Imaging Strain in Nanostructures ESRF and ILL Summer School 2017 Report by Jan Bendix Hagedorn
Jan Bendix Hagedorn Imaging Strain in Nanostructures Contents 1 Introduction 2 2 Project Summary 3 2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Strain in Semiconductor Structures . . . . . . . . . . . . . . . . 3 2.1.2 The K-Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Building a Model in Comsol . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.3 Physics and Boundary Conditions . . . . . . . . . . . . . . . . . 8 2.2.4 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Computation and Visualization . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3 Sources 15 1
Jan Bendix Hagedorn Imaging Strain in Nanostructures 1 Introduction During the four weeks of the ESRF and ILL Student Summer Programme 2017, I worked under the supervision of Ga´ etan Girard in the X-Ray Nanoprobe Group at the ESRF. The members of the Group at beamline ID01 have developed an imaging technique called Quick Mapping, or K-Map for short, that aims to resolve lattice strain and tilt in small crystalline samples. The purpose of my work was to provide a refer- ence for the measurements obtained through the K-Map. I obtained these references using the Comsol Multyphysics software to run finite element simulations of strain in semiconductor nanostructures modeled after the samples investigated by my supervisor. With this report I aim to provide a summary of my work at the ESRF as well as an overview of the data acquired through the simulations and how it could be used in the future. As I had no prior experience in experimental diffraction, much of my time was spend studying the concepts investigated and the methodology employed by the group at beamline ID01. I will attempt to reflect this in my report. Beyond the work described in this report, the Summer School gave me a glimpse of the workings of a large scale research facility such as the ESRF. The lectures held for our group by scientists of both the ESRF and ILL provided me with an overview of the numerous interesting fields of science present on the EPN Campus. These experiences combined with the opportunity to meet like minded students from all over Europe, made me consider my stay in Grenoble as a valuable addition to my education. 2
Jan Bendix Hagedorn Imaging Strain in Nanostructures Figure 1: Epitaxial growth of a strained SiGe layer 2 Project Summary 2.1 Motivation 2.1.1 Strain in Semiconductor Structures Strain plays an important role in semiconductor structures on the nanoscale because it can alter the electrical properties of a material. In a strained crystal the lattice parameters differ from those in an unstrained crystal. The subsequent change in the electric potential affects the electronic band structure. Strained crystals can be grown by epitaxy as illustrated in figure 1 [Berthelon et al. 2017]. The silicon-germanium layer in this example adopts the horizontal lattice parameter of the silicon it is grown on, bringing the atoms closer together than they would be in unstrained silicon-germanium and resulting in an in plane strain ( ǫ xx , ǫ yy ) The material is stretched in the vertical direction to compensate, creating an out of plane strain ( ǫ zz ). This surface based effect would be negligible for a bulk material but in a nanostructures such as epitaxial films it has significant effects. By purposely engineering semiconductor structures to be stressed, these effects can be used to increase the performance of certain elements for example metaloxidesemi- conductor field-effect transistors or MOSFETs for short [Maiti and Maiti, 2012]. With strain thus being an important property of modern electronic devices, imaging tech- niques that are able to resolve it on small scales become interesting. One such technique has been developed by scientists working on microdiffraction at the ESRF’s beamline ID01. 3
Jan Bendix Hagedorn Imaging Strain in Nanostructures Figure 2: Diffractometer used at ID01 [ID01 Homepage] 2.1.2 The K-Map Quick mapping is an imaging method based on scanning x-ray diffraction microscopy (SXDM). Where techniques such as atomic force microscopy, scanning electron mi- croscopy or transmission electron microscopy can only probe the sample surface or require the sample to be specifically prepared for measurements (e.g. in thin slices), SXDM is able to probe a sample volume without limitations to its shape or situation. The method is sensitive to the crystal lattice parameter [Evans et al. 2012] and thus to the local strain. To produce a K-Map of a sample it is mounted on the piezo stage in the center of the diffractometer (see figure 2). The sample is positioned so that the incoming microbeam is diffracted in the area that is to be investigated. The motions of hexapod and piezo stage are remote controlled and a microscope is used for visual feedback. The detector is then moved to capture a single Bragg reflex, that is chosen based on the investigated strain component. Measurements of at least three different reflexes, corresponding to non parallel crystal planes, are needed to obtain full information about the strain. The sample is then moved along the x and y directions given by the orientation of the piezo stage. For every point of this scan the intensity around the chosen Bragg peak is measured with the two dimensional detector. Step size can be chosen depending on the size of the investigated area. Quasi continuous measurements, supported by a software package developed at ID01, allow for much faster scanning times than an SXDM conducted in a step wise fashion. The procedure is repeated with the sample 4
Jan Bendix Hagedorn Imaging Strain in Nanostructures Figure 3: Schematics of a K-Map measurement [Chahine et al. 2014] tilted at different angles, producing measurements along a rocking curve at each point. This results in a five dimensional data set consisting of x - and y -coordinates, angle of incidence ω and scattering angles 2Θ and ν (see figure 3). [Chahine et al. 2014] From the three angles measured at each point, an image of the Bragg peak in three dimensional Q -Space can be obtained. The position of the peak in Q -Space yields information about strain and tilt of the lattice at the measured point in real space, since the scattering vector Q is connected to the orientation and relative distance of scattering planes: d hkl = 2 π 2 π = | � � Q 2 x + Q 2 y + Q 2 Q | z � � tilt [ ◦ ] = 180 Q z π arccos � Q 2 x + Q 2 y + Q 2 z 2.2 Building a Model in Comsol 2.2.1 Geometry The model geometry is determined directly by the investigated samples. Comsol allowed me to create geometries for simulations via the built in CAD software. All model dimensions were expressed in parametric form to allow for easy rescaling of the created objects. 5
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