Insight into physical processes controlling
the mechanical properties of the wurtzite
group-III nitride family
著者
I Yonenaga, M Deura, Y Tokumoto, K Kutsukake,
Y Ohno
journal or
publication title
Journal of Crystal Growth
volume
500
page range
23-27
year
2018-08-06
URL
http://hdl.handle.net/10097/00128835
Insight into physical processes controlling the mechanical properties of the wurtzite group-III nitride family
I. Yonenaga1,*, M. Deura1,#, Y. Tokumoto1,$, K. Kutsukake1,+, Y. Ohno1
1Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
Abstract
The mechanical properties and elastic moduli of wurtzite-structured nitrides (BN, AlN, GaN and InN) and AlGaN nitride alloy are evaluated by micro- and nano-indentation studies at room temperature (RT), and the physical process controlling the properties of the family is discussed. The hardness of BN, AlN, GaN and InN varies depending on the a-axis lattice constant a as an (n ~ −6), whereas the Young’s, shear and bulk moduli of the nitrides vary as
an (n ~ −5).The properties are governed by the atomic bonding. A homology of indentation hardness scaled using the shear modulus and the magnitude of the Burgers vector for nitrides is observed. The yield strength and stress-intensity factor of the nitrides at RT are presumed. The alloy-hardening effect in AlGaN alloy is weak compared with that in InGaN alloy.
PACS: 62.20.de; 62.20.Qp; 81.05.Ea
Keywords: A1. Hardness; A1. Elastic moduli; A1. Indentation; B1. Nitrides; B1. Nitride
alloys
* Corresponding author: Tel: +81 22 215 2040; fax: +81 22 215 2041
E-mail address: [email protected] (I. Yonenaga)
# Present affiliation: School of Engineering, University of Tokyo $ Present affiliation: Institute of Industrial Science, University of Tokyo
1. Introduction
Boron nitride (BN), aluminum nitride (AlN), gallium nitride (GaN) and indium nitride (InN) are members of the group-III nitride family of the wide-bandgap semiconductors in the wurtzite structure. Members of this semiconductor family have potential applications in optoelectronic devices such as blue and ultraviolet light-emitting devices/photodetectors, high-power/temperature/frequency electronic devices, a n d high-power switches and are chemically stable substrates for various materials. Many of the physical properties required for realizing these applications have been thoroughly reported [1].
The mechanical properties of individual nitrides, especially GaN and AlN, have been investigated experimentally and theoretically, whereas comparatively little is known about those of the broader nitride family. Controlling strains (stresses) in modern devices requires knowledge of the elastic parameters (Young’s and shear moduli), Poisson’s ratio and the yield strength of the epitaxial thin films of suitable thickness on foreign substrates with/without buffer layers. These parameters provide important indications of the transition from elastic and plastic deformation. These elastic/plastic parameters can also provide the basic information necessary to suppress or reduce the generation of grown-in dislocations that adversely affect the optical and electrical performance of nitride devices, and also to explore a new field of applications in sensors and actuators such as surface acoustic wave devices in microelectromechanical systems (MEMS).
Given the importance of the elastic moduli and yield strength in explaining the performance and applications of the group-III nitrides, we have conducted room temperature (RT) micro-indentation and nano-indentation tests on GaN, AlN and InN, and quite recently, BN [2-12]. We have also determined the temperature dependences of the micro-hardness of GaN and AlN were determined [2-5,7]. From a fundamental viewpoint, comparing the elastic parameters and yield strength of the nitrides to gain insights into the underlying physical mechanisms controlling the elastic and plastic properties of materials is important. We herein
summarize the hardness and elastic moduli of wurtzite-structured nitrides (BN, AlN, GaN and InN) and ternary nitride alloys (AlGaN [13] and InGaN [14]) on the basis of our original data [2-13]. In addition, the experimental results are discussed in comparison with some ab
initio predictions to identify future research topics.
2. Hardness and elastic moduli of nitrides
2.1. Experimental procedure and samples
Hardness implies resistance to local deformation. To evaluate hardness, we used a diamond indenter to conduct impression experiments on the (0001) basal-plane surfaces of the samples. The micro-indentation and nano-indentation hardness were determined with Vickers and Berkovich diamond indenters under a load P of 0.5–2 N and 44 mN in maximum, respectively. The hardness H was defined as P/A where A is the contact area of each indentation test. Here, the micro-indentation hardness and nano-indentation hardness are denoted as Hv and HNI. The Young’s modulus Ec along the [0001] c-axis of the nitrides was
evaluated from the unloading stiffness of the load–penetration depth (P–h) curves obtained in the nano-indentation experiments. In the isotropic approximation, the bulk and shear moduli (B and G, respectively) of the nitrides were calculated using the relations
B = Ec/3(1 − 2), (1)
G = Ec/2(1 + ), (2)
where is the Poisson’s ratio. Detailed procedures of the indentation tests are described elsewhere [2,4,6,11,12].
The samples used in hardness tests can be considered quality-highest and thickest among the available nitride samples. A BN sample was prepared from a hexagonal BN bulk crystal by the direct conversion method under a high uniaxial pressure of 10 GPa at 850˚C [12]. Free-standing AlN and GaN crystals 0.5 mm thick were grown by hydride-vapor-phase
epitaxy (HVPE) and were removed chemically from the substrates of Si and -Al2O3,
respectively [2,4]. InN crystals 0.5–4 m thick were grown on a GaN buffer on -Al2O3
substrates by plasma-assisted molecular beam expitaxy (p-MBE) [11]. Details of the growth of the respective nitrides can be found in the respective literatures. Notably, grown-in dislocations in InN (≈ 1010 cm-2) do not substantially affect its properties because local
deformation proceeds via dislocations (> 1013 cm-2) freshly generated and distributed beneath
the indenter [9].
2.2. Indentation hardness
Table 1 summarizes the mechanical parameters of the nitrides together with some of their basic crystalline parameters at RT [2,4,6,11-13,15-22]. The data in this table were obtained mainly from our experimental results, including unpublished ones. The upper part of the table shows the bandgap at 300 K, a- and c-axis lattice constants, magnitude of the
a-dislocation Burgers vector, ionicity [15], phase-transition pressure from wurtzite to rock
salt structure [16,17] and stacking fault energy [18]. The a lattice constant is equal to the magnitude of the a-dislocation Burgers vector. The lower part shows the micro- and nano-indentation hardness: Young’s, shear and bulk moduli: Poisson’s ratio and yield stress. The bottom line indicates stress-intensity factor (fracture toughness) determined from the micro-indentation hardness experiments. The stress-intensity factor characterizes fracture of crack formation/generation in a material.
The HV of the nitrides tend to be smaller than their HNI, which is commonly
observed in materials such as dislocation-free silicon and originates from a difference in the deformation volume related to penetration of the indenter under the applied load. In addition, the Hv is affected by the phase transition and cracking during indentation when the
deformation volume is large. The transition from elastic to plastic deformation, like the onset of plastic deformation (i.e., yield strength), increases with decreasing sample size from macro/microscale to nanoscale [23,24]. BN is t h e hardest material among the nitride family,
whereas InN is the softest. Fig. 1 shows the dependence of the hardnesses HV and HNI of the
nitrides on their a lattice constant.
Though the range of a is rather limited, HNI shows a correlation with the a-axis
lattice constant in the wurtzite-structured nitrides as described by the following relation:
HNI ≈ A1an, n ~ −6, (3)
where A1 is a constant.
A semiconductor crystal is brittle at RT, where obtaining the yield stress is difficult. Tabor proposed that yield stresses are approximately equal to one-third of the indentation hardness (~ H/3) in metallic crystals [21]. If we adopt this, the yield stress of BN, AlN, GaN and InN at RT is estimated to be 18, 6, 5 and 2.5 GPa, respectively, as shown in Table 1. Indeed, Nowak et al. reported a yield strength (critical resolved shear stress) for GaN of ~ 7.5 GPa at RT, as measured by the nano-indentation [25]. The aforementioned yield stresses can be used as an apparent measure of the onset of plastic deformation under the exclusion of any effects of phase transition during indentation experiments.
The experimentally determined stress-intensity factors KIC of the nitrides range
from approximately 0.5 to 3 MPam1/2. Gerberich et al. proposed a model [22];
KIC ~ A2[G(H/3)b]1/2, (4)
where A2 is a constant and b is the magnitude of the Burgers vector of a-dislocation.
According to this model, the KIC of BN can be presumed to be ~ 4.5 MPam1/2. In the future,
accurate knowledge of KIC of AlN should be established because the experimentally obtained
value is rather scattered, as reported in Table 1.
The experimentally determined or derived elastic moduli of the nitrides decrease in the order of Ec, B and G with the exception of BN. The Poisson’s ratio adopted for the
estimation was 0.064 [12]. This value is rather small, compared with those of other members. Generally, experimental knowledge of is rather limited and further confirmation should be conducted.
Fig. 2 shows the nitrides’ Ec and derived B and G values based on our
nano-indentation experiments, plotted against their a-axis lattice constant. Ec, B and G of InN
are much lower than those of GaN and AlN. Strangely, the G of BN is lower than its B, possibly because of the low value of . As evident in Eqs. (1) and (2), B is more sensitive than G to variations of . A clear relation is observed between the Ec, B and G values and the
a-axis lattice constant of the nitrides, described as
Ec, G ≈ A3 an, n ~ −5, (5)
where A3 is a constant. Sher et al. proposed that hardness is governed by the atomic bonding
distance d as d−5 – d−11, depending on the covalency and ionicity, in cubic-type
semiconductors [26]. Parameter a is proportional to d. Thus, bonding character controls the elastic properties of semiconductors irrespective of the crystal structure. Eq. (5) shows that covalency rather than iconicity may be a key factor, as deduced from the difference between the group-III nitrides (III–V) and II–VI compounds such as ZnO [11].
Table 2 shows the elastic stiffness set of the nitrides evaluated by ab initio calculations by Wright [27] and Shimada et al. [28]. The Young’s, shear and bulk moduli and the Poisson’s ratio of the nitrides were derived from the aforementioned stiffness set. For example,
. (7)
The theoretically derived Young’s modulus Ec of the nitrides is compared with that
experimentally determined in terms of dependence on the a lattice parameter in Fig. 3. The elastic moduli decrease qualitatively with increasing a lattice constant in both experimental and theoretical estimations, although some scatters in the magnitudes of Ec between
experimental and theoretical values of the nitrides is clearly observed. For example, the experimental values of Ec are larger than the theoretical one for AlN and InN, whereas vice
versa for BN and GaN. The theoretically derived elastic stiffness values c12 and c33 of GaN
are somewhat large compared with those of AlN and InN (Table 2). Indeed, such a theoretical estimation depends on the model and method used. Though elastic constants can be measured experimentally by methods such as Brillouin scattering and X-ray diffraction, there are some limitations related to the quality and size of samples. Evaluation of the Young’s moduli along the ሾ112ത0ሿ and ሾ11ത00ሿ directions by nano-indentation tests will be useful to validate elastic constants presumed theoretically. Indeed, nano-indentation can be applied to small samples and thin films.
2.4. Homology
The hardness of the semiconductors with a hexagonally closed-packed (hcp) structure shows a universal relationship with respect to the dependence on temperature T [10]. The measured values of Hv for GaN and AlN are scaled by G and plotted against kBT/Gb3 for
the crystals in Fig. 4, where G is the shear modulus, b is the magnitude of the Burgers vector of dislocation, and kB is the Boltzmann constant. The term Gb3 represents the energy of a
minimum length b of dislocation. The hardness data for BN and InN are limited to RT; however, they are included into the diagram in Fig. 4, which shows that they fall into a universal relation, irrespective of the differences in the bandgap, ionicity [15], stacking fault
energy [18,19], etc. The dependence of homology on the dislocation energy can be explained by the hardness being a good measure of resistive strength against initiation of plastic deformation controlled by collective motion of dislocations in a crystal.
3. Ternary nitride alloys
3.1. Alloy samples and experimental procedure
Samples were prepared from (0001)-oriented AlxGa1-xN thin films with a thickness
of 0.8 or 1 m on c-oriented sapphiresubstrates where alloy fraction x was 0.56, 0.61, 0.81, 0.89, 0.92 or 0.97. The HNI was determined by indentation tests with a Berkovich diamond
indenter under a load of 32 mN in maximum for the (0001) basal plane surfaces of the samples at RT [13]. The Young’s modulus Ec along the [0001] c-axis of the alloys was
evaluated in the same manner as noted in the previous section.
3.2. Alloying effect on hardness and Young’s modulus
The AlxGa1-xN alloys exhibited a hardness of 16.5−19.5 GPa depending on the
alloy fraction, with a maximum at x ~ 0.5. The Young’s modulus of the AlGaN alloys varied almost linearly with the alloy fraction x; from GaN to AlN. To clarify the alloying effect in AlGaN, nano-indentation hardness data were normalized to be Hnor(x) by the following
relation:
Hnor(x) = HNI(x) / {HNI(0) + x[HNI(1) − HNI(0)]}, (8)
where HNI(x), HNI(0) and HNI(1) are the measured hardness of AlxGa1-xN, GaN and AlN,
respectively. Fig. 5 plots the variation of Hnor(x) of AlGaN against the alloy fraction x,
together with the variation of the normalized Young’s modulus Enor(x), similarly defined for
Ec(x). The variations of H and E indicate that the alloy-hardening effect in AlGaN is small
effect due to the solid solution, as we previously reported [13,29,30]. Because the most plausible origin of the alloy-hardening effect in III−V alloy semiconductors is the size difference of the constituent group-III atoms [29,31], the aforementioned result is reasonable for AlGaN alloys. Further studies of InGaN alloys where In is atomically much larger than Ga will be important to verify the aforementioned alloy-hardening model in ternary nitride alloys.
4. Conclusions
Based on the results of micro- and nano-indentation tests at RT, mechanical properties and elastic moduli of the wurtzite-structured nitrides (BN, AlN, GaN and InN) and AlGaN nitride alloy were summarized and discussed comprehensively to elucidate the underlying physical mechanisms:
(1) The hardness decreased in the order BN, AlN, GaN and InN, dependent on the a-axis lattice constant as an (n ~ −6) at RT. The yield stresses of the nitrides were deduced to be 18,
6, 5 and 2.5 MPa for BN, AlN, GaN and InN, respectively.
(2) The stress-intensity factor, which characterizes fracture and cracking, for AlN, GaN and InN were determined to be 0.5–3 MPam1/2, whereas that of BN was deduced to be ~ 4.5
MPam1/2, an extremely high value.
(3) The Young’s, shear and bulk moduli of the nitrides at RT depended on the a-axis lattice constant as an (n ~ −5) and were likely controlled by the covalent bonding character.
(4) Indentation hardness of the group-III nitrides scaled by G and b showed homology. (5) Almost no alloy-hardening effect was found in the AlGaN ternary nitride alloy.
References
[1] H. Morkoç, Handbook of Nitride Semiconductors and Devices, Vol. 1 (Wiley-VCH,
Weinheim, 2008).
[2] I. Yonenaga, T. Hoshi, A. Usui, Hardness of bulk single-crystal gallium nitride at high temperatures, Jpn. J. Appl. Phys. 39 (2000) L200-L201.
[3] I. Yonenaga, T. Hoshi, A. Usui, High temperature hardness of bulk single crystal GaN, MRS Internet J. Nitride Semicond. Res. 5S1 (2000) W3.9 (1-5).
[4] I. Yonenaga, A. Nikolaev, Y. Melnik, V. Dmitriev, High-temperature hardness of bulk single-crystal AlN, Jpn. J. Appl. Phys. 40 (2001) L426-L427.
[5] I. Yonenaga, Thermo-mechanical stability of wide-bandgap semiconductors: high temperature hardness of SiC, AlN, GaN, ZnO and ZnSe, Physica B 308-310 (2001) 1150-1152.
[6] I. Yonenaga, T. Shima, M. H. F. Marcel, Nano-indentation hardness and elastic moduli of bulk single-crystal AlN, Jpn. J. Appl. Phys. 41 (2002) 4620-4621.
[7] I. Yonenaga, Hardness of bulk single-crystal GaN and AlN, MRS Internet J. Nitride Semicond. Res. 7 (2002) 6 (1-4).
[8] I. Yonenag, T. Suzuki, Indentation hardnesses of semiconductors and a scaling rule, Philos. Mag. Lett. 82 (2002) 535-542.
[9] Y. Tokumoto, K. Kutsukake, Y. Ohno, I. Yonenaga, Dislocation structure in AlN films induced by in situ nanoindentation, J. Appl. Phys. 112 (2012) 093526; Erratum, ibid. 112 (2012) 129902.
[10] I. Yonenaga, Evaluation of dislocation mobility in wurtzite semiconductors, Mater. Res. Soc. Symp. Proc. 1741 (2015) AA13, http://dx.doi.org/10.1557/opl.2015.61.
[11] I. Yonenaga, Y. Ohkubo, M. Deura, K. Kutsukake, Y. Tokumoto, Y. Ohno, A. Yoshikawa, X. Q. Wang, Elastic properties of indium nitrides grown on sapphire substrates determined by nano-indentation: In comparison with other nitrides, AIP Advances 5 (2015) 077131.
[12] M. Deura, K. Kutsukake, Y. Ohno, I. Yonenaga, T. Taniguchi, Nanoindentation measurements of a highly oriented wurtzite-type boron nitride bulk crystal, Jpn. J. Appl. Phys. 56 (2017) 030301.
[13] Y. Tokumoto, H. Taneichi, Y. Ohno, K. Kutsukake, H. Miyake, K. Hiramatsu, I. Yonenaga, Nanoindentation hardness and elastic modulus of AlGaN alloys, Extended abstracts of the 10th Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) (Kyoto, IEEE, 2013), p. TuPH-3.
[14] R. Nowak, T. Soga, M. Umeno, Surface deformation of the InGaN thin films deposited on a sapphire substrate, Thin Sol. Films. 295(1997) 193-198.
[15] J. C. Phillips, Bonds and Bands in Semiconductors (Academic Press, New York, 1973). [16] M. Ueno, A. Onodera, O. Shimomura, K. Takemura, X-ray observation of the structural phase transition of aluminum nitride under high pressure, Phys. Rev. B 45 (1992) 10123-10126.
[17] M. Ueno, M. Yoshida, A. Onodera, O. Shimomura, K. Takemura, Stability of the wurtzite-type structure under high pressure: GaN and InN, Phys. Rev. B 49 (1994) 14-21.
[18] L. Nistor, S. Nistor, G. Dinca, J. Van Landuyt, D. Schoemaker, V. Copaciu, P.
Georgeoni, N. Arnici, High-resolution electron microscopy and electron spin resonance studies on cubic boron nitride crystals made by high-pressure/high-temperature synthesis Diamond and Related Materials 8 (1999) 738-742.
[19] S. Takeuchi, K. Suzuki, Stacking fault energies of tetrahedrally coordinated crystals, Phys. Stat. Sol. (a) 171 (1999) 99-103.
[21] D. Tabor, Indentation hardness: fifty years on a personal review, Philos. Mag. A 74 (1996) 1207-1212.
[22] W. W. Gerberich, W. M. Mook, C. B. Carter, R. Ballarini, A crack extension force correlation for hard materials, Int. J. Fracture 148 (2007) 109-116.
[23] W.W. Gerberich, J. Michler, R. Ghisleni, F. Östlund, D.D. Stauffer, R. Ballarini, Scale effects for strength, ductility, and toughness in “brittle” materials, J. Mater. Res. 24 (2009) 898-906.
[24] I. Yonenaga, An overview of plasticity of Si crystals governed by dislocation motion, Eng. Fracture Mech. 147 (2015) 468-479.
[25] R. Nowak, M. Pessa, M. Suganuma, M. Leszczynski, I. Grzegory, S. Porowski, F. Yoshida, Elastic and plastic properties of GaN determined by nano-indentation of bulk crystal, Appl. Phys. Lett. 75 (1999) 2070-7072.
[26] A. Sher, A. B. Chen, W. E. Spicer, Dislocation energies and hardness of semiconductors, Appl. Phys. Lett. 46 (1985) 54-56.
[27] A. F. Wright, Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN, J. Appl. Phys. 82 (1997) 2833-2839.
[28] K. Shimada, T. Sota, K. Suzuki, First-principles study on electronic and elastic
properties of BN, AlN, and GaN, J. Appl. Phys. 84 (1998) 4951-4958.
[29] I. Yonenaga, K. Sumino, Mechanical strength of GeSi alloy, J. Appl. Phys. 80 (1996) 3244-3247.
[30] I. Yonenaga, in: G. Kissinger, S. Pizzini (Eds.) Silicon, germanium, and their alloys (CRC Press, London, 2015), Chat. 2，pp. 23-60.
[31] M. Ichimura, A. Sasaki, Solution hardening due to a nonrandom atom arrangement in III-V ternary ally semiconductors, Jpn. J. Appl. Phys. 27 (1988) L176-L178.
Table 1. Experimentally determined mechanical parameters and basic crystalline parameters at RT of BN, AlN, GaN and InN nitrides [2,4,6,11-13,15-22]. Bandgap energy (Eg), a- and
c-lattice constant (a, c), iconicity (f), phase transition pressure (PPT), stacking fault energy (),
micro- and nano-indentation hardness (HV and HNI), Young’s, shear and bulk moduli (Ec, B
and G), Poisson’s ratio (), yield stress (y) and stress-intensity factor (KIC).
Table 2. Theoretically derived elastic stiffness set [c11, c12, c13, c33 and c44, in (GPa)] and
Young’s, shear and bulk moduli [Ec, G and B, in (GPa)] and Poisson’s ratio () of BN, AlN
Figure captions
Fig. 1. Hardness of nitrides dependent on the a-axis lattice constant. The open and solid symbols are for micro-indentation hardness HV and nano-indentation hardness HNI,
respectively.
Fig. 2. Young’s moduli Ec, shear moduli G and bulk moduli B of nitrides dependent on the
a-axis lattice constant. The circle, triangle and square symbols are for Ec, G and B,
respectively.
Fig. 3. Comparison of the a-axis lattice constant dependence of Young’s moduli Ec of nitrides
measured experimentally and estimated by ab initio calculation [26,27]. The solid and open symbols are for experimental results and theoretical estimations, respectively.
Fig. 4. The relation of Hv /G vs kBT/Gb3 for the nitrides.
Fig. 5. Normalized hardness and Young’s modulus of AlxGa1-xN alloy dependent on the alloy
fraction x [13]. The result of In0.1Ga0.9N [14] is superimposed. Red and blue lines are eye
