Elastic Constant Effect on the Critical Thickness of an Epilayer
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Tong-Yi Zhang Department of Mechanical Engineering Hong Kong University of Science and Technology Clear Water Bay, Kowloon, Hong Kong
ABSTRACT The effect of elastic constants on the critical thickness of an epilayer is investigated. The results indicate that the self energy of the dislocation is controlled by the soft phase between the epilayer and the substrate, while the interaction energy only depends on the elastic constants of the epilayer. It is easier for a dislocation to be formed if the substrate is softer than the epilayer, and consequently the critical thickness is smaller. On the other hand, a soft epilayer can have a large thickness without any mismatch dislocation.
INTRODUCTION The critical thickness of a strained epilayer on an isomorphic substrate has been studied for a long time. Frank and van der Merwe [1] first proposed that the critical thickness can be determined by minimizing the total energy of the system. Matthews and Blakeslee [2] assumed a critical balance between the action of the force which arises as a result of lattice mismatch on a propagating segment of a threading dislocation and the additional line tension associated with the newly created length of interfacial dislocation. Freund [3] systematically studied the
threading dislocation. Willis and co-workers [4,5,6] developed a rigorous treatment for the stability of dislocation arrays. Zhang et al. [7] calculated work hardening for dislocation generation, which had been observed experimentally [8]. In these works, however, the epilayer is assumed to have the same elastic constants as its substrate. In general, the epilayer has different elastic constants from its substrate. The elastic constant effect on the critical thickness has not been deeply investigated. Willis et al. [4] and Gosling and Willis [9] did formulate, via the Fourier transformation, the stress field of dislocations in the interface between an epilayer and its substrate with different elastic properties. In the present work, the stress and displacement fields are formulated using both the superposition principal and the Fourier transformation. Then the effect of elastic constants on the critical thickness is investigated.
ANALYSIS
Figure 1 shows an epilayer with a thickness of h deposited on an infinitely thick substrate. The interface between the epitaxial layer and its substrate is chosen to be the xI axis. Both the epilayer and substrate are assumed to be mechanically isotropic such that in-plane and anti-plane deformation can be treated separately. A dislocation with a Burgers vector 325 Mat. Res. Soc. Symp. Proc. Vol. 356 01995 Materials Research Society
Figure 1.
A dislocation located in an interface, strained epilayer and its substrate.
X2 =0,
between a
b=[b1 ,b2 ,b3] is located at the origin. In the present work, energies are calculated per length of dislocation line or per thickness, and only the formation energy of the dislocation is of interest inasmuch as the total mismatch strain energy approaches infinity in the infinite body. The formation e
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