High-temperature annealing induced electrical compensation in UID and Sn doped β-Ga₂O₃ bulk samples: The role of V_Ga–Sn complexes

The modification of the structural, optical, and electrical properties of n-type conducting β-Ga₂O₃ by high-temperature annealing has been reported in various studies.^1–7 High-temperature annealing is a standard approach in semiconductor technology. High-temperature annealing has been applied for two a priori contradictory purposes: (i) the transformation of n-type conductive layers in high resistive ones or (ii) on the contrary to increase the carrier concentration in n-type doped samples. It is equally applied after ion implantation for dopant activation and annealing of structural damage.^8–10 It has recently been applied for the optimization of enhancement mode β-Ga₂O₃U-shaped trench vertical MOSFETS⁵ to obtain high resistive layers. These annealing were performed in the temperature range of 900–1200 °C under either O₂ or N₂ atmospheres and have been applied to thin films and also to bulk samples. The importance of the nature of the shallow donor (SD), Si or Sn, has not been investigated; both give rise to shallow effective mass donors but occupy different lattice sites. Si is a shallow donor when substituting on a fourfold coordinated Ga1 site, whereas Sn is a shallow donor on a sixfold coordinated Ga₂ lattice site. It may seem surprising that high-temperature annealing in the same temperature range can be used to reduce and increase the carrier concentration. For example, Tadjer et al.¹ reported the effect of 3 h annealing of Si and Sn doped EFG bulk samples in either N₂ or O₂ atmospheres, which showed an increase in the carrier concentration for annealing at 1000 °C under N₂, whereas a strong reduction was observed for annealing under O₂ at 1150 °C. The formation of intrinsic acceptors is generally evoked to explain the compensation, and we have shown recently that indeed Ga vacancy defects are responsible for the electrical compensation.² 

The standard techniques in electrical measurements, Hall effect, and deep level transient spectroscopy (DLTS) cannot identify the microscopic structure of the annealing induced defects. For example, a number of electron traps at E_C—0.62 eV, E_C—0.82 eV, E_C—1.00 eV, E_C—2.16 eV, E_C—4.40 eV have been evidenced in EFG grown bulk samples, but without clear identification.¹¹ We have shown recently² by EPR spectroscopy that a V_Ga related defect is responsible for the electrical compensation by high-temperature annealing. EPR spectroscopy is a useful complementary approach for such studies,^12–20 as it identifies equally the chemical nature of the defects and allows a quantitative analysis by spin counting. EPR spectroscopy, which can be applied to thin films as well as bulk samples, is a volume sensitive technique and analyzes the total volume of bulk and thin film samples. Various extrinsic defects such as Ir, Mg, Zn, Fe, Cu, Ni as well different V_Ga related centers have been investigated in β-Ga₂O₃ by EPR. Some of them (Fe, Cr, Cu) are present as native defects in the EFG grown bulk materials and lead to partial compensation. In specific charge states (Fe³⁺, Cr³⁺, Cu²⁺), they are paramagnetic and can be analyzed by EPR. The main parameters determined in EPR experiments are the electron spin S, Landé g-tensor, the central and distant hyperfine interaction and the point symmetry; these parameters can be compared to first-principles calculations and allow to build a microscopic model. In the wide-bandgap semiconductor Ga₂O₃, these defects have more than one charge transition level and their charge states can be used to monitor the Fermi-level position.

Our previous results² have already shown that the effects of the annealing are not limited to a micron-thick surface layer but modify the properties in the entire volume of typically 600 μm thick bulk samples. In this work, we have investigated the effect of high-temperature annealing of 650 μm thick substrates for two different series of samples: UID doped (−201) and Sn doped (001) oriented bulk samples with carrier concentrations of 2 × 10¹⁷ and 5 × 10¹⁸ cm⁻³, respectively.

UID doped (−201) and Sn doped (001) oriented 650 μm thick bulk samples have been purchased from Novel Crystal Technology. The carrier concentrations were, respectively, (N_D–N_A) = 2 × 10¹⁷ cm⁻³ and (N_D–N_A) = 5 × 10¹⁸ cm⁻³. The samples were cut in 5 × 6 mm² pieces and were furnace annealed under O₂ atmosphere at T = 900 °C, T = 1000 °C, T = 1100 °C, 1200 °C for 6 h. The samples were heated to the annealing temperatures at a rate of 5 °C/min and cooled under the same conditions.

The EPR measurements were performed with a Bruker X-band spectrometer in the temperature range of T = 4 K and T = 300 K. We applied standard 100 kHz field modulation, which results in first-derivative Lorentzian or Gaussian EPR lineshapes. Spin concentrations were determined by double integration of the EPR spectrum and comparison with a spin standard sample (Cr:Al₂O₃) purchased from the National Bureau of Standards (NBS). The EPR spectra were taken under thermal equilibrium conditions and under low temperature in situ photoexcitation with a UV Hg light source. The EPR spectra are simulated with the EasySpin program using Gaussian lineshapes. The photoluminescence spectra were taken at T = 4 K with a UV excitation (266 nm).

The EPR parameters of different V_Ga–Sn complexes were calculated by density functional theory (DFT) calculations using the Quantum ESPRESSO package^21,22 in their EPR active (S = 1/2) singly negative charge state. In particular, we calculated the g tensor and the hyperfine (hf) interactions with the neighboring Ga nuclei. The defect structures (ground states, excited states as well as Slater–Janak transition states) are modeled within periodic boundary conditions using 160 atom containing supercells, and a 2 × 2 × 2 Monkhorst–Pack k-point sampling, norm-conserving pseudopotentials and a plane-wave basis set with a 950 eV energy cutoff. All defect structures are fully relaxed (forces below 10⁻⁴ Ry/Bohr) using the standard HSE hybrid functional²³ to describe the exchange-correlation interaction of the many-particle system. For the HSE-relaxed structures, the EPR parameters are calculated within linear magnetic response using the gauge-including projector-augmented wave (GIPAW) method^24,25 and using the semi-local PBE functional.²⁶ This combined HSE-PBE approach yields highly accurate hf splittings but tends to underestimate the deviation of the elements of the electronic g tensor.

EPR spectroscopy can be applied to the study of conduction electrons (CEs), the so-called conduction electron spin resonance (CESR), shallow donors and to paramagnetic centers such as intrinsic point defects. The distinction between CESR and SD EPR spectroscopy has to be taken into account for the determination of defect concentrations as CE follow a Pauli-like magnetism whereas paramagnetic defects have a Curie-like magnetism. For n-type conducting samples doped with Si or Sn shallow donors with respective ionization energy of E_D = 36 meV or 56 meV, the donors will be ionized at T = 300 K and magnetic resonance will measure the CESR. At temperatures below T < 60 K, the carriers will freeze out and the paramagnetic, neutral shallow donors can be quantitatively analyzed.

The neutral shallow donors and conduction electrons in β-Ga₂O₃ have been studied previously by different authors.^27–32 Their spin Hamiltonian parameters have been determined as electron spin S = 1/2, g-tensor with principal values of g₁₁ = 1.9572, g₂₂ = 1.9602, and g₃₃ = 1.9622 with the g₂₂ aligned with the crystal b axis. Contrary to the case of transition metal impurities, the EPR linewidth of SD is extremely temperature dependent due to motional narrowing. This occurs when the donor electrons are delocalized in an impurity band or are thermally emitted in in the conduction band. We have shown previously that the EPR donor linewidth can be used for the analysis of the electrical transport properties and gives insight the variable range hopping conduction observed in n-type Ga₂O₃.^27,28 Typical experimental EPR linewidth are ΔB < 1 G at T = 300 K and ΔB = 60 G at T = 4 K, if the carriers are fully localized.²⁸ This unusual behavior has been analyzed in more detail in Ref. 28 and described to thermally activated delocalization of the donor electrons and variable range hopping transport at intermediate temperatures.

In Fig. 1(a), we show SD EPR spectra at T = 4 K for the UID samples annealed at 900, 1000, 1100, 1200 °C, respectively. The EPR spectra were taken under identical conditions and we observe comparable intensities and linewidth irrespective of the annealing temperature. At T = 60 K [Figs. 1(b) and 1(c)], the linewidths are in the range of 15–18 G, which demonstrates that the donor electrons are still mobile and not yet fully localized. At T < = 40 K, the linewidth increases further up to 60 G. At T = 4 K, the donor electrons are fully localized given the thermal ionization energy of the effective mass donor of E = 36 meV. By a double integration of the donor signals at T = 4 K, we obtain the spin concentration [Fig. 1(d)]. We observe within the error bars a decrease by 40% to 1.3 × 10¹⁷ cm⁻³ for the 900 and 1000 °C annealed samples and a further 20% decrease after the 1100 and 1200 °C annealing. Surprisingly, the annealing has only slightly reduced the neutral donor concentration from 1.7 × 10¹⁷ to 0.8 × 10¹⁷ cm⁻³ and the samples are still n-type conductive at T = 300 K.

In Fig. 2(a), we show the shallow donor EPR spectra at T = 4 K for the Sn doped Ga₂O₃ samples for the different annealing temperatures. The linewidth increases [Fig. 2(b)] with the annealing temperature, indicating increased electrical compensation. But only for the 1200 °C annealed sample has the linewidth increased to ΔB = 60 G, demonstrating that the carriers are fully localized. In Fig. 2(c), we show the variation of the EPR linewidth with temperature for the 1200 °C annealed sample. Its variation is different from the case of the UID doped samples, which will be analyzed in more detail in another paper. In Fig. 2(d), we compare the SD concentrations measured at T = 4 K. We observe a monotonous decrease but as the donor electrons are still not localized only relative concentrations can be measured. In the 1200 °C annealed sample, the linewidth of 60 G shows complete localization and thus the spin concentration can be quantitatively determined by comparison with a spin standard sample. We obtain a value [Sn°]=0.9 × 10¹⁶ cm⁻³. Thus, the neutral SD concentration has been reduced from initially 5 × 10¹⁸ cm⁻³ by two orders of magnitude.

In the UID samples, no new paramagnetic defect is observed after the annealing. This is different from the Sn doped samples, in which a V_Ga related paramagnetic defect is generated by the annealing. The fingerprints of paramagnetic V_Ga centers are a spin S = 1/2, g-values g > 2.00, typical for oxygen hole centers, and strong hyperfine interaction with neighboring Ga atoms. Intrinsic V_Ga centers are triple acceptors and could thus efficiently compensate n-type samples. Their detection by EPR requires the (2−) charge state and thus particular Fermi-level positions. If the Fermi-level is pinned on the (3−/2−) level, this defect can be observed at thermal equilibrium by EPR in the paramagnetic 2− charge state with S = 1/2. Its observation after 1000 °C annealing indicates a shift of the Fermi-level to about E_C—2.0 eV.

In Fig. 3(a), we show for the 1000 °C annealed sample the experimental EPR spectrum of the V_Ga related defect and its simulation with the EasySpin program. We obtain the following spin Hamiltonian parameters: electron spin S = 1/2, principal values of the g-tensor: g₁₁ = 2.0423, g₂₂ = 2.0160, g₃₃ = 2.0024 and a hyperfine interaction with two equivalent Ga atoms with A(⁶⁹Ga) = 29 G. As the Ga atoms have a nuclear spin I = 3/2 and two isotopes (⁶⁹Ga, ⁷¹Ga) with different nuclear moments and isotopic abundances of 60% and 40%, respectively, the hf interaction with two Ga atoms gives rise to a characteristic multiplet structure. It should be stressed that the spin Hamiltonian parameters are different from the ones reported for the irradiation induced V_Ga centers.³³ In Fig. 3(b), we show the angular variation of the V_Ga center in the crystal b plane, from which the g-values g₂₂ and g₃₃ are obtained. The third value g₁₁ is obtained from a measurement with the magnetic field aligned B//b. The Sn doped samples become increasingly compensated with the annealing temperature, which would a priori imply an increased V_Ga concentration. However, the EPR intensity of the (2−) charged V_Ga center has a more complicated variation due to the importance of the Fermi-level position. As frequently observed in high bandgap materials, UV photoexcitation at low temperatures allows to modify the equilibrium spin concentrations and is also efficient in this case [Figs. 3(c) and 3(d)].

The increased V_Ga EPR spectrum remains stable after the excitation is shut off. In the 1100 °C annealed sample, the V_Ga spectrum is no longer observed before photoexcitation but is observed after UV excitation. In the 1200 °C annealed sample, the V_Ga²⁻ spectrum is not observed in thermal equilibrium; only a lower intensity spectrum can be generated by UV photoexcitation. This shows that after the 1100 °C anneal the Fermi-level is below its charge transition level (−2/1−) and most of the V_Ga centers are in the 1− charge state not observable by EPR. The fraction of the V_Ga centers which can be transformed in the EPR active 2− charge state by electron transfer from the VB to the V_Ga¹⁻ center depends on the light source (wavelength, intensity) and is in competition with photoinduced charge transfer to the impurities Cr, Fe, Cu, and Mn equally present in these samples.^34,35 The spin concentration of the EPR active fraction of V_Ga is rather small, of the order of 5 × 10¹⁶ cm⁻³, which is related to the Fermi-level position required for its observation.

We have equally investigated the PL spectra from 10 to 300 K of the UID and Sn doped samples with/without oxygen annealing in the UV and visible spectral range. PL spectra were measured using a 266 nm excitation. This spectrometer uses a xenon lamp as the excitation source. In Ga₂O₃, various PL and CL spectra have been reported.^36–38 They are called the UV, blue, and green bands, which have been tentatively, assigned to O and Ga vacancy centers. In Fig. 4, we show the photoluminescence spectra of the UID and Sn samples before and after 1200 °C annealing. Before annealing, the PL spectra are similar for the two types of samples with the UV band dominating. After the highest annealing of T = 1200 °C, the UID sample shows only the UV band 370 nm and a weak spectrum centered at λ = 550 nm, whereas the spectrum at 550 nm becomes highly dominating in the Sn doped sample. The broad PL spectrum at 550 nm has not yet been reported and we assign it based on first-principles calculations to the recombination on the V_Ga defect, which as will be shown below, is attributed to a V_Ga–Sn complex. In Ref. 38, a PL band with similar wavelength has been theoretically predicted for V_Ga–Si complexes.

Ga vacancy defects, are intrinsic defects, which due to their triple acceptor configuration (3–/2–/1–) will modify the electrical properties of thin films and bulk crystals. In the case of monoclinic β-Ga₂O₃ with two distinct Ga lattice sites and three distinct O lattice sites (O₁, O₂, O₃), a variety of Ga vacancy configurations may be formed, as discussed in Refs. 33 and 39–41. In addition to the simple V_Ga1 und V_Ga2 configurations, more complex Ga vacancy models such as V_Ga1–Ga_i–V_Ga1 have been proposed.⁴² Indeed, scanning transition electron microscopy (STEM) measurements⁴³ have directly visualized these V_Ga1–Ga_i–V_Ga1 split vacancy complexes. According to first-principles calculations, they are more stable than the simple vacancies. V_Ga centers. They have been studied by different techniques such as positron annihilation spectroscopy (PA), cathodoluminescence (CL), deep level transient spectroscopy (DLTS), and EPR spectroscopy.^44–47 

Previously, already three different V_Ga centers have been evidenced by EPR.^33,39–41 They have been observed after high-energy particle irradiation or high-temperature annealing but were not observed by EPR as native defects. Particle irradiation with energies close to the displacement threshold for Ga or O atoms is a standard technique to generate vacancy defects.⁴⁷ V_Ga defects are actually oxygen hole centers, where the hole is localized on one of the first nearest oxygen neighbors of the Ga vacancy. A common property of the Ga vacancy defects is a g-tensor with principal values g > 2.00 and a hyperfine interaction (HF) interaction with two or more nearest neighbor Ga atoms. Proton irradiation, electron irradiation, or neutron irradiation have been shown to generate the same V_Ga center, observed by EPR in the paramagnetic 2− charge state. The analysis of its spin Hamiltonian parameters³³ discarded the simple model of a monovacancy and favored the one of a split vacancy complex. Low temperature optical excitation transforms this V_Ga center in a different metastable configuration. This photo-excited variant of the V_Ga center has also been attributed to a self-trapped hole center,⁴⁸ but this model has been discarded recently.⁴⁹ The thermal stability of the radiation induced V_Ga center is low and they anneal out at temperatures of T > 650 °C.⁴⁷ 

The V_Ga center observed after high-temperature annealing of Sn doped n-type material does not fit to any of the previous models discussed in Ref. 33. A similar defect was reported in Si doped and 1450 °C annealed materials,⁴¹ but with slightly different g-tensor values. A common key-property of these thermally induced V_Ga centers is an increased value of the hf interaction with two Ga neighbors, which is about twice the value of the irradiation induced V_Ga²⁻. The experimental and calculated EPR parameters of the different V_Ga centers are compared in Table I.

Our results have shown the importance of the carrier concentration and/or the chemical nature of the dopant, Si or Sn, for the electrical compensation of n-type β-Ga₂O₃ by high-temperature annealing. As this V_Ga center is not observed in the UID doped annealed samples, where the n-type conductivity is associated with Si shallow donors, but only in Sn doped samples after annealing we have considered the formation of V_Ga–Sn complexes. These defect complexes are EPR-active with spin S = 1/2 in the single negative charge states due to the binding with donor atoms. We have calculated the spin properties of the most stable V_Ga–Sn complexes in this charge state. Indeed, both Si and Sn donors as well as V_Ga centers have been shown to become mobile at temperatures above T = 1000°C^44,50; Sn donors diffuse via the formation of Sn–V_Ga complexes. We restrict our DFT calculations of V_Ga–Sn_Ga2 complexes to the case of nearest neighbor (nn) configurations. For more distant configurations, there are many different possibilities, with varying distances and orientations, which should give rise to a distribution of EPR parameters. Since in our EPR experiment there is no hint to such a distribution, we limit our calculations to nearest neighbor (nn) complexes. Previous calculations have shown (i) that Sn prefers to occupy the Ga₂ sublattice site, also in the case of pairing with V_Ga vacancies, and (ii) V_GaSn complexes, are more stable in the two split vacancy configurations, V_Ga1–Sn_ib–V_Ga1 (V^ib_GaSn) and V_Ga1–Sn_ic–V_Ga1 (V^ic_GaSn), than as a simple nn neighbor pair V_Ga1Sn_Ga2. We have also considered two possibilities not reported before, where the Sn atom does not host the interstitial position of the Sn split vacancy configurations, but changes position with one of the neighboring in-plane Ga₂ lattice sites. From the nn neighbor pair V_Ga1Sn_Ga2 these configurations can be formed gaining energy, if one of the Ga1 neighbors is relaxing toward the V_Ga1 position, occupying one of the sixfold coordinated ib/ic interstitial sites. According to our HSE total energy calculations, these configurations in their EPR-active 1− charge state are higher in energy than the V_Ga1–Sn_ib–V_Ga1 ground state configuration (Fig. 5), but actually by 0.4 eV (V_Ga1–Ga_ib–V_Ga1–Sn_Ga2) and 0.8 eV (V_Ga1–Ga_ic–V_Ga1–Sn_Ga2) lower in energy than the simple V_Ga1Sn_Ga2 pair.

Our DFT calculations show (Table I) that the models V_Ga1–Sn_ic–V_Ga1 and V_Ga1–Ga_ic–V_Ga1–Sn_Ga2 can be clearly ruled out. In these models, the unpaired electron is localized on a threefold coordinated O₃ atom dangling bond. They would give rise to an additional hf interaction with a third Ga ligand with hf splittings of 25 and 15 G, respectively. This is incompatible with the experimental hf interaction observed in this work. Furthermore, the orientation of the g-tensors is different from our results. Although both ic-related complexes provide only slightly enhanced formation energies (∼0.1 eV above the V_Ga1–Sn_ib–V_Ga1 ground state), they are obviously not observed in the EPR measurements. According to our total energy calculations, this can be explained by their charge transition levels, which are situated more than 3.2 eV below the conduction band minimum. Assuming a Fermi-level close to midgap, these Vn_GaSn complexes will be in their diamagnetic 2− charge state, not observable by EPR.

The spin distribution of the other two V_Ga-related defect models is only marginally modified by the presence of the Sn donor atom. The unpaired electron is always predominantly localized on an O₁ oxygen atom. The hf splitting calculated for the two equivalent Ga ligands remains almost unaffected and does not allow us to determine the position of the Sn donor atom, also in the case of the nn neighbor V_Ga1–Sn_Ga2 pair. For the latter, however, the calculated g-tensor shows an inverted orientation of the g₂₂ and g₃₃ principal axes. The medium value g₂₂ is not oriented along the crystal c axis (as in experiment), but close to the a* direction, so that this model can also be excluded. The two remaining models however provide almost the same g tensor (see Table I). The largest component of the g tensors is nevertheless smaller than the experimental value. This discrepancy might be compared with the case of intrinsic V_Ga-related defects, where similarly underestimated g₁₁ values have been calculated using almost the same method.³³ 

In order to discriminate further between the two remaining models, we have also calculated the related photoluminescence (PL) spectra corresponding to a recombination with an extra electron toward the diamagnetic (V_GaSn)²⁻ defect. Following Ref. 38, the peak position is computed by assuming recombination of the EPR-active state with a conduction band (CB) electron. In fact, the CB minimum provides for all investigated defects the lowest excited energy level from which PL emission into the diamagnetic 2− ground state configuration is possible. Due to the strong dispersion of the lowest conduction band around the gamma-point, recombination with the EPR-active defect states explains the large width of the PL band. Table II shows the peak positions calculated for the most stable V_GaSn_Ga2 complexes. Again, the ic-related split vacancy configurations do not fit to the experimentally observed energy range. It is the model of the V_Ga1–Sn_ib–V_Ga1 split vacancy complex that provides the best agreement with the experiment. With a calculated PL peak position of 2.19 eV, it nearly coincides with the experimental value of 2.23 eV. In the EPR-active negative charge state, it provides the lowest formation energy (see also Table II) with a Sn binding energy of 1.16 eV, which further supports the V_Ga1–Sn_ib–V_Ga1 model.

The electrical compensation of Sn doped n-type β-Ga₂O₃ bulk samples by high-temperature annealing under oxygen is attributed to the combined action of V_Ga1 formation and Sn diffusion giving rise to the formation of V_Ga–Sn complexes. These defects, which we attribute to the split vacancy complex V_Ga–Sn_ib–V_Ga, have a high thermal stability and deep charge transition level slightly above midgap, making them interesting for microelectronic applications, where highly resistive layers are required.^5,6 The formation of V_Ga–Sn complexes will lead to electrical compensation in two ways: (i) due to the acceptor properties of the V_Ga–Sn_i–V_Ga defect and (ii) the associated reduction of the Sn shallow donor concentration due to the complex formation. The issue whether the difference in the compensation for the Si and Sn doped samples observed in this study is due to the chemical nature and site occupation of the dopant (Si, Sn) or to the different Fermi-level position has to be investigated in a future study.

The authors gratefully acknowledge the Paderborn Center for Parallel Computing (PC²) for the provided computational resources, as well as funding by the Deutsche Forschungsgemeinschaft (DFG) from TRR 142/3-2024, Project No. 231447078, support from the French National Agency (ANR) project “GOPOWER” Grant No. CE-50 N0015-01, and the National Natural Science Foundation of China under Grant Nos. 61925110, U23A20358, 62234007, and 62474170. This work was partially carried out at the Center for Micro and Nanoscale Research and Fabrication of USTC.

The authors have no conflicts to disclose.

H. J. von Bardeleben: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (equal); Writing – original draft (lead). Xuanze Zhou: Conceptualization (equal); Funding acquisition (equal); Investigation (equal). Jingbo Zhou: Conceptualization (equal); Investigation (equal). Guangwei Xu: Conceptualization (equal); Investigation (equal). Shibing Long: Conceptualization (equal); Investigation (equal); Resources (equal). U. Gerstmann: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Writing – original draft (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.