TEM analysis of stress in GaInAs/(001)InP epitaxial systems.
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TEM analysis of stress in GaInAs/(001)InP epitaxial systems. André Rocher, Martiane Cabié, Anne Ponchet and Nicolas Bertru* CEMES-CNRS, BP 4347, F-31055 Toulouse, France *LENS, INSA, Rennes, F-35043, France ABSTRACT A Transmission Electron Microscopy analysis of misfit stress based on the Stoney formula is proposed. It is applied to the GaInAs/(001)InP system to determine the residual stress for layers thicker than the critical thickness. The measured stress corresponds well to the value calculated using the elasticity theory and the nominal lattice mismatch: the structure is always nearly fully strained even for an epilayer two times larger than the critical thickness. Very few segments of misfit dislocation are observed indicating that the plastic relaxation is not active yet. A tentative explanation, based on the difficulty to create the core of a misfit dislocation, is explored. INTRODUCTION The elastic strain applied to an epitaxial layer is one of the most important parameters in the engineering of the modern opto- and micro-electronic devices. Since it modifies the energy band gap, it allows the tuning of the emission wave length of quantum wells. This elastic strain is due to the accommodation of the lattice mismatch f existing between an epilayer and its substrate. When this epilayer is thin enough, all the models of epitaxy admit that the lattice mismatch is fully accommodated by a purely elastic deformation of the layer. Following the elasticity theory, this elastic strain is necessary associated with a stress directly related to the lattice mismatch. The in plane component of this stress is given as the product of the biaxial elastic modulus of the layer Ml and the lattice mismatch f by the equation: σ = -Ml*f
(1)
We have developed a Transmission Electron Microscopy (TEM) method to measure this elastic stress due to a lattice mismatch in epitaxial systems [1,2]. This method is based on the curvature of the sample induced by a stress relaxation which exists for all mono or polycrystalline strained bilayers. In this case, there exists a relationship, the Stoney formula, between the stress and the radius of curvature [3]. In this paper, the misfit stress is studied in the GaInAs/(001)InP heterostructure for two different ternary compositions giving a tensile and compressive stress in the epilayer. EXPERIMENTS The principle of the stress measurement by TEM is based on the Stoney formula modified to take into account the sub-micrometer thickness of the substrate [4]: σ =
Ms t s2 t * * F( l ) 6 tl * R ts
(2)
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where σ is the in-plane component of the stress applied by the lattice mismatch in the epilayer, Ms the biaxial elastic modulus of the substrate, R the radius of curvature, ts and tl the substrate and epilayer thicknesses. The function F(tl/ts) has been introduced by Freund et al to take into account the relaxation effect induced by the specimen bending [4]; when tl/ts
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