Growth of Ga2O3 by furnace oxidation of GaN studied by perturbed angular correlations

Ga2O3 is a promising material for use in “solar-blind” UV-detectors which can be produced efficiently by oxidation of GaN. In this study we focus on the evolution of the oxide layer when GaN is heated in air. The experimental method applied is the perturbed angular correlation (PAC) spectroscopy of γ-rays emitted by radioactive nuclides, here 111Cd and 181Ta, whose parent nuclei are ion implanted into films of GaN grown on sapphire. As the emission pattern for nuclei in GaN is clearly distinct from that of nuclei in Ga2O3, the fraction of probe nuclei in the oxide layer can be directly measured and allows to follow the time dependent growth of the oxide on a scale of less than 100 nm. Additional measurements were carried out with the oxidized sample held at fixed temperatures in the temperature range from 19 K to 973 K showing transitions between the hyperfine interactions of 111Cd in the oxide matrix both at high and low temperatures. A model for these transitions is proposed.


Introduction
Ga 2 O 3 is a transparent wide band gap semiconductor which can be used for high-efficiency, "solar blind" UV photodetectors. However, the controlled production of high quality films of monoclinic β-Ga 2 O 3 which are essential for the fabrication of such detectors is still difficult. In a recent study Weng et. al. [1] presents a feasible and efficient way to grow Ga 2 O 3 by furnace oxidation of GaN. This is an important step forward since thermal oxidation is a simple, cheap and clean process. In this study we focus on the details of the evolution of the oxide layer when oxidized at 1223 K in dry air. The experimental method applied is the perturbed angular correlation (PAC) technique of γ -rays emitted by probe nuclides, here 111 In and 181 Hf, which are ion implanted into the GaN samples [2]. It allows to measure the electric field gradient (EFG) at the crystal site of the probe nuclei. Since the EFG for nuclei in GaN is clearly distinct from that of nuclei in Ga 2 O 3 , the fraction of probe nuclei in the oxide layer can be directly measured. This allows us to follow the time dependent growth of the oxide on a scale of less than 100 nm and at the same time monitor the quality of the crystal lattice in the vicinity of the probe nuclei. Since they are not uniformly distributed inside the sample, the layer thickness has to be deduced by comparing the measurement results with the lateral distribution of nuclei.

Experimental technique and data analysis
The PAC probes 111 In (T 1/2 = 2.8 d) and 181 Hf (T 1/2 = 42.4 d) decay by electron capture (EC) to 111 Cd and β − -decay to 181 Ta, respectively. In both cases an excited state of the daughter nuclide is populated and decays further by emission of a γ -γ -cascade, passing a spin-5/2 state. The half life of this intermediate state is T 1/2 = 85 ns for 111 Cd and T 1/2 = 10.8 ns for 181 Ta [3,4]. The hyperfine interaction of the EFG produced by the charge distribution in the crystal lattice with the quadrupole moment of the nuclear state is detected by the PAC technique.
The emission directions of the two γ in the γ -γ -cascade are correlated by W ( ). When subjected to an EFG, transitions between the hyperfine levels of the spin-5/2 intermediate state introduce a time modulation of the angular correlation pattern by a perturbation factor G kk (t): with the anisotropy coefficient A kk depending upon the multipolarities and spins of the decay transitions. P k (cos ) are Legendre polymomials.
The ω n are the transition frequencies between the hyperfine sublevels of the intermediate state which depend on the asymmetry parameter η and the spin-independent quadrupole interaction constant ν q of the EFG: where V xx , V yy and V zz are the components of the diagonalized EFG tensor. A Lorentzian frequency distribution with relative width δ is taken into account by the exponential in (2). For the remainder of this article, the quadrupole interaction constant ν q will be used.
In our experiments we measure the angular correlation using a conventional four-detector fast-slow coincidence set-up with LSO scintillation detectors [5,6]. For each measurement 12 coincidence spectra were collected with relative angles of θ = 90 • or 180 • between the emission directions of the γ rays. The coincidence spectra contain information on the number of nuclear decays measured with a delay time t between both γ rays observed in a given detector combination. Thus, each detected decay contributes one count to the corresponding coincidence spectrum. Each spectrum contains statistical information of typically 10 6 probe nuclei.
We get the perturbation factor by calculating the ratio where W (θ, t) is the geometric mean of all spectra with relative angle θ . In (4) it is already taken into account that i distinct hyperfine interactions due to different electronic environments may exist in the sample, with a fraction f i of the probe nuclei subjected to these.

Sample preparation and oxidation
6 μm thick GaN grown on saphire was ion implanted with either 111 In or 181 Hf at the Bonn isotope separator (BONIS) with an implantation energy of 160 keV each. For these conditions, Monte Carlo simulations with SRIM [7] show the maximum of the ion distribution profile at a depth of 40 nm for 111 In and 25 nm for 181 Hf (Fig. 1). Nearly all probe ions are deposited within 100 nm and 70 nm beneath the surface, respectively. Their Rapid thermal annealing at 1273(3) K for 2 min in nitrogen atmosphere removes most of the damage due to the ion implantation as can be shown with PAC measurements after the annealing. These are indicated by 0 min oxidation time in Figs. 2 and 3. A second piece of GaN used as proximity cap helps to suppress nitrogen diffusion out of the sample. At these temperatures, diffusion of the implanted nuclei should be negligible [8].
Immediately before the first oxidation step, the surface of the sample is wet etched with diluted hydrochloric acid for 3 min to remove the native oxide [9]. There was no contamination of the diluted acid with 111 In, so it can be assumed that the GaN layer is not affected by this procedure as was recently shown by Zhuang et al. [10].
For the oxidation, the sample is placed in a tube furnace preheated to 1223(3) K to prevent a reformation of the native oxide layer during temperature increase. The oxygen for the chemical reaction is simply provided by the ambient air.
Oxidation steps of 5 min each were performed followed by PAC measurements at room temperature to study the development of the oxide. The overall oxidation time was chosen such that the volume containing the PAC probes was completely oxidized as indicated by the results of the measurements. For 111 In, an oxidation time of 80 min was more than sufficient, so the measurements with 181 Hf were stopped after 70 min already. This procedure proved reproducible with various samples and independent of the length of the individual oxidation steps.
Additional measurements were carried out in vacuum with the oxidized sample held at fixed temperatures in the temperature range from 19 K to 973 K. A furnace similar to the one presented in [11] was used for measurements at or above room temperature and a commercial cryostat for measurements at low temperatures.

Results
After the annealing step described above, 84(3) % of the Cd probes show the quadrupole interaction constant characteristic for probes on regular, undisturbed Ga sites in GaN. This value is in good agreement with previous studies [12]. For Ta, however, it is only about half of what would be reached normally, noticeable in the anisotropy at t = 0 ns in Fig. 3. This is due to an unusually high dose of stable Hf which had contaminated the 181 Hf ion beam during the implantation. Thus, about half of the Hf are situated either in lattice sites strongly disturbed by neighboring Hf atoms or in regions amorphized by the implantation, leading to a large quadrupole interaction constant, which cannot be resolved by the PAC set-up. This fraction does not anneal and shows no involvement in the oxidation. Therefore, in the following analysis only the fraction of Ta probes on regular Ga sites is considered.
Selected spectra following the development of the oxide with oxidation time are presented in Figs. 2 and 3 for 111 In and 181 Hf, respectively. Least square fits of (2) to the data yield the fraction of probes in different surroundings given by distinct hyperfine interactions in the sample. The prominent fractions resulting from the fits are shown in Fig. 4.

Identification of the contributing interactions
First we will identify the hyperfine interactions (HFIs) in GaN and Ga 2 O 3 . The characteristics of these HFIs are compiled in Table 1, together with their development with oxidation time.
Before the start of the oxidation process, the predominant HFI can be attributed to 111 Cd or 181 Ta on Ga locations in the regular GaN matrix (Cd Ga (N) and Ta Ga (N), respectively) [13][14][15]. The EFGs associated with these interactions are both axially symmetric (η = 0) and single crystalline.
In the Ta-implanted sample, one prominent interaction emerges with oxidation time which we identify with 181 Ta on the Ga II lattice site in Ga 2 O 3 [16] (Ta Ga (Ox)). As it is known in the literature [17][18][19], atoms with a significantly larger ionic radius than Ga, such  [15,20].
With 111 Cd however, two distinct interactions can be associated with the probes on Ga II sites. One clearly defined interaction (Cd Ga (Ox)), present at 27(5) % of probes after oxidation, is the interaction of 111 In in a nominal and defect-free Ga 2 O 3 matrix [18,19].
The second, strongly attenuated interaction is present at 64(6) % of probes after oxidation (Cd Ga (Def)). The stronger attenuation can be seen in the spectra at larger delay times t. We will assume that this interaction is present at nuclei on Ga II sites with nearby electronic defects [18,19] and we identify both Cd Ga (Ox) and Cd Ga (Def) with 111 Cd in the oxide. The fraction of probes in a Ga 2 O 3 matrix is then given by the sum of the fractions of the two HFIs. We will validate this assumption later in this article by showing, that by variation of the sample temperature, Cd Ga (Def) can be reversibly switched to Cd Ga (Ox) and vice versa.

Evolution of the oxide layer with oxidation time
Due to the conversion of the nitride, the fraction f N of probes in this environment (X Ga (N), with X being either Cd or Ta) decreases with oxidation time (Fig. 4), which can phenomenologically described by a falling exponential f N (t) = A + f N (t = 0) · e −t/τ N , with τ N = 12(2) min for 111 Cd and 13(1) min for 181 Ta.
The development of the oxide gives rise to Ta Ga (Ox) and both Cd Ga (Ox) and Cd Ga (Def) with oxidation time. The sum of the corresponding probe fractions (f ox (Cd) and f def (Cd)) is shown in Fig. 4 as open squares. For both probes this can be described as f Ox (t) = Table 1 Time frames of the oxidation for measurements with 111 Cd and

Reversible switching of interactions with temperature in 111 Cd implanted samples
The temperature dependent measurements were carried out with two new samples prepared as described above, due to the comparatively short half-life of 111 In. One sample was used solely for high temperature measurements up to 973 K in a PAC furnace [11]. With another sample, measurements were made covering the full temperature range from 19 K to 973 K. For comparison, measurements with 181 Ta at high temperatures were performed with the same sample used for oxidation measurements in the previous section. Figure 5 shows some selected spin precession curves for the Cd-implanted samples. As we focus on probes in the oxide layer, Fig. 6a and b show only the fraction of probes in either X Ga (Ox) or X Ga (Def) so the sum of the fractions shown does not necessarily add up to 100 %.
The thermal history of the samples starts at RT with increasing temperature until reaching 973 K, decreasing T to RT and for sample 3 continuing at 19 K until arriving again at RT.
Although to a different extent, both sample 2 and 3 show an increase of Cd Ga (Ox) with sample temperature starting at approx. 600 K, which reversibly reduces when returning to RT. A similar, although less pronounced, increase is seen at temperatures below 200 K. At both high and low temperatures a lesser fraction of probes are subjected to Cd Ga (Def). If this was due to some change in crystalline structure, we would expect a similar behavior for 181 Ta. And although there seems to be a slight increase of Ta Ga (Ox) when stepping up in temperature (Fig. 6c), the uncertainties coming from the least square fits prevent any concise conclusion. Within errors we see therefore no significant thermal behavior for the 181 Ta probes.
We conclude that Cd Ga (Def) is an electronic defect coupled to 111 Cd which can detrap thermally to be responsible for the switching between Cd Ga (Ox) and Cd Ga (Def) with temperature. As previously assumed, both interactions should thus belong to nuclei in the oxide matrix, one with and one without this coupled electronic defect.
While thermal detrapping may explain the high temperature branch and is consistent with previous models [18,19], this does not explain the rise of Cd Ga (Ox) at low temperatures. We will present a detailed model for both the high and low temperature behavior in the discussion.

Evolution of the oxide layer with oxidation time
As shown above, perturbed angular correlations can give the fraction of implanted probe atoms in distinct lattice or electronic environments. We can thus derive the fraction of probes still in a GaN environment and of probes in the Ga 2 O 3 layer of the sample for each step of the oxidation process. In case of probe 181 Ta this information is simply given by the fraction of probes in Ta Ga (Ox). For 111 Cd we assume the combination of Cd Ga (Ox) and Cd Ga (Def) to be a valid representation. GaN will oxidize to Ga 2 O 3 externally, i.e. the oxide layer will start forming on top of the sample and continue to grow following an oxidation front into the sample. Hence it should be possible to estimate the position of the oxidation front with time. For this, we take the experimental probe fractions at a certain oxidation time (Fig. 6) and relate these to the accumulated fraction of probes up to a certain depth in the source material (Fig. 1). When no oxide has formed yet, the position of the oxidation front is set to 0 nm with higher values indicating the penetration depth of the oxidation front in the source material. This is not equivalent to an estimation of the oxide thickness, as this would require detailed knowledge about the microscopic restructuring of the material, the resulting lattice structure and parameters, all of which is not accessible by PAC alone. As was mentioned earlier, the probes are not deposited homogeneously in the samples and due to this, estimating the position of the oxidation front has to rely on the simulation data of the probe distributions given by SRIM. For GaN the depth profile of implanted species should be well estimated by SRIM and very little prone to diffusion during annealing [8]. But, due to the inhomogeneous distribution, once a large majority of probes are inside the oxidized region, small uncertainties in the experimental probe fraction translate to large uncertainties in the estimated position.
The result of this estimation is given by the filled symbols in Fig. 7 and indicates a more than 20 nm layer already present in the Cd-implanted sample before oxidation, as the interaction Cd Ga (Def) is already present at this stage. At larger oxidation times there would be a corresponding offset for that sample as compared to the Ta-implanted sample.
If we assume, that Cd Ga (Def) represents both a highly damped defect in the nitride as well as in the oxide that cannot be separated in our least square fits as their characteristics are very similar, we get the open symbols in Fig. 7. For this, we scale the fraction f def according to the magnitude of the probe fraction in oxide environment, i.e. we calculate f def · f ox /(f ox +f N ) and add that to f ox . By definition the oxide vanishes at oxidation time 0 min, but we also get a fine match between the oxidation process in this estimation and the process in the Ta-implanted sample.

Model for the reversible switching of interactions with temperature in 111 Cd implanted samples
After oxidation, we assume both interactions Cd Ga (Ox) and Cd Ga (Def) to represent Cd probes on Ga II lattice sites in the oxide. The first is in good agreement with the literature [18,19] and the latter can be at least reduced, in one sample even switched off, just by raising the temperature to the samples. To show this reversible switching more clearly, we calculated f * ox = f ox /(f ox + f def ) which is the ratio of Cd on defect-free Ga II lattice sites Although the extent is different for the two samples under investigation, variation of the sample temperature allows to alter the predominant HFI for the majority of probes in both samples. Lines are given to guide the eye to all Cd on Ga II lattice sites in the oxide (Fig. 8). The so calculated reduced fraction f * ox shows a minimum from approximately RT to 600 K for both samples under investigation. Although the extent is different for the two samples under investigation, variation of the sample temperature allows to reversibly alter the predominant HFI for the majority of probes in both samples. The thermal activation energies for these transitions are 19(1) meV for the low temperature transition and 56(1) meV or 59(3) meV, respectively, for the two samples at high temperatures.
An electron hole coupled to the Cd-probes is the most likely electronic defect. The 111 In on Ga sites are embedded isovalent in the 3 + charge state in the oxide [17,21]. During the EC-decay to 111 Cd, an initial hole is created in an inner shell of the probe, which relaxes to the valence band. An additional undefined number of holes are generated by accompanying Auger processes, leaving the nuclei in a much higher charge state [22,23]. These holes can recombine with free electrons, are thus mobile and in a semiconducting material the relaxation process is expected to be resolved on a pico-second time frame [24]. Unless an at least meta-stable defect with lifetimes of tens of nanoseconds is formed, these holes cannot perturb the 111 Cd intermediate state.
Although proposed for some time [27], it was only recently established that Ga 2 O 3 can form self-trapped holes (STH) [25,28,29]. These are local lattice distortions generated by a hole which are energetically more favorable on a local scale than the non-distorted lattice and can thus trap the hole generating the distortion, introducing a stable defect state in the band gap. The most prominent experimental effect attributed to these STH is an UV emission band in the photo luminescence spectrum [25,28,29]. A certain activation energy E B is required for the free hole to be trapped. Such defects can become mobile again when passing another, significantly higher potential barrier (E B + E ST ). Figure 9 is an adaptation of the formation model from Varley et al. [25], who could show the formation of these defects in Ga 2 O 3 with ab-initio calculations. In these calculations a free valence band  [25], lattice coordinates from [26]) hole stabilizes only at O I next to Ga II sites after passing a potential barrier of 0.1 eV. The corresponding distortion of the lattice around this site was calculated to be around 8 % (see supplemental material of [25]). The STH can escape with an activation energy of 0.63 eV to move back to the Ga site or with 0.4 eV when moving to equivalent oxygen positions along the crystal b-axis. If these activation energies could be provided purely thermally, this could explain the higher fraction of defect-free probes at low temperatures and the transition with increasing temperature starting above 150 K. The second transition at higher temperatures starting around 600 K could then be attributed to the mobilization of the STH, which is in line with the previous models of holes localized next to the probes provided in the literature [18].
The thermal activation energies deduced from the experiments, 19(1) meV for the low temperature and 56-59 meV for the high temperature transition, are significantly lower than the energies required for formation or relaxation in [25]. But in our case we are not in a pristine Ga 2 O 3 lattice, but in a lattice doped with In/Cd probes. From ab-initio calculations by Blanco et al. [17], local lattice distortions of 0.15Å (approx. 7 % of next neighbor bond lengths) are already expected around Indium on Ga II sites and we would expect even larger distortions after the EC-decay due to the higher cadmium charge state in the lattice. Further, a free valence band hole would not have to be trapped next to the probe, as the probes would generate adjacent holes during the EC-decay. Both mechanisms could facilitate the formation or relaxation of the STH and thus lower the corresponding activation energies.
This model would not apply to 181 Ta in Ga 2 O 3 , as the tantalum charge state 5 + being positive relative to the lattice would suppress the coupling of holes to the probe. We propose this model of post-EC hole trapping in the distorted lattice around In/Cd probes, with activation energies for formation and relaxation of this stable defect realized purely thermally, to explain the increased fraction of probes in a defect-free Ga 2 O 3 matrix both at temperatures higher and lower than room temperature. While at higher temperatures an increase of free electrons can contribute to the relaxation, for low temperatures we can rule out jump-diffusion mechanisms, as we would expect these to be suppressed by phononinteraction at temperatures significantly below 150 K. So we know of no other model to describe the low temperature behavior satisfyingly.
Varley et al. [25] carried out further ab-initio calculations showing STH formation in Al 2 O 3 , TiO 2 , SnO 2 , In 2 O 3 and MgO, most of which show similar high temperature defect relaxation with PAC using 111 Cd [30], and no STH formation in ZnO and SiO 2 , which do not show this effect in PAC measurements with 111 Cd. Here Ga 2 O 3 and In 2 O 3 show the highest tendency for STH formation. Low-temperature PAC measurements of all of these materials are sparsely published, so it would be interesting to check whether some of the materials also show the increase of defect-free interactions at low temperatures and whether this model could also be applicable to these materials.

Summary and conclusions
In this article, we follow the evolution of the Ga 2 O 3 oxide layer by furnace oxidation of GaN with the experimental method of perturbed angular correlations. Experiments are performed at room temperature in between oxidation steps. The probe nuclei 111 Cd and 181 Ta are introduced into 6 μm thin nitride layers grown on sapphire by ion implantation of the parent nuclei 111 In and 181 Hf. Both types of probes are incorporated on substitutional Ga sites in the lattice.
Over the course of the oxidation we see a decrease of the signal from probes in the nitride and an increase of the corresponding signal in the oxide. While for 181 Ta this is represented by a single hyperfine interaction (Ta Ga (Ox)), we attribute two disctinct interactions for 111 Cd on Ga II sites in the oxide (Cd Ga (Ox) and Cd Ga (Def)).
Regarding the temporal evolution of the oxide, we estimate the position of the oxidation front in the material with time by correlating the fractions of probe nuclei in the oxide matrix with the SRIM-simulated implantation profiles. While this gives reasonable results with 181 Ta, the presence of the defect Cd Ga (Def) at room temperature prevents concise results with 111 Cd. As it would require detailed microscopic knowledge of the oxidation process around the probes and the resulting lattice parameters, the true thickness of the formed oxide layer is not directly accessible with this approach.
The validity of the above attribution of Cd Ga (Ox) and Cd Ga (Def) to probes on substitutional Ga II lattice sites is checked in measurements at various sample temperatures ranging from 19 K to 973 K. These show that Cd Ga (Def) represents a purely electronic defect which can be trapped or de-trapped depending on the temperature. They furthermore show that Cd Ga (Ox) is especially pronounced both at temperatures below 150 K and above 750 K, but suppressed between room temperature and 600 K. We adapt a model of self-trapped holes in Ga 2 O 3 for both the high and low temperature behavior of the Cd Ga (Ox) and Cd Ga (Def) interplay, which could be checked by additional temperature-dependent PAC measurements or ab-initio simulations on Cd-doped materials where self-trapped holes are expected.