Finite element modelling of strained nanowire heterostructures

Abstract

When two materials with different lattice constants are grown together, this generates stress between them, and therefore strain. This strain causes them to have different thermal and electrical properties, and this is especially important on the nanoscale where changes have large impacts.

This project is intended to see if COMSOL can be used as a tool to model how materials respond to lattice mismatch induced strain. One nanowire consisting of three segments was generated. One middle segment of indium phosphide surrounded by indium gallium phosphide, based on locally made nanowires. It is also intended to serve as a base point for further direct research based on data points generated from the project's simulations.

The COMSOL Multiphysics' engine is used to generate simulations of nanowires using a Finite Element Method. The goal with this work is as a demonstration of how this can be easily replicated in the future. The variables tested were wire radius, the thickness of the middle InP, and percentage gallium in the InGaP segments.

The results of the simulations match the theory well, but due to time and scope constraints they could not be compared to the experimental nanowires used as a foundation for the project, so this should be treated as a first step in determining how useful COMSOL is for practically modelling nanowires.

Popular Abstract

Crystals are materials where the atoms are regularly structured. Unlike non-crystalline materials, one point in a grain of salt will look the same as any other point. If two crystals are made of different elements, the structure of how atoms are placed in relation to each other and the distance between atoms will be different. This means that when one crystal is grown onto a different kind of crystal, the atoms will not line up perfectly. If a crystal with a large distance between atoms is grown onto a crystal with a narrow distance between atoms, they will pull and push each other and try to make each other align. This kind of material stretching is called strain, and affects how well the materials handle electricity and heat.

When most materials are heated up, they expand at a certain rate depending on their composition. If you have two materials in contact with very different expansion rates, this can cause the bonding between them to crack, or break entirely. Therefore when constructing components on the nanoscale, like those used in computer processors, one needs to consider not only what materials to use but also how they behave together. Testing this once in a lab is feasible, but if one can simulate it on a computer it is both cheaper and faster for different conditions and materials. The aim of this project is to test how close one can get to the physical world by using simulations.

For the project, experimental data of locally grown nanowires is used as a basis for the model, and as a comparison for the developed model. To get data on how the strain affects the material, one needs its diffraction pattern. When one shoots light at an object, it hits the electrons in it, the electrons get energized and need to re-stabilize by releasing photons of their own. These released photons form the material’s diffraction pattern, which is unique for each material. A software called COMSOL is used to create a model, and the software MATLAB is used to process the results. MATLAB was used because COMSOL treats materials as if they were uniform blocks of matter, and cannot model individual atoms, which is needed to produce the diffraction patterns.

In COMSOL one can create essentially any two or three dimensional shape. Many different packages can be downloaded depending on what area of physics one wants to explore, such as fluid or heat flow. For this project the focus is the packages handling strain and solid mechanics. The base model was a wire with a width of less than 100 nanometers and three segments of alternating materials, two indium gallium phosphide segments surrounding a segment of indium phosphide.

Once a model is set up, it is very easy to set up different parameters for the size and composition of the nanowire. The software has to make a lot of approximations, so not everything will be practically applicable, but it is an acceptable trade-off for speed and simplicity. Calculating the strain and stretching of a material from the difference in atomic distance (in technical terms lattice spacing) is virtually impossible to do analytically for anything but the most basic of geometric shapes. For this to work, COMSOL uses something called the Finite Element Method (FEM). FEM takes one large object and divides it into many elements, each small enough to calculate how the an element behaves and how it affects its neighbours. A numerical approximation of the equations in the analytical model is used. This gives a straightforward calculation for the computer, and a very good approximation of the physical world’s case.

This project and model is not intended to be a giant leap in our understanding of material science, but a small step forward and a tool for future use. There is currently no one straightforward way to simulate nanowire strain, but by making a model and testing its validity, I hope to create something that can be used, copied or adapted for future work in the field.

• author: Grape Wyke, Alexander
• supervisor: Jesper Wallentin; Susanna Hammarberg
• organization: Synchrotron Radiation Research; Department of Physics
• course: FYSK02 20181
• year: 2019
• type: M2 - Bachelor Degree
• subject: Physics and Astronomy
• keywords: Strain, nanowire, heterostructure, physics, nanophysics, COMSOL, simulation, lattice
• language: English
• id: 8975122
• date added to LUP: 2019-05-09 14:54:57
• date last changed: 2019-05-09 14:54:57