A pathway to highly conducting Ge-doped AlGaN

Si and Ge are the typical donors employed in Al_xGa_1−xN exhibiting low ionization energies (<30 meV) for x < 0.8 and x < 0.5, respectively.^1–6 They provide controllable n-type conductivity at room temperature, which makes them practical for optoelectronic and electronic applications. However, Si-doped alloys tend to crack at high doping levels; it was proposed that this is due to the Fermi level effect causing high vacancy concentrations when free carrier concentrations exceed ∼10¹⁹cm⁻³ and the associated vacancy-mediated dislocation climb.⁷ In contrast to these observations, there are several reports of crack-free, heavily Ge-doped GaN and AlGaN with free carrier concentrations in the 10²⁰cm⁻³ and high 10¹⁹cm⁻³ ranges, respectively, via MOCVD and MBE.^8–12 In addition to the mechanical challenges, electrical conductivity in both Si- and Ge-doped AlGaN alloys is characterized by a knee behavior, where the conductivity at first increases with dopant concentration, reaches a plateau (“knee”) at intermediate dopant concentrations, and then drops precipitously with increasing dopant concentration.^10,13–15 On the low doping side of this curve, C_N and edge dislocations are expected to be the main acceptor-type compensators, limiting the control of low carrier concentrations and maximum achievable mobility.^13,16,17 On the high doping side (above the conductivity knee), it has been predicted that dopants can incorporate as complexes with metal vacancies rather than the shallow donors and, depending on their charge state, act as compensators.^18,19 As such, V_III–nSi_III/V_III–nGe_III complexes are expected to be the common compensators present in the high doping regime, accounting for the self-compensation in AlGaN.^{10,13,15,18–20} Si- and Ge-doped Al_0.3Ga_0.7N shows apparent differences in the formation of corresponding complexes, V_III–nGe_III and V_III–nSi_III, leading to different distributions among the possible complexes, where n = 1, 2, and 3.¹⁰ While Ge doping shows higher achievable carrier concentrations for a wider range of dopant concentrations, Si doping results in a sharper decrease in free carrier concentration at high doping and lower maximum carrier concentration under the same growth condition. Consequently, this would suggest that Ge complexes have higher formation energies than the Si equivalents, making Ge a more effective dopant in AlGaN.¹⁰ Moreover, the complex-type distribution (different n's), as a function of dopant concentration, can be hypothesized to establish other differences between the two dopants. This would make a significant difference in the observed knee shape exhibited by doping either with Si or Ge.

At higher Al compositions (above 50% Al content), Ge undergoes a DX transition seemingly limiting the viability of Ge as a donor in the Al-rich AlGaN.^5,9 However, recent results suggest that Ge has a deep donor (0/+1) behavior instead of the typical DX (−1/+1) Fermi level pinning, indicating that high conductivity in Al-rich AlGaN should be possible at high enough Ge doping levels.²¹ This makes Ge a viable donor even for the Al-rich compositions. However, the knee behavior would still be observed due to the donor–vacancy complex formation. Hence, controlling the formation of complexes should be an integral part of the pathway to highly conducting Ge-doped Al-rich AlGaN or even AlN.^22,23

Point defect and impurity incorporation, such as C_N and vacancy-dopant complexes, depends in MOCVD on various growth conditions, that is, growth temperature, V/III ratio, diluent gas, reactor pressure, etc.^14,24–26 A general framework that is independent of growth method is established by exploiting the dependence of point defect formation energy on chemical potential and Fermi level as part of a defect-control toolbox. Both approaches have been developed as universally applicable point defect control methods and have been successfully used for control of C_N and V_III–nSi_III in III-nitrides.^13,26,27 In regards to the chemical potential control (CPC) method, Reddy et al. have established a systematic framework that relates growth parameters to process supersaturation and finally to chemical potentials of reactants that directly influence the defect formation energy. This allows for a systematic approach that yields growth parameters that maximize the formation energy of a specific defect, thus reducing its incorporation or stabilizing a specific charge state.^13,16,26 Accordingly, the formation energy of V_III–nSi_III complexes in Si doped Al_0.7Ga_0.3N was increased by tuning the growth environment to be “metal-rich.”¹³ The maximum achievable carrier concentration in AlGaN alloys is an important parameter for electronic and optoelectronic applications; however, complex formation is a critical limitation to the practical applications of n-type doping in AlGaN.²⁸ 

In this article, we apply the CPC framework to manage self-compensation and complex formation in Ge-doped Al_0.4Ga_0.6N with the goal of determining the doping limits and to understand the driving forces for compensation.

All Al_0.4Ga_0.6N films were grown on c-oriented sapphire wafers in a vertical, low-pressure (20 Torr), RF-heated, MOCVD reactor. Triethylgallium (TEG), trimethylaluminum (TMA), and ammonia were used as gallium, aluminum, and nitrogen precursors, respectively. The sapphire substrate surface was exposed to H₂ at 1100 °C for 7 min and a subsequent NH₃ ambient at 950 °C for 4 min. A low temperature AlN nucleation layer (20 nm) was deposited at 650 °C and then annealed at 1050 °C for 15 min to obtain Al-polarity prior to the growth of a 200 nm thick AlN layer at 1200 °C that served as an Al-polar AlN template. Subsequently, 350 nm thick Ge-doped Al_0.4Ga_0.6N layers were grown, using germane (1000 ppm in nitrogen) as the Ge precursor. The dopant concentration was varied between 1 × 10¹⁸ and 2 × 10²⁰cm⁻³ and confirmed by secondary ion mass spectroscopy (SIMS) with details provided elsewhere.⁵ The AlGaN layers were grown under H₂ diluent, at 1000 or 1100 °C, and V/III ratios of 400, 1400, and 4200, corresponding to about 0.3, 1, and 3 slm NH₃ flow rates, respectively. The total metal organic flow rate was 33 μmol/min. Growth rate was constant at about 700 nm/h. The dislocation density in the AlN template (∼10¹⁰cm⁻²) and Al content in AlGaN epilayers were estimated from x-ray diffraction (XRD) measurements using a Philips X'Pert materials research diffractometer with a Cu anode and using methods described elsewhere.²⁹ Defect centers were investigated by photoluminescence (PL) and the spectra were acquired using a pulsed ArF excimer laser (λ = 193 nm) along with a Princeton Instruments Acton SP2750 0.75 m high-resolution monochromator with a 150 g/mm grating and a PIXIS: 2KBUV cooled charge-coupled device camera. Electrical characterization was performed using Hall measurements (Ecopia HMS-5500) in the van der Pauw configuration at room temperature.

According to the grand canonical formalism, the defect formation energy depends on the constituents’ chemical potentials and the position of the Fermi level. Similar to Si doping, V_III–nGe_III complexes start forming on the high doping side (above 10¹⁹cm⁻³ for 40% Al-content), acting as the drivers of self-compensation.¹³ Equation (1) describes the formation energy of these defects,^13,18

Here, n = 1, 2, and 3 correspond to the number of Ge atoms in the complex, t = 2, 1, 0 correspond to the charge state of the complex and μ_III = x μ_Al + (1−x) μ_Ga and μ_Ge are the metal and Ge chemical potentials, respectively. The metal chemical potential is related to the process supersaturation and, as such, can be controlled via the typical MOCVD growth parameters.^26,30,31 In this investigation, the NH₃ flow rate and growth temperature were used as the two main growth “knobs” to control process supersaturation and complex formation in Ge doped Al_0.4Ga_0.6N within the CPC framework. Figure 1 shows the change of metal chemical potential as a function of NH₃ flow rate (or V/III ratio) at a constant temperature. The change in the chemical potential is referenced to 0.1 slm NH₃ flow rate at 1000 °C and a constant total metal organic flow rate of 33 μmol/min. An increase in the NH₃ flow rate reduces the metal chemical potential and the formation energy of V_III–nGe_III, as described in Eq. (1). Therefore, a higher incorporation of these complexes is expected.

Figure 2 shows the effect of the NH₃ flow rate on the carrier concentration vs Ge concentration in Al_0.4Ga_0.6N. Changing of the NH₃ flow rate leads to the following changes in the self-compensation behavior: (a) a change in the self-compensation onset, as marked by the peak carrier concentration (the “knee”), (b) change in the shape of the “knee,” and (c) change in the onset of the sharp drop in carrier concentration.

Previously, the maximum carrier concentration in Si-doped Al_0.7Ga_0.3N was successfully increased within the CPC framework. However, no significant change in the knee shape was observed by changing the growth environment.¹³ For Si doping in AlGaN,^10,13 a metal-rich condition leads to an increase in the formation energy of the complexes, increasing the maximum achievable carrier concentration. However, a sharp decrease in the carrier concentration is observed right after the knee. In other words, the growth environment determines the formation energy of V_III–nSi_III complexes but does not directly influence the complex-type distribution as suggested by the shape of the carrier concentration vs Si concentration plot. This implies that there is a single dominating complex type for self-compensation in the high Si doping regime that seems to be independent of the growth conditions. Ge doping, on the other hand, shows a knee shape that is strongly influenced by the growth environment. This suggests that the V_III–nGe_III complex distribution should also change using the CPC, consistent with the predictions by Washiyama et al.¹⁰ 

V_III–nGe_III complexes can be either charged or neutral, depending on the number of Ge atoms in the complex form. The formation energy of the charged ones, such as (V_III–Ge_III)⁻² and (V_III–2Ge_III)⁻¹, reduce with a slope of 1 and 2, respectively, as the Ge chemical potential increases as described in Eq. (1). Moreover, their formation faces the opposing electrostatic force due to the Fermi level position and they have high incorporation only when the Fermi level is close to the conduction band. In other words, sharp reduction in the carrier concentration due to the compensation makes the charged complexes energetically less favorable because of the Fermi level effect. On the other hand, the formation of neutral complexes is independent of the Fermi level position; thus, there is no electrostatic driving force to influence their formation. Their formation energy reduces faster with the Ge chemical potential than that of charged complexes (with slope of 3). This suggests that (V_III–3Ge_III)⁰ will eventually be the dominant complex for high Ge doping concentrations independent of the growth condition. While the neutral complexes are expected to be stable under high doping conditions, the onset of their formation and the stability of any charged complexes still depends on the growth conditions.

As shown in Fig. 2, the maximum carrier concentration shows about a fivefold increase from 8 × 10¹⁸cm⁻³ to 4 × 10¹⁹cm⁻³ as the NH₃ flow rate decreases from 3 to 0.3 slm, supporting the predicted changes in the self-compensation behavior. This enhancement in the peak position is due to the increase in the formation energy of all complexes under the metal-rich condition. The impact of NH₃ on the formation energy for each individual complex type needs further investigation. Here, the doping range can be divided into the three regimes: 1—low doping, where the compensation is dominated mostly by C_N and results in the deviation of the carrier concentration from the ideal line; 2—medium doping, showing a plateau in the carrier concentration. In this doping regime, charged complexes are expected to be dominant, showing the balance between the Fermi level and Ge chemical potential effects. Finally, 3—high doping regime, in which a sudden sharp drop in the electron concentration is observed as Ge concentration increases, resulting in the Fermi level to shift away from the conduction band. In this doping regime, neutral complexes are dominating, and their formation is enhanced by increasing Ge concentration without any opposing driving force.

To further illustrate the above, the medium doping regime in Fig. 2 has been shaded for each NH₃ flow rate. Ge concentrations before and after the shaded areas are considered as low and high doping regimes, respectively. Clearly, a change in the growth conditions changes the onset for each regime. This can be explained by the stability of different V_III–nGe_III complexes. According to Eq. (1), for heavily doped alloys, where $(n+1)μIII≪nμGe$⁠, the formation energy is mainly determined by the dopant chemical potential (μ_Ge) and depends less on the growth environment represented by μ_III. At the onset of self-compensation, the dopant chemical potential is not yet significant, that is, $(n+1)μIII≫nμGe$⁠, and the concentration of complexes is still much lower than the dopant concentration. Here, each complex formation energy will be governed mainly by μ_III according to Eq. (1). In this respect, the formation energy of the higher order (higher n) complexes is more sensitive to the change in the metal chemical potential. As such, higher order complexes should be energetically favorable at lower μ_III, or so-called “metal-poor” (N-rich) growth conditions and high concentration of Ge donors. On the other hand, charged complexes are expected to be stable over a wider Ge concentration under “metal-rich” condition.

As observed in Fig. 2, for a 3 slm NH₃ flow rate, the peak carrier concentration, corresponding to the onset of self-compensation, occurs at a lower Ge concentration (8 × 10¹⁸cm⁻³). In addition, the shaded area extends to 3 × 10¹⁹cm⁻³ of Ge, which is much lower than for other growth conditions. Therefore, neutral complexes are expected to be more dominant under this N-rich growth condition. At lower NH₃ flow rates (1 slm), the formation of charged complexes dominates near the onset of self-compensation, leading to an apparent constant carrier concentration. This is followed by a sharp drop in the carrier concentration after the neutral complex formation becomes more likely with increasing Ge concentration. Consequently, the extension of the shaded areas corresponding to the dominancy of the charged complexes changes from 3 × 10¹⁹cm⁻³ to 7 × 10¹⁹cm⁻³ and to 1 × 10²⁰cm⁻³ by decreasing NH₃ flow rate from 3 to 1 and 0.3 slm, respectively. Thus, the stability of the charged over neutral complexes can be successfully controlled via the CPC method. From this, a more metal-rich (lower NH₃ flow) process has two effects: 1—it inhibits the complex formation, leading to the higher maximum achievable carrier concentration and an onset of self-compensation at higher Ge concentrations; 2—it stabilizes the charged complexes over the neutral ones. At higher doping levels, around 1 × 10²⁰cm⁻³, all carrier concentrations converge to the same value, independent of the NH₃ flow rate. At this point, the influence of nμ_Ge dominates the change in μ_III.

It is worth noting that C_N is also considered to be a compensator in n-type AlGaN. Contrary to the vacancy-related complexes, the formation energy of C_N increases for metal-poor growth conditions.¹³ This behavior has also been observed for GaN and Al-rich AlGaN.^13,16,26 However, the compensation by C_N plays a more pivotal role in the low doping regimes. This is seen in Fig. 2 by the deviation from the linear regime before the knee, which occurs at higher Ge concentrations at a lower NH₃ flow rate. This suggests a higher compensation by C_N under the metal-richer conditions. It is worth mentioning that mobility shows a knee behavior with Ge concentration as well. In the low doping regime, mobility values drop to about 5 cm²/Vs. The mobility collapse due to the carbon and dislocations has been shown previously for GaN.¹⁶ At Ge concentration corresponding to the highest carrier concentration, mobility shows its maximum values reaching to about 50 cm²/Vs. After the onset of self-compensation, mobility decreases due to the formation V_III–nGe_III complexes acting as scattering centers. Consequently, at very high doping levels, mobility drops to about 3 cm²/Vs.

To further illustrate the role of the III-metal chemical potential in complex formation, PL spectra from samples grown under different NH₃ flow rates were acquired. Figure 3(a) shows the room temperature PL spectra of Al_0.4Ga_0.6N:Ge grown under 1 and 3 slm of NH₃. Near-band edge emission at 4.25 ± 0.05 eV corresponds to a 40 ± 1% Al content. The defect luminescence at 2.2 eV is related to V_III–nGe_III and is similar to the one observed for V_III–nSi_III.^10,13,14 Washiyama et al. predicted this observation based on a model developed to describe the general V_III–n•donor complex formation.¹⁰ By increasing the NH₃ flow rate from 1 to 3 slm, the normalized intensity (I_complex/I_NBE) of the defect peak increased. This change corresponded to an increase in the concentration of vacancy–dopant complexes. Figure 3(b) shows the variation of I_complex/I_NBE with the NH₃ flow rate for a Ge concentration of ∼5 × 10¹⁹cm⁻³. This concentration is high enough to facilitate complex formation but lower than when the μ_Ge becomes dominant. This further illustrates that an increase in the NH₃ flow rate makes the complex formation energetically more favorable and results in a higher intensity of the 2.2 eV peak in the PL spectra. However, the defect peak is broad and complexes with different charge states (n values) are not clearly resolved under these PL experimental conditions.

In addition to the ammonia flow rate or V/III ratio, growth temperature is another process control “knob” strongly influencing process supersaturation. For Si doping, it has been shown that V_III–nSi_III complex formation increases with temperature, resulting in a reduction in the conductivity.^13,14 However, the behavior of Ge complexes is markedly different. Figure 4(a) shows the knee behavior in the carrier concentration in Al_0.4Ga_0.6N:Ge at growth temperatures of 1000 and 1100 °C. A decrease in the growth temperature by 100 °C does not show any noticeable change in the maximum carrier concentration; however, the sharp reduction in carrier concentration starts at higher dopant concentrations. As discussed earlier, the sharp decrease in the carrier concentration is attributed to the formation of neutral complexes. The shaded area (medium doping), corresponding to the charged complexes, seems to be wider under lower growth temperature. Therefore, charged complexes seem to be stable over a wider Ge concentration. The CPC method was implemented successfully to change the onset of neutral complex formation from a Ge concentration of 6 × 10¹⁹ to 1 × 10²⁰cm⁻³. This significant change in the dominant complex type is illustrated by an almost three orders of magnitude reduction in carrier concentration observed at a Ge concentration of 8 × 10¹⁹cm⁻³. From this, we can conclude that self-compensation is more sensitive to the growth temperature than the change in metal chemical potential through the change in the NH₃ flow rate. Figure 4(b) shows the V_III–nGe_III luminescence in Al_0.4Ga_0.6N:Ge for different growth temperatures for a constant Ge concentration of 8 × 10¹⁹cm⁻³. NBE is at 4.2 ± 0.1 eV which corresponds to 40 ± 2% Al composition. Consistent with the observations in the carrier concentration, the increase in growth temperature leads to an increase in the intensity of the mid-gap luminescence peak corresponding to an increase in the complex concentration.

In general, CPC method enables both (1) the control of the V_III–nGe_III complex concentration and (2) stabilization of a specific complex configuration or charge state. Under lower NH₃ flow rates and lower growth temperatures, all vacancy–donor complexes have a higher formation energy, resulting in a higher maximum achievable carrier concentration. Furthermore, these growth conditions seem to favor the formation of charged complexes, where nμ_Ge is not the dominating factor in the complex formation energy. A detailed quantitative analysis is outside the scope of this work; however, this qualitative discussion presents the fundamental elements necessary for establishing dopant engineering in ultra-wide bandgap semiconductors.

In conclusion, the chemical potential control framework was used to suppress the formation of V_III–nGe_III complexes that were identified as the main compensators in heavily Ge-doped AlGaN. Their formation was controlled through the metal chemical potentials, with a metal-rich environment favoring lower concentrations of these complexes. In addition, a metal-rich environment led to the possibility of controlling the abundance of various vacancy–donor complexes, selectively favoring charged complexes over the neutral ones. The metal-rich conditions were realized by a low growth temperature (1000 °C) and a low NH₃ flow rate (0.3 slm). The highest achieved carrier concentration of 4 × 10¹⁹cm⁻³ resulted in a conductivity of 166 Ω⁻¹cm⁻¹ in Al_0.4Ga_0.6N grown on sapphire substrates. The conductivity data were supported by a decrease in the intensity of the 2.2 eV peak in the PL spectra, which has been attributed to the vacancy–donor complexes. Although the neutral complexes (V_III–3Ge_III)⁰ ultimately start forming at high Ge concentrations, causing a sharp drop in the carrier concentration, the CPC method can selectively stabilize the charged complexes for a wide range of Ge concentrations, resulting in a doping plateau. This work allows for the control of the knee behavior in AlGaN alloys, which plays a pivotal role in the doping efficiency and achievable conductivity in ultra-wide bandgap semiconductors.

The authors acknowledge funding in part from AFOSR (Nos. FA9550-17-1-0225, FA9550-19-1-0114, and FA9550-19-1-0358), NSF (Nos. ECCS-1508854, ECCS-1916800, and ECCS-1653383), and ARO (No. W911NF-16-C-0101).

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

The authors have no conflicts to disclose.