### Abstract

A model was developed to calculate the elastic fields, including strain energy density, in multilayers grown epitaxially on a planar substrate. This model works well for compliant and non-compliant substrates. In particular we illustrate the model for four layer heterostructure and apply it for graded Ge (Si
_{x}Ge
_{1-x}) grown on a planar silicon substrate. Using the equations for static equilibrium and Hooke's law for isotropic materials under a plane stress condition, the elastic fields associated with each layer were calculated. The strain partitioning in this model reduces to the limiting case of a two-layer structure available in the literature. As it turns out here, strain partitioning is a function of the bulk unstrained lattice parameters, elastic constants and thicknesses of the layers. The model was qualitatively verified by comparing the strain energy density with the dislocation density away from a relatively thick substrate. This model helps shed some light on the factors important in achieving defect free multilayers for optoelectronic devices.

Original language | English |
---|---|

Title of host publication | Materials Research Society Symposium Proceedings |

Editors | P.M. Anderson, T. Foecke, A. Misra, R.E. Rudd |

Pages | 37-42 |

Number of pages | 6 |

Volume | 821 |

Publication status | Published - 2004 |

Externally published | Yes |

Event | Nanoscale Materials and Modeling - Relations Among Processing, Microstructure and Mechanical Properties - San Francisco, CA, United States Duration: 13 Apr 2004 → 16 Apr 2004 |

### Other

Other | Nanoscale Materials and Modeling - Relations Among Processing, Microstructure and Mechanical Properties |
---|---|

Country | United States |

City | San Francisco, CA |

Period | 13/4/04 → 16/4/04 |

### Fingerprint

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials

### Cite this

*Materials Research Society Symposium Proceedings*(Vol. 821, pp. 37-42). [P2.10]

**Modeling the elastic fields in epitaxially grown multilayers.** / Vanamu, Ganesh; Khraishi, Tariq A.; Datye, Abhaya K.; Zaidi, Saleem H.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Materials Research Society Symposium Proceedings.*vol. 821, P2.10, pp. 37-42, Nanoscale Materials and Modeling - Relations Among Processing, Microstructure and Mechanical Properties, San Francisco, CA, United States, 13/4/04.

}

TY - GEN

T1 - Modeling the elastic fields in epitaxially grown multilayers

AU - Vanamu, Ganesh

AU - Khraishi, Tariq A.

AU - Datye, Abhaya K.

AU - Zaidi, Saleem H.

PY - 2004

Y1 - 2004

N2 - A model was developed to calculate the elastic fields, including strain energy density, in multilayers grown epitaxially on a planar substrate. This model works well for compliant and non-compliant substrates. In particular we illustrate the model for four layer heterostructure and apply it for graded Ge (Si xGe 1-x) grown on a planar silicon substrate. Using the equations for static equilibrium and Hooke's law for isotropic materials under a plane stress condition, the elastic fields associated with each layer were calculated. The strain partitioning in this model reduces to the limiting case of a two-layer structure available in the literature. As it turns out here, strain partitioning is a function of the bulk unstrained lattice parameters, elastic constants and thicknesses of the layers. The model was qualitatively verified by comparing the strain energy density with the dislocation density away from a relatively thick substrate. This model helps shed some light on the factors important in achieving defect free multilayers for optoelectronic devices.

AB - A model was developed to calculate the elastic fields, including strain energy density, in multilayers grown epitaxially on a planar substrate. This model works well for compliant and non-compliant substrates. In particular we illustrate the model for four layer heterostructure and apply it for graded Ge (Si xGe 1-x) grown on a planar silicon substrate. Using the equations for static equilibrium and Hooke's law for isotropic materials under a plane stress condition, the elastic fields associated with each layer were calculated. The strain partitioning in this model reduces to the limiting case of a two-layer structure available in the literature. As it turns out here, strain partitioning is a function of the bulk unstrained lattice parameters, elastic constants and thicknesses of the layers. The model was qualitatively verified by comparing the strain energy density with the dislocation density away from a relatively thick substrate. This model helps shed some light on the factors important in achieving defect free multilayers for optoelectronic devices.

UR - http://www.scopus.com/inward/record.url?scp=14944365969&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14944365969&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:14944365969

VL - 821

SP - 37

EP - 42

BT - Materials Research Society Symposium Proceedings

A2 - Anderson, P.M.

A2 - Foecke, T.

A2 - Misra, A.

A2 - Rudd, R.E.

ER -