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[Masataka Tansho](https://orcid.org/0000-0001-7986-3199), [Takayuki Suehiro](https://orcid.org/0000-0001-9444-9738), [Tadashi Shimizu](https://orcid.org/0000-0003-1202-8185)

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[Constancy of the quadrupolar interaction product in nanocrystalline gallium nitride revealed by 71Ga MAS NMR shift distribution](https://mdr.nims.go.jp/datasets/883be023-3eae-4487-a71a-f9b678beaed3)

## Fulltext

1 Constancy of the Quadrupolar Interaction Product in Nanocrystalline Gallium Nitride Revealed by 71Ga MAS NMR Shift Distribution Masataka Tansho a,∗, Takayuki Suehiro b, and Tadashi Shimizu a a High Field NMR Group, Research Center for Advanced Measurement and Characterization, National Institute for Materials Science (NIMS), 3-13 Sakura, Tsukuba 305-0003, Japan b Sialon Group, Research Center for Functional Materials, National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba 305-0044, Japan AUTHOR INFORMATION * Corresponding Author E-mail address: tansho.masataka@nims.go.jp (M. Tansho)   mailto:TANSHO.Masataka@nims.go.jp    2 ABSTRACT  The question of whether the broad 71,69Ga nuclear magnetic resonance (NMR) signal of hexagonal gallium nitride (h-GaN) at 530–330 ppm is related to the Knight shift (caused by the presence of carriers in semiconductors) is the subject of intense debate. The intensity increase observed for the narrower 71Ga magic angle spinning (MAS) NMR signals above 1050 °C suggests that the broader signals do not reflect the decomposition of h-GaN. Herein, we utilized 71Ga multi-quantum (MQ) MAS NMR spectroscopy to reveal that the quadrupolar interaction products for the broad signal of nanocrystalline h-GaN are almost constant in the entire shift range that we investigated, equaling 1.7 ± 0.1 MHz or similar values. Since the above parameter is sensitive to the local chemical symmetry around the Ga atom, the NMR shift distribution is considered not to be related to that of the chemical environment. Consistent with the most recent reports, including those on double-resonance 15N{71Ga} measurements, the Knight shift may be ascribed to defects serving as shallow donors and populating the conduction band. Thus, MQMAS measurements performed using a low-field NMR instrument or by choosing half-integer quadrupole nuclei with a large quadrupole constant such as 69Ga are expected to provide important information for each Knight shift value and for analyzing the nature of semiconductors other than GaN.  Taxonomy:  Add minimum of 2 AND maximum of 6 topics Analytical Chemistry Analysis ,   Industrial Inorganic Chemistry ,   Physical Inorganic Chemistry ,   Nanoparticles ,       Inorganic Materials   ,   Magnetochemistry  https://www.evise.com/evise/faces/pages/submission/Submission.jspx?_adf.ctrl-state=abchi58pj_98https://www.evise.com/evise/faces/pages/submission/Submission.jspx?_adf.ctrl-state=abchi58pj_98https://www.evise.com/evise/faces/pages/submission/Submission.jspx?_adf.ctrl-state=abchi58pj_98https://www.evise.com/evise/faces/pages/submission/Submission.jspx?_adf.ctrl-state=abchi58pj_98https://www.evise.com/evise/faces/pages/submission/Submission.jspx?_adf.ctrl-state=abchi58pj_98    3   GRAPHICAL ABSTRACT       KEYWORDS: semiconductor; carrier distribution; Knight shift; MQMAS; quadrupole coupling constant; defect; Korringa rule; chemical shift axis; NMR shift.        4 1. Introduction Magic-angle spinning nuclear magnetic resonance (MAS NMR) spectroscopy of inorganic solids provides valuable information on their local chemical structure. Although such structural information is typically extracted from chemical shifts, nuclear quadrupole coupling constants are similarly informative for quadrupolar nuclei with spins of I > 1/2, such as 71Ga (I = 3/2) and 69Ga (I = 3/2) [1]. In the past 30 years, gallium nitride with a hexagonal wurtzite structure (h-GaN), one of the most industrially valuable semiconductors, has been continuously investigated by NMR [2–11]. The Ga NMR signals of GaN are often known to comprise two signals: a sharp one at 330–324 ppm and a broad one at 530–330 ppm, although only one sharp 27Al and one sharp 11B MAS NMR signal are observed for hexagonal wurtzite–structured AlN and BN, respectively [2,12]. The sharp peaks in the above cases can be explained by a pseudo-tetrahedral MN4 coordination (M = Ga, Al, B), which is reasonable for the hexagonal wurtzite structure. On the other hand, the broad peak can be explained by either the distribution of impurities and defects [4b–d,7,9] or that of the Knight shift related to conduction electrons (as suggested by Yesinowski et al.) [5,6,8b]. In the latter case, the shift could be related to the concentration of charge carriers in the semiconductor (n) [5,6,10,11] and is probably a function of n1/3 [13]. Using a Korringa-type plot of the spin-lattice relaxation time (T1) of 71Ga, Yesinowski et al. [6] showed that the broad signal was mainly attributable to the Knight shift. Subsequently, Schwenzer et al. [9] showed that T1 values experimentally determined by inversion-recovery measurements are significantly shorter than those expected in the case of the Knight-shift-only influence. They concluded that the broad shift distribution is due to nearest-neighbor inhomogeneities by ruling out large shift contributions from quadrupolar broadening using the similarity in line shape     5 between the 71 Ga NMR spectra along the F1 dimension and the F2 dimension of multi-quantum (MQ) MAS data [9]. Additionally, Yesinowski et al. [11] demonstrated that the dependence of T1 on the saturation-recovery pulse technique implies that the true T1 of the broad signal is not overly short compared to the simulated value. Moreover, Yesinowski et al. [14] utilized analyses including double-resonance 2D 15N{71Ga} measurements to reveal that 71Ga, 14N, and 15N NMR spectra were mutually spatially correlated on a subnanometer scale, with this correlation being reasonable for the nature of the Knight shift. This evidence points toward an origin of the distribution in terms of spatially varying Knight shifts on the nanometer scale for randomly sited defects or dopants, even when the larger-scale concentration is uniform and not variable [14]. Herein, we carried out 71Ga MAS NMR analysis on polycrystalline h-GaN samples prepared under a flow of ammonia [1,4a,8a,8b] under different conditions to clarify the nature of the abovementioned broad signal. The results of 71Ga MQMAS NMR measurements were then compared to the typical 71Ga results obtained for other gallium compounds [15,16]. Although h-GaN has previously been characterized by 71Ga MQMAS (a two-dimensional NMR technique) [9], we decided to employ this powerful technique to separate isotropic and quadrupolar shifts [17] and discuss the quadrupolar interaction product (PQ) by choosing the same 71Ga nucleus.  2. Experimental  2.1. Preparation of GaN samples     6  Commercial GaN (Sigma-Aldrich Co., 99.99%) and Ga2O3 (Sigma-Aldrich Co., 99.99%) powders were used as starting materials to prepare GaN powders via two distinct synthetic routes.  In route (i), commercial yellow GaN powder was heat-treated for various periods in a flowing NH3–1.5 vol% CH4 atmosphere at 1100 °C which produced gray powders, whereas in route (ii), GaN powders were synthesized by reduction–nitridation of Ga2O3 in the same atmosphere at 900 °C for various times, or at various temperatures for a constant time of 4 h [1,4a,8a].  Powders prepared via route (ii) were yellow when synthesized below 1000 °C and gray when the synthesis temperature exceeded 1000 °C.  The detailed synthetic procedure has been reported in our previous work and references therein [1], and the impurity carbon content was found to be as low as 0.03 wt%. The nitrogen and oxygen contents of the as-obtained GaN samples were determined by selective hot-gas extraction (TC-436, LECO Co.). Samples prepared via route (i) using a heat treatment time of 1 h (sample A) and via route (ii) by a 5-h heating at 900 °C (sample B) were shown to have compositions of Ga1N1.000(6)O0.0116(5) and Ga1N0.992(6)O0.069(5), respectively. The phase composition and crystallite size of synthesized powders were analyzed by X-ray diffraction (XRD; SmartLab, Rigaku, 45 kV, 200 mA) using Cu Kα1 radiation, and no crystallographic impurities were observed for samples A and B (Fig. 1). Based on the line broadening of XRD peaks, the crystallite sizes of samples A and B were 89 and 33 nm, respectively. An appreciable a-b plane orientation was observed for sample B (Figs. 1b and c) [8b].       7   Figure 1.  XRD patterns of (a) sample A, (b) sample B, and (c) simulated pattern of h-GaN (ICSD No. 54698).      8  2.2. Solid-state NMR   All NMR measurements were performed on a JEOL ECA 500-MHz NMR spectrometer (71Ga resonance frequency = 152 MHz) using 3.2-mm double resonance MAS probes (Chemagnetics Inc.) without temperature control. All samples were spun at 20 kHz and referenced to 0 ppm utilizing 1.0 M aqueous Ga(NO3)3 as a standard. One-dimensional spectra were acquired by performing 64 scans using a 1.2-μs single-pulse sequence, which corresponded to π/2 pulses for both sharp and broad h-GaN signals (see Supporting Information). The relaxation delay was set to 20 s [6], which was sufficient for comparing the amplitudes of the above two signals. In contrast, the three-pulse (3.6, 1.3, and 15 μs) MQMAS sequence with a zero-quantum filter proposed by Amoureux et al. [18] was employed for 71Ga MQMAS NMR measurements. Accumulation time was set to 1680 scans, and the relaxation delay was set to 0.5 s, which was sufficient to obtain a good signal-to-noise ratio for the broad signal in view of the shorter T1 [6,9,11].  3. Results and discussion Figs. 2–4 show the 71Ga MAS NMR spectra of samples prepared under various reaction conditions, revealing the presence of narrow and broad signals. Specifically, narrow signals were clearly demonstrated by the pseudo-tetrahedral GaN4 coordination that is reasonable for the     9 hexagonal wurtzite structure [2–9]. Moreover, the asymmetrical broadening observed for the narrow signals was larger for sample (ii) below 1050 °C. Although only the sharp signal could be observed for sample (i) at first glance, the broad signal could also be observed upon magnification (Fig. 2(c)) [4a,8a]. Since the intensity of the broad signal did not increase with increasing heat treatment time at 1100 °C, this signal did not reflect decomposition. On the other hand, an intensity increase without sharpening was observed for the sharp signal with time, accompanied by an intensity increase of spinning sidebands. Therefore, previous studies suggest that the fraction related to the broad peak in sample (i) progressively decreased upon heat treatment in NH3–1.5 vol% CH4 at 1100 °C [4a,8b].       10 Figure 2. (a) 71Ga MAS NMR spectra of samples (i) heat-treated at 1100 °C for different time periods. Spectra in (b) correspond to expansions of those in (a) in the region 400–250 ppm, and spectra in (c) correspond to expansions of those in (a) by a factor of ten, with asterisks denoting spinning sidebands.  Fig. 3 shows that the intensity of the broad signal of sample (ii) increased with increasing reaction time at 900 °C. Although the reported GaN decomposition temperatures span a wide range from below 800 °C to above 1100 °C and depend on the applied conditions and the type of GaN sample [8a], the decomposition temperature of sample (ii) was concluded to exceed 1100 °C in view of the reduction–nitridation of Ga2O3 in NH3 flow [19]. Therefore, the broad signal cannot be rationalized by such decomposition but probably reflects the presence of conduction band electrons originating from the presence of oxygens as shallow electron donors at N sites, as has been suggested previously for GaN materials [14]. The increased width of the sharp signal in Fig. 3 compared to that observed in Fig. 2 was ascribed to the poor crystallinity of sample B.      11  Figure 3. (a) 71Ga MAS NMR spectra of samples (ii) synthesized at 900 °C for different time periods. Spectra in (b) are expansions of those in (a) from 400 to 250 ppm, and spectra in (c) are expansions of those in (a) by a factor of five.  Fig. 4 shows the 71Ga MAS NMR spectra of samples (ii) synthesized under different conditions, revealing that with increasing temperature, the sharp signal of the GaN4 structure narrowed below 1050 °C, as reported previously [4a], and became more intense above 1050 °C. On the other hand, the broad signal intensified and shifted downfield at temperatures below 1050 °C, while becoming less intense at temperatures above 1050 °C. The different behaviors observed above and below 1050 °C were in good agreement with the observed sample colors (gray and yellow, respectively). Therefore, the behavior of the sharp signal with increasing     12 temperature was concluded to reflect an increase in crystallinity below 1050 °C and an increase in the fraction of the sharp peak above 1050 °C [4a,8b]. The asymmetrical width of the narrow signals was thought to reflect the crystallinity distribution. On the contrary, the broad signal decrease above 1050 °C did not reflect the decomposition of GaN but rather was related to the decrease of the oxygen-rich fraction and then developed into the sharp peak by nitridation of the oxygen-rich fraction [5a,8b].       13    Figure 4. (a) 71Ga MAS NMR spectra of samples (ii) synthesized at different temperatures for 4 h. Spectra in (b) are expansions of those in (a) from 400 to 250 ppm, and spectra in (c) are expansions of those in (a) by a factor of 20.      14 To understand the above behavior, samples A and B were characterized by 71Ga MQMAS NMR (Fig. 5), wherein (a”) and (b”) correspond to ×10 transverse expansions of (a’) and (b’) after anti-clockwise rotation by 45° for easy viewing.  For the sharp signal, the narrower widths in the F1 dimension compared to those in the F2 dimension could best be explained by the decrease in the remaining second-order quadrupolar width in the F1 dimension. Although the obtained spectra were similar to those recorded by Schwenzer et al. [9], featuring a diagonally aligned broad signal, precise analysis performed herein allowed us to extract more information.        15 Figure 5. 71Ga MQMAS NMR spectra of (a) sample A and (b) sample B, with chemical shift axes shown in red and blue, respectively, and asterisks denoting spinning sidebands. (a’) and (b’) are the results of anticlockwise rotation of (a) and (b) by 45°, respectively. (a’’) and (b’’) correspond to ×10 transverse expansions of (a’) and (b’), respectively.  For simple crystalline compounds with a low extent of disorder, MQMAS signals observed after a shearing transformation are aligned parallel to the F2 axis because of the second-order quadrupolar shift, as reported for gallophosphate, GaPO-34 [15]. Since a similar alignment parallel to the F2 axis was detected for the sharp signals at 330–324 ppm, one can consider the pseudo-tetrahedral GaN4 structures in h-GaN to result from a simple local structure with weakly pronounced chemical disorder. However, this is not the case for the results in this study. For crystallographically disordered materials such as Ga-rich zeolites, the signals become island-shaped because of the local structure distribution [16]. For sheared three-quantum MQMAS spectra, the positions of lines in the F1 dimension are given by δ = δiso – (10/17)δqis,                                                                                         (1) where δiso and δqis are the isotropic chemical shift and the second-order quadrupolar shift, respectively. The positions of experimental resonances (δF1 and δF2) in the F1 and F2 dimensions of the sheared MQMAS spectrum allow δiso and the quadrupolar interaction product PQ (identical to the second-order quadrupolar effect (SOQE)) to be calculated as      16 δiso = (17/27)δF1 + (10/27)δF2,                                                                                                        (2) PQ = (680/27)1/2 × 10–3 × νL(δF1 – δF2)1/2,                                                          (3) where νL is the Larmor frequency, and PQ is related to the quadrupole coupling constant CQ by PQ = CQ (1 + η2/3)1/2, with the asymmetry parameter η taking values between 0 and 1 [17].  Since the diagonally aligned broad signals are almost parallel to the chemical shift axis at small δqis values, the NMR shift distributions of the broad signal are related not to the quadrupolar shift but to the isotropic shift. To clarify this situation, δF2, δF1–δF2, and PQ for selected δF1 values are listed in Tables 1 and 2.   Table 1. δF2, δF1–δF2, and PQ values for selected δF1 values of the broad signal of sample A. δF1/ppm δF2/ppm δF1–δF2/ppm PQ/MHz 500.0 495.0 ± 0.5 5.0 ± 0.5 1.7 ± 0.1 450.0 445.0 ± 0.5 5.0 ± 0.5 1.7 ± 0.1 400.0 395.0 ± 0.5 5.0 ± 0.5 1.7 ± 0.1 350.0 345.0 ± 0.5 5.0 ± 0.5 1.7 ± 0.1  Table 2. δF2, δF1–δF2, and PQ values for selected δF1 values of the broad signal of sample B.     17 δF1/ppm δF2/ppm δF1–δF2/ppm PQ/MHz 500.0 495.0 ± 0.5 5.0 ± 0.5 1.7 ± 0.1 450.0 445.0 ± 0.5 5.0 ± 0.5 1.7 ± 0.1 400.0 395.0 ± 0.5 4.5 ± 0.5 1.6 ± 0.1 350.0 345.0 ± 0.5 4.0 ± 0.5 1.5 ± 0.1  As a result, for all δF1 values, the same PQ of 1.7 MHz and nearly same PQ of 1.7–1.5 MHz with distributions of  ± 0.1 MHz were observed in the 71Ga spectra of h-GaN for sample A and sample B, respectively, whereas for GaO4 coordination, PQ or CQ varied between 1.2 and 11 MHz, depending on the local structure [15,16,20]. Therefore, the local structural disorder represented by the broad line must be negligible for sample A and very small for sample B in the whole range of 500–350 ppm. Here, it should be noted that the “chemical shift axis” is related not only to the chemical shift distribution but also to the distribution of all other isotropic NMR shifts. Moreover, assuming η = 0 for the axially symmetric structure of the pseudo-tetrahedral GaN4 coordination in h-GaN for sample A, all values of CQ, broad for shifts of 500–350 ppm become identical to PQ = 1.7 ± 0.1 MHz and equal the CQ, narrow values of 1.72–1.76 MHz reported for the sharp signal in the range of 330–324 ppm [3]. This coincidence implies that the local structure of the broad signal must be identical to that of the sharp one. The above finding can also be     18 explained by nutation experiments considering the identical π/2 pulse lengths of both signals (see Supporting Information). The obtained CQ, broad values are difficult to rationalize assuming that the nature of the broad shift reflects the structural distribution. However, the NMR shift distribution maintaining the same CQ is easily understood if the nature of the broader NMR shift reflects the distribution of the Knight shift, since this distribution is affected by the distribution of carriers. It is worth noting that defects are not directly correlated to the broad NMR signal via the chemical shift, although they can be related to it via the Knight shift. Oxygen shallow donors [5a,8b,14], or whatever shallow donors are responsible for Knight shifts in sample B, might produce more of a field gradient than whatever shallow donors exist in sample A.  4. Conclusion The broad lines in the F1 axis of the MQMAS spectra were thought to reflect chemical shift distribution, and the quadrupolar interaction was concluded to be negligible at first glance [9]. However, the NMR shift distribution of the broad 71Ga MAS NMR signal of h-GaN was almost unrelated to the chemical shift but was rather related to the Knight shift [5,6,8b], which, in turn, reflected the presence of defects acting as shallow donors that populate the existing conduction band with electrons. This conclusion was drawn based on the constant PQ value of 1.7 ± 0.1 MHz or the almost constant PQ value of 1.7–1.5 ± 0.1 MHz observed in the range of 500–350 ppm, as revealed by 71Ga MQMAS measurements. Assuming the asymmetry parameter η to equal zero for axially symmetric GaN4 coordination, the CQ, broad of sample A becomes identical to PQ and equals the well-known CQ, narrow value of 1.72–1.76 MHz of h-GaN [3]. Hence, our     19 study supports the conclusion drawn by Yesinowski et al. [14] that NMR analysis reveals electronic disorders in the form of broad distributions (Knight shifts) of local metallic properties, which are shown to be spatially correlated on the subnanometer scale. The conclusion that quadrupolar parameters can be obtained for each Knight shift value is interesting and broadly relevant to conducting and degenerately doped semiconductor materials beyond GaN that manifest Knight shifts and often contain quadrupolar half-integer spin nuclei.  ASSOCIATED CONTENT Supporting Information The following files are available free of charge: nutation experiment details (PDF) AUTHOR INFORMATION Corresponding Author *E-mail: tansho.masataka@nims.go.jp ORCID Masataka Tansho: 0000-0001-7986-3199 Notes The authors declare no competing financial interests.  ACKNOWLEDGMENT     20  We express our gratitude to Mr. K. Deguchi and Mr. S. Ohki for their help with NMR measurements and thank Mr. Y. Yajima of NIMS for his assistance with chemical analyses.  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