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Anisotropic electromechanical properties of GaN ceramics caused by polarisation
Ceramics International xxx (xxxx) xxx–xxx
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Anisotropic electromechanical properties of GaN ceramics caused by polarisation GuoShuai Qina,b, Chunsheng Lub, Muhammad Umaira, MingHao Zhaoa,c,d,∗ a
School of Mechanics and Safety Engineering, Zhengzhou University, Zhengzhou, Henan, 450001, China School of Civil and Mechanical Engineering, Curtin University, Perth, WA, 6845, Australia c School of Mechanical Engineering, Zhengzhou University, Zhengzhou, Henan, 450001, China d Henan Key Engineering Laboratory for Anti-fatigue Manufacturing Technology, Zhengzhou University, Zhengzhou, Henan, 450001, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Piezoelectric semiconductor ceramics Polarisation direction Anisotropy Electromechanical properties GaN
Based on three-point bending tests and finite element modelling, effects of polarisation directions are investigated on the mechanical and electrical properties of GaN piezoelectric semiconductor ceramics (PSCs). It is shown that polarisation leads to anisotropic electromechanical properties of PSCs. For GaN samples polarised along the vertical direction, their conductive capabilities enhance by nearly 50%, and however, there are almost no changes in ones with horizontal polarisation. Bending strengths of samples with vertical polarisation increase by 11.6% because piezoelectric charges are driven along the polarisation direction under mechanical loading. It is the correlation between mobility and polarisation direction that largely affects the fracture toughness of GaN PSCs. These experimental findings indicate that, in contrast to traditional ceramics, the electromechanical properties of GaN ceramics can be tailored through polarisation directions.
1. Introduction Piezoelectric semiconductor ceramics (PSCs) are a kind of advanced functional electronic materials with piezoelectric and semiconductive properties [1–3]. When loading on a PSC structure, a piezoelectric potential field is stimulated by ions polarisation, which drives carries to move and redistribute. Such a unique synergy makes PSCs exhibit a variety of novel electromechanical coupling behaviours, and thus, numerous modern products such as piezoelectric charge-coupled devices [4–6] and energy conversion supplies [7–11] have been developed. Polarisation is a key procedure in preparation of piezoelectric ceramics [12–15]. It has been demonstrated that [16–23], due to correlation between the domains switch and mechanical stress near defects, their mechanical properties can be appreciably affected by poling. To the best of our knowledge, however, there are little researches on conductive PSCs, with particular attention on the excellent semiconductor properties. The piezoelectric properties of PSCs are often omitted, and their electromechanical properties are thought to be isotropy and unaffected by polarisation. In fact, piezoelectricity may have an appreciable impact, especially on the electromechanical behaviour with different poling directions. Under external loading, the redistribution of carriers driven along polarisation direction may result in changes of physical and mechanical properties of PSCs [24–26]. Unlike
∗
insulating piezoelectric ceramics, however, to achieve a polarisation electric field in PSCs, a huge and even unrealistic poling current would be required. Thus, polarisation is difficult to achieve and there is no available report on the effects of polarisation direction in PSCs. That is, the actual role of polarisation direction remains unclear in improving performance of PSCs structures and further research is necessary. In this paper, GaN ceramics, a typical kind of PSCs, are investigated by using comprehensive experimental tests and numerical calculations. It is expected to clarify the influence of polarisation direction on their electromechanical properties such as conductivity, strength and fracture toughness. Further, whether there is a relationship is discussed between the mechanical properties of GaN ceramics and an electric load. 2. Experimental procedures As a representative material of third generation conductors, GaN has excellent functional properties and multi-field coupling characteristics [27–29]. Here, samples were produced by pressing GaN powder in a vacuum furnace at 480 °C. The purity of a manufactured GaN PSC is 99.999%, which represents an n-type semiconductor. According to the three-point bending strength test standard [30] and a single-edge precracked beam fracture test method [31,32], samples with
Corresponding author. School of Mechanical Engineering, Zhengzhou University, Zhengzhou, China. E-mail address: [email protected] (M. Zhao).
https://doi.org/10.1016/j.ceramint.2019.10.285 Received 5 August 2019; Received in revised form 13 October 2019; Accepted 30 October 2019 0272-8842/ © 2019 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Please cite this article as: GuoShuai Qin, et al., Ceramics International, https://doi.org/10.1016/j.ceramint.2019.10.285
Ceramics International xxx (xxxx) xxx–xxx
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Fig. 1. Schematic diagrams of a GaN sample polarised along (a) x-axis and (b) y-axis directions.
40 × 3 × 4 mm3 were processed for electromechanical coupling tests. To investigate the correlation between the conductivity, strength, fracture toughness and polarisation direction of PSCs, an interlayer polarisation method was developed with a specialized polarisation device. Samples were divided into three groups, including polarised PSCs along x (horizontal) and y (vertical) directions, as well as ones without polarisation. During polarisation, two poly tetra fluoro ethylene (PTFE) plates of 0.6 mm-thick were set along polarisation direction and silver paste was plated on the outer surface of a plate as an electrode, as illustrated in Fig. 1. Taking the voltage dividing of a PTFE plate into account, DC voltages of 90 kV (horizontal polarisation) and 16 kV (vertical polarisation) were applied to silver electrode, respectively. This makes a poling electric field of up to 24 kV cm−1, which is almost three times of the coercive field of PSCs (8.19 kV cm−1). To avoid discharging, all samples were polarised in a polymethyl methacrylate (PMMA) container filled with silicone oil bath. Under a polarised electric field, free electrons gather at the surface layer of a GaN sample and generate an induced electrical field, which leads to domain switch and finally attains a saturated polarisation intensity. After polarising, X-ray diffraction (XRD) measurements of these three kinds of samples were carried out and their corresponding diffraction patterns are shown in Fig. 2. It is seen that intensities of three strongest diffraction peaks for specimens with x- and y-axis polarisation are different. For a sample polarised along x-axis, the strongest intensity appears at the (101) diffraction peak, indicating a preferred orientation. However, in the case of y-axis polarisation, the strongest diffraction peak is (002), that is, the principal plane of grains is probably consisted of (002) crystal faces. Thus, the grain orientation in PSCs may be affected by polarisation. In consideration of insulation between the loading system and conductive PSCs, pressure head and support jigs were produced by alumina ceramic (see Fig. 3(a)). Silver paste was coated at two ends of a sample to act as electrode, and silver wire (with a diameter of 0.2 mm) was welded to electrode to connect to power supply for providing an
Fig. 2. X-ray diffraction patterns of GaN samples with x- or y-axis and without polarisation.
applied voltage. A mechanical force loaded at the middle of a specimen increases monotonically with a loading rate of 0.05 N/s until fracture. Due to inevitable scatter of experimental results, a total of 12 samples were tested under each testing condition. All mechanical and electrical loads were automatically recorded. For fracture tests, a pre-crack was processed in a three-point bending sample (at the centre of tensile surface) by using a specific diamond disc of 0.06 mm-thick, and its notch depth was controlled in a range of 1.4–2.4 mm. At the bottom of a notch, there is an obvious arc shape with a diameter of 20–50 μm (see 2
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Table 1 Material constants of GaN ceramics (polarised along x-axis) used in finite element analysis. Elastic constant (GPa)
C11 = 286.7 C12 = 103.2 C13 = 134.6 C33 = 293.4 C44 = 21.8
The physical and mechanical behaviours of n-type PSCs are dominated by Newton's law, Poisson's equation, and Boltzmann transport equation [35], that is
(1b)
1 Ji, i = 0, q
(1c)
−
where σij, Di and Ji are the components of stress, electric displacement and current density, respectively. q is the electronic charge, and Δn = n – n0, representing deviation between the random carrier concentration (n) and initial carrier density (n0 = 1.29 × 1023 m−3). Constitutive equations of n-type PSCs can be represented as [35,36].
σij = cijkl εkl − eijk Ek ,
(2a)
Di = eikl εkl + κij Ej,
(2b)
Ji = q (nμij Ej + dij Δn, j ),
(2c)
e31 = −0.57 e15 = −0.53 e33 = 0.71
ε11 = 10.5 ε33 = 9.2
μ11 = 1418 μ33 = 396
d11 = 36.86 d33 = 10.04
As shown in Fig. 4, the current transport performance in samples polarised along y-axis increases by about 50%, and however, there is a little change in ones with x-axis polarisation. This indicates that the conductive capability of PSCs can be regulated with polarisation direction, which is easier and more effective than doping. To clarify its physical mechanisms, we measured the electron mobility of samples with different polarisation directions, and found that the horizontal mobility (μ11 = 653 cm2 V−1 s−1) with y-axis polarisation is higher than that (μ11 = 380 cm2 V−1 s−1) of unpolarised ones [37,38]. For PSCs polarised along x-axis, the horizontal mobility (μ33) remains almost unchanged (see Table 1). That is, the electron mobility (perpendicular to polarisation direction) can be largely enhanced by polarising. This is mainly attributed to the domain switch generated by polarisation. A high-speed carrier transport channel perpendicular to polarisation direction was formed at the domain wall [40], which can promote carrier transmission. In addition, domain flipping along polarisation direction provides the extra energy for electrons to escape constraint of covalent bonds and further stimulates more valence electrons to enter a conduction band. The excited electrons move rapidly on the transport channel and result in an increase of conductivity perpendicular to
3. Numerical analysis
Di, i = −qΔn,
(cm2 V−1 s−1)
Diffusion coefficient (cm2 s−1)
Migration rate
4. Results and discussion
Fig. 3(b, c)), which can reduce the influence of notch passivation [33,34].
(1a)
Relative dielectric constant (κij/κ0)
electron mobility. According to the experimental conditions, GaN PSCs were connected to Ag electrodes and constituted a Schottky contact [38]. Therefore, Schottky electrical boundary conditions [38,39] were used in finite element calculations. Moreover, to meet the Debye length of GaN PSCs [35,38], grids in a Schottky contact region must be refined in numerical modelling.
Fig. 3. (a) Illustration of experimental configuration with a span distance (s) of 30 mm in electromechanical bending tests. (b) Morphology of a pre-crack tip in a GaN sample, with the three-dimensional bottom view (c) tested by a microscope (Leica, DVM5000).
σij, j = 0,
Piezoelectric constant (C m−2)
Where cijkl , eijk , κij , μij and dij are material constants of elastic, piezoelectric, dielectric, migration and diffusion, respectively. Here, it is worth noting that a concrete constitutive formulation is dependent on polarisation direction. The strain εij and the electric field Ei are related to the mechanical displacement u and the electric potential φ through
εij =
1 (ui, j + uj, i ), 2
Ei = −φ, i .
(3) (4)
Generally, it is quite difficult to study a nonlinear multi-field problem of PSCs by an analytic method. Therefore, a finite element method was adopted to analyse the electromechanical properties by using a customized partial differential equation tool in COMSOL Multiphysics, with relevant material constants (x-axis polarisation) as listed in Table 1. In contrast to samples unpolarised [37] and polarised along yaxis [38], there is an obvious change of piezoelectric coefficients and
Fig. 4. The current-voltage characteristics of samples under different polarisation directions without loading, in which lines represent corresponding numerical results. 3
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Fig. 5. The bending strength of samples with different polarisation directions versus an applied electric voltage.
Fig. 7. (a) Variation of KIC for three kinds of samples with an applied voltage (Va) and (b) their current density distributions versus the ratio of a crack tip spacing to a notch depth (i.e., r/a), where inset shows discharging of a sample polarized along y-axis during fracture testing.
Fig. 8. Scanning electron microscope photographs of fracture surfaces of samples polarised along (a) y-axis and (b) x-axis directions under an applied voltage of 5 V. (c) and (d) are enlarged graphs of the corresponding rectangle regions in (a) and (b), respectively.
Fig. 6. (a) Distributions of piezoelectric polarisation charges in unpolarised and polarised samples along x = 0 under a load of 4 N, where nephogram shows the carrier concentration near surface with y-axis polarisation. (b) The maximum horizontal stress versus a mechanical load (P) under different polarisation directions.
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concentrated at the crack tip, resulting in melting of materials. It is obvious to see that tested results are agreement with numerical analysis in Fig. 7(b).
polarisation direction. Thus, under the experimental schedule as illustrated in Fig. 3(a), the x-axis polarisation has little effect on horizontal mobility. Based on the tested parameters and experimental conditions, numerical simulations were performed to further confirm the effect of electron mobility on conductivity. As shown in Fig. 4, the current transport properties of GaN PSCs are strongly dependent on polarisation direction. Here, it is worth noting that, to clarify underlying physical mechanisms, more experimental and theoretical studies are still needed. According to experimental results in Fig. 5, bending strength (defined as the maximum bending stress) of samples with y-axis polarisation increases by 11.6% in comparison to that of unpolarised ones, and however, such an enhancing phenomenon does not appear in the case of x-axis polarisation. When polarised along y-axis, piezoelectric charges are driven and gathered on top and bottom surfaces under mechanical loading (see Fig. 6(a)). In contrast, there are no observed changes in unpolarised GaN PSCs because of non-piezoelectricity. Redistribution of carriers leads to an electric field concentration on top and bottom surfaces. According to the constitutive relation (Eq. (2a)), the reduced maximum stress at fracture (i.e., σxx at x = 0, y = −t ) results in enhancement of bending strength due to concentration of an electric field. It is seen in Fig. 6(b) that there is a distinct deviation of stress between unpolarised and polarised (along y-axis) GaN PSCs. For samples with x-axis polarisation, piezoelectric charges are driven along the horizontal direction and thus, there are no concentration of carriers and electric fields at the location of fracture. Therefore, similar to samples without polarisation, the maximum stress is not affected by polarising (see Fig. 6(b)), which is consistent with that observed in experiments. It is seen from Fig. 5 that, as increase of voltage, bending strengths decrease with the fastest one occurring along y-axis polarisation. For piezoelectric ceramics, bending strength decreases in the range of Curie temperature [17,37]. Due to the thermoelectric effect of PSCs, when an electric voltage is added up to 12 V, the average temperature of unpolarised samples is 139 °C. The corresponding temperatures of other two types of samples are 142 °C (x-axis polarisation) and 174 °C (y-axis polarisation), respectively. Under the same voltage, samples with y-axis polarisation have the highest temperature rise and thus, the decreasing trend of bending strength is the fastest (see Fig. 5). Fig. 7(a) shows that fracture toughness (KIC, i.e., the critical stress intensity factor [32]) of samples polarised along y-axis increase with applied electric loads. However, samples polarised along x-axis is just opposite. Here, increase of the fracture load is attributed to electro-plastic deformation [41,42], which was triggered by the high current density and discharging near a crack tip (see Fig. 7(b)). The accumulation of current density causes a very high temperature and makes materials near a crack tip malleable, and thus an increase of KIC. Due to the Joule heat, temperature of the tested sample increases with electric load and the thermal influence plays a leading role. According to the correlation between the fracture strength and testing temperature [17,37], KIC would be reduced. For samples with x-axis polarisation and unpolarised ones, because mobility in the x-axis direction does not significantly increase, the current density near a crack tip is much lower than that of samples polarised along y-axis at the same voltage (see Fig. 7(b)). The temperature rise at the crack tip is not enough to form an electro-plastic zone and thus, KIC continuously decreases with electrical load (see Fig. 7(a)). As shown in Fig. 8(a), under an applied voltage of 5 V, there is an obvious ablation area on fracture surface of a sample with y-axis polarisation. Grains were melted and re-solidified (Fig. 8(c)), indicating a high temperature near the crack tip and the discharging during crack propagation (see Fig. 7(b)). However, for samples polarised along xaxis, fractograph looks uniform and smooth, and grains show a typical lamellar structure (see Fig. 8(b, d)). Such a difference of fractographs is mainly due to anisotropy of conductivities, which is caused by diverse polarisation directions. Under the same electrical voltage load, the current density of y-axis polarised sample is much larger, which is
5. Conclusions In this paper, the influence of polarisation directions on the electrical and mechanical properties of GaN PSCs has been clarified based on experimental and numerical studies. In comparison with unpolarised GaN PSCs, the conductive capability of samples with vertical polarisation increases by about 50%, and however, there is a little change in GaN PSCs with horizontal polarisation. This is mainly due to mobility and diffusivity that are related to polarisation directions of PSCs. That is, mobility along perpendicular polarisation largely increases with polarising. Owing to piezoelectricity and redistribution of piezoelectric polarisation charges, the average bending strength of samples with vertical polarisation enhances by 11.6%, but with the applied electric load, it quickly decreases. Besides, the anisotropic fracture behaviour is resulted by different polarisation directions. Thus, varying polarisation directions can be applied to tailor the electromechanical properties of GaN PSCs, and thus, the correct choice of a polarisation direction is crucial in manufacture and design of GaN devices. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors declare the following financial interests/personal relationships which may be considered as potential competing interests. Acknowledgements This work has been supported by the National Natural Science Foundation of China (No. 11572289). References [1] R.S. Withers, Electron devices on piezoelectric semiconductors: a device model, IEEE Trans. Ultrason. Ferroelectr. 31 (1984) 117–123. [2] G.J. Rees, Strained layer piezoelectric semiconductor devices, Microelectron. J. 28 (1997) 957–967. [3] O. Akira, T. Norihiko, K. Yuko, S. Takuya, H. Satoh, Y. Haruyasu, Dielectric activity and ferroelectricity in piezoelectric semiconductor Li-doped ZnO, Jpn. J. Appl. Phys. 35 (1996) 5160–5162. [4] C.L. Zhang, X.Y. Wang, W.Q. Chen, Propagation of extensional waves in a piezoelectric semiconductor rod, AIP Adv. 6 (2016) 045301. [5] J.S. Yang, Y.C. Song, A.K. Soh, Analysis of a circular piezoelectric semiconductor embedded in a piezoelectric semiconductor substrate, Arch. Appl. Mech. 76 (2006) 381–391. [6] X.D. Wang, J. Zhou, J.H. Song, J. Liu, N.S. Xu, Z.L. Wang, Piezoelectric field effect transistor and nanoforce sensor based on a single ZnO nanowire, Nano Lett. 6 (2006) 2768–2772. [7] P.X. Gao, J.H. Song, J. Liu, Z.L. Wang, Nanowire piezoelectric nanogenerators on plastic substrates as flexible power sources for nanodevices, Adv. Mater. 19 (2007) 67–72. [8] F.S. Hickernell, The piezoelectric semiconductor and acoustoelectronic device development in the sixties, IEEE. Trans. Ultrason. Ferroelectr. 52 (2005) 737–745. [9] W.Z. Wu, X.N. Wen, Z.L. Wang, Taxel-addressable matrix of vertical-nanowire piezotronic transistors for active and adaptive tactile imaging, Science 340 (2013) 952–957. [10] S.Q. Fan, W.L. Yang, Y.T. Hu, Adjustment and control on the fundamental characteristics of a piezoelectric PN junction by mechanical-loading, Nano Energy 52 (2018) 416–421. [11] P. Li, F. Jin, J.S. Yang, Effects of semiconduction on electromechanical energy conversion in piezoelectrics, Smart Mater. Struct. 24 (2015) 025021. [12] A.D. Prewitt, J.L. Jones, Effects of the poling process on piezoelectric properties in lead zirconate titanate ceramics, Ferroelectrics 419 (2011) 39–45. [13] T.M. Kamel, G.D. With, Poling of hard ferroelectric PZT ceramics, J. Eur. Ceram. Soc. 28 (2008) 1827–1838. [14] R. Rianyoi, R. Potong, A. Ngamjarurojana, A. Chaipanich, Poling effects and piezoelectric properties of PVDF-modified 0-3 connectivity cement-based/lead-free 0.94(Bi0.5Na0.5) TiO3-0.06BaTiO3 piezoelectric ceramic composites, J. Mater. Sci. 52 (2018) 345–355.
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Ceramics International journal homepage: www.elsevier.com/locate/ceramint
Anisotropic electromechanical properties of GaN ceramics caused by polarisation GuoShuai Qina,b, Chunsheng Lub, Muhammad Umaira, MingHao Zhaoa,c,d,∗ a
School of Mechanics and Safety Engineering, Zhengzhou University, Zhengzhou, Henan, 450001, China School of Civil and Mechanical Engineering, Curtin University, Perth, WA, 6845, Australia c School of Mechanical Engineering, Zhengzhou University, Zhengzhou, Henan, 450001, China d Henan Key Engineering Laboratory for Anti-fatigue Manufacturing Technology, Zhengzhou University, Zhengzhou, Henan, 450001, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Piezoelectric semiconductor ceramics Polarisation direction Anisotropy Electromechanical properties GaN
Based on three-point bending tests and finite element modelling, effects of polarisation directions are investigated on the mechanical and electrical properties of GaN piezoelectric semiconductor ceramics (PSCs). It is shown that polarisation leads to anisotropic electromechanical properties of PSCs. For GaN samples polarised along the vertical direction, their conductive capabilities enhance by nearly 50%, and however, there are almost no changes in ones with horizontal polarisation. Bending strengths of samples with vertical polarisation increase by 11.6% because piezoelectric charges are driven along the polarisation direction under mechanical loading. It is the correlation between mobility and polarisation direction that largely affects the fracture toughness of GaN PSCs. These experimental findings indicate that, in contrast to traditional ceramics, the electromechanical properties of GaN ceramics can be tailored through polarisation directions.
1. Introduction Piezoelectric semiconductor ceramics (PSCs) are a kind of advanced functional electronic materials with piezoelectric and semiconductive properties [1–3]. When loading on a PSC structure, a piezoelectric potential field is stimulated by ions polarisation, which drives carries to move and redistribute. Such a unique synergy makes PSCs exhibit a variety of novel electromechanical coupling behaviours, and thus, numerous modern products such as piezoelectric charge-coupled devices [4–6] and energy conversion supplies [7–11] have been developed. Polarisation is a key procedure in preparation of piezoelectric ceramics [12–15]. It has been demonstrated that [16–23], due to correlation between the domains switch and mechanical stress near defects, their mechanical properties can be appreciably affected by poling. To the best of our knowledge, however, there are little researches on conductive PSCs, with particular attention on the excellent semiconductor properties. The piezoelectric properties of PSCs are often omitted, and their electromechanical properties are thought to be isotropy and unaffected by polarisation. In fact, piezoelectricity may have an appreciable impact, especially on the electromechanical behaviour with different poling directions. Under external loading, the redistribution of carriers driven along polarisation direction may result in changes of physical and mechanical properties of PSCs [24–26]. Unlike
∗
insulating piezoelectric ceramics, however, to achieve a polarisation electric field in PSCs, a huge and even unrealistic poling current would be required. Thus, polarisation is difficult to achieve and there is no available report on the effects of polarisation direction in PSCs. That is, the actual role of polarisation direction remains unclear in improving performance of PSCs structures and further research is necessary. In this paper, GaN ceramics, a typical kind of PSCs, are investigated by using comprehensive experimental tests and numerical calculations. It is expected to clarify the influence of polarisation direction on their electromechanical properties such as conductivity, strength and fracture toughness. Further, whether there is a relationship is discussed between the mechanical properties of GaN ceramics and an electric load. 2. Experimental procedures As a representative material of third generation conductors, GaN has excellent functional properties and multi-field coupling characteristics [27–29]. Here, samples were produced by pressing GaN powder in a vacuum furnace at 480 °C. The purity of a manufactured GaN PSC is 99.999%, which represents an n-type semiconductor. According to the three-point bending strength test standard [30] and a single-edge precracked beam fracture test method [31,32], samples with
Corresponding author. School of Mechanical Engineering, Zhengzhou University, Zhengzhou, China. E-mail address: [email protected] (M. Zhao).
https://doi.org/10.1016/j.ceramint.2019.10.285 Received 5 August 2019; Received in revised form 13 October 2019; Accepted 30 October 2019 0272-8842/ © 2019 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Please cite this article as: GuoShuai Qin, et al., Ceramics International, https://doi.org/10.1016/j.ceramint.2019.10.285
Ceramics International xxx (xxxx) xxx–xxx
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Fig. 1. Schematic diagrams of a GaN sample polarised along (a) x-axis and (b) y-axis directions.
40 × 3 × 4 mm3 were processed for electromechanical coupling tests. To investigate the correlation between the conductivity, strength, fracture toughness and polarisation direction of PSCs, an interlayer polarisation method was developed with a specialized polarisation device. Samples were divided into three groups, including polarised PSCs along x (horizontal) and y (vertical) directions, as well as ones without polarisation. During polarisation, two poly tetra fluoro ethylene (PTFE) plates of 0.6 mm-thick were set along polarisation direction and silver paste was plated on the outer surface of a plate as an electrode, as illustrated in Fig. 1. Taking the voltage dividing of a PTFE plate into account, DC voltages of 90 kV (horizontal polarisation) and 16 kV (vertical polarisation) were applied to silver electrode, respectively. This makes a poling electric field of up to 24 kV cm−1, which is almost three times of the coercive field of PSCs (8.19 kV cm−1). To avoid discharging, all samples were polarised in a polymethyl methacrylate (PMMA) container filled with silicone oil bath. Under a polarised electric field, free electrons gather at the surface layer of a GaN sample and generate an induced electrical field, which leads to domain switch and finally attains a saturated polarisation intensity. After polarising, X-ray diffraction (XRD) measurements of these three kinds of samples were carried out and their corresponding diffraction patterns are shown in Fig. 2. It is seen that intensities of three strongest diffraction peaks for specimens with x- and y-axis polarisation are different. For a sample polarised along x-axis, the strongest intensity appears at the (101) diffraction peak, indicating a preferred orientation. However, in the case of y-axis polarisation, the strongest diffraction peak is (002), that is, the principal plane of grains is probably consisted of (002) crystal faces. Thus, the grain orientation in PSCs may be affected by polarisation. In consideration of insulation between the loading system and conductive PSCs, pressure head and support jigs were produced by alumina ceramic (see Fig. 3(a)). Silver paste was coated at two ends of a sample to act as electrode, and silver wire (with a diameter of 0.2 mm) was welded to electrode to connect to power supply for providing an
Fig. 2. X-ray diffraction patterns of GaN samples with x- or y-axis and without polarisation.
applied voltage. A mechanical force loaded at the middle of a specimen increases monotonically with a loading rate of 0.05 N/s until fracture. Due to inevitable scatter of experimental results, a total of 12 samples were tested under each testing condition. All mechanical and electrical loads were automatically recorded. For fracture tests, a pre-crack was processed in a three-point bending sample (at the centre of tensile surface) by using a specific diamond disc of 0.06 mm-thick, and its notch depth was controlled in a range of 1.4–2.4 mm. At the bottom of a notch, there is an obvious arc shape with a diameter of 20–50 μm (see 2
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Table 1 Material constants of GaN ceramics (polarised along x-axis) used in finite element analysis. Elastic constant (GPa)
C11 = 286.7 C12 = 103.2 C13 = 134.6 C33 = 293.4 C44 = 21.8
The physical and mechanical behaviours of n-type PSCs are dominated by Newton's law, Poisson's equation, and Boltzmann transport equation [35], that is
(1b)
1 Ji, i = 0, q
(1c)
−
where σij, Di and Ji are the components of stress, electric displacement and current density, respectively. q is the electronic charge, and Δn = n – n0, representing deviation between the random carrier concentration (n) and initial carrier density (n0 = 1.29 × 1023 m−3). Constitutive equations of n-type PSCs can be represented as [35,36].
σij = cijkl εkl − eijk Ek ,
(2a)
Di = eikl εkl + κij Ej,
(2b)
Ji = q (nμij Ej + dij Δn, j ),
(2c)
e31 = −0.57 e15 = −0.53 e33 = 0.71
ε11 = 10.5 ε33 = 9.2
μ11 = 1418 μ33 = 396
d11 = 36.86 d33 = 10.04
As shown in Fig. 4, the current transport performance in samples polarised along y-axis increases by about 50%, and however, there is a little change in ones with x-axis polarisation. This indicates that the conductive capability of PSCs can be regulated with polarisation direction, which is easier and more effective than doping. To clarify its physical mechanisms, we measured the electron mobility of samples with different polarisation directions, and found that the horizontal mobility (μ11 = 653 cm2 V−1 s−1) with y-axis polarisation is higher than that (μ11 = 380 cm2 V−1 s−1) of unpolarised ones [37,38]. For PSCs polarised along x-axis, the horizontal mobility (μ33) remains almost unchanged (see Table 1). That is, the electron mobility (perpendicular to polarisation direction) can be largely enhanced by polarising. This is mainly attributed to the domain switch generated by polarisation. A high-speed carrier transport channel perpendicular to polarisation direction was formed at the domain wall [40], which can promote carrier transmission. In addition, domain flipping along polarisation direction provides the extra energy for electrons to escape constraint of covalent bonds and further stimulates more valence electrons to enter a conduction band. The excited electrons move rapidly on the transport channel and result in an increase of conductivity perpendicular to
3. Numerical analysis
Di, i = −qΔn,
(cm2 V−1 s−1)
Diffusion coefficient (cm2 s−1)
Migration rate
4. Results and discussion
Fig. 3(b, c)), which can reduce the influence of notch passivation [33,34].
(1a)
Relative dielectric constant (κij/κ0)
electron mobility. According to the experimental conditions, GaN PSCs were connected to Ag electrodes and constituted a Schottky contact [38]. Therefore, Schottky electrical boundary conditions [38,39] were used in finite element calculations. Moreover, to meet the Debye length of GaN PSCs [35,38], grids in a Schottky contact region must be refined in numerical modelling.
Fig. 3. (a) Illustration of experimental configuration with a span distance (s) of 30 mm in electromechanical bending tests. (b) Morphology of a pre-crack tip in a GaN sample, with the three-dimensional bottom view (c) tested by a microscope (Leica, DVM5000).
σij, j = 0,
Piezoelectric constant (C m−2)
Where cijkl , eijk , κij , μij and dij are material constants of elastic, piezoelectric, dielectric, migration and diffusion, respectively. Here, it is worth noting that a concrete constitutive formulation is dependent on polarisation direction. The strain εij and the electric field Ei are related to the mechanical displacement u and the electric potential φ through
εij =
1 (ui, j + uj, i ), 2
Ei = −φ, i .
(3) (4)
Generally, it is quite difficult to study a nonlinear multi-field problem of PSCs by an analytic method. Therefore, a finite element method was adopted to analyse the electromechanical properties by using a customized partial differential equation tool in COMSOL Multiphysics, with relevant material constants (x-axis polarisation) as listed in Table 1. In contrast to samples unpolarised [37] and polarised along yaxis [38], there is an obvious change of piezoelectric coefficients and
Fig. 4. The current-voltage characteristics of samples under different polarisation directions without loading, in which lines represent corresponding numerical results. 3
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Fig. 5. The bending strength of samples with different polarisation directions versus an applied electric voltage.
Fig. 7. (a) Variation of KIC for three kinds of samples with an applied voltage (Va) and (b) their current density distributions versus the ratio of a crack tip spacing to a notch depth (i.e., r/a), where inset shows discharging of a sample polarized along y-axis during fracture testing.
Fig. 8. Scanning electron microscope photographs of fracture surfaces of samples polarised along (a) y-axis and (b) x-axis directions under an applied voltage of 5 V. (c) and (d) are enlarged graphs of the corresponding rectangle regions in (a) and (b), respectively.
Fig. 6. (a) Distributions of piezoelectric polarisation charges in unpolarised and polarised samples along x = 0 under a load of 4 N, where nephogram shows the carrier concentration near surface with y-axis polarisation. (b) The maximum horizontal stress versus a mechanical load (P) under different polarisation directions.
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concentrated at the crack tip, resulting in melting of materials. It is obvious to see that tested results are agreement with numerical analysis in Fig. 7(b).
polarisation direction. Thus, under the experimental schedule as illustrated in Fig. 3(a), the x-axis polarisation has little effect on horizontal mobility. Based on the tested parameters and experimental conditions, numerical simulations were performed to further confirm the effect of electron mobility on conductivity. As shown in Fig. 4, the current transport properties of GaN PSCs are strongly dependent on polarisation direction. Here, it is worth noting that, to clarify underlying physical mechanisms, more experimental and theoretical studies are still needed. According to experimental results in Fig. 5, bending strength (defined as the maximum bending stress) of samples with y-axis polarisation increases by 11.6% in comparison to that of unpolarised ones, and however, such an enhancing phenomenon does not appear in the case of x-axis polarisation. When polarised along y-axis, piezoelectric charges are driven and gathered on top and bottom surfaces under mechanical loading (see Fig. 6(a)). In contrast, there are no observed changes in unpolarised GaN PSCs because of non-piezoelectricity. Redistribution of carriers leads to an electric field concentration on top and bottom surfaces. According to the constitutive relation (Eq. (2a)), the reduced maximum stress at fracture (i.e., σxx at x = 0, y = −t ) results in enhancement of bending strength due to concentration of an electric field. It is seen in Fig. 6(b) that there is a distinct deviation of stress between unpolarised and polarised (along y-axis) GaN PSCs. For samples with x-axis polarisation, piezoelectric charges are driven along the horizontal direction and thus, there are no concentration of carriers and electric fields at the location of fracture. Therefore, similar to samples without polarisation, the maximum stress is not affected by polarising (see Fig. 6(b)), which is consistent with that observed in experiments. It is seen from Fig. 5 that, as increase of voltage, bending strengths decrease with the fastest one occurring along y-axis polarisation. For piezoelectric ceramics, bending strength decreases in the range of Curie temperature [17,37]. Due to the thermoelectric effect of PSCs, when an electric voltage is added up to 12 V, the average temperature of unpolarised samples is 139 °C. The corresponding temperatures of other two types of samples are 142 °C (x-axis polarisation) and 174 °C (y-axis polarisation), respectively. Under the same voltage, samples with y-axis polarisation have the highest temperature rise and thus, the decreasing trend of bending strength is the fastest (see Fig. 5). Fig. 7(a) shows that fracture toughness (KIC, i.e., the critical stress intensity factor [32]) of samples polarised along y-axis increase with applied electric loads. However, samples polarised along x-axis is just opposite. Here, increase of the fracture load is attributed to electro-plastic deformation [41,42], which was triggered by the high current density and discharging near a crack tip (see Fig. 7(b)). The accumulation of current density causes a very high temperature and makes materials near a crack tip malleable, and thus an increase of KIC. Due to the Joule heat, temperature of the tested sample increases with electric load and the thermal influence plays a leading role. According to the correlation between the fracture strength and testing temperature [17,37], KIC would be reduced. For samples with x-axis polarisation and unpolarised ones, because mobility in the x-axis direction does not significantly increase, the current density near a crack tip is much lower than that of samples polarised along y-axis at the same voltage (see Fig. 7(b)). The temperature rise at the crack tip is not enough to form an electro-plastic zone and thus, KIC continuously decreases with electrical load (see Fig. 7(a)). As shown in Fig. 8(a), under an applied voltage of 5 V, there is an obvious ablation area on fracture surface of a sample with y-axis polarisation. Grains were melted and re-solidified (Fig. 8(c)), indicating a high temperature near the crack tip and the discharging during crack propagation (see Fig. 7(b)). However, for samples polarised along xaxis, fractograph looks uniform and smooth, and grains show a typical lamellar structure (see Fig. 8(b, d)). Such a difference of fractographs is mainly due to anisotropy of conductivities, which is caused by diverse polarisation directions. Under the same electrical voltage load, the current density of y-axis polarised sample is much larger, which is
5. Conclusions In this paper, the influence of polarisation directions on the electrical and mechanical properties of GaN PSCs has been clarified based on experimental and numerical studies. In comparison with unpolarised GaN PSCs, the conductive capability of samples with vertical polarisation increases by about 50%, and however, there is a little change in GaN PSCs with horizontal polarisation. This is mainly due to mobility and diffusivity that are related to polarisation directions of PSCs. That is, mobility along perpendicular polarisation largely increases with polarising. Owing to piezoelectricity and redistribution of piezoelectric polarisation charges, the average bending strength of samples with vertical polarisation enhances by 11.6%, but with the applied electric load, it quickly decreases. Besides, the anisotropic fracture behaviour is resulted by different polarisation directions. Thus, varying polarisation directions can be applied to tailor the electromechanical properties of GaN PSCs, and thus, the correct choice of a polarisation direction is crucial in manufacture and design of GaN devices. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors declare the following financial interests/personal relationships which may be considered as potential competing interests. Acknowledgements This work has been supported by the National Natural Science Foundation of China (No. 11572289). References [1] R.S. Withers, Electron devices on piezoelectric semiconductors: a device model, IEEE Trans. Ultrason. Ferroelectr. 31 (1984) 117–123. [2] G.J. Rees, Strained layer piezoelectric semiconductor devices, Microelectron. J. 28 (1997) 957–967. [3] O. Akira, T. Norihiko, K. Yuko, S. Takuya, H. Satoh, Y. Haruyasu, Dielectric activity and ferroelectricity in piezoelectric semiconductor Li-doped ZnO, Jpn. J. Appl. Phys. 35 (1996) 5160–5162. [4] C.L. Zhang, X.Y. Wang, W.Q. Chen, Propagation of extensional waves in a piezoelectric semiconductor rod, AIP Adv. 6 (2016) 045301. [5] J.S. Yang, Y.C. Song, A.K. Soh, Analysis of a circular piezoelectric semiconductor embedded in a piezoelectric semiconductor substrate, Arch. Appl. Mech. 76 (2006) 381–391. [6] X.D. Wang, J. Zhou, J.H. Song, J. Liu, N.S. Xu, Z.L. Wang, Piezoelectric field effect transistor and nanoforce sensor based on a single ZnO nanowire, Nano Lett. 6 (2006) 2768–2772. [7] P.X. Gao, J.H. Song, J. Liu, Z.L. Wang, Nanowire piezoelectric nanogenerators on plastic substrates as flexible power sources for nanodevices, Adv. Mater. 19 (2007) 67–72. [8] F.S. Hickernell, The piezoelectric semiconductor and acoustoelectronic device development in the sixties, IEEE. Trans. Ultrason. Ferroelectr. 52 (2005) 737–745. [9] W.Z. Wu, X.N. Wen, Z.L. Wang, Taxel-addressable matrix of vertical-nanowire piezotronic transistors for active and adaptive tactile imaging, Science 340 (2013) 952–957. [10] S.Q. Fan, W.L. Yang, Y.T. Hu, Adjustment and control on the fundamental characteristics of a piezoelectric PN junction by mechanical-loading, Nano Energy 52 (2018) 416–421. [11] P. Li, F. Jin, J.S. Yang, Effects of semiconduction on electromechanical energy conversion in piezoelectrics, Smart Mater. Struct. 24 (2015) 025021. [12] A.D. Prewitt, J.L. Jones, Effects of the poling process on piezoelectric properties in lead zirconate titanate ceramics, Ferroelectrics 419 (2011) 39–45. [13] T.M. Kamel, G.D. With, Poling of hard ferroelectric PZT ceramics, J. Eur. Ceram. Soc. 28 (2008) 1827–1838. [14] R. Rianyoi, R. Potong, A. Ngamjarurojana, A. Chaipanich, Poling effects and piezoelectric properties of PVDF-modified 0-3 connectivity cement-based/lead-free 0.94(Bi0.5Na0.5) TiO3-0.06BaTiO3 piezoelectric ceramic composites, J. Mater. Sci. 52 (2018) 345–355.
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