PSI - Issue 23

Atsushi Kubo et al. / Procedia Structural Integrity 23 (2019) 372–377 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction

Wide-bandgap semiconductors such as silicon carbide (SiC) and gallium nitride (GaN) are widely used for power devices. In power devices, such semiconducting materials undergo complex stress conditions caused by various factors; semiconducting materials are connected to other materials with different lattice constants, coefficients of thermal expansion, etc., resulting in a lattice misfit at the interface; Since power devices have complicated geometries [see, e.g., Jones et al. (2016); Udrea and Fujihira (2017)], the mechanical condition of semiconductors is accordingly complexified by structural constraint; mechanical deformation is also induced by electric current, with which dislocation motion was observed in SiC-based devices [Skowronski and Ha (2006)]. Thus, it is required to understand the fundamental mechanical properties, especially strength of semiconductors under complex loading conditions for a more reliable and efficient design of power devices. One of the most essential properties related to mechanical strength is the strength of the perfect crystal, namely the ideal strength, and thus it has been intensively investigated for various solid materials (including metals and ceramics) using the first- principles approaches [Černý et al. (2013); Ogata et al. (2004)]. Nevertheless, there is still only limited knowledge of mechanical properties and deformation/fracture processes in semiconductors under complex deformation conditions, besides several precedent studies regarding the ideal strength of semiconductors and related materials [Umeno et al. (2011 ); Umeno and Černý (2008); Umeno et al. (2015); Černý et al. (2013)]. In this study, we extend a recent work by the present authors [Umeno et al. (2015)], and perform ideal strength analyses for SiC, GaN and aluminum nitride (AlN) with several typical crystal structures using a first principles calculation approach. The deformation and fracture behaviors under multiaxial compression and tension are discussed. First-principles calculations based on the density functional theory (DFT) [Kohn and Sham (1965)] were performed for the ideal strength analysis, using Vienna Ab-initio Simulation Package (VASP) [Kresse and Hafner (1994); Kresse and Furthmüller ( 1996A); Kresse and Furthmüller ( 1996B)]. The projector augmented wave (PAW) method [Blöchl (1994); Kresse and Joubert (1999)] was adopted for calculation of core electrons. The exchange-correlation potential term was evaluated by the generalized gradient approximation (GGA) with the formulation by Perdew et al. (1996) The cutoff energy of plane waves was set for SiC, GaN and AlN to 1000 eV, 1200 eV and 1000 eV, respectively. Tensile stress-strain (  -  ) relationships were obtained for typical crystal structures (polytypes) of SiC, GaN and AlN, as listed in Table 1 and shown in Fig. 1(a). All the crystal structures examined in this study consist of tetrahedra of atoms with fourfold coordination stacked in different ways. Note that 2H and 3C structures are identical to the wurtzite and zincblende structures, respectively, and several crystal orientations in different crystal structures are equivalent to each other; e.g.,  110  direction in zincblende (3C) structure is equivalent to  2110  in wurtzite (2H) and 4H structures;  111  direction in zincblende (3C) structure equivalent to  0001  in wurtzite (2H) and 4H structures. In most cases, the smallest orthogonal simulation cells were chosen for convenience of calculation. 2. Methodology

Table 1. Examined materials, crystal structures and directions of tension.

System

Crystal structure 2H (wurtzite) 3C (zincblende)

Direction of tension

SiC

 2110  ,  1100  ,  1101  ,  0001 

 100  ,  110  ,  111 

4H

 2110  ,  1100  ,  0001   2110  ,  1100  ,  0001 

GaN

wurtzite

zincblende

 100  ,  110  ,  111 

AlN

wurtzite

 2110  ,  1100  ,  0001 

zincblende

 100  ,  110  ,  111 