.^108–111  These data indicate that $αp$ is several times larger than $αn$ (at least below 3.3 MV/cm), and therefore the impact of ionization due to holes likely dominates the avalanche breakdown effect. The electric field dependences of $αp$ were consistent in reports by Cao et al.¹⁰⁹  and Maeda et al.,¹¹¹  whereas Baliga and Ji et al. suggested smaller values.^108 ,110  Figure 1.3 plots the reported breakdown electric field values, E_b, against the net doping concentration, N,^{76 ,111–115}  based on the values provided in Table 1.4, and it is important to compare these data. In the case of a punch-through (PT) type device, the drift layer is fully depleted at the breakdown voltage, and the maximum electric field for a PT design is, in principle, higher than that for a non-punch-through (NPT) unit such as that reported by Ozbek and Baliga.¹¹⁶  This is the case because the distance over which avalanche multiplication takes places is shorter in a PT design as compared to an NPT design. Thus, when examining the relationship between E_b and N as an intrinsic property of GaN, data acquired from PT designs^116–120  should be excluded. A second important point is that the assumed static relative permittivities, $εS||$⁠, are different among various researchers.

The net doping concentration, N, can be obtained from capacitance-voltage (C-V) analyses via the equation

where N_d and N_a are the donor and acceptor concentrations in a p-n junction, C is the junction capacitance, and A is the junction area. In addition, the breakdown electric field, E_b, can be expressed as

where V_d and V_b are the breakdown voltage and the build-in potential of the p-n junction. Therefore, assuming different values for $εS||$ will result in variations in the estimated values for both N and E_b. Here, we recalculated N and E_b values using the $εS||$ value of 10.4.⁷²  During this process, in the case that a paper did not provide a $εS||$ value, $εS||$ was estimated based on the relationship between V_b and E_b in the report. As indicated in Table 1.4, N′ and N are the original reported net donor concentration and the values recalculated using $εS||=10.4$⁠, respectively. The solid line in Fig. 1.2 shows the simulated E_b data based on the impact ionization coefficients determined by Maeda et al.,¹¹¹  and it is evident that the experimental data lie close to the simulated line. The maximum discrepancy of 10% can possibly be attributed to the error in estimating the area over which the C-V data were acquired, in-plane variations in the doping concentration, or fluctuations in the impact ionization coefficients throughout the low electric field region. Since the performance of a power device is proportional to $Ecrit3$⁠, more precise studies may be required in the future.

The control of conductivity via impurity doping using extrinsic sources is vital to the fabrication of power devices. Silicon (Si), germanium (Ge), and oxygen atoms (O) can all act as shallow donors in GaN, although O doping is typically avoided because it can lead to lattice expansion, significant visible light absorption,¹²¹  and the formation of point defect complexes.¹²²  Figure 1.3 plots the resistivity of GaN as a function of the Si and/or Ge doping concentrations.^{89 ,123–127}  The conductivity of Si- and Ge-doped GaN layers is seen to perfectly match the line conforming to $ρ=1.247×1012Ndoping−0.7675$ over a wide doping range. This result confirms that both Si and Ge can function as good shallow donors for GaN. It should be noted, however, that this equation is simply used for the purpose of fitting the data, and resistivity is more properly expressed as $ρ=1/qnμ$⁠, where n is the carrier concentration. The conduction mechanism in this concentration range is different from that in the doping range, where the ionization energy, ΔE_d, plays a key role, and Table 1.5 plots ΔE_d values for a Si-donor as a function of N_d.¹²⁸  Si atoms on Ga sites (Si_Ga) can function as shallow donors and are 92% ionized in the case of N_d = 10¹⁶ cm⁻³ at 300 K. In the case of an N_d less than approximately 2 × 10¹⁷ cm⁻³, the conduction mechanism is based on a scattering mechanism in a non-degenerated semiconductor.^88 ,89  The equation for ΔE_d also indicates that the ionization energy reaches zero at $Nd~1.3×1018cm−3$⁠,⁸⁹  which is in good agreement with a report by Wolos et al.¹²⁹  Above this N_d value, Si-doped GaN can be treated as a degenerated semiconductor exhibiting conduction.¹³⁰  In the intermediate doping range (on the order of 5 × 10¹⁷ cm⁻³), hopping conduction occurs parallel with conduction band transport via electrons thermally excited from impurity bands.¹²⁹  In contrast, in the low doping regime around and below 10¹⁶ cm⁻³, carrier compensation resulting from acceptor-like deep levels significantly reduces the electron concentration and increases the resistance of the drift layer in a power device, although this effect is not obvious in Fig. 1.3 because a log scale has been applied. This issue is discussed in more detail in Chapter 3. In contrast, a high degree of n-type doping is needed for the substrate in a vertical power device. The thickness of commercial freestanding GaN substrates is typically in the range of 0.3–0.5 mm. For a 1 kV class vertical GaN device, the target on-state resistance is on the order of 1 mΩ cm²;⁴²  therefore, the contribution of the substrate resistance should be less than 10%. Figure 1.3 indicates that a substrate thickness of 0.3 mm associated with doping above 10¹⁹ cm⁻³ meets the target, although various technical issues arise at such high doping levels, as discussed later in this section.

It is well known that p-type doping is quite different from n-type doping. Magnesium (Mg) atoms act only as shallow acceptors in GaN, but the associated ionization energy is relatively high at $245±25meV$ at the low limit of N_a,¹³¹  such that the free hole concentration in a Mg-doped p-type GaN layer will be low. The N_a range over which degeneracy occurs is expected to be above 10²⁰ cm⁻³,¹³¹  but high Mg doping (more than 2 × 10¹⁹ cm⁻³) significantly reduces the hole concentration.^132–135  Consequently, it becomes difficult to form a p-type ohmic contact with low resistivity. The reduction of free holes in the high doping regime is related to defect formation, as discussed in Chapter 4. In addition, as indicated in Table 1.1, the intrinsic hole mobility is approximately 42 times lower than that in n-type GaN; therefore, an electronic device using holes as the majority carrier is impractical. In the case of a unipolar power device using electrons, the space charges generated via Mg acceptors (rather than free holes) are used to control the electric field distribution and the threshold voltage in a FET. This p-type layer does not necessarily require a high free hole concentration but does necessitate the precise control of N_a, so that the carrier compensation resulting from donor-like deep levels provides an effective acceptor concentration. Chapter 3 provides further focus on the appearance of deep levels in p-type layers.

Impurity doping affects not only conductivity but also other material properties. Specifically, thermal conductivity, κ, can be reduced by the presence of both threading dislocations and impurity scattering.¹³⁶  The film thickness also affects κ because of boundary scattering,¹³⁶  and so a wide range of thermal conductivity values has been reported.^{127 ,136–139}  In the case of undoped 1-mm-thick GaN layers with low threading dislocation densities (<10⁷ cm⁻²), the κ values at 300 K exceeded 250 W m⁻¹ K⁻¹.^136 ,138  In addition, the incorporation of O likely reduces thermal conductivity,¹³⁹  possibly due to the formation of complexes with vacancies.¹⁴⁰  Paskov et al. reported a gradual decrease in κ with increases in the Si concentration over the range of 1.6 × 10¹⁶ to 7 × 10¹⁸ cm⁻³ because of phonon-free-electron scattering,¹²⁴  while Oshima et al. found almost identical κ values (approximately 200 W m⁻¹ K⁻¹ at 300 K for an n of approximately 10¹⁹ cm⁻³) for Si-doped and Ge-doped GaN samples.¹²⁷  Moreover, thermal conductivity is reduced with increases in temperature due to increases in the scattering rate. Thus, when simulating the energy losses in a vertical GaN power device, it is important to consider that the κ value depends on the doping concentration, the sample thickness, the dislocation density, and the operational temperature.

Impurity doping affects the propagation of threading dislocations, and high levels of Si doping can induce tensile stress by interacting with threading edge dislocations in a process known as dislocation climb.^141 ,142  The tensile stress due to Si doping sometimes causes three-dimensional growth, whereas Ge doping provides an improved morphology because of a lower degree of stress.¹⁴²  This effect can possibly modify the threading dislocation density in the case that a thick GaN layer is grown on a foreign substrate. Oshima et al. found that the threading dislocation density increased with increases in the Si doping concentration, whereas the dislocation density was slightly decreased at higher Ge concentrations. This difference was ascribed to the smaller extent of lattice distortion involved with the location of a Ge atom at a Ga site (Ge_Ga) compared to substitution by Si.¹²⁷  Since a vertical GaN power device requires a highly conductive GaN substrate, the possibility of higher doping levels can be an advantage of Ge doping.

A radio frequency power device requires a high resistivity substrate, and this can be obtained by introducing impurities to compensate for carriers. Fe atoms are typically used for this purpose, with a doping limit of at least 10¹⁹ cm⁻³.³⁵  However, the ionization energy of Fe is in the range of 0.5–0.6 eV, resulting in insufficient resistivity values at elevated temperatures.^{36 ,143 ,144}  In addition, Fe atoms are likely to segregate on the growth surface, leading to unintentional incorporation into the upper epitaxial layer.¹⁴⁵  Fe atoms incorporated into the epitaxial layer have been shown to cause current collapse in a lateral device¹⁴⁶  and electron compensation in an n-type drift layer within a vertical GaN power device. C atoms in GaN have a greater ionization energy of 0.85–1 eV^{33 ,144 ,147}  compared to Fe, and so improve the high temperature resistivity. C doping leads to an abrupt depth profile without diffusion or segregation,³²  but a C-doped buffer layer can also serve as a source of current collapse in an HEMT.³¹  The deep levels formed by doping with Fe and C atoms in GaN are discussed in detail in Chapter 3. Finally, manganese (Mn) atoms in GaN tend to generate deep levels around the midgap, and so are more favorable candidates as dopants when attempting to produce a high-resistivity substrate.¹⁴⁴  Even so, the segregation and diffusion properties of Mn in GaN are still unclear even though these are important with regard to devices formed on doped layers.

This chapter discussed the history of the study of defects in GaN and reviewed the physical properties of this compound as determined experimentally. The information presented herein can be summarized as follows.

• Freestanding GaN substrates have been developed with applications in LDs, and means of lowering threading dislocation densities have been researched so as to prolong the lifetimes of these devices.

• Point defects are known to degrade the threshold current density in LDs. In addition, deep levels associated with impurities can act as sources of current collapse in lateral electronic devices.

• The high current capacity of vertical GaN power devices requires a large active area that can involve several threading dislocations at the current level of a freestanding GaN substrate. In addition, a point defect concentration is not negligible compared with a carrier concentration in an n-type drift layer in conjunction with a high blocking voltage. Accordingly, a vertical GaN power device is likely to be sensitive to the presence of defects.

• The intrinsic physical properties of GaN are provided in Table 1.1. However, at present, there remains some uncertainty concerning parameters such as the effective mass of holes and the degree of anisotropy in GaN. When reporting research results, it is more important to indicate the parameters used than to select specific values.

• The breakdown voltage and the breakdown field values are summarized in Fig. 1.2 and Table 1.4. As indicated by the data in Table 1.3, these values are affected by the doping concentration as a result of their relationship with the impact ionization coefficients.

• The doping properties of Si and Ge as shallow donors are very similar in terms of the effects of resistivity (Fig. 1.3) and thermal conductivity. However, greater doping can be advantageous in the case of Ge as a means of reducing the resistivity of a freestanding GaN substrate.

• Mg functions solely as a shallow acceptor in GaN but the ionization energy of this element is quite high, as can be seen in Table 1.5. Thus, it can be challenging to form a p-type ohmic contact having low resistivity.

• The ionization energies of the high resistivity dopants Fe, C, and Mn are summarized in Table 1.5, which also provides the applicable temperature ranges. The segregation and diffusion properties of impurities are also important in terms of avoiding the incorporation of dopants in the active layer.