An Analytical Solution for Inhomogeneous Strain Fields Within Wurtzite GaN Cylinders Under Compression Test

Abstract

Compression test on solid circular cylinders of finite length is a popular method in obtaining the compressive strength, the elastic moduli and the electronic properties of semiconductors ( Goroff & Kleinman, 1963; Pollak & Cardona, 1968). It was found that, by generating a strain field, the external stress may significant change the electronic energy structures and the optoelectronic behavior of semiconductors (Suzuki & Hensel, 1974; Mathieu et al, 1979; Bir & Pickus, 1974; Singh, 1992; Pollak, 1990). Several methods have been used to investigate the effect of stress and strain on band structures (Jiang & Singh, 1997; Hasegawa, 1963). For example, the multiband effective-mass theory was employed to study the electronic and optical-absorption properties of uniaxially stressed quantum wells, the envelope-function approximation was used to describe the electronic structure of superlattices and quantum wells under arbitrary uniaxial stress, the effect of uniaxial and hydrostatic strain on the optical constants and the electronic structure of Copper was investigated, the strain dependence of effective masses in tetrahedral semiconductor under uniaxial stress was also studied. In all of these studies, the homogeneous strain distributions induced by an external uniform stress were considered. Pollak (1990) made good review on the effect of homogeneous strain on band structures and electronic properties of semiconductors. However, friction effect on the end surfaces is ignored in all of these studies. It has long been recognized that friction inevitably exists between two end surfaces of cylinders and the loading platens under compression test. The strain and stress distributions within cylinder are very sensitive to the external load acting on the surface of cylinders (Wei et al, 1999). Although numerous efforts have been made to reduce the friction between the semiconductor cylinder and the loading platens, end friction inevitably exists. Techniques developed to reduce end friction include the insertion of Telfon sheet, lubrication, iron brush contact, and the use of a loading platen of the same Poisson's ratio as the cylinder. Nevertheless, the stress distributions within cylinders under compression are normally nonuniform, and inhomogeneous strain fields are thus induced within semiconductor cylinders. Although the analytical solution for finite cylinders under arbitrary external load was obtained (Chau & Wei, 1999), the solution is for isotropic materials with force boundary condition only. Experimental results show that wurtzite GaN is a kind of transversely