An extended Stoney's formula including nonlinear deformation for large size wafer of multilayers with arbitrary thicknesses

SCRIPTA MATERIALIA

卷:186

Article

Li, Mengda¹  Wu, Jiejun¹  He, Jinmi²  Liu, Nanliu³  Han, Tong¹  Zhang, Guoyi^1,2,3  Yu, Tongjun¹ 

[1] Peking Univ, Res Ctr Wide Gap Semicond, Sch Phys, State Key Lab Artificial Microstruct & Mesoscop P, Beijing 100871, Peoples R China

[2] Sino Nitride Semicond Co Ltd, Dongguan 523500, Peoples R China

[3] Peking Univ, Dongguan Inst Optoelect, Dongguan 523808, Guangdong, Peoples R China

关键词: Layered structures;    Residual strain;    Wafer curvature;    Fracture;    GaN;   

DOI  :  10.1016/j.scriptamat.2020.04.006

来源: Elsevier

【 摘 要 】

Applying the principle of minimum potential energy in an invariant plane reference frame, we obtain a concise curvature-strain equation for large size thick multilayered wafer, which incorporates strain due to nonlinear deformation. This equation manifests itself as Stoney's or other famous formulas for specific cases, and clarifies their relations and physical origins. We find nonlinear deformation greatly suppresses wafer bending and verify this effect experimentally in 2-4 in. GaN/sapphire systems. Such mechanical analysis provides a foundation of curvature control which is crucial in wafer fabrication for electronics and photonics. (C) 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

【 授权许可】

Free