Study of Interface Stress Property of Gan-Sapphire Hetero-Thick-Film System

作者: 李 佳 , 刘辉召 , 齐浩然 :河北工业大学理学院,天津; 史俊杰 , 吴洁君 :北京大学宽禁带半导体研究中心,人工微结构和介观物理国家重点实验室,物理学院,北京;

关键词: GaN膜蓝宝石应力界面GaN Film Sapphire Stress Interface

考虑两条假设:a) 去除Stoney模型中膜厚远小于基底厚度的近似条件,考虑GaN膜的厚度和基底蓝宝石的厚度相当。b) 把GaN的膜厚考虑成非均匀的,随面内径向坐标r变化。在此两条假设基础上研究了GaN-蓝宝石异质厚膜体系的曲率和界面剪切应力,其中将GaN的膜厚取为坐标r的正弦函数,且研究了从系统中心到边缘膜厚的薄–厚–薄和厚–薄的两种变化模式,计算结果表明系统的曲率不再是常量而是随坐标r变化的变量,界面剪切应力在整个半径R范围内出现方向的转变,转变点正好对应曲率取极值的点,可见曲率对界面剪切应力有重要影响,根本原因来源于我们考虑了GaN膜厚的非均匀性。

Abstract: Based on two hypothesis: a) eliminating the approximate condition that the thickness of film is far less than that of substrate adopted by Stoney model, and considering that the film thickness of GaN is comparable to that of Sapphire substrate; b) taking the GaN film as a film with non-uniform thickness which changes with r, we investigate the curvature and interface shear stress of GaN- Sapphire hetero-thick-film system. In addition, we take the film thickness of GaN as sinusoidal function of r, and study two types of film thickness variation, i.e. the thin-thick-thin model and thick-thin model. The results reveal that the system curvature is not a constant but a variable which changes with r. The interface shear stress shows a behavior of direction transition within the range of R, and transition point just corresponds to the extreme point of curvature, indicating that the curvature has a significant influence on the interface shear stress, which originates from our consideration of the non-uniform film thickness for GaN.

文章引用: 李 佳 , 史俊杰 , 吴洁君 , 刘辉召 , 齐浩然 (2014) GaN-蓝宝石异质厚膜体系界面应力特性研究。 力学研究, 3, 55-64. doi: 10.12677/IJM.2014.34006


[1] Chung, K., Lee, C.-H. and Yi, G.-C. (2010) Transferable GaN layers grown on ZnO-coated graphene layers for optoelectronic devices. Science, 330, 655-657.

[2] Taniyasu, Y., Kasu, M. and Makimoto, T. (2006) An aluminium nitride light-emitting diode with a wavelength of 210 nanometres. Nature, 441, 325-328.

[3] Zhang, S., Shi, J.-J., Zhang, M., Yang, M. and Li, J. (2011) First-principles investigation on optical properties of GaN and InGaN alloys. Journal of Physics D: Applied Physics, 44, 495304.

[4] Stoney, G.G. (1909) The tension of metallic films deposited by electrolysis. Proceedings of the Royal Society of London, 82, 172-175.

[5] Floro, J.A., Lucadamo, G.A., Chason, E., Freund, L.B., Sinclair, M., Twesten, R.D. and Hwang, R.Q. (1998) SiGe island shape transitions induced by elastic repulsion. Physical Review Letters, 80, 4717.

[6] Freund, L.B., Floro, J.A. and Chason, E. (1999) Extensions of the Stoney formula for substrate curvature to configure- tions with thin substrates or large deformations. Applied Physics Letters, 74, 1987-1989.

[7] Timoshenko, S.P. (1925) Analysis of bi-metal thermostats. Journal of the Optical Society of America, 11, 233-255.

[8] Freund, L.B. and Suresh, S. (2003) Thin film materials: Stress, defect formation, and surface evolution. Cambridge University Press, London.

[9] Barghout, K. and Chaudhuri, J. (2004) Calculation of residual thermal stress in GaN epitaxial layers grown on techno- logically important substrates. Journal of Materials Science, 39, 5817-5823.

[10] Hlramatsu, K., Detchprohm, T. and Akasakl, I. (1993) Relaxation mechanism of thermal stresses in the heterostructure of GaN grown on sapphire by vapor phase epitaxy. Japanese Journal of Applied Physics, 32, 1528-1533.

[11] Touloukian, Y.S., Kirby, R.K., Taylor, R.E. and Lee, T.Y.R., Eds. (1977) Thermophysical properties of matter. Plenum Press, New York.

[12] Murrayy, C.E. and Noyan, I.C. (2002) Finite-size effects in thin-film composites. Philosophical Magazine A, 82, 3087- 3117.

[13] Itoh, N., Rhee, J.C., Kawabata, T. and Koike, S. (1985) Study of cracking mechanism in GaN/α-Al2O3 structure. Journal of Applied Physics, 58, 1828.