# Defect Structure Determination of GaN Films in GaN/AlN/Si Heterostructures by HR-TEM, XRD, and Slow Positrons Experiments

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{e}, L

^{s}) found in the 690 nm GaN film, were associated with the better effective positron diffusion length (L

_{eff}) of ${L}_{\mathrm{eff}}^{\mathrm{GaN}2}$ = 43 ± 6 nm.

## 1. Introduction

^{2}V

^{−1}s

^{−1}) of the two-dimensional electron gas (formed at interfaces with e.g., AlN) that leads to low channel resistance and high current density (>1 A mm

^{−1}), and a breakdown field of 3.3 MV cm

^{−1}that is 11 times higher than that of silicon (0.3 MV cm

^{−1}) [4,5]. GaN is widely used in applications that require either n-type or p-type doped semiconductors for charge carrier injection in different devices [6]. New methods of obtaining Ga based films using liquid Ga [7,8] for reactive depositions have emerged in recent years and the fundamentals behind liquid metal enabled synthesis, along with the related surface functionalization aspects [9] showed promising possibilities concerning the growth of GaN thin films. Despite this, the fabrication of defect-free GaN films still possesses interest in some fields, such as field assisted positron moderation [10].

^{−2}, is greatly reduced by atomic scale defects which can trap positrons.

_{2}O

_{3}, ZnO, TiO

_{2}, SiC, with different orientations [15]. The stable phase of gallium nitride is the α-phase wurtzite structure. However, epitaxial layers can be achieved with the coexistence of wurtzite and zinc-blende (β-phase) phases due to the stacking sequence of nitrogen and gallium atoms. Both structures have polar axes and they do not have an inversion symmetry [16].

## 2. Materials and Methods

#### 2.1. Materials

^{13}cm

^{−2}, and an electron mobility of over 2000 cm

^{2}V

^{−1}s

^{−1}. The two wafers, were further labeled as GaN300/Si and GaN700/Si, where the number stands for the claimed thickness of the GaN film, expressed in nm. No further details on structure, defects, and interfaces were made available by the producer.

#### 2.2. Structural Analysis

#### 2.2.1. Microstructural Characterization

^{®}(Oxford, England), and images of simulated crystals were generated using CrystalMaker

^{®}, a software by CrystalMaker Software Ltd., Oxford, England [18].

#### 2.2.2. Defect Structure Determination

_{α}= 1.5418 Å) and a HyPix-3000 high-resolution detector (Rigaku, Neu-Isenburg, Germany), in 0D mode. The data (ω—rocking curves of selected symmetrical and asymmetrical reflections) were recorded in double-axis configuration, in the parallel beam mode, using a parabolic mirror (cross beam optics module) and a four bounce Ge-220 monochromator (Rigaku, Neu-Isenburg, Germany), resulting in an axial divergence of the beam of 0.003° in the vertical diffraction plane of the goniometer. A narrow incidence slit of 1 mm was used to avoid the effect of sample curvature on the measurements. On the detector side, receiving slits (RS) of RS1 = 4 mm, and RS2 = 38.5 mm were used (open detector configuration), so that all diffuse scattering from the sample was accounted for. The wafers were first aligned with respect to the Si substrate, in order to avoid any measurement errors due to sample misalignment, then the rocking curve measurement of the selected GaN planes was performed.

_{i}is the integrated peak intensity and I

_{backgr}is the background intensity. The A and B parameters were obtained by integral fitting on the experimental data. A and B describe the dislocation density and the dislocation correlation range, respectively, and can be expressed as:

_{B}is the Bragg angle at which the diffraction interference takes place, according to the geometry described in Ref. [19]. Both f and g can be computed so that the density of dislocations, as well as the characteristic dislocation correlation length, can be obtained for either edge or screw defects, marked by the superscripts “e” and “s” in Equation (3). For edge dislocations, an asymmetrical lattice plane of the GaN network was considered, while for screw dislocations, a symmetrical plane of the same sample was used. For symmetric Bragg reflections (so, for screw dislocations), the setup implies that ψ = π/2 and ϕ = θ

_{B}, resulting in f = 1/8π and g = 2π, respectively [19].

#### 2.3. Doppler Broadening Spectroscopy

_{γ}≈ 511 keV. The longitudinal component of the annihilation pair momentum, p

_{L}, determines the energy shift due to Doppler broadening, ΔE

_{γ}= 511-E

_{γ}= p

_{L}c/2, where c is the speed of light. The Doppler broadening spectra of the annihilation radiation are sensitive to the electron momentum distribution of the site where the positron annihilated, since, the momentum distribution of the electrons in defects differs from that of electrons in the bulk material [20].

_{+}= 0.5 to 25 keV. Each of the experimental spectra was collected over a period of 8 min for a fixed E

_{+}, resulting in statistics of ~5 × 10

^{5}counts in the 511 keV region. The shape of the annihilation peak was analyzed by the sharpness parameter, S, defined as the sum of counts, in the central region of the peak (|ΔE

_{γ}| < 0.78 keV), relative to the total peak counts (N

_{tot}), determined in the range between 500 and 522 keV. The triplet state of positronium (Ps) decays by emitting 3-gamma rays when it does not interact with the electrons of the material. The ratio, F

_{Ps}, between the counts in the valley region (from 450 to 500 keV) in the energy spectrum to N

_{tot}can give a relative estimate of the Ps emitted from the surface.

^{-3}can be described, according to Ref. [21], by:

_{0}= 1.13 z

_{m}, and the mean penetration depth is

_{0}is the density of the substrate. In the analysis of the experimental data, densities of 2.33, 3.26 and 6.15 g cm

^{−3}were used for the Si substrate, AlN buffer layer, and GaN film, correspondingly.

_{m}, and E

_{+}, the experimental data S(E

_{+}) and F

_{Ps}(E

_{+}) represents depth profiles. The VEPFITsoftware (Delft University of Technology, Delft, Netherlands) was used to fit the experimental data [22]. In addition to the implantation, the processes that have to be taken into account to solve the positron transport problem are diffusion, drift (in case of electric field), and trapping or annihilation of free positrons. Surface related processes, such as Ps emission and positron surface trapping, are incorporated within the model. The influence of epithermal positrons, and that of thermal positrons which diffuse back to the surface, is also taken into account in the VEPFIT software.

_{+}) is fitted using a model described by:

_{+}) = S

_{e}F

_{e}(E

_{+}) + S

_{s}F

_{s}(E

_{+}) + ∑ S

_{i}F

_{i}(E

_{+})

_{e}(E

_{+}) + F

_{s}(E

_{+}) +∑ F

_{i}(E

_{+}) = 1, where F

_{e}(E

_{+}) is the fraction of epithermal positrons annihilated at the surface, and F

_{s}(E

_{+}) and F

_{i}(E

_{+}) are the fractions of thermalized positrons annihilated at the surface and in the i-th layer. S

_{e}, S

_{s}, and S

_{i}are characteristic parameters, respectively, corresponding to the annihilation of epithermal positrons and of thermalized positrons at the surface and in the bulk of i-th virtually uniform layer. VEPFIT uses discretization as a fast method of solving numerically the positron transport problem to obtain the fractions of annihilated positrons from the above described states. One of the parameters which is derived from the fit is the effective positron diffusion length (L

_{eff}) for each layer. L

_{eff}is limited by the layer defects and is described by:

^{+}is the positron diffusion coefficient, λ

_{b}is the annihilation rate of positrons in a defect-free material, and the product between the defect density, n

_{t}, and the positron trapping rate, k

_{t}, for vacancies, usually holds the value of 10

^{15}s

^{−1}.

_{Ps}(E

_{+}), is useful in the interpretation of the experimental results. Both depth profiles S(E

_{+}) and F

_{Ps}(E

_{+}) can be fitted simultaneously by one and the same VEPFIT model.

## 3. Results and Discussion

#### 3.1. Microstructural Characterization

#### 3.1.1. TEM

#### 3.1.2. XRD

^{s}, and another one for the ($10\overline{1}5$) plane, to determine the edge characteristics ${\rho}_{\mathrm{d}}^{\mathrm{e}}$ and L

^{e}. The collected and simulated omega scans, along with their respective full width at half maximum (FWHM), are shown in Figure 4.

^{e}= 0.32 nm and for screw dislocations - b

^{s}= 0.52 nm. Parameters f

^{e}and g

^{e}, f

^{s}, and g

^{s}are calculated with Equation (3), and with the help of the extracted A and B, a series of threading dislocation densities and correlation lengths were calculated, the results being summarized in Table 1. The total threading dislocation density, ${\rho}_{\mathrm{d}}^{\mathrm{t}}$, is calculated as the sum of the two component densities (screw and edge), while the mean distance between two dislocations is given by r

_{d}= 1/${({\rho}_{\mathrm{d}}^{\mathrm{t}})}^{1/2}$ [28]. As shown in Table 1, the thicker GaN film manifests defect densities ${\rho}_{\mathrm{d}}^{\mathrm{e}}$ = 2.24 × 10

^{11}cm

^{−2}and ${\rho}_{\mathrm{d}}^{\mathrm{s}}$ = 1.35 × 10

^{10}cm

^{−2}, both lower than those of the thinner one, ${\rho}_{\mathrm{d}}^{\mathrm{e}}$ = 4.19 × 10

^{11}cm

^{−2}and ${\rho}_{\mathrm{d}}^{\mathrm{s}}$ = 1.85 × 10

^{10}cm

^{−2}. In the GaN700/Si wafer, the values for the dislocations correlation lengths, L

^{e}= 41 nm and L

^{s}= 220 nm, are higher compared to the corresponding values of the GaN300/Si wafer, L

^{e}= 27 nm and L

^{s}= 107 nm. The dislocation correlation length, also known as screening range, corresponds to the average size of cells in which the total Burger vector is equal to zero. The correlation lengths values suggest a reduced scattering of X-rays for the GaN film from the GaN700/Si wafer, also indicated by the smaller values of the FWHM, depicting a better quality of the film.

#### 3.2. Positron Implantation Profile

_{+}) for the GaN300/Si and GaN700/Si are shown in Figure 5. The sharp initial decrease of S for E

_{+}≲ 1 keV was due to annihilated epithermal positrons. Because of their high kinetic energy in the moment of annihilation, S

_{e}did not reflect the material structure. At E

_{+}≳ 1 keV, it can be seen that S slowly increased with E

_{+}in the GaN film range, while approaching the AlN buffer layer, a stronger increase starts (at E

_{+}≳ 11 keV) and tends to reach a saturation level in the Si substrate (better seen in Figure 5b). Full saturation can be expected at high enough energies (E

_{+}> 25 keV) to have all implanted positrons annihilated entirely in the Si substrate.

^{2}) of 1.47 and 1.40 for GaN700/Si and GaN300/Si, respectively, and also, into long L

_{eff}~ 100 nm for the GaN film in both cases. The curves of the preliminary fits were very close to the fits showed in Figure 5. However, the best fit parameters revealed that the S

_{s}~ 0.445 was found to be lower than S

_{GaN}~ 0.455 (specific to positrons annihilated in GaN film). No Ps was formed in the bulk of GaN, however, at the surface, the branching ratio showed that 12% of the positrons formed Ps [13]. The triplet state of Ps (o-Ps) annihilates in vacuum into three gamma rays that do not contribute to the 511-keV peak. Statistically, 25% of Ps is singlet form (p-Ps). The p-Ps annihilation in vacuum was characterized by a narrow Doppler shift distribution curve, thus, with a high S [31]. For sample-detector longitudinal geometry, the emission of Ps at low incident positron energy may cause asymmetry in the Doppler broadened peak [32]. It is caused by a shift of the centroid of the p-Ps contribution and may lead to an increase of the annihilation peak width. However, for the geometry described in Section 2.3, if Ps is emitted from the surface, the centroid of the p-Ps contribution will not be shifted. Therefore, S

_{s}should have a larger value than S

_{GaN}. As this relationship is not fulfilled for the preliminary fit results, it can be concluded that this type of fit is physically incorrect. Our attempts to force S

_{s}to be greater (or at least equal) than S

_{GaN}, without any increase in the number of layers of the model, led to bad fits with χ

^{2}> 7. The latter indicates depth inhomogeneity of the GaN film.

_{+}, which is typical for materials with long effective positron diffusion length (reported as ${L}_{\mathrm{eff}}^{\mathrm{DF}}$ = 135 nm) [33]. For Mg-doped p-type GaN, a sharp decrease in S was observed for E

_{+}≲ 1 keV, similarly to what can be seen in Figure 5. Uedono et al. explain this behavior by the created local electric field due to band bending near the surface, which suppresses the back diffusion of the thermalized positrons to the surface [34]. As a result, less Ps is formed at the surface by the thermalized positrons, and the positron diffusion length is shortened in a near surface layer. Based on the above reasoning, the number of the layers of the fitting model is changed by splitting the GaN film into sublayers (GaN1 and GaN2). In order to have a better understanding of the near surface positron annihilation, simultaneous fit of S(E

_{+}) and F

_{Ps}(E

_{+}) were performed by VEPFIT. Reasonable fits (see Figure 5) were obtained with two sublayers of the GaN film (4-layer model). The best fit parameters are summarized in Table 2.

_{eff}. For GaN700/Si, the value S

_{GaN1}= 0.4456 ± 0.0004 is lower than S

_{GaN2}= 0.4456 ± 0.0004 and this relationship indicates lower quality of the GaN2 sublayer compared to GaN1. The fact that ${L}_{\mathrm{eff}}^{\mathrm{GaN}1}$ = 13.1 ± 0.4 nm is shorter than ${L}_{\mathrm{eff}}^{\mathrm{GaN}2}$ = 43 ± 6 nm seems to contradict the latter statement. However, the short ${L}_{\mathrm{eff}}^{\mathrm{GaN}1}$ can be explained by the presence of local electric field directed inward the surface. Using the detector resolution and the S determination range given in Section 2.3, the characteristic parameter for p-Ps annihilation, S

_{p}

_{-Ps}, was estimated to be 0.95. If the branching ratio of Ps formation by thermalized positrons on the surface is 12% [13], the p-Ps annihilation contribution will be 3%. This should lead to an 0.028 increase in S

_{s}, compared to S

_{GaN1}. As can be seen in Figure 5b, the S

_{s}(see the parameter’s stair at E

_{+}= 0) was very close to S

_{GaN1}, indicating strong reduction in the Ps formation due to back-diffusion of thermalized positrons to the surface. The results for GaN300/Si in Figure 5a can be explained analogously.

_{eff}< 60 nm values of positron diffusion length in GaN are due to positron interaction with dislocations. The dislocations can shorten L

_{eff}by enhanced scattering of thermal positrons on them, and while vacancies tend to reside along them, they induce negative charge densities [36], trapping positrons more efficiently. In the case of the present study, the TEM analysis and the XRD defect assessment pointed out higher dislocation densities in the GaN film of the GaN300/Si wafer compared to GaN700/Si wafer (see Table 1). This is in agreement with the shorter effective positron diffusion length ${L}_{\mathrm{eff}}^{\mathrm{GaN}2}$ = 22 ± 6 nm (higher ${S}_{\mathrm{GaN}2}$ = 0.4558 ± 0.0004) in the GaN300/Si wafer, compared to ${L}_{\mathrm{eff}}^{\mathrm{GaN}2}$ = 43 ± 6 nm (${S}_{\mathrm{GaN}2}$ = 0.4536 ± 0.0003) in GaN700/Si wafer. Another explanation for the last relationships could be that the highly defect GaN/AlN interface region in the GaN film, has stronger influence on the S

_{GaN2}and ${L}_{\mathrm{eff}}^{\mathrm{GaN}2}$ for the thinner GaN film.

_{+}) points increased rather smoothly with the increase of E

_{+}in the region of the AlN buffer layer (see Figure 5a,b) and the specific parameters for the AlN (see Table 2) are determined by large uncertainties even with no electric field. So, further complications of the model are not reasonable to be applied.

## 4. Conclusions

^{11}cm

^{−2}, ${\rho}_{\mathrm{d}}^{\mathrm{s}}$ = 1.85 × 10

^{10}cm

^{−2}, ${\rho}_{\mathrm{d}}^{\mathrm{t}}\text{}$= 4.37 × 10

^{11}cm

^{−2}), implying a lower quality of the GaN film, compared to the one in the GaN700/Si wafer (${\rho}_{\mathrm{d}}^{\mathrm{e}}$ = 2.24 × 10

^{11}cm

^{−}

^{2}

_{,}${\rho}_{\mathrm{d}}^{\mathrm{s}}$ = 1.35 × 10

^{10}cm

^{−}

^{2}, ${\rho}_{\mathrm{d}}^{\mathrm{t}}$ = 2.35 × 10

^{11}cm

^{−}

^{2}). This was also supported by the higher dislocation correlation lengths found in the GaN700/Si wafer (L

^{e}= 41 nm and L

^{s}= 220 nm) as well as the larger mean distance between two dislocations (r

_{d}= 21 nm) which corresponded to larger average size of cells in which the total Burger vector is equal to zero, implying a higher crystallinity of the GaN film, compared to the one in the GaN300/Si (L

^{e}= 27 nm, L

^{s}= 107 nm, r

_{d}= 15 nm). Elemental diffusion studies carried out by TEM have shown that outside each layer boundary, both Al and Ga cross their respective layer interface to a certain depth, justifying the need of using a model that includes two different GaN layers (for each wafer) to explain the results from the DBS studies. Because both wafers were grown using the same method, in similar conditions, the improvement in crystallinity of the top GaN film is associated with the decreased lengths for elemental interfusion, relative to the GaN film width. While atomic displacements intermediate defect formation and propagation, a shorter length of non-stoichiometry in the GaN film induces a better quality of the top film, lowering the amount of defects and thus improving the positron moderation capacity of the material. The studied materials, because of their high amounts of edge and screw dislocations, diffusion, and partial non-stoichiometry, still imply several limitations in their use in the field of positron moderation. The positron data revealed the lack of uniformity in defect depth distribution, a fact that could not be observed in HR-TEM, nor in XRD. Therefore, using a positron-based complementary technique holds significant value for structural characterization. The DBS experiment assessed the effective positron diffusion length for both wafers, with a larger value of ${L}_{\mathrm{eff}}^{\mathrm{GaN}2}$ = 43 ± 6 nm (${S}_{\mathrm{GaN}2}$ = 0.4536 ± 0.0003), corresponding to the GaN film found in the GaN700/Si wafer, compared with ${L}_{\mathrm{eff}}^{\mathrm{GaN}2}$ = 22 ± 6 nm (${S}_{\mathrm{GaN}2}$ = 0.4558 ± 0.0004) for the GaN film in the GaN300/Si wafer.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Tsai, Y.L.; Lai, K.Y.; Lee, M.J.; Liao, Y.K.; Ooi, B.S.; Kuo, H.C.; He, J.H. Photon management of GaN-based optoelectronic devices via nanoscaled phenomena. Prog. Quantum Electron.
**2016**, 49, 1–25. [Google Scholar] [CrossRef] - Pampili, P.; Parbrook, P.J. Doping of III-nitride materials. Mater. Sci. Semicond. Process.
**2017**, 62, 180–191. [Google Scholar] [CrossRef] - Kuech, T.F. III-V compound semiconductors: Growth and structures. Prog. Cryst. Growth Charact. Mater.
**2016**, 62, 352–370. [Google Scholar] [CrossRef] - Meneghini, M.; Tajalli, A.; Moens, P.; Banerjee, A.; Zanoni, E.; Meneghesso, G. Trapping phenomena and degradation mechanisms in GaN-based power HEMTs. Mater. Sci. Semicond. Process.
**2018**, 78, 118–126. [Google Scholar] [CrossRef] - Roccaforte, F.; Fiorenza, P.; Greco, G.; Nigro, R.L.; Giannazzo, F.; Iucolano, F.; Saggio, M. Emerging trends in wide band gap semiconductors (SiC and GaN) technology for power devices. Microelectron. Eng.
**2018**, 78, 118–126. [Google Scholar] [CrossRef] - Flack, T.J.; Pushpakaran, B.N.; Bayne, S.B. GaN Technology for Power Electronic Applications: A Review. J. Electron. Mater.
**2016**, 45, 2673–2682. [Google Scholar] [CrossRef] - Carey, B.J.; Ou, J.Z.; Clark, R.M.; Berean, K.J.; Zavabeti, A.; Chesman, A.S.; Russo, S.P.; Lau, D.W.; Xu, Z.Q.; Bao, Q.; et al. Wafer-scale two-dimensional semiconductors from printed oxide skin of liquid metals. Nat. Commun.
**2017**, 8, 14482. [Google Scholar] [CrossRef] - Syed, N.; Zavabeti, A.; Messalea, K.A.; Della Gaspera, E.; Elbourne, A.; Jannat, A.; Mohiuddin, M.; Zhang, B.Y.; Zheng, G.; Wang, L.; et al. Wafer-Sized Ultrathin Gallium and Indium Nitride Nanosheets through the Ammonolysis of Liquid Metal Derived Oxides. J. Am. Chem. Soc.
**2019**, 141, 104–108. [Google Scholar] [CrossRef] - Daeneke, T.; Khoshmanesh, K.; Mahmood, N.; De Castro, I.A.; Esrafilzadeh, D.; Barrow, S.J.; Dickey, M.D.; Kalantar-Zadeh, K. Liquid metals: Fundamentals and applications in chemistry. Chem. Soc. Rev.
**2018**, 47, 4073–4111. [Google Scholar] [CrossRef] - Merrison, J.P.; Charlton, M.; Deutch, B.I.; Jorgensen, L.V. Field assisted positron moderation by surface charging of rare gas solids. J. Phys. Condens. Matter
**1992**, 4, L207–L212. [Google Scholar] [CrossRef] - Hugenschmidt, C. Positrons in surface physics. Surf. Sci. Rep.
**2016**, 71, 547–594. [Google Scholar] [CrossRef] [Green Version] - Beling, C.D.; Fung, S.; Ming, L.; Gong, M.; Panda, B.K. Theoretical search for possible high efficiency semiconductor based field assisted positron moderators. Appl. Surf. Sci.
**1999**, 149, 253–259. [Google Scholar] [CrossRef] - Jørgensen, L.V.; Schut, H. GaN-a new material for positron moderation. Appl. Surf. Sci.
**2008**, 255, 231–233. [Google Scholar] [CrossRef] - Kukushkin, S.A.; Osipov, A.V.; Bessolov, V.N.; Medvedev, B.K.; Nevolin, V.K.; Tcarik, K.A. Substrates for epitaxy of Gallium Nitride:new materials and techniques. Rev. Adv. Mater. Sci.
**2008**, 17, 1–32. [Google Scholar] - Yam, F.K.; Low, L.L.; Oh, S.A.; Hassan, Z. Gallium nitride: An overview of structural defects. In Optoelectronics—Materials and Techniques; IntechOpen Limited: London, UK, 2011; pp. 99–136. [Google Scholar]
- Ambacher, O. Growth and applications of Group III-nitrides. J. Phys. D Appl. Phys.
**1998**, 31, 2653–2710. [Google Scholar] [CrossRef] - Schneider, C.A.; Rasband, W.S.; Eliceiri, K.W. NIH Image to ImageJ: 25 years of image analysis. Nat. Methods
**2012**, 9, 671–675. [Google Scholar] [CrossRef] - Palmer, D.C. CrystalMaker; Begbroke: Oxfordshire, UK, 2014. [Google Scholar]
- Kaganer, V.M.; Brandt, O.; Trampert, A.; Ploog, K.H. X-ray diffraction peak profiles from threading dislocations in GaN epitaxial films. Phys. Rev. B Condens. Matter Mater. Phys.
**2005**, 72, 045423. [Google Scholar] [CrossRef] [Green Version] - Tuomisto, F.; Makkonen, I. Defect identification in semiconductors with positron annihilation: Experiment and theory. Rev. Mod. Phys.
**2013**, 85, 1583–1631. [Google Scholar] [CrossRef] [Green Version] - Van Veen, A.; Schut, H.; de Vries, J.; Hakvoort, R.A.; Ijpma, M.R. Analysis of positron profiling data by means of “VEPFIT”. AIP Conf. Proc.
**1991**, 218, 171–198. [Google Scholar] - Van Veen, A.; Schut, H.; Clement, M.; de Nijs, J.M.M.; Kruseman, A.; IJpma, M.R. VEPFIT applied to depth profiling problems. Appl. Surf. Sci.
**1995**, 85, 216–224. [Google Scholar] [CrossRef] - Yu, H.; Ozturk, M.K.; Ozcelik, S.; Ozbay, E. A study of semi-insulating GaN grown on AlN buffer/sapphire substrate by metalorganic chemical vapor deposition. J. Cryst. Growth
**2006**, 293, 273–277. [Google Scholar] - Lahreche, H.; Vennéguès, P.; Tottereau, O.; Laügt, M.; Lorenzini, P.; Leroux, M.; Beaumont, B.; Gibart, P. Optimisation of AlN and GaN growth by metalorganic vapour-phase epitaxy (MOVPE) on Si (1 1 1). J. Cryst. Growth
**2000**, 217, 13–25. [Google Scholar] [CrossRef] - Mánuel, J.M.; Morales, F.M.; García, R.; Aidam, R.; Kirste, L.; Ambacher, O. Threading dislocation propagation in AlGaN/GaN based HEMT structures grown on Si (111) by plasma assisted molecular beam epitaxy. J. Cryst. Growth
**2012**, 357, 35–41. [Google Scholar] [CrossRef] - Yamaguchi, M.; Yamamoto, A.; Tachikawa, M.; Itoh, Y.; Sugo, M. Defect reduction effects in GaAs on Si substrates by thermal annealing. Appl. Phys. Lett.
**1988**, 53, 2293–2295. [Google Scholar] [CrossRef] - Bogusławski, P.; Rapcewicz, K.; Bernholc, J.J. Surface segregation and interface stability of AlN/GaN, GaN/InN, and AlN/InN {0001} epitaxial systems. Phys. Rev. B
**2000**, 61, 10820–10826. [Google Scholar] [CrossRef] [Green Version] - Romanitan, C.; Gavrila, R.; Danila, M. Comparative study of threading dislocations in GaN epitaxial layers by nondestructive methods. Mater. Sci. Semicond. Process.
**2017**, 57, 32–38. [Google Scholar] [CrossRef] - Zubiaga, A.; García, J.A.; Plazaola, F.; Tuomisto, F.; Zúñiga-Pérez, J.; Muñoz-Sanjosé, V. Positron annihilation spectroscopy for the determination of thickness and defect profile in thin semiconductor layers. Phys. Rev. B
**2007**, 75, 205–305. [Google Scholar] [CrossRef] [Green Version] - Schultz, P.J.; Tandberg, E.; Lynn, K.G.; Nielsen, B.; Jackman, T.E.; Denhoff, M.W.; Aers, G.C. Defects and Impurities at the Si/Si(100) Interface Studied with Monoenergetic Positrons. Phys. Rev. Lett.
**1988**, 61, 187–190. [Google Scholar] [CrossRef] - Jean, Y.C.; Mallon, P.E.; Schrader, D.M. Principles and Applications of Positron and Positronium Chemistry; World Scientific Publishing Co.Pte.Ltd.: Singapore, 2003. [Google Scholar]
- Van Petegem, S.; Dauwe, C.; Van Hoecke, T.; De Baerdemaeker, J.; Segers, D. Diffusion length of positrons and positronium investigated using a positron beam with longitudinal geometry. Phys. Rev. B Condens. Matter Mater. Phys.
**2004**, 70, 115410. [Google Scholar] [CrossRef] [Green Version] - Uedono, A.; Ishibashi, S.; Tenjinbayashi, K.; Tsutsui, T.; Nakahara, K.; Takamizu, D.; Chichibu, S.F. Defect characterization in Mg-doped GaN studied using a monoenergetic positron beam. J. Appl. Phys.
**2012**, 111, 014508. [Google Scholar] [CrossRef] - Krause-Rehberg, R.; Leipner, H.S. Positron Annihilation in Semiconductors—Defect Studies; Springer-Verlag: Berlin/Heidelberg, Germany, 1999. [Google Scholar]
- Saleh, A.S.; Elhasi, A.M. Investigation of Positron Annihilation Diffusion Length in Gallium Nitride. Am. J. Mod. Phys.
**2014**, 3, 24–28. [Google Scholar] [CrossRef] [Green Version] - Pi, X.D.; Coleman, P.G.; Tseng, C.L.; Burrows, C.P.; Yavich, B.; Wang, W.N. Defects in GaN films studied by positron annihilation spectroscopy. J. Phys. Condens. Matter
**2002**, 14, L243–L248. [Google Scholar] [CrossRef] - Puska, M.J.; Lanki, P.; Nieminen, R.M. Positron affinities for elemental metals. J. Phys. Condens. Matter
**1999**, 1, 6081–6094. [Google Scholar] [CrossRef] - Makkonen, I.; Snicker, A.; Puska, M.J.; Mäki, J.M.; Tuomisto, F. Positrons as interface-sensitive probes of polar semiconductor heterostructures. Phys. Rev. B Condens. Matter Mater. Phys.
**2010**, 82, 041307. [Google Scholar] [CrossRef] [Green Version] - Hu, Y.F.; Shan, Y.Y.; Beling, C.D.; Fung, S.; Xie, M.H.; Cheung, S.H.; Tu, J.; Brauer, G.; Anwand, W.; Tong, D.S. GaN Thin Films on SiC Substrates Studied Using Variable Energy Positron Annihilation Spectroscopy. In Materials Science Forum; Trans Tech Publications Ltd.: Zurich-Uetikon, Switzerland, 2001; Volume 363, pp. 478–480. [Google Scholar]

**Figure 1.**High-resolution transmission electron microscopy (HR-TEM) micrographs and selected area electron diffraction (SAED) patterns showing the display of atom planes in respect to their respective interfaces for: (

**a**) GaN300/Si–Si/AlN interface, (

**b**) GaN300/Si–AlN/GaN interface, (

**c**) GaN700/Si–Si/AlN interface, (

**d**) GaN700/Si–AlN/GaN interface.

**Figure 2.**HR-TEM micrographs with display of simulated crystal lattices near the interface between Si substrate and AlN buffer layer in (

**a**) GaN300/Si, (

**c**) GaN700/Si and between AlN buffer layer and GaN film for (

**b**) GaN300/Si, (

**d**) GaN700/Si.

**Figure 3.**STEM micrographs with EDS mapping and elemental line profiles for (

**a**) GaN300/Si, (

**c**) GaN700/Si, and TEM micrographs showing the overview of the two wafers, (

**b**) and (

**d**), respectively.

**Figure 4.**Experimental and simulated omega scans around (

**a**) (0 0 0 4) planes of GaN in GaN300/Si, (

**b**) ($10\overline{1}5$) planes of GaN in GaN300/Si, (

**c**) (0 0 0 4) planes of GaN in GaN700/Si, (

**d**) ($10\overline{1}5$) planes of GaN in GaN700/Si. Abbreviations: FWHM, full width at half maximum.

**Figure 5.**Plotted depth profiles S(E

_{+}) of (

**a**) GaN700/Si and (

**b**) GaN300/Si. The experimental errors are in the order of the experimental point size. The stairs represent the best parameters obtained by the fit of a 4-layer model to the experimental data by the VEPFIT software. The upper part of figure is the experimental data and the best fit of the relative Ps fraction, F

_{Ps}(E

_{+}).

**Table 1.**Dislocation densities and correlation lengths for GaN in the GaN300/Si and GaN700/Si samples. The uncertainty of the presented values is within the least significant digit.

Sample | ${\mathit{\rho}}_{\mathbf{d}}^{\mathbf{e}}$ [cm^{−2}]
| ${\mathit{\rho}}_{\mathbf{d}}^{\mathbf{s}}$ [cm^{−2}]
| ${\mathit{\rho}}_{\mathbf{d}}^{\mathbf{t}}$ [cm^{−2}]
| r_{d} [nm] | L^{e} [nm] | L^{s} [nm] |
---|---|---|---|---|---|---|

GaN300/Si | 4.19 × 10^{11} | 1.85 × 10^{10} | 4.37 × 10^{11} | 15 | 27 | 107 |

GaN700/Si | 2.24 × 10^{11} | 1.35 × 10^{10} | 2.35 × 10^{11} | 21 | 41 | 220 |

**Table 2.**Best fit parameters obtained by VEPFIT from the S(E

_{+}) and F

_{Ps}(E

_{+}) depth profiles. The values without error margins are fixed parameters.

Sample | GaN300/Si χ^{2} = 1.15 | GaN700/Si χ^{2} = 1.73 | |||||
---|---|---|---|---|---|---|---|

Layer | L_{eff} [nm] | S | d [nm] | L_{eff} [nm] | S | d [nm] | |

GaN | Sublayer | ||||||

GaN1 | 14.3 ± 0.5 | 0.4501 ± 0.0006 | 50 | 13.1 ± 0.4 | 0.4456 ± 0.0004 | 50 | |

GaN2 | 22 ± 6 | 0.4558 ± 0.0004 | 300 | 43 ± 6 | 0.4536 ± 0.0003 | 640 | |

AlN | 26 ± 10 | 0.4957 ± 0.0019 | 105 | 4 ± 33 | 0.4707 ± 0.0032 | 85 | |

Si | 245 | 0.5254 ± 0.0005 | - | 245 | 0.5264 ± 0.0011 | - |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ene, V.L.; Dinescu, D.; Djourelov, N.; Zai, I.; Vasile, B.S.; Serban, A.B.; Leca, V.; Andronescu, E.
Defect Structure Determination of GaN Films in GaN/AlN/Si Heterostructures by HR-TEM, XRD, and Slow Positrons Experiments. *Nanomaterials* **2020**, *10*, 197.
https://doi.org/10.3390/nano10020197

**AMA Style**

Ene VL, Dinescu D, Djourelov N, Zai I, Vasile BS, Serban AB, Leca V, Andronescu E.
Defect Structure Determination of GaN Films in GaN/AlN/Si Heterostructures by HR-TEM, XRD, and Slow Positrons Experiments. *Nanomaterials*. 2020; 10(2):197.
https://doi.org/10.3390/nano10020197

**Chicago/Turabian Style**

Ene, Vladimir Lucian, Doru Dinescu, Nikolay Djourelov, Iulia Zai, Bogdan Stefan Vasile, Andreea Bianca Serban, Victor Leca, and Ecaterina Andronescu.
2020. "Defect Structure Determination of GaN Films in GaN/AlN/Si Heterostructures by HR-TEM, XRD, and Slow Positrons Experiments" *Nanomaterials* 10, no. 2: 197.
https://doi.org/10.3390/nano10020197