Finite element modelling of nonlinear elastic and piezoelectric properties of InN and InGaN QDs

Paweł Dłużewski 1Grzegorz Jurczak 1Pierre Ruterana 2,4S. P. Lepkowski 3

1. Polish Academy of Sciences, Institute of Fundamental Technological Research (IPPT PAN), Świętokrzyska 21, Warszawa 00-049, Poland
2. Laboratoire CRISMAT - UMR 6508, ISMRA et Universite de Caen, 6 Boulevard de Marechal JUIN, Caen 14050, France
3. Polish Academy of Sciences, Institute of High Pressure Physics (UNIPRESS), Sokolowska 29/37, Warszawa 01-142, Poland
4. SIFCOM, UMR6176, CNRS-ENSICAEN, 6 Bld Maréchal Juin, Caen 14050, France


We investigate elastic and electric properties of wurtzite InGaN/GaN heterostructures with inhomogeneous indium composition. Distortion field and continuous fluctuation of chemical composition extracted by means of digital processing of the HRTEM images are used as the input data for the nonlinear FE calculations. This data are input to FE mesh in the form of nodal variables for extended nodal freedom degrees taking into account the fixed: nodal source distortions, chemical distribution and electric charge distribution as well as the wanted: nodal displacements and electrostatic potential distribution. To model a whole considered crystal region we use 27-node (brick) elements with quadratic shape functions assuring the compatibility condition between coupled fields (source distortions, displacements, chemical composition and electrostatic potential). This is an essential condition to avoid the extra effects including artificial residual stresses and caused by FE incompatibilities. We solve a boundary-value problem for piezoelectricity to calculate residual stresses and strains existing in a such heterostructure for the given (fixed) electric charge distribution. We obtain also the resulting electrostatic potential distribution. To do this we use finite element method based on nonlinear anisotropic piezoelectricity. During calculation we take into account piezoelectric polarization as well as the spontaneous polarisation of the wurtzite crystals.

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Presentation: invited oral at E-MRS Fall Meeting 2005, Symposium A, by Paweł Dłużewski
See On-line Journal of E-MRS Fall Meeting 2005

Submitted: 2005-05-30 14:49
Revised:   2009-06-07 00:44
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