Self-compensation in Ge- and Si-doped Al0.3Ga0.7N has been investigated in terms of the formation of III vacancy and donor-vacancy complexes. Both Ge- and Si-doped AlGaN layers showed a compensation knee behavior with impurity compensation (low doping regime), compensation plateau (medium doping regime), and self-compensation (high doping regime). A maximum free carrier concentration of 4–5 × 1019 cm−3 was obtained by Ge doping, whereas Si doping resulted in only half of that value, ∼2 × 1019 cm−3. A DFT calculation with the grand canonical thermodynamics model was developed to support the hypothesis that the difference in self-compensation arises from the difference in the formation energies of the VIII-n•donor complexes relative to their onsite configurations. The model suggested that the VIII-2•donor and VIII-3•donor complexes were responsible for self-compensation for both Ge- and Si-doped AlGaN. However, a lower free carrier concentration in Si-doped samples was due to a high VIII-3•Si concentration, resulting from a lower energy of formation of VIII-3•Si.

Germanium (Ge) is known as a shallow donor in GaN that allows for free carrier concentrations exceeding 1020 cm−3.1–5 Kirste et al. proposed the possibility of plasmonic applications using heavily Ge-doped GaN with a carrier concentration of up to 2.4 × 1020 cm−3.5 They observed bandgap renormalization and band filling with the corresponding Moss–Burstein shift in Ge-doped GaN at low temperatures. This allowed for the observation of a bulk and surface plasma resonances, as confirmed by infrared ellipsometry, at 2.8 μm and 5 μm, respectively. Ajay et al. demonstrated the highest carrier concentration reported to date in Ge-doped GaN as 6.7 × 1020 cm−3.1 Unlike Si, which is the most commonly employed dopant for the III-nitrides, heavy Ge doping does not induce tensile stress and surface roughening.3 Gordon et al. have proposed by hybrid functional calculations that high carrier concentrations may also be possible in AlGaN by Ge doping.6 When the Al mole fraction is higher than 0.52, however, some models predict that Ge undergoes a DX transition where Ge is slightly displaced from the substitutional III-site. As Ge in the DX configuration no longer behaves as a shallow donor, the carrier concentration is expected to be significantly lower than the Ge concentration. This expected decrease in carrier concentration has been experimentally observed at Al mole fractions above 0.5 in Ge-doped AlGaN.7–9 

In addition, conductivity in Si-doped AlGaN is reduced when the Si concentration exceeds a certain maximum carrier concentration, i.e., Si doping shows “knee” behavior, arising from self-compensation. Harris et al. have identified VAl-n•Si complexes as the primary compensators in highly Si-doped AlN by density functional theory (DFT) calculations using hybrid exchange-correlation functionals.10 Their calculations indicated that the formation of VIII-n•Si with n = 2, 3 became more favorable in the self-compensation regime; thus, the Fermi level decreased with Si concentration, resulting in lower carrier concentrations. We have reported that the onset of self-compensation in Si-doped AlGaN depended on the chemical potentials in the growth environment.11 The formation energy of the compensating point defects was modified through chemical potential control (CPC), which in turn depended on the vapor supersaturation of the growth species. The supersaturation was varied by growth temperature and NH3 partial pressure. The highest conductivity reported in Si-doped Al0.7Ga0.3N of 160 S/cm with a carrier concentration of 3 × 1019 cm−3 was achieved under metal-rich conditions, which increased the formation energy of VIII-related point defects.11 Therefore, a better understanding of compensating point defects is necessary to achieve highly conductive AlGaN layers.

Although a decrease in carrier concentration with increasing Al mole fraction in Ge-doped AlxGa1−xN (x < 0.5) has been observed experimentally,7–9 i.e., below the composition leading to the DX transition, little is known about the nature of the compensation mechanism. In this study, self-compensation in heavily Ge-doped AlGaN is investigated. The electronic properties of Ge-doped AlGaN are compared with Si-doped samples as a way to contrast possible compensation mechanisms. Based on the Hall effect measurement and DFT calculations, we propose that electrically neutral VIII-3•donor and acceptor-type VIII-2•donor complexes are responsible for the observed self-compensation and that Ge is a better choice for highly conductive AlxGa1−xN layers (x < 0.5) due to a lower probability for VIII–3•Ge formation as compared to VIII–3•Si formation.

AlGaN layers were grown on AlN templates on c-plane sapphire substrates in a vertical, rf-heated, low-pressure MOCVD reactor equipped with an open showerhead. A sapphire substrate surface was exposed to H2 at 1100 °C for 7 min and annealed in NH3 ambient at 950 °C for 4 min. A 20-nm-thick AlN nucleation layer was deposited at 650 °C and annealed at 1050 °C for 15 min to obtain Al-polarity.12 A 300-nm-thick AlN template was grown on the nucleation layer at temperatures ranging from 1150 °C to 1250 °C. The reactor total pressure was kept constant at 20 Torr for all growth runs. Trimethylaluminum (TMA), triethylgallium (TEG), and NH3 were used as Al, Ga, and N precursors, respectively. GeH4 (1000 ppm in N2) and SiH4 (10 ppm in N2) were used as the Ge and Si dopant source, respectively. Subsequently, the 500-nm-thick n-type AlGaN layers were grown on top of 500-nm-thick unintentionally doped AlGaN layers at 1000 °C in H2 diluent gas with 1 slm NH3 flow rate for both dopant types and concentrations. X-ray diffraction measurements were carried out using a Philips X'Pert materials research diffractometer to determine the Al mole fraction in the AlGaN layers.13 Indium metal was employed as Ohmic contact for the Hall effect measurement in the Van der Pauw geometry. Room temperature photoluminescence (PL) was measured to characterize the optical properties of the AlGaN layers. Si and C concentrations were obtained from secondary ion mass spectroscopy (SIMS), while the Ge concentration was determined by comparing the electrical properties of Ge-doped AlGaN with ones of Si-doped AlGaN.

Since all of the AlGaN samples in this study were grown under the same growth conditions, except Ge and Si precursor flow rates, the difference in the VIII-donor induced compensation in Ge-doped and Si-doped AlGaN layers arose from the dopant type, i.e., formation energy of VIII-n•donor complex. A relatively high growth rate of ∼1.5 μm/h with high metalorganic flow rates and low growth temperature of 1000 °C enhances the formation of carbon impurities on nitrogen sites (CN),11 which are main acceptor-type compensators.14 However, these high supersaturation conditions were necessary to suppress the formation of VIII-n•donor complexes to obtain a high free carrier concentration, which was the purpose of this study.

The Al mole fraction targeted in this study was determined based on the following requirements: (1) Ge does not undergo the DX transition. Blasco et al. and Bagheri et al. have shown a steep increase in the Ge donor activation energy with increasing Al mole fraction above 0.5, resulting in an abrupt drop in the carrier concentration.8,9 Since the free carrier concentration is significantly reduced by the DX center formation in Ge-doped AlGaN in the above-mentioned studies,8,9 the Al mole fraction above 0.5 is undesirable to investigate the self-compensation. (2) When the Al mole fraction is lower than 0.24, the observed carrier concentration was similar to the Ge concentration in GaN.8 This observation suggests that self-compensation is not significant at low Al mole fractions. In contrast, more than one order of magnitude lower carrier concentration than Ge concentration in AlGaN at an Al mole fraction of 0.36 has been observed. Taking into account the Al mole fraction below the DX transition, the reduction of the free carrier concentration is considered to be a consequence of compensation. From these criteria, an Al mole fraction between 0.3 and 0.4 was employed in this study.

The electronic properties of Ge- and Si-doped AlGaN layers as a function of donor concentration are displayed in Fig. 1. Three different doping regimes were clearly observed in Ge-doped AlGaN in Fig. 1(a): low, middle, and high doping regimes. In the low doping regime ([Ge]<4 × 1019 cm−3), impurity compensation plays the main role and the electronic properties are determined by the acceptor-type impurities. From the SIMS measurement, the CN concentration was estimated to be ∼1 × 1019 cm−3. Due to the CN defects, the mobility collapse was also confirmed in this low doping regime in Fig. 1(a).15 For both Ge-doped and Si-doped samples, the mobility collapse is seen in Figs. 1(a) and 1(b) at ∼1 × 1019 cm−3, which corresponds to the C concentration. As the C concentration was identical in Ge-doped and Si-doped samples, the mobility collapse (or sharp decrease in carrier concentration) occurred at the same donor concentration, ∼1–2 × 1019 cm−3. As the Si concentration was known from the SIMS measurements, the Ge concentration was estimated by observing the mobility collapse in the low doping regime. In addition, threading dislocations also act as carrier compensators in this regime. As suggested by Kyle et al., threading dislocations introduce acceptor-type charge trap states in n-type GaN.16 The threading dislocations can be compensators with one acceptor charge per c-lattice constant. This translates into acceptor-type trap density of low 1017 cm−3 in our AlGaN layers.11 By comparing the compensation levels between CN (∼1 × 1019 cm−3) and threading dislocations (low 1017 cm−3), the main compensator in the low doping regime is attributed to the CN defect.

FIG. 1.

Free carrier concentration and Hall mobility in (a) Ge-doped and (b) Si-doped AlGaN as a function of donor (Ge and Si) concentration. Both Ge-doped and Si-doped AlGaN layers exhibit a decrease in carrier concentration with increasing donor concentration (self-compensation) in the high doping regime.

FIG. 1.

Free carrier concentration and Hall mobility in (a) Ge-doped and (b) Si-doped AlGaN as a function of donor (Ge and Si) concentration. Both Ge-doped and Si-doped AlGaN layers exhibit a decrease in carrier concentration with increasing donor concentration (self-compensation) in the high doping regime.

Close modal

In the middle doping regime, a linear increase in the carrier concentration was observed as a function of Ge concentration. As the Ge concentration increased from 1 × 1020 cm−3 to 2 × 1020 cm−3, the carrier concentration remained relatively constant at 4–5 × 1019 cm−3, indicating the onset of self-compensation. With a further increase in the Ge concentration in the high doping regime, the carrier concentration exhibited an abrupt drop due to self-compensation ([Ge]>2 × 1020 cm−3). The carrier concentration sharply decreased from 4 × 1019 cm−3 to 3 × 1018 cm−3, while the Ge concentration increased from 2 × 1020 cm−3 to 4 × 1020 cm−3. As seen in Fig. 1(a), Hall mobility also decreased in this regime, indicating a high concentration of carrier scattering centers. Si-doped AlGaN samples in Fig. 1(b) also exhibited a similar behavior in different doping regimes. Here, complexes between the cation vacancy (VIII) and donor were found responsible for compensation.11 

One may claim that the secondary phase such as GexNy layer could be formed due to the heavy Ge doping when exceeding the solubility limit of Ge.4,17 However, Ge-doped samples used in this study did not exhibit any significant change in their properties with increasing Ge doping concentration. Although Ge-doped samples showed a high density of hexagonal pits, the surface morphology (not shown) did not change at a Ge concentration from ∼7 × 1019 cm−3 (maximum carrier concentration) to ∼2 × 1020 cm−3 (highest Ge concentration in this work), suggesting that the crystallographic symmetry maintained in this Ge concentration range. PL spectra also confirmed no abrupt change in the optical properties by high Ge doping. Furthermore, electrical properties in Fig. 1 were continuously changed with the Ge concentration, as observed in Si-doped samples. The results indicate that the Ge concentration up to ∼2 × 1020 cm−3 did not result in the secondary phase formation in our AlGaN samples.

Compensation mechanisms due to the CN and threading dislocations in the low doping regime depend on growth parameters and can be assumed to be the same for both dopants under the same growth conditions. The behavior of the two dopant in AlGaN is displayed in Fig. 2. For Ge-doped AlGaN, the maximum achieved carrier concentration was 4–5 × 1019 cm−3, which was more than twice as high as for Si-doped samples (2 × 1019 cm−3). For both dopants, the carrier concentrations strongly decreased beyond the maximum carrier concentration. The beginning of the self-compensation in Si-doped samples corresponded to the carrier concentration of ∼2 × 1019 cm−3 at [Si] ∼6 × 1019 cm−3, while the carrier concentration in Ge-doped AlGaN increased up to ∼5 × 1019 cm−3 at [Ge] ∼1.4 × 1020 cm−3. In addition, a high pit density of ∼1010 cm−2 was observed on Si-doped AlGaN surface with the Si concentration for the maximum carrier concentration (∼2 × 1019 cm−3), while the pit density was relatively low at low 109 cm−2 in Ge-doped samples at a carrier concentration of ∼4 × 1019 cm−3.

FIG. 2.

Carrier concentration in Al0.3Ga0.7N as a function of donor concentration ([Ge] or [Si]). The black dashed line indicates a linear relationship between donor and carrier concentrations.

FIG. 2.

Carrier concentration in Al0.3Ga0.7N as a function of donor concentration ([Ge] or [Si]). The black dashed line indicates a linear relationship between donor and carrier concentrations.

Close modal

Since the [CN] and dislocation density were the same for both sets of samples, there must be a difference in the formation of the related VIII–n•donor complexes between the two different donors. As such, the following hypothesis can be formulated: the difference in self-compensation arises from the difference in the formation energies of the VIII+n•donor complexes relative to their onsite configurations, i.e., VIII–n•Ge or VIII–n•Si vs substitutional GeIII or SiIII. Such differences have been predicted for Si- and Ge-doped GaN,18 and the differences in efficacy between silicon and germanium in AlN are well known.6 To further elaborate on this hypothesis, we developed a computational model based on density functional theory and supported by the asphalt point defect simulation informatics suite (supplementary material).19 Developing an accurate model that considers the alloy explicitly presents significant computational challenges due to the number of unique configurations of multimember complexes as well as inherently random occupation of Al and Ga atoms on cation sites in AlxGa1−xN. To circumvent this challenge, we have developed a scheme for projecting computationally obtained defect thermodynamics and the electronic density of states from the endmembers (AlN and GaN) into the alloy, as a first approximation.

Point defects including on-site, DX, vacancies, and multi-donor complexes with up to three donors were simulated in AlN and GaN. Harris et al. describe the set of unique configurations for multi-member–vacancy complexes VIII–n•Si (n = 1, 2, 3) in the wurtzite structure.10 From that set, we consider only those that have been shown to have a considerable effect on compensation, as described in much more depth by Baker et al.18 This set includes unique configurations of the following for both Ge and Si: three single-donor vacancy complexes, seven two-donor vacancy complexes, and six three-donor vacancy complexes. Even with results interpolated from explicit point defect simulations in AlN and GaN, still a significant number of simulations was needed to take into account the different charge states of VIII–n•Si and VIII–n•Ge complexes and other defects needed to complete the charge balance model.

For the interpolation, the finite-size-corrected DFT, total energies of every charge state of every defect and bulk supercell were linearly interpolated as

EEalloytot=nEAlNtot+(1n)EGaNtot,

where n is the fraction of aluminum. Chemical potentials were similarly interpolated. The densities of states presented unique challenges in this respect. They were decomposed into valence and conduction bands, and the number of states per unit energy was linearly interpolated. Lastly, the interpolated bands were re-assembled with the band edges set to the linearly interpolated valence band and a band-bowing-corrected interpolated conduction band edge.20 

These interpolated data were then used to calculate the concentrations of on-site donors and multi-donor–vacancy complexes in Ge- and Si-doped Al0.3Ga0.7N layers as a function of dopant concentration. Percentages of donors forming multi-donor–vacancy complexes relative to remaining on-site defects are shown in Fig. 3. Solid lines represent the percentages of Ge (red) and Si (blue) remaining on-site as a function of increasing donor concentration and dashed lines represent the percentages of Ge and Si, which form multi-donor–vacancy complexes. These complexes, labeled VIII–n•Ge and VIII–n•Si, contain the single-, two-, and three-donor–vacancy complexes described previously. In the low doping limit, both impurities predominantly incorporate as on-site donors. As the impurity concentration increases, the on-site donors begin to be compensated by multi-donor-vacancy complexes. Comparing the two impurities in Fig. 3, it is found that the percentage of on-site Si drops off faster than on-site Ge, and in the high doping regime, multi-Si–vacancy complexes increase at a faster rate than multi-Ge–vacancy complexes. Further model analysis of multi-donor–vacancy complexes reveals that these percentages are highly sensitive to the donor concentration. As the donor concentration increases to high doping regimes, VIII–2•donor and VIII–3•donor complexes dominate the total multi-donor–vacancy complex concentration, while single-donor–vacancy complex concentration remains relatively low. These multi-donor–vacancy complexes have previously been shown to contribute to self-compensation.10 As seen in Fig. 3, the concentration of the VIII–3•donor is higher in Si-doped samples in comparison to Ge-doped ones. Due to the rapid increase in the VIII–3•Si concentration with the increasing Si doping level, the on-site Si concentration is lower than that of on-site Ge for all doping concentrations. This indicates that a higher % of Si atoms is consumed to form VIII–3•Si in the high Si-doped regime. The model offers three basic predictions based on the VIII–n•donor complex formation hypothesis: (1) the onset of self-compensation occurs at lower doping levels for Si-doped AlGaN; (2) Ge doping leads to a higher peak carrier concentration (under the same growth conditions), and (3) as the nature of the donor complexes is similar, a qualitative similar optical emission transition (deep luminescence peak) is expected.10 

FIG. 3.

Percentages of defects that form multi-donor vacancy complexes relative to remaining on-site. Solid lines represent percentages of on-site defects and dashed lines represent the total of multi-donor vacancy complexes VIII-n•Ge and VIII-n•Si, where n = 1, 2, and 3.

FIG. 3.

Percentages of defects that form multi-donor vacancy complexes relative to remaining on-site. Solid lines represent percentages of on-site defects and dashed lines represent the total of multi-donor vacancy complexes VIII-n•Ge and VIII-n•Si, where n = 1, 2, and 3.

Close modal

The first two predictions are consistent with the Hall measurements presented in Figs. 1 and 2. To validate the third prediction, room temperature PL measurements were carried out using a series of Ge- and Si-doped Al0.4Ga0.6N layers grown with reduced C concentration, i.e., lower metalorganic flow rates. Figure 4 displays the PL spectra from the Ge- and Si-doped AlGaN samples. As expected from our previous study of Si-doped AlGaN,11 the defect luminescence regarding VIII and donor complex appears with increasing donor concentration, while the CN peak was observed in the low doping condition. As seen in Fig. 4(a), when the [Ge] is relatively low, the dominant defect luminescence originates from the CN defect, whereas the VIII–n•Si peak appears in the self-compensation regime. The same trend is also observed in Si-doped AlGaN layers shown in Fig. 4(b). In order to characterize the difference in concentrations of VIII-n•Si and VIII-n•Ge, the relative intensities to the near band edge peak are plotted in Fig. 4(c). In the low doping regime, there is no clear difference between Ge- and Si-doped samples. A sharp increase in the VIII-n•Si peak was observed in Si-doped samples at [Si] ∼3 × 1019 cm−3, whereas a higher Ge concentration (∼1 × 1020 cm−3) was needed for the increase in the VIII–n•Ge peak. This result suggests that the VIII–n•Ge concentration is lower than the VIII-n•Si concentration at the same donor concentration, which agrees with predictions (1) and (3) and leads to the observed higher carrier concentrations in Ge-doped AlGaN. As such, Ge offers a technological advantage as a shallow donor over Si for highly conductive AlxGa1−xN layers (x < 0.5) based on the nature of the self-compensation. This realization is an example of dopant engineering in ultra-wide bandgap semiconductors, where dopant selection is not only based on (1) being a shallow “hydrogenic” donor but (2) also dependent on the compensating complexes that form with the dopant and (3) their corresponding formation energies.

FIG. 4.

Room temperature PL spectra from (a) Ge-doped and (b) Si-doped AlGaN. Defect peaks due to CN at ∼2.7 eV and VIII-n•D at ∼2.1 eV are observed in both Ge- and Si-doped AlGaN. VIII-related defect peak intensity as a function of donor concentration is summarized in (c).

FIG. 4.

Room temperature PL spectra from (a) Ge-doped and (b) Si-doped AlGaN. Defect peaks due to CN at ∼2.7 eV and VIII-n•D at ∼2.1 eV are observed in both Ge- and Si-doped AlGaN. VIII-related defect peak intensity as a function of donor concentration is summarized in (c).

Close modal

In summary, self-compensation in Ge- and Si-doped Al0.3Ga0.7N layers has been investigated in terms of III vacancy and donor-vacancy complex (VIII-n•Ge and VIII-n•Si) formation. Both Ge- and Si-doped AlGaN exhibited a compensation knee behavior composed of impurity compensation, compensation plateau, and self-compensation. A maximum free carrier concentration of 4–5 × 1019 cm−3 was obtained by Ge doping, whereas the carrier concentration achieved in Si-doped samples was only half of that value, ∼2 × 1019 cm−3. DFT calculations with the grand canonical thermodynamics computational model supported the hypothesis that the difference in self-compensation arose from the difference in the formation energies of the VIII-n•donor complexes relative to their onsite configurations. The model predicted that the major point defects contributing to self-compensation were VIII-2•donor and VIII-3•donor complexes for both Ge- and Si-doped AlGaN. The increase in the on-site Si concentration with doping was not as significant as that of Ge due to the more rapidly increasing VIII–3•Si concentration, resulting from the lower formation energy of VIII–3•Si. These predictions are consistent with the observed difference in carrier concentration and photoluminescence spectra. This is a good example of dopant engineering in ultra-wide bandgap semiconductors beyond the common rules for traditional semiconductors.

See the supplementary material for the DFT calculations.

The authors gratefully acknowledge funding in part from AFOSR (Nos. FA-95501710225 and FA9550-1910114); NSF (Nos. ECCS-1916800, ECCS-1508854, ECCS-1610992, DMR-1508191, and ECCS-1653383); ARO (Nos. W911NF-1520068, W911NF-16C0101, and W911NF-1810415); and DOE (No. DE-SC0011883). This work was performed in part at the Analytical Instrumentation Facility (AIF) at North Carolina State University, which is supported by the State of North Carolina and the NSF (Award No. ECCS-2025064). The AIF is a member of the North Carolina Research Triangle Nanotechnology Network (RTNN), a site in the National Nanotechnology Coordinated Infrastructure (NNCI).

The data that support the findings of this study are available within the article.

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