Three-Dimensional Lattice Matching of Epitaxially Embedded Nanoparticles
ORAL
Abstract
Since Mathews and Blakeslee developed a theory of atomic lattice matched thin films in 1974, epitaxy has been modeled using 2D lattice-matching considering only the in-plane strain $\left( {\varepsilon_{IP}^{\ast } } \right)$. Here, we present a 3D model to predict the conditions at which epitaxially encased nanoparticles relax by plastic deformation, including the out-of-plane lattice mismatch $\left( {\varepsilon_{OP}^{\ast } } \right)$. The critical particle length $\left( {L_{C} } \right)$ at which defect formation proceeds is determined by balancing the resulting reduction in strain energy from a dislocation, with the corresponding increase in the energy of formation. Our results use a modified Eshelby inclusion technique for an embedded nanoparticle, shedding new light on the epitaxy of nanostructures. By tailoring $\varepsilon_{IP}^{\ast } $ and $\varepsilon _{OP}^{\ast } $, $L_{C} $ can be increased to 70{\%} beyond the case of encapsulation in a homogenous matrix. An InAs nanoparticle embedded in GaN $\left( {\varepsilon_{IP}^{\ast } =\varepsilon_{OP}^{\ast } =-0.072} \right)$ results in $L_{C} =10.8$ nm. However, it can be increased to $16.4$ nm when grown on GaAs and surrounded by InSb $\left( {\varepsilon _{IP}^{\ast } =-0.072,\varepsilon_{OP}^{\ast } =+0.065} \right)$, and a maximum of $18.4$ nm if the particle is capped by an alloy with $\varepsilon _{OP}^{\ast } =+0.037$. This effect, which we term ``3D Poisson-stabilization'', provides a means to increase the strain tolerance and modify the strain state in epitaxial heterostructures through the engineering of $\varepsilon_{OP}^{\ast } $.
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Authors
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Brelon May
The Ohio State University
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Peter Anderson
The Ohio State University
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Roberto Myers
The Ohio State University