Use of the curvature method to determine the misfit stress of epitaxial semiconducting systems: the case of samples thin
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Use of the curvature method to determine the misfit stress of epitaxial semiconducting systems: the case of samples thinned for TEM observation. A. Ponchet, M. Cabié, L. Durand, M. Rivoal and A. Rocher CEMES-CNRS, BP 94347, F-31055 Toulouse, France
ABSTRACT The curvature method which allows to measure the stress in epitaxial layers has been adapted to transmission electron microscopy observations. The samples thinned by the substrate side present some particular mechanical characteristics. The ratio between the substrate thickness and the layer thickness should be taken into account. The experimental conditions allowing a reliable determination of the stress have been established. A finite element calculation has been used to show that the dimensions of the area where the measure is performed can not systematically be neglected. This method has been applied to the semiconducting systems Ga1-xInxAs/GaAs and Ga1-xInxAs/InP. INTRODUCTION The stress in the heterostructures grown by epitaxy constitutes an important parameter in the engineering of opto- and microelectronic components. For instance it is one of the main parameters used to monitoring the wave-length emission of quantum wells. The stress is due to the accommodation of the lattice mismatch existing between the substrate and the epilayer. The theoretical value of the in-plane component of the stress σmisfit is related to the lattice mismatch f by the well-known formula in which El and νl are the Young’s modulus and Poisson’s ratio of the layer, respectively: σ misfit = −
El f 1−νl
The stress in the epilayer bends the sample to minimize the total elastic energy. The resulting curvature can be used to determine directly the in-plane component of the misfit stress σmisfit [1]. We present here the analysis of the curvature performed by Transmission Electron Microscopy (TEM) on plan-view samples in semiconducting systems. The samples thinned for TEM observations present particular structural characteristics which will be examined.
PRINCIPLE OF THE STRESS MEASUREMENT The relationship between the curvature radius and the in plane component σ of the epitaxial stress is given by the Stoney formula [1] σ=
Es t2 s 6 (1−ν s ) t l
1 1 − R R0
(1)
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in which tl and ts are the layer and substrate thickness, respectively, R is the radius of curvature of the sample and R0 the radius of curvature of the substrate before deposit, Es and νs are the Young’s modulus and Poisson’s ratio of the substrate, respectively. Our approach consists in adapting the curvature method to TEM experiments. As detailed elsewhere [2], the curvature radius and the substrate thickness can be determined in the same zone by bend contour analysis of bright and dark field images, respectively. In classical samples with a substrate thickness larger than 300 µm, typical curvature radii are in the range of 100 m and are measured by an optical method. In this work, the samples are thinned by the substrate side to allow plan-view observations and the sample thickness does not
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