Critical thickness of an epilayer grown on a finite substrate with different elastic constants

This study addresses the problem of the critical thickness of an epilayer g rown on a finite substrate with different elastic constants. The principle of superposition and Fourier integral methodology are used to solve the dis placement and stress fields that satisfy the boundary conditions. The chang e in strain energy caused by the introduction of a misfit dislocation is de fined as the dislocation formation energy E-t. Meanwhile, the epilayer thic kness, corresponding to E-t = 0 is the epilayer critical thickness h(c). Th is investigation reveals a promising characteristic of using a thin substra te, namely that when the substrate is very thin and the shear modulus ratio of epilayer over substrate is 1/10, then if the corresponding h(c) is smal ler than the substrate thickness, h(c) will decrease as the shear modulus r atio increases. However, if the corresponding h(c) is greater than the subs trate thickness, h(c) markedly increases with an increase of the shear modu lus ratio, becoming infinite. When the substrate is very thin, the h, also increases rapidly with the epilayer (substrate) Poisson ratio and finally r eaches infinity; however, the pattern differs from that of the variation in the ratio of the shear modulus. If the substrate becomes thinner and trans forms into a diaphragm structure, the epilayer critical thickness reaches i nfinity, regardless of the magnitude of the shear modulus ratio, epilayer, and substrate Poisson ratio. Results obtained when the epilayer and substra te share identical elastic constants are compared with those of Zhang et al . and Fruend and Nix. The present result lies between those obtained in the se two earlier studies. (C) 2001 Elsevier Science B.V. All rights reserved.