Mg-doping and free-hole properties of hot-wall MOCVD GaN Open Access

Mg doping of GaN is essential for obtaining epitaxial layers with $p$-type conductivity for GaN-based devices such as light-emitting diodes (LEDs), normally-off high electron mobility transistors (HEMTs), and $p$-$n$ diodes. Metal-organic chemical vapor deposition (MOCVD) is the technique of choice to grow large-scale GaN-based device structures and $p$-type doping in MOCVD GaN:Mg with free-hole concentrations in the range of $1016$–$1018$ cm$−3$ has successfully been demonstrated.^1–3 

As-grown MOCVD Mg-doped GaN layers have limited or no $p$-type conductivity due to the formation of Mg–H complexes.⁴ Originating from the pyrolysis of hydrogen carrier gas and from the ammonia precursor cracking, atomic H is abundant in the MOCVD processes. The incorporated hydrogen must dissociate from the Mg–H complexes and out-diffuse to render GaN $p$-type, which requires post-growth treatment of the as-grown material.^5,6 The activation is typically achieved via ex situ rapid or regular thermal annealing under N$2$ atmosphere. Due to the large Mg acceptor ionization energy, the free-hole concentration at room temperature is much lower than the Mg doping concentration. For this reason, high Mg concentration should be incorporated in GaN to reduce the ionization energy.^1,7 However, above a certain level, typically in the low 10$19$ cm$−3$ range, a further increase in Mg concentration leads to a reduction in free-hole concentrations.^1,3,8 The latter is often associated with the formation of pyramidal inversion domains (PIDs).^2,9 It has been shown that Mg atoms segregate at the PID (0001) boundaries rendering Mg atoms electrically inactive.³ Other works have suggested that the nitrogen vacancy, V$N$⁠, and its complexes (e.g., Mg-V$N$⁠) play a role in the compensation of Mg acceptors at high dopant concentrations.^10,11 In addition, any donors, e.g., unintentional impurities such as Si and O or native defects such as Ga interstitials, will interfere negatively with the desired $p$-type conductivity. Notably, C is a major impurity in MOCVD due to the metal-organic precursor molecules cracking. The roles of C as a trap and compensation defect in GaN:Mg have been extensively discussed. Density functional theory calculations showed that C occupying Ga site is a shallow donor and it has the lowest formation energy for Fermi level positions close to the valence band maximum.¹² Experimentally, it was demonstrated that the C incorporation leads to an increased donor concentration and a reduction in hole mobility, which was attributed to a donor-like +1/0 state of C$N$⁠.³ Variation of growth conditions, such as V/III ratio, precursor, and gas flows, is expected to affect impurity incorporation and defect formation energies and, hence, their densities might influence the degree of passivation/compensation of Mg acceptors. Therefore, optimization and tuning of the growth process is explicitly necessary for acquiring low impurity and native defect levels in GaN:Mg. In addition, a characteristic delay in Mg incorporation relative to the onset of Cp2Mg precursor flow is common to MOCVD of Mg-doped GaN. Various measures including pre-flow of Cp2Mg to the reactor and purposeful design of the heat zone in the reactor¹³ have been adopted.

Continuous efforts in further improving $p$-type conductivity and free-hole properties, including both growth and post-growth acceptor activation, are undertaken to further the progress in GaN-based device performance.^3,14 Despite the numerous investigations, no study exists on the capability of hot-wall MOCVD to deliver high-quality GaN:Mg layers with $p$-type conductivity. Because of its concept and the range of high deposition temperatures (up to 1400–1600 $°$C) achievable, the hot-wall MOCVD has successfully complied to conditions required for deposition of epitaxial layers of Al(Ga)N of semiconductor quality^15,16 and reflected in demonstrating exciton luminescence in photoluminescence measurements¹⁷ and Mg-doped Al$0.85$Ga$0.15$N layers with low resistivity at room temperature.¹⁸ Recently, a room-temperature mobility above 2200 cm$2/Vs$ of two-dimensional electron gas (2DEG) AlGaN/GaN HEMT heterostructures,^19,20 a GaN$−$SiC hybrid material for high-frequency and power electronics,²¹ and state-of-the-art N-polar AlN epitaxial layers²² using hot-wall MOCVD have been demonstrated. The hot-wall MOCVD concept enables reduced temperature gradients in both vertical and horizontal directions. It further allows for independent control of the gas phase chemistry over the substrate and the growth species surface diffusion, which may be exploited to control defect formation and impurity incorporation in a wider growth window.

In this work, we report a systematic study of Mg-doped GaN epitaxial layers grown by hot-wall MOCVD. A detailed investigation of the effects of growth and doping conditions on the incorporation of Mg, H, and C impurities is presented and discussed in terms of Ga supersaturation. The results are evaluated in relation to extended defects, revealed by transmission electron microscopy as well as x-ray diffraction and surface morphology, and correlated with the electrical and free-hole properties of the GaN:Mg layers obtained by Hall-effect and capacitance–voltage measurements. As a result, a comprehensive picture of hot-wall MOCVD of GaN:Mg is established, demonstrating the capabilities of this technique to deliver state-of-the-art $p$-type GaN.

A hot-wall MOCVD reactor in horizontal configuration was utilized for the epitaxial growth of all layers. Chemical–mechanical polished 4H-SiC substrates with on-axis $(0001)$ orientation were used after wet chemical cleaning treatment. Before growth, the cleaned substrates were annealed and etched with hydrogen at 1340 $°$C in the MOCVD reactor. AlN nucleation layers (NLs) with a thickness of $∼50$ nm were grown at 1250 °C with a V/III ratio of 1258, followed by growth of 500 nm-thick Mg-doped GaN layers. The growth process was performed under a constant ammonia (NH$3$⁠) flow (2 l/min), a mixture of N$2$ and H$2$ as carrier gases, and a constant pressure of $100$ mbar. NH$3$⁠, trimethylaluminum (TMAl), trimethylgallium (TMGa), and bis(cyclopentadienyl)magnesium (Cp$2$Mg) were used as the N, Al, Ga, and Mg precursors, respectively. The growth conditions of the GaN:Mg layers are summarized in Table I. The unintentionally doped (UID) GaN reference sample and the Mg-doped GaN samples with Mg doping concentration ranging from $2.45×1018$ cm⁻³ up to $1.10×1020$ cm⁻³ are denoted as M$0$ and M$1$–M$9$⁠, respectively. Several sets of Mg-doped GaN layers were grown by systematically varying one of the following growth parameters: (i) Cp$2$Mg/TMGa ratio—samples M$1$–M$5$ grown under optimized conditions with low carrier gas flows, where the Cp$2$Mg/TMGa is varied between 0.033% and 0.5% and samples M$7$ and M$8$ grown with high carrier gas flows with Cp$2$Mg/TMG of 0.335% and 0.5%, respectively; (ii) V/III ratio—samples M$4$⁠, M$6$⁠, and M$7$ grown with Cp$2$Mg/TMGa of 0.335% and V/III ratios of 906, 1811, and 453, respectively; and (iii) growth temperature (⁠$Tg$⁠)—samples M$8$ and M$9$ with $Tg=1120°$C and $Tg=1040°$C, respectively. In addition, a sample, M$opt$ was grown on 1 $μ$m-thick undoped GaN using the conditions of M$3$⁠. The Mg acceptors were activated using optimized ex situ annealing process at 900 °C in N$2$ atmosphere in a rapid thermal processing equipment.

The Mg and the background impurity (H, C, Si, O) depth profiles in as-grown and annealed samples were measured by secondary ion mass spectroscopy (SIMS). The detection limit was $1×1016$ cm⁻³ for Mg, $1×1017$ cm⁻³ for H, (3–5)$×1015$ cm$−3$ for Si and O, and $1×1015$ cm⁻³ for C. The average concentrations for all the elements were estimated using the SIMSview program from EAG Labs.²³ The surface morphology of the layers was studied by atomic force microscopy (AFM) using a Veeco Dimension 3100 scanning probe microscope in tapping mode. Both $5×5μ$m$2$ and $80×80μ$m$2$ images were acquired. Spectroscopic ellipsometry measurements were performed on a J. A. Woollam RC$2$-XI ellipsometer in the ultraviolet-visible spectral range (0.7–$5.9$ eV) for the determination of the layer thicknesses. The crystalline quality of the layers was evaluated by high-resolution x-ray diffraction (HRXRD) using a PANalytical Empyrean diffractometer. A hybrid monochromator consisting of a parabolic x-ray mirror and a two-bounce Ge(⁠$220$⁠) crystal resulting in CuK$α1$ radiation with wavelength $λ$ = 1.540 597 4 Å at the incident x-ray beam and a symmetric three-bounce Ge(⁠$220$⁠) analyzer on the detector side was used. HRXRD $2θ−ω$ scans of the symmetric 0006 and the asymmetric $101¯5$ Bragg peaks were used for the determination of the $c$ and $a$ lattice parameters, respectively. The screw- and edge-type dislocation densities, $NS$ and $NE$⁠, were estimated using the tilt and twist angles, $αS$ and $αE$⁠, respectively,^24,25 and the lattice parameters of a bulk GaN,²⁶ 

The tilt angle was determined by the Williamson–Hall plots of the symmetric $0002$⁠, $0004$⁠, and $0006$ diffraction peaks of GaN,²⁵ and the magnitude of the Burger vector along the $c$-axis (⁠$bc=0.5185$ nm) was used for an estimation of the screw-type dislocation density. For the edge dislocation density estimation, a method is proposed by Srikant et al.,²⁴ where the full-width at half-maximum (FWHM) of the rocking curves from the asymmetric $101¯1$⁠, $101¯2$⁠, $101¯3$⁠, $101¯4$$101¯5$⁠, and $303¯2$ diffraction peaks and the Burger vector along the $a$-axis (⁠$ba=0.3189$ nm) are used.

The structural quality of selected samples was further assessed by transmission electron microscopy (TEM) using the double corrected Linköping FEI Titan$3$ 60-300 microscope, operated in scanning TEM (STEM) mode and 300 kV. Images were acquired using annular dark-field (ADF) and annular bright-field (ABF) detectors (collection angles $∼21$–200 and $∼4$–43 mrad, respectively), revealing both atomic number and strain contrast. Electron energy loss spectroscopy (EELS) thickness measurements were performed by acquisition using a Gatan GIF Quantum detector with $10$ ms exposure time, $0.25$ eV/channel dispersion (⁠$−50.0$ to $462.0$ eV), and convergence and collection angles of $22.0$ and $15.0$ mrad, respectively. Calculations were done in the embedded function in Gatan Digital Micrograph software. Samples were mechanically cut and mounted in Ti grids, followed by mechanical thinning and Ar-ion milling (Gatan PIPS Model 691). This produced two projection directions: $[11¯00]$ and $[112¯0]$⁠.

The free-hole concentration and mobility of the as-grown and annealed samples were determined by Hall-effect measurements performed at room temperature in Van der Pauw configuration using a Linseis HCS1 instrument. For this purpose, Ni/Au (⁠$5$ nm/$250$ nm) ohmic contacts were deposited by thermal evaporation and annealed at 450 °C in air. Note that the Hall-effect measurements of as-grown and annealed samples were performed on the same piece for a given growth condition. The effective dopant concentration $NA−ND$ in samples M$1$–M$8$ was extracted by capacitance–voltage (C–V) measurements, using a Hg-probe setup with a 4284A LCR meter from Agilent. The C–V data were acquired in series measurement mode in the 1–10 kHz frequency range.

The concentrations of Mg dopants, H and C impurity, the root mean square surface roughness, the density of screw and edge type dislocations, and the free-hole concentration in as-grown GaN and the free-hole concentration, mobility, and resistivity of the respective thermally activated GaN samples are summarized in Table II.

Figure 1 shows the Mg and H concentrations in the GaN:Mg layers as a function of the ratio between the dopant precursor and the TMGa in the gas phase, Cp$2$Mg/TMGa. As expected, Cp$2$Mg/TMGa has a significant effect on the Mg incorporation. For samples M$1$–M$5$ grown under optimized growth conditions of V/III ratio of 906 and growth rate of 0.60–0.70 $μm$/h, [Mg] increases linearly with Cp$2$Mg/TMGa. A maximum Mg concentration of $∼6.0×1019$ cm⁻³ at Cp$2$Mg/TMGa = 0.5% is reached. We deduce a dopant incorporation efficiency of 0.24 from the dependence of the atomic fraction of magnesium [Mg]/[Ga] in the lattice as a function of the Cp$2$/TMGa flux ratio in the vapor phase (see Fig. S1 in the supplementary material). The observed trends (Fig. 1 and Fig. S1 in the supplementary material) are consistent with the previously reported results for MOCVD GaN:Mg layers.^2,8,27,28 We note that the characteristic delay in Mg incorporation, typical for MOCVD processes, is also observed in our experiments. The abruptness of the Mg doping profile can be influenced by increasing the hydrogen carrier flow as reported elsewhere.²⁹ 

In order to explore the limitations in Mg incorporation levels, additional GaN:Mg layers, M$6$ - M$9$⁠, with the two highest Cp$2$Mg/TMGa ratios of 0.335% and 0.5% but with different V/III ratios, temperatures, and growth rates were prepared. Samples M$6$ and M$7$ were grown with the same Cp$2$Mg/TMGa ratio of $0.335%$ as for sample M$4$ but with twice as high V/III ratio of 1811 and reduced by half V/III ratio of 453, respectively. It can be noted that for a constant CpMg/TMGa ratio, the increase in the V/III ratio leads to $1.5$ times lower Mg concentration, bringing it below the threshold for PID formation (for details on PID, see Sec. III B). When the V/III is decreased to 453, a significant increase in [Mg] to 7.0$×1019$ cm$−3$ is observed (M$7$⁠). This is almost three times higher compared to the respective [Mg] in M$4$ with a V/III ratio of 906. Note that higher gas carrier flows of H$2=25$ and N$2=12$ l/min (Table I) were used for M$7$ but their ratio was kept the same as for the case of samples M$0$–M$6$⁠. A detailed study on the effects of carrier gas flows and composition is reported elsewhere.²⁹ In the next step, a GaN:Mg with the same growth parameters as for M$7$ but with a Cp$2$Mg/TMGa of 0.5% was grown (sample M$8$⁠) to investigate whether Mg incorporation can be further boosted by increasing Cp2Mg/TMGa at these specific growth conditions. Interestingly, [Mg] in M$8$ is found to be $6.7×1019$ cm⁻³, which is very similar to [Mg] in M$7$⁠. This indicates that at low V/III ratios a saturation of Mg incorporation is already reached at a Cp$2$Mg/TMGa of 0.335%. The lower V/III ratio is associated with a higher growth rate, which can shift the balance from Mg atom substitutionally replacing a Ga atom toward remaining as an adatom providing potential explanation for the observed Mg saturation. Finally, a GaN:Mg with a V/III ratio of 453, Cp$2$Mg/TMGa ratio of 0.5% but at a lower temperature of 1040 °C—M$9$ was grown (the rest of the samples were all grown at 1120 °C). This also led to a slightly different growth rate of 1.20 $μ$m/h compared to M$8$⁠. The lower growth temperature resulted in high Mg incorporation level in the range of $∼1×1020$ cm⁻³.

Within the medium-to-high Mg concentration range up to 2.4$×1019$ cm$−3$⁠, [H] follows closely [Mg] being slightly lower than the expected 1:1 ratio (see Fig. 1, Table II, and Fig. S2 in the supplementary material). Consequently, as-grown GaN:Mg exhibits $p$-type conductivity even before the annealing, as will be discussed later (see Sec. III C). The H levels in all GaN:Mg layers with [Mg] above $2.4×1019$ cm⁻³ are below $∼3×1019$ cm⁻³, being significantly lower than the respective [Mg] in agreement with earlier observations^1,2 (see Fig. 1 and Fig. S2 in the supplementary material).

Our results indicate that the Mg incorporation, as expected, is directly related to the Cp$2$Mg/TMGa ratio, more specifically to the Mg precursor flow in the reactor. In addition, V/III ratio, growth rate, growth temperature, and pressure are impacting the growth process and, hence, incorporation of impurities and formation of native defects. It has been demonstrated that for MOCVD growth the concept of supersaturation, which measures the deviation from the thermodynamic equilibrium, is suitable to evaluate the impact of growth conditions in their complexity.³⁰ Therefore, we present in Fig. 2 [Mg] as a function of the Ga supersaturation. The latter was calculated following Ref. 30 and the respective growth parameters in Table I. Notably, the supersaturation has a strong effect on the incorporated [Mg] for samples with a constant Cp$2$Mg/TMGa ratio. For instance, at Cp$2$Mg/TMGa of 0.335%, the decrease in supersaturation from 160 (M$4$⁠) to 79 (M$6$⁠) results in 65% decrease in [Mg] while increasing it to 184 (M$7$⁠) leads to a steep rise of [Mg] by 165%. When the Ga supersaturation for constant Cp$2$Mg/TMGa of 0.5% increased from $184$ (M$8$⁠) to $1000$ (M$9$⁠) [Mg] is increased by 65%. For the first case (M$4$⁠, M$6$⁠, and M$7$⁠), the increase in Ga supersaturation was achieved by varying the TMGa flow and by decreasing the growth temperature for the latter case (M$8$–M$9$⁠). The ratio F (the ratio of the input mole fraction of H$2$ to the total amount of the two carrier gases, H$2$ and N$2$⁠), which also strongly affects the supersaturation, is the same for all samples. These observations show that the Mg incorporation in GaN is a multi-dimensional process and the trends related to different growth parameters, e.g., V/III ratio, growth temperature, and carrier gas composition, can be assessed by taking into account only the Cp$2$Mg precursor flow and the Ga supersaturation. Clearly, Mg incorporation follows the same trend as Ga supersaturation, i.e., the available Ga species in the reaction. Since Mg atoms compete with Ga atoms for incorporation at the same lattice site, at a constant Ga supersaturation the balance of Mg/Ga atoms incorporation is shifted more toward the Mg side when the Cp$2$Mg precursor flow, i.e., the available Mg atoms in the reaction are increased.

O and Si impurity levels in our GaN:Mg layers were found to be at the SIMS detection limit of (3–5)$×1015$ cm$−3$ in all samples. Hence, only C from the unintentional impurities is further discussed in its potential role as a compensating donor and a trap affecting the free-hole properties. The respective C concentrations in the GaN:Mg films are presented in Fig. 3 as a function of Ga supersaturation. An overall linear increase in [C] with increasing Ga supersaturation is evident independently of whether the change in supersaturation is achieved via varying V/III ratio or growth temperature. The increase in [C] at constant supersaturation could be associated with an increase in the Cp$2$Mg/TMGa ratio.³¹ 

As can be seen from Table II, a small variation of the screw-type dislocations density upon increasing the Mg concentration is observed in the as-grown GaN:Mg layers. The $NS$ remains very similar to the value found in the undoped GaN layer. On the other hand, $NE$ increases from (5–6)$×108$ cm$−2$ to (7–9)$×108$ cm$−2$ for [Mg] $≥2.4×1019$ cm$−3$⁠. For comparison, in Mg doped InN layers, the edge dislocation density remains similar with increasing Mg, while screw dislocation density increases accompanied by a polarity inversion.³² 

STEM analysis was performed to provide further insight into the microstructure of the GaN:Mg layers. The results shown in Fig. 4 verify that extended defects are not generated in layers doped with Mg up to $1.6×1019$ cm⁻³ [Figs. 4(a) and 4(b)]. For [Mg] = $2.4×1019$ cm⁻³ (sample M$4$⁠), sporadic PID defects are present [Figs. 4(c) and 4(e)]. Incorporating more Mg (sample M$8$ with [Mg]=$6.7×1019$⁠) leads to a notable increase in PID density [Fig. 4(d)]. The average width of the PIDs in the latter case is estimated to be $5.4±0.9$ nm [Fig. 4(d)], in range with the previously reported values.^2,3 Polarity inversion inside the pyramids is confirmed by annular bright-field (ABF) STEM (see Fig. S3 in the supplementary material). STEM analysis further revealed segregation of Mg at the PID (⁠$0001$⁠) facet (Fig. S3 in the supplementary material) in concordance with earlier observations.^2,3 Additionally, our comprehensive EELS analysis reveals that Mg atoms are segregated not only at the (⁠$0001$⁠) planes of the PIDs, but they are also found at their inclined facets (further details on the EELS analysis will be reported elsewhere).

A crude estimate of the PID density results in a range between $1.9$ and $8.9×1016$ cm$−3$ by sampling different regions of M$8$ [Fig. 4(d)]. The extended range originates from a thickness measurement by EELS acquired in an adjacent region. An estimate of the number of Mg atoms associated with the PIDs can be obtained by following Narita et al.,^2,3 for calculating the Mg atoms bound to the top facet and adding the herein observed segregation of Mg to the side facets. Accordingly, [Mg] bound to the PIDs in M$8$ is estimated to be from $1.6×1019$ to $7.7×1019$ cm$−3$⁠. We expect the actual value to be on the higher end of the range since the PID density measurement was performed close to an edge where the measured thickness is on the lower end of our estimate. In comparison, the difference between [Mg] and [H] in this sample as measured by SIMS amounts to $5.3×1019$ cm$−3$ (Table II and Fig. S2 in the supplementary material). It is, therefore, inferred that the difference between [Mg] and [H] at doping levels above $2.4×1019$ cm$−3$ can be accounted for by Mg segregated at all the interfaces of the PIDs.

The presence of PIDs is also expected to affect the surface morphology, in particular, for the high-defect-density layers with [Mg] $≥2.4×1019$ cm$−3$⁠. The UID GaN and GaN:Mg layers M$0$–M$5$ grown with the optimal growth conditions exhibit step-flow growth mode and the terrace size is similar for the undoped and doped layers up to [Mg] of $6.1×1019$ cm$−3$ as can be seen from the $5×5μ$m$2$ micrographs in Fig. 5. The root-mean-square (RMS) roughness for M$0$–M$5$ is in the range of 0.15–0.26 nm. However, on a larger scale, changes in morphology could be observed already at moderate Mg concentrations. Figure 6 shows representative $80×80μ$m$2$ micrographs of selected samples. It is seen that already for Mg doping of $1.6×1019$ cm$−3$ (M$3$⁠) there is a slight increase in RMS as compared to M$1$⁠. The RMS of sample M$4$⁠, for which sporadic PIDs start to appear, is further increased by a factor of two (Fig. 6). With a further increase in Mg concentration, one can observe well defined hexagonal hillocks [Fig. 4(d)]. Their density and height is increasing with increasing [Mg], which is manifested in higher RMS surface roughness. This surface deterioration can be correlated with the enhanced PID density that takes place with increasing [Mg]. Previously, it was shown that for [Mg]  $≥1.0×1020$ cm⁻³ the formation of hexagonal hillocks and platelets can be associated with a polarity inversion to N-polar GaN.^33–35 Our results indicate that this is a gradual process that starts already at [Mg] = $2.4×1019$ cm⁻³ and is associated with the PID formation in the overall Ga-polar GaN. Note that this is not accompanied by any noticeable increase in screw dislocation densities as earlier suggested for the case of full polarity inversion in GaN³³ and experimentally observed for InN.³² For example, samples M$3$ and M$8$ have very similar $NS$ (Table II) while their PID density differs by orders of magnitude.

Figure 7 shows the net acceptor concentration $NA−ND$ and the free-hole concentrations in the annealed samples. The relative difference between Mg and H concentrations with respect to the total Mg concentration, ([Mg]–[H])/[Mg] in the as-grown GaN:Mg is plotted as a function of [Mg] in Fig. 8. Assuming that all H binds to the available Mg$Ga$⁠,³⁶ this fraction represents the total amount of Mg atoms not bound to H and it may include: (i) Mg$Ga$ acceptors not passivated by H and/or (ii) Mg incorporated at a different site in the GaN crystal lattice, e.g., Mg interstitial and Mg segregated on the PID facets. Two distinct behaviors of (⁠$NA−ND$⁠)/$p$ and ([Mg]–[H])/[Mg] can be discerned below and above [Mg] = $2.4×1019$ cm$−3$⁠, respectively.

Up to $2.4×1019$ cm$−3$⁠, the $NA−ND$ follows closely [Mg], indicating that Mg is incorporated as an acceptor within this doping range. A certain fraction between 4% and 21% of [Mg] remains non-passivated by H (Fig. 8 and Table II). Since all Mg atoms are incorporated as acceptors (Fig. 7), this result implies that [Mg]–[H])/[Mg] represents the fraction of Mg atoms of type (i), i.e., the isolated Mg$Ga$ acceptor not passivated by H.³⁷ As a result, as-grown GaN:Mg manifests a net $p$-type conductivity with free hole concentration in the low to high $1016$ cm$−3$ range (samples M$2$⁠, M$3$⁠, and M$6$⁠, see Table II). These findings are very interesting since they are contrasted with previous reports, where [H] is equal to or larger than^2,8 Mg and indicates the expanded opportunities offered by the hot-wall MOCVD concept. The higher the non-passivated Mg fraction, the higher the free-hole concentration in the as-grown GaN:Mg for this doping range. It has been shown theoretically that higher amounts of H during growth can be used to increase acceptor incorporation and decrease the density of compensating native defects via tuning the Fermi level position.³⁶ We speculate that the hot-wall environment may play a role in an enhanced dissociation of molecular hydrogen to atomic hydrogen, which is beneficial for $p$-type doping. Details on exploring carrier gas composition for increasing the non-passivated Mg acceptor and free-hole concentrations are presented elsewhere.²⁹ It is instructive to compare samples M$3$ and M$6$ with the same [Mg] but significantly different levels of non-passivated Mg of $1×1018$ cm$−3$ and $3×1018$ cm$−3$⁠, respectively. The comparison reveals that M$6$ having three times larger fraction of non-passivated Mg exhibits four times higher free-hole concentration before annealing with regard to M$3$⁠. Assuming ionization energy of 180–200 meV corresponding to N$A$ of $1×1018$ cm$−3$ and 3$×1018$ according to Ref. 7, the maximum free-hole concentrations in the as-grown M$3$ and M$6$ layers are expected to be in the mid and high $1016$ cm$−3$ range, respectively. The $p0$ values measured for M$3$ and M$6$ are lower indicating a certain degree of compensation. We recall that M$6$ is grown at a higher V/III ratio as compared to M$3$⁠, i.e., at lower supersaturation (Table I), and exhibits significantly lower levels of C (Table II and Fig. 3). Under the N-rich conditions, typically employed in MOCVD growth, C$Ga$ acting as a donor has the lowest formation energy in $p$-type GaN.¹² Although [C] is at least two orders of magnitude lower than the non-passivated isolated Mg acceptors ([Mg]–[H]), it is close to the observed free-hole concentrations in the as-grown layers and will interfere negatively with the $p$-type conductivity. This can explain the observed lower free-hole concentration before annealing in M$3$ as compared to M$6$⁠. After annealing, the free-hole concentration in M$6$ is also higher as compared with M$3$⁠, correlating with $NA−ND$⁠. In this case, $NA−ND$ is dominated by the thermally activated Mg acceptors resulting from the dissociation of H from the Mg–H complexes in the as-grown samples.

The increase in Mg concentration above $2.4×1019$ cm$−3$ leads to a decrease in $NA−ND$⁠, which becomes significantly lower than [Mg] (Fig. 7), consistent with previous reports.^2,8 The C–V measurements show that 72%–92% of the incorporated Mg atoms are not electrically active. This doping range corresponds to [H] $≪$ [Mg] in the as-grown samples as can be seen from Fig. 1 and Fig. S2 in the supplementary material and the respective fraction of Mg not bound to H is in the range of 74%–84% with no distinct dependence on [Mg] (Fig. 8). These results imply that the number of Mg atoms not binding to H in the as-grown layers could account to a large extent for the difference between the net acceptor and Mg concentrations in the respective samples after annealing. In other words, the fraction ([Mg]–[H])/[Mg] corresponds to scenario (ii) in which Mg incorporates at non-acceptor sites in the GaN crystal lattice.

This is reflected in a significant reduction of free-hole concentration in the annealed samples (Fig. 7). Note that the lower the $NA−ND$ (Fig. 7) the lower the free-hole concentration in the as-grown (Table II) and annealed (Fig. 7) samples. Our STEM analysis shows that the observed large fraction of electrically inactive Mg could potentially be explained by the estimated concentration of Mg segregated at the PIDs. However, the fraction of Mg not bound to H is very similar for samples M$5$⁠, M$7$⁠, and M$8$ (Fig. 8) while their $NA−ND$ differs significantly (Fig. 7). For example, sample M$5$ with an inactive Mg fraction of 84% has more than twice as high net acceptor concentration than M$8$ with 74% of inactive [Mg] non-bound to H, while the opposite could be expected. In fact, in M$5$⁠, the concentration of Mg–H complexes before annealing is $9.6×1018$ cm$−3$ (assuming all available H binds to Mg), which compares well with the $NA−ND$ of $1.7×1019$ cm$−3$ after annealing. This suggests that no significant concentrations of compensating donors, most notably V$N$ and its complexes with Mg, are generated. In samples M$7$ and M$8$⁠, the Mg–H levels before annealing are slightly higher as compared to M$5$⁠, while $NA−ND$ are significantly lower, i.e., (5–8)$×1018$ cm$−3$⁠, indicating that compensating defects are present in large densities. Both M$7$ and M$8$ are grown at a lower V/III ratio, which can explain an enhanced formation of V$N$ in this case. Our findings strongly suggest that compensating donors, likely V$N$ and its complexes with Mg are generated for highly Mg doped GaN grown at higher supersaturation and which play a significant role in the observed reduction of free-hole concentration (Fig. 7). The increase in [Mg] above $1×1020$ does not alter the fraction of non-passivated electrically inactive Mg. In this case, however, the high [C] levels of $3.1×1017$ cm$−3$⁠, due to the significantly lower growth temperature, lead to additional compensation and the GaN layer shows semi-insulating behavior.

It has been shown that by growing GaN:Mg on GaN substrates, with significantly lower density of dislocations, the free-hole concentration in the homoepitaxial layers can be significantly enhanced.³⁸ To reduce the dislocation density in our heteroepitaxial case, we grew M$opt$ consisting of a 550-nm-thick GaN:Mg layer on 1-$μ$m-thick undoped GaN buffer layer using the same growth conditions as for sample M$3$⁠. Both screw- and edge-type dislocation densities of M$opt$ show the lowest values of $1.6×107$ cm$−2$ and $4.3×108$ cm$−2$⁠, respectively, among all samples (Table II). $NS$ and $NE$ in GaN:Mg are likely to be even lower since the measured dislocation densities are averaged over the entire layer thickness. The free-hole concentration in the as-grown M$opt$ is increased more than twice as compared to the respective value in M$3$⁠. If a similar approach is employed for lower Mg doping levels, e.g., such as in M$2$⁠, free-hole concentrations in the low to mid $1017$ cm$−3$ range can be potentially achieved without the need of thermal activation. The free-hole concentration of $8.4×1017$ cm$−3$ and the resistivity of $0.77$ $Ω$ cm in the annealed sample are among the best results reported in the literature.^3,38 These results demonstrate that the hot-wall MOCVD capabilities can be expanded to deliver state-of-the art $p$-type GaN enabling development of power diodes and vertical transistors, and normally-off HEMTs, for example.

We have explored hot-wall MOCVD for the growth of Mg doped GaN. It is found that the efficiency of Mg dopant incorporation is similar to the earlier reported MOCVD results. A detailed study of growth and doping conditions’ impacts on the incorporation of Mg, H, and C is presented and the findings are discussed in terms of Ga supersaturation. Our results indicate that Ga supersaturation can be conveniently used as a universal parameter for the optimization of Mg incorporation and C reduction in MOCVD of GaN instead of multiple growth parameters independently used for the same purpose.

In the low doping range ([Mg] $≤2.4×1019$ cm$−3$⁠), a large fraction (up to 21%) of active Mg acceptors (not passivated by H) is evidenced in as-grown material, resulting in free-hole concentrations in the low-to-high $1016$ cm$−3$ range. Hence, hot-wall MOCVD addresses a practical challenge related to the realization of as-grown p-GaN without the need for ex situ post-growth annealing for Mg activation. These results provide an intriguing opportunity to exploit the technique for delivering lightly p-type doped material required in device heterostructures, e.g., vertical MOSFETs,³⁹ and simplifying the device fabrication process. In the annealed samples, $NA−ND$ is found to closely follow [Mg], indicating that all Mg atoms are incorporated as acceptors, where 96% are activated by thermal dissociation of H during post-growth annealing.

In the high doping range above $2.4×1019$ cm$−3$⁠, increased Mg leads to the generation of PIDs. It is shown that this can be correlated with the formation of hexagonal hillocks, the density and height of which increase with increasing [Mg]. This gradual surface morphology deterioration can be clearly observed in large-scale AFM imaging while on a smaller scale the morphology and surface roughness remain virtually unchanged. STEM analysis reveals segregation of Mg at the PIDs, sufficient to account for the observed amount of electrically inactive Mg not passivated by H. However, generation of V$N$ and its complexes with Mg$Ga$ need to be invoked to explain the considerably lower free-hole and net acceptor concentrations measured in the highly doped GaN:Mg grown at high supersaturation.

Under optimized growth conditions, high-quality GaN:Mg with a resistivity of 0.77 $Ω$ cm and a free-hole concentration of $8.4×1017$ cm$−3$ corresponding to Mg acceptor activation of 5.25% has been demonstrated. These results and the established comprehensive picture of GaN:Mg growth via hot-wall MOCVD substantiate the expanded capabilities of the technique to deliver state-of-the-art $p$-type GaN for the development of power diodes and transistors.

See the supplementary material for additional details about Mg and H incorporation in the studied layers as well as on the structure of the observed pyramidal defects as revealed by STEM.

This work is performed within the framework of the competence center for III-Nitride technology, C3NiT—Janzén supported by the Swedish Governmental Agency for Innovation Systems (VINNOVA) under the Competence Center Program Grant No. 2016-05190, Linköping University, Chalmers University of Technology, Ericsson, Epiluvac, FMV, Gotmic, Hexagem, Hitachi Energy, On Semiconductor, Saab, SweGaN, and UMS. We further acknowledge support from the Swedish Research Council VR under Award No. 2016-00889, Swedish Foundation for Strategic Research under Grant Nos. RIF14-055, RIF14-0074, and EM16-0024, and the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University, Faculty Grant SFO Mat LiU No. 2009-00971. The KAW Foundation is also acknowledged for support of the Linköping Electron Microscopy Laboratory.

The authors have no conflicts to disclose.

The data that support the findings of this study are available within the article and its supplementary material.