[1] [1] Yang J S, Zhou H G. Amplification of acoustic waves in piezoelectric semiconductor plates［J］. Inter. J. of Solids & Structures, 2005, 42(11/12): 3171-3183.

[2] [2] Rees G J. Strained layer piezoelectric semiconductor devices［J］. Microelectronics J., 1997, 28(8/10): 957-967.

[3] [3] Withers R S. Electron devices on piezoelectric semiconductors: A device model［J］. IEEE Trans. on Sonics & Ultrasonics, 1984, 31(2):117-122.

[4] [4] Erturk A, Inman D J. Issues in mathematical modeling of piezoelectric energy harvesters［J］. Smart Materials and Structures, 2008, 17(6): 65016.

[5] [5] Wu W, Wang Z L. Piezotronics and piezo-phototronics for adaptive electronics and optoelectronics［J］. Nat. Rev. Mater., 2016, 24(34): 23-24.

[6] [6] Wen X N, Wu W Z, Pan C F, et al. Development and progress in piezotronics［J］. Nano Energy, 2015, 14: 276-295.

[7] [7] Liu Y, Zhang Y, Yang Q, et al. Fundamental theories of piezotronics and piezo-phototronics［J］. Nano Energy, 2015, 14: 257-275.

[10] [10] Pan Z W, Dai Z R, Wang Z L. Nanobelts of semiconducting oxides［J］. Science, 2001, 291(5510): 1947-1949.

[11] [11] Gao P X, Ding Y, Mai W, et al. Conversion of zinc oxide nanobelts into superlattice-structured nano helices［J］. Science, 2010, 309(5741): 1700-1704.

[12] [12] Zhang C L, Wang X Y, Chen W Q, et al. An analysis of the extension of a ZnO piezoelectric semiconductor nanofiber under an axial force［J］. Smart Materials and Structures, 2017, 26(2): 025030.

[13] [13] Cheng R, Zhang C L, Chen W Q, et al. Piezotronic effects in the extension of a composite fiber of piezoelectric dielectrics and nonpiezoelectric semiconductors［J］. J. of Appl. Phys., 2018, 124(6): 064506.

[14] [14] Wang G L, Liu J X, Liu X L, et al, Extensional vibration characteristics and screening of polarization charges in a ZnO piezoelectric semiconductor nano-fiber［J］. J. of Appl. Phys., 2018, 124: 094502.

[15] [15] Yang G, Du J, Wang J, et al. Extension of a piezoelectric semiconductor fiber with consideration of electrical nonlinearity［J］. Acta Mechanica, 2018, 229: 4663-4676.

[16] [16] White D L. Amplification of ultrasonic waves in piezoelectric semiconductors［J］. J. of Appl. Phys., 1963, 63(1): 199-200.

[17] [17] Deng F, Deng Q, Shen S P. A three-dimensional mixed finite element for flexoelectricity［J］. J. of Appl. Mechanics: Trans. of the ASME, 2018, 85: 031009.

[18] [18] Sze S M, Ng K K. Physics of Semiconductor Devices［M］. New York: Wiley, 2006.

[19] [19] Qin G S, Ma S J, Lu C S, et al, Influence of electric field and current on the strength of depoled GaN piezoelectric semiconductive ceramics［J］. Ceramics International, 2018, 44: 4169-4175.

[20] [20] Tagantsev A K. Theory of flexoelectric effects in crystals［J］. Zhurnal Eksperimentalnoii Teroreticheskoi Fiziki, 1985, 88: 2108-2122.

[21] [21] Zhou W, Chen P, Chu B. Flexoelectricity in ferroelectric materials［J］. IET Nanodielectrics, 2019, 2(3): 83.

[22] [22] Deng Q. Size-dependent flexoelectric response of a truncated cone and the consequent ramifications for the experimental measurement of flexoelectric properties［J］. J. of Appl. Mechanics-Trans. of the Asme, 2017, 84(10): 101007.

[23] [23] Lam D C C, Yang F, Chong A C M, et al. Experiments and theory in strain gradient elasticity［J］. J. of the Mechanics & Physics of Solids, 2003, 51(8): 1477-1508.