Transmission Electron Microscopy of III-V Nanowires and Nanotrees

Transcription

1 Transmission Electron Microscopy of III-V Nanowires and Nanotrees Lisa S. Karlsson Doctoral Thesis 2007 Faculty opponent: Dr. Zuzanna Liliental-Weber Materials Sciences Division Lawrence Berkeley National Laboratory University of California Division of Polymer & Materials Chemistry Department of Chemistry Sweden Akademisk avhandling som för avläggande av filosofie doktorsexamen vid tekniska fakulteten vid Lunds universitet kommer att offentligen försvaras vid Fysiska institutionen, Sölvegatan 14, hörsal B, måndagen den 3 december 2007, kl

2 c Lisa S. Karlsson, 2007 Division of Polymer & Materials Chemistry Department of Chemistry Lund University P. O. Box 124 SE Lund Sweden Printed in Sweden by Media-Tryck, Lund October, 2007 ISBN:

3 The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them -SIR WILLIAM BRAGG

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5 Abstract In this work, the morphology and crystal structure of epitaxial semiconductor nanowire structures grown by metal-organic vapour phase epitaxy (MOVPE) are studied by electron microscopy methods. In particular, the three-dimensional structure of nanowires and nanotrees has been characterised by scanning electron microscopy (SEM), high-resolution transmission electron microscopy (HRTEM) and multi-slice (MS) simulations. It has been found that the repeated lamellar twinning often observed in III-V 111 B nanowires tends to form a morphology bound by {111} facets only. When this structure is viewed parallel to the twin planes in 110,azig-zag appearance is found as two of the {111} facet types are in the zone. When rotated 30 around the growth axis to a 11 2 direction the edges between the {111} facets align to seemingly flat side facets. Also, the twin planes are clearly distinguishable in 110 but are less pronounced in 11 2, due to alignment of the atomic columns in the latter case. Two possible twin types have previously been reported in literature, a rotation twin 60 around the growth axis of the nanowire and a mirror twin 180 over the twin plane. The dominating type in this study, as found from MS-simulations, is the rotation twin type with III-V bonding over the twin plane. Viewing directions of the nanowires non-parallel to the twin plane will show two different crystal orientations in neighbouring twin segments, as a consequence of twinning. These are crystallographically related as they share a common (111) twin plane and can be indexed based on stereographic projections. MS-simulations showed that both twin types would have the same appearance in HRTEM-images of the studied low index zones 100, 1 10, and The corresponding zone axes in the neighbouring segments were indexed to 1 2 2, 11 4 and 11 5 in the first three cases. Moreover, the appearance of the nonoverlapping regions in these viewing directions confirmed a suggested three-dimensional model with only {111} facets. To mediate the nanowire growth, Au seed nanoparticles are often used to define the position and diameter of the nanowires. The influence of the interaction between the Au seed nanoparticles and the substrate and nanowire structures during growth was investigated for GaAs. The effects of annealing prior to growth and of different termination procedures during cooling after growth were studied by ex situ EDS-analysis. It was found that the Au seed particles are stable in contact with GaAs nanowires when kept at As-rich conditions during annealing, growth and cooling. However, if Ga-rich conditions are used, alloying between Au and Ga occurs readily and the composition of the seed nanoparticles changes with growth temperature. These observations are consistent with the ternary Au-Ga-As phase diagram where a Au-GaAs-As tie-triangle dominates at As-rich conditions and GaAsalloy tie-lines are found on the Ga-rich side. Therefore, it was concluded that the Au seed particles are solid during growth, in our MOVPE-system, but that the situation can change if alloying is allowed to occur during annealing. For Au-In-As the situation is different as there is no tie-line of Au-InAs and the seed particles will alloy more readily with the substrate. In fact, to stabilise the growth of InAs nanotrees pre-alloyed Au-In seed nanoparticles were used. 5

6 By sequential nanowire growth using previously grown nanowires as free-standing substrates more complex, so called nanotree structures, can be grown. Due to the similarity of a tree the respective growth sequences are labelled trunk, branch, and leaf. For III-V nanotrees of predominantly zinc blende structure the nanowire growth was found to adopt the 111 B growth directions irrespective of growth sequence. However, a single crystalline transition section was found close to the base of branches and/or leaves nucleating on a twinned region. This section was believed to form during low supersaturation conditions in the initial stage of growth. If nucleation occurred on a single crystalline section, fully single crystalline leaves would form. Similarly, when nucleating at the very base of a branch, fully twinned leaves would grow. Heteroepitaxial growth of InP on GaP resulted in a topotaxial growth behaviour with InP branches or leaves crawling parallel to or spiralling around the previously grown nanowires. Only the top section of the previously grown GaP nanowires would form InP in the 111 B growth direction. This led to the conclusion that the nucleation conditions of the two generations are different. Thanks to the limited diameter of the nanowire structures, HRTEM-images with atomic resolution can be obtained on as grown samples with minimal sample preparation. Based on the appearance of these images, the 3D structure of the nanowires can be characterised using MS-simulations. Also, Moiré patterns and double diffraction of overlapping crystalline materials can be used to determine the relative orientation of sequentially grown nanowire structures as well as neighbouring twin segments. 6

7 Preface The basis of this thesis is the work I performed during my time as a PhD-student at Lund University in I started out working on characterisation of aerosol nanoparticles together with my supervisors Jan-Olle Malm and Knut Deppert in January During the first two years, I gradually worked my way through the transmission electron microscopes available at the national Centre for High-Resolution Electron Microscopy (nchrem) at Lund University. This involved obstacles such as the old XEDS-system of the 200kV instrument, the art of adjusting astigmatism using a TV-screen on the 400kV and pulling out the TEM-holder without breaking the vacuum of the 300kV field-emission gun instrument. Meanwhile, I looked at nanoparticle samples of Au, Ag (or Ag 2 S?), Ga, Sm, Au-Ga, Ni and In-Se produced by Martin N A Karlsson, Brent A Wacaser and Zsolt Geretovszky at the Division of Solid State Physics. The publications of this work was summarized in a licenciate dissertation in September 2005 based on Paper X, XII, XVII, XVIII and XIX. About this time, I also got involved in the characterisation of GaP nanotrees in a project together with Kimberly A Dick. From this point, the focus of my work switched to nanowire structures. While carrying out a statistical study of twin segments in GaP 111 B nanowires, Jonas Johansson and I started to work on a three-dimensional model based on the observed nanowire morphology (Paper I). This led to several possible structural models that resulted in me taking a self-study course in multi-slice simulations. This became very useful during the final self-dilating project on GaAs 111 B nanowires together with Kimberly A Dick, where rather peculiar effects appeared in some of the HRTEM-images (Paper II). During my PhD I have had the opportunity to visit Prof Angus Kirkland s group at the Department of Materials in Oxford on a number of occasions, to study image reconstruction techniques. I learned a lot during these visits and found out that there is such a thing as a theoretical microscopist. I have also struggled to implement focal series reconstructions on the studied samples with varying degree of success. This made me realise that things sometimes take longer than anticipated. I also had the opportunity to participate in a number of international microscopy conferences. The starting point was Scandem 2003 in Oslo after only half a year as a PhD-student, followed by EMC in Antwerp in Last year I managed to get to IMC-16 in Sapporo and this spring I attended MSMXV in Cambridge. I have always enjoyed the open-minded discussions during these meetings, although I must confess that it was a lot to grasp in the beginning. So how did I end up in microscopy? Well, to be honest I ve always been told I had an eye for details and colour, whether for spotting birds in a tree or working through a Christmas jigsaw puzzle in different shades of brown. Early on my dad was testing my ability to read the topography based on the height contours of a map by asking: Does this slope go up or down? upon which I would reply without hesitation and always correctly. I also remember my fascination for the stereo spectacles he used for studying aerial photographs and the three-dimensional effect they generated. The next fascination came when I encoun- The licenciate degree is an optional degree often taken half-way through the PhD-period in Sweden. 7

8 tered the polarising optical microscope techniques used to determine the mineral content of thin polished wafers of rocks and ores during my undergraduate studies in Geology. Although, I must admit that the different shades of pale yellow to pink of the ore samples were a disappointment. After a switch to the Department of Chemistry, I ended up doing my diploma work on fluorescence microscopy of solutions containing DNA and gemini surfactants (see Paper XXI). Following a brief career within the coatings industry, I applied for a PhD-position resulting in this thesis. With electron microscopy I entered a completely new field, as described above, and by now my eyes are well-adjusted to intense shades of green, from the fluorescent screen, together with subtle variations in grey. My studies on phase diagrams and crystallography from mineralogy, physical chemistry and inorganic chemistry have finally come to good use and I can t help feeling that I have finally closed the loop. Now I am looking forward to the next one! Lisa S Karlsson Lund, October

9 Contents List of papers 11 1 Introduction 15 2 Entering the world of electron microscopy The TEM hardware The magic of image formation X-ray energy dispersive spectroscopy (XEDS) Electron energy loss spectroscopy (EELS) Crystallography and twin defects of III-V semiconductors Crystal structures Twinning Crystal growth on the nanoscale Growth systems Nanowire growth and growth mechanism Alloying and phase diagrams Aerosol nanoparticle generation D-characterisation of III-V nanowires Structural characterisation of GaP and GaAs nanowires Side-facets Twin segment statistics Interaction of seed nanoparticle and substrate/nanowire 49 7 Structural aspects of III-V nanotrees 51 8 Outlook for future explorers 53 Populärvetenskaplig sammanfattning 55 Acknowledgements 61 References 63 My contributions 69 9

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11 List of papers This thesis is based on the following papers, referred to in the text as Paper I-V. I. Structural properties of 111 B-oriented III-V nanowires J. Johansson, L. S. Karlsson, C. P. T. Svensson, T. Mårtensson, B. A. Wacaser, K. Deppert, L. Samuelson and W. Seifert. Nature Materials 2006, 5, II. Understanding the 3D-structure of GaAs 111 B nanowires L. S. Karlsson, K. A. Dick, J. B. Wagner, J.-O. Malm, K. Deppert, L. Samuelson and L. R. Wallenberg. Accepted for publication in Nanotechnology, III. Composition of the Au seed particle of GaAs 111 B nanowires: A growth study L. S. Karlsson, K. A. Dick, K. Deppert, J.-O. Malm, L. Samuelson and L. R. Wallenberg. Manuscript in progress, IV. Improving InAs nanotree growth with composition-controlled Au-In nanoparticles K. A. Dick, Zs. Geretovsky, A. Mikkelsen, L. S. Karlsson, E. Lundgren, J.-O. Malm, J. N. Andersen, L. Samuelson, W. Seifert, B. A. Wacaser and K. Deppert. Nanotechnology 2006, 17, V. Crystal structure of branched epitaxial III-V nanotrees L. S. Karlsson, M. W. Larsson, J.-O. Malm, L. R. Wallenberg, K. A. Dick, K. Deppert, W. Seifert and L. Samuelson. NANO 2006, 1,

12 Papers not included The following papers are not included due to overlapping content or dealing with topics out of the scope of this thesis. Those cited in the text are referred to as Paper VI-XXI. VI. Electrospraying of colloidal nanoparticles for seeding of nanostructure growth P. H. M. Böttger, B. Zhaoxia, D. Adolph, K. A. Dick, L. S. Karlsson, M. N. A. Karlsson, B. A. Wacaser and K. Deppert. Nanotechnology 2007, 18, VII. Directed growth of branched nanowire structures K. A. Dick, K. Deppert, L. S. Karlsson, M. W. Larsson, W. Seifert, L. R. Wallenberg and L. Samuelson. MRS Bulletin 2007, 32, VIII. The structure of 111 B oriented GaP nanowires J. Johansson, L. S. Karlsson, C. P. T. Svensson, T. Mårtensson, B. A. Wacaser, K. Deppert and L. Samuelson. Journal of Crystal Growth , IX. Position-controlled interconnected InAs nanowire networks K. A. Dick, K. Deppert, L. S. Karlsson, W. Seifert, L. R. Wallenberg and L. Samuelson. Nano Letters 2006, 6, X. Size determination of Au aerosol nanoparticles by off-line TEM/STEM observations L. S. Karlsson, K. Deppert and J.-O. Malm. Journal of Nanoparticle Research 2006,8, XI. Au-free epitaxial growth of InAs nanowires B. Mandl, J. Stangl, T. Mårtensson, A. Mikkelsen, J. Eriksson, L. S. Karlsson, G. Bauer, L. Samuelson, and W. Seifert. Nano Letters 2006, 6, XII. Aerosol phase generation of In-Se nanoparticles Zs. Geretovszky, K. Deppert, L. S. Karlsson, M. N. A. Karlsson, J.-O. Malm and M. Mühlberg. Journal of Nanoscience & Nanotechnology 2006,6, XIII. Growth and characterization of defect free GaAs nanowires B. A. Wacaser, K. Deppert, L. S. Karlsson, L. Samuelson and W. Seifert. Journal of Crystal Growth, 2006, 287,

13 List of papers XIV. Growth and optical properties of strained GaAs-Ga x In 1 x P core-shell nanowires N. Sköld, L. S. Karlsson, M. W. Larsson, M.-E. Pistol, W. Seifert, J. Trädgårdh and L. Samuelson. Nano Letters 2005, 5, XV. A new understanding of Au-assisted growth of III-V semiconductor nanowires K. A. Dick, K. Deppert, L. S. Karlsson, L. Samuelson and W. Seifert. Advanced Functional Materials 2005, 15, XVI. Experimental evidence for non-uniform flow in a horizontal evaporation/condensation aerosol generator T. A. Damour, S. H. Ehrman, M. N. A. Karlsson, L. S. Karlsson and K. Deppert. Aerosol Science & Technology 2005, 39, XVII. Compaction of agglomerates of aerosol nanoparticles: A compilation of experimental data K. Deppert, M. N. A. Karlsson, M. H. Magnusson, L. S. Karlsson, J.-O. Malm and N. S. Srinivasan. Journal of Nanoparticle Research 2005,7, XVIII. Size-controlled nanoparticles by thermal cracking of iron pentacarbonyl M. N. A. Karlsson, K. Deppert, B. A. Wacaser, L. S. Karlsson and J.-O. Malm. Applied Physics A 2005, 80, XIX. Size- and composition controlled Au-Ga alloy aerosol nanoparticles M. N. A. Karlsson, K. Deppert, L. S. Karlsson, M. H. Magnusson and J.-O. Malm. Aerosol Science & Technology 2004, 38, XX. Phase behaviour of an Ionic Surfactant with Mixed Monovalent/Polymeric Counterions A. Svensson, L. Piculell, L. Karlsson, B. Cabane and B. Jönsson. Journal of Physical Chemistry B 2003, 107, XXI. Compaction of DNA by Gemini Surfactants: Effects of Surfactant Architecture L. Karlsson, M. C. P. van Eijk and O. Söderman. Journal of Colloid Interface Science 2002, 252,

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15 Chapter 1 Introduction The world of nanotechnology is essentially the growth and characterisation of materials on the atomic scale. To be able to control processes at this size scale, rather sophisticated tools are required. The experiments need to be designed for processes occurring on a size scale that the human eye is not capable of observing. This means that the techniques used to grow and study these structures becomes the link to understanding them. As a scientist it is sometimes frustrating when your experimental set-up becomes a black box, where trialand-error is the only successful approach. However, it is not a bad starting point, and as one gains increasingly more knowledge about the processes, the number of possibilities of controlling them will follow. This also means that the science will only progress as far as the available techniques are capable of going. This is particularly true when it comes to microscopy-related techniques where the obtainable resolution is essentially the information limit. To reach atomic resolution the use of an electron beam for image formation was a crucial step taken by Knoll and Ruska in the early 1930 s [1]. Due to the wave character of the electron, the wavelength of the beam could be controlled by the input energy from the electron source. This led to an improvement of resolution in comparison with light microscopy. Together with the development of electron optics the capabilities of the transmission electron microscope (TEM) progressed significantly and the first resolved lattice images were published some 20 years later [2]. Since then, the technical improvements in the field have been followed by the choice of studied structures. The state-of-the-art TEMs of today are equipped with monochromator electron sources [3] and aberration correctors [4] and are capable of a point resolution in the sub-ångström regime. Thus, the field of TEM is now experiencing a leap in obtainable resolution and interesting research is expected to follow. In fact, the field left the micro regime a long time ago and recently the alternative term nanoscopy has come of use. Controlled crystal growth can be obtained using a seed or substrate crystal to mediate the growth. If the crystal structure and orientation of the grown crystal is set by that of the seed or substrate crystal it is referred to as epitaxial growth. Using this technique thin crystalline films can be grown in a controlled way layer-by-layer. By directing the growth at localised areas using either seed particles or masks, one-dimensional wires can be grown using the same technique. For a semiconductor material the restriction in size to the nanoscale will affect the motion of its electrons, resulting in quantized states of their kinetic energy. So called nanowires are therefore referred to as 1D-structures, as the movement of the electrons is limited to only one direction. This property will affect the electrical characteristics of the structure and can be used to design electrical and optical devices [5, 6, 7]. The large surfaceto-volume ratio of nanowire structures also makes them suitable for sensor applications For example with the foundation of the Centre for Electron Nanoscopy (CEN) at DTU, Copenhagen. 15

16 Chapter 1 [7] where grafting of chosen sensor molecules to the nanowires surface sensitises them to specific target molecules. Also, complex inter-branched structures (Paper IX) can be grown by sequential nanowire growth in preferred crystal orientations. In this thesis, the morphology and crystal structure of III-V nanowire structures have been studied by TEM and related methods. In particular the three-dimensional structure has been characterised on the atomic scale and a structural model has been postulated. Also, the role of the Au seed nanoparticle has been investigated by ex situ compositional analysis and fits of measured lattice spacings. Based on these findings a deeper understanding of nanowire growth may lead to further possible improvement of the crystalline quality of the nanowires. 16

17 Chapter 2 Entering the world of electron microscopy In order to study crystal structures on the atomic level, advanced instruments with stateof-the-art resolution are needed. The transmission electron microscopes (TEMs) have this ability and the field is now advancing into the sub-ångström (Å) resolution regime. As chemical bonds are found on the length scale of Ångströms, this opens up the possibility of characterisation at an truly atomic level. The prerequisite for this is the use of an electron beam to probe the sample. However, as the studied material also contains electrons there will be interactions affecting the formation of the image, resulting in generation of X-rays and energy transfer to the sample. The interaction processes are utilised in compositional characterisation using X-ray electron energy dispersive spectroscopy (XEDS) and electron energy loss spectroscopy (EELS). These are additional techniques often added to the TEMinstrument, which give the possibility of very precise and localised compositional and structural characterisation. To facilitate the interpretation of the output from the instrument one must be familiar with the concepts behind all of these techniques. This will be discussed in the following sections after an explanation of the build-up of the TEM-instrument used in this work. 2.1 The TEM hardware To be able to control the electron beam the TEM-instrument consists of a column with an electron gun at the top followed by a series of electromagnetic lenses (Figure 2.1). The electron gun of the instrument used in this work is a field-emission gun (FEG), generating the electrons by exposing a fine tip of ZrO 2 -coated W (Schottky emitter) to an intense electric field. Earlier instruments were often equipped with so called thermionic guns where heat was used to overcome the work function (Φ)ofafinetip of LaB 6 or W. The advantages of the FEG are that it has a longer life-time and generates a more intense beam with more narrow energy spread. The latter being important when it comes to resolution of the instrument (see subsection 2.2.6). The condenser lens package situated above the sample in the column serves to focus the beam onto the sample, and is, together with the electron gun, sometimes referred to as the illumination system. Two operational modes can be chosen for this system: a parallel beam for the formation of a shadow image or a condensed beam to probe the sample point by point. The former is used in conventional TEM (CTEM) and high-resolution TEM (HRTEM) and the latter in scanning TEM (STEM). All three methods can generate a representative image of the sample but by slightly different processes. The objective lens package below or at the sample is mainly used in CTEM and HRTEM and is often called the image formation system. This package is very important for the resolution in the formed image and therefore the objective lens needs to be kept in a good condition. Severe aberrations in 17

18 Chapter 2 Figure 2.1: A cross-section of a TEM column from JEOL Ltd., Japan. In principle the TEM is built up by three different lens systems; the illumination system, the image formation system and the projection system. this particular lens package largely deteriorates the quality of the obtained data (see section 2.2). The lens package situated at the bottom of the column consists of the projector lenses, which only purpose is to translate the formed image to the acquisition equipment - the CCD-camera. These lenses should not affect the quality of the formed image but will be used to obtain different magnifications in combination with the previous lens packages. Additionally the column is equipped with a number of apertures with variable size. These are used to limit the width of the electron beam exposing the sample (condenser aperture) or to limit the output of the transmitted beam onto the CCD (objective aperture). 2.2 The magic of image formation Despite the heading there is nothing magical about image formation, it follows very specific rules. However, there are many exceptions to these rules, and the exact process dominating is material dependent and can even vary within the same sample. The duality of the electrons, described as both waves and discrete charged particles, plays a very important part in these processes. In principle the particle nature of the electrons can be described as scattering and the wave nature as diffraction. However, as both processes occur, the terminology quickly becomes intermixed. 18

19 Entering the world of electron microscopy Scattering Scattering can occur by two principle types: elastic or inelastic. In case of an elastic scattering event the electron changes its direction with maintained velocity and energy. For the inelastic event both direction and velocity will be altered, with some of the energy being transferred to the sample. Depending on the degree of energy transfer and the material in the sample, this could lead to beam damage to the sample. If the electron is transmitted, its energy loss could be used to analyse the composition of the sample (see section 2.4). For very thick samples the electrons could be scattered more than once, both elastically and inelastically, making the prediction of the electrons path through the sample rather difficult to trace. Two terms related to the wave property of the electrons often used together with scattering are coherent and incoherent. A fully coherent beam has all of its electrons in the same phase while the incoherent does not. Generally an elastically scattered beam is coherent and an inelastically scattered beam is incoherent. It is important to remember that electrons are strongly scattered due to their charge and will be affected by both electron cloud and atom cores in the sample Diffraction When it comes to diffraction two concepts need to be considered: kinematical and dynamical diffraction. In kinematical diffraction single diffraction is dominating; this is valid for very thin samples only. For dynamical diffraction, multiple diffraction events occur as the electron beam passes through the sample. In this case, some electrons are even said to be absorbed due to repeated inelastic scattering. Also, the incident and scattered beams are coupled as multiple diffraction can contribute to the incident beam. The distribution of diffracted electrons in reciprocal space is referred to as the diffraction pattern and can be analysed to determine the crystallinity and structure of the sample. When it comes to dynamical diffraction the relative intensity of the diffraction spots will change with sample thickness and atomic number, Z. For diffraction due to crystallinity the Bragg condition [8] must be fulfilled. This means that constructive interference of diffracted electron waves occurs at the Bragg angle, θ B. Although this process is often described as reflection of the electron beam at crystal planes, this is not the physical reality Contrast Based on the concepts of scattering and diffraction the origin of contrast in the generated image can be discussed. Without contrast there would be nothing to see in the image and no information about the sample would be obtained. Hence, the undulations in the formed image are a crucial prerequisite for microscopy in general. There are several processes contributing to contrast, often at the same time, but there are four distinct types that can be defined: massthickness, Z, diffraction and phase contrast. Mass-thickness contrast simply means that areas of larger mass or thickness will appear darker. In this case, scattering is more pronounced in electron dense areas and multiple diffraction can occur, in both cases reducing the amount of electrons passing through the sample in a forward direction. For Z-contrast, scattering increases with atomic number as the electron cloud is more dense and the atomic core is highly charged. Z-contrast is closely related to mass-thickness contrast - both are types of amplitude contrast - but is specifically used for electrons scattered to large angles. Dedicated detectors which collect transmitted electrons at high angles only can be used to emphasize this phenomena. As highly scattering areas contribute more electrons to these angles the contrast of the image is inverted when the forward scattered electrons are omitted. This 19

20 Chapter 2 technique is known as dark-field (DF) or high-angular annular dark-field (HAADF), where the latter is used in STEM mode. Diffraction contrast is related to the degree of diffraction occurring in the sample, where an amorphous area will scatter less than a crystalline area and therefore appear brighter. Also, a crystal oriented in a zone with several fringes present will appear darker than in a zone with only one lattice spacing. Hence, a crystalline particle appearing darker than equally sized neighbouring particles is most likely closer to a highly diffracting zone. Phase contrast appears whenever more than one beam contributes to the image and interference occurs. This is true for fringes observed in HRTEM-images but also at lower magnifications in Moiré patterns (see subsection 2.2.5). Another widely used type of phase contrast is Fresnel contrast generated by a phase shift at abrupt interfaces of two materials of different potential. This contrast is seen as fringes at the interface and is sensitive to defocus. In practice it is often used to find the minimum-contrast-defocus at a sample edge or interface Kikuchi diffraction A specific type of diffraction used in this work is Kikuchi diffraction [9]. The origin of Kikuchi diffraction is incoherently scattered electrons travelling in all directions, often referred to as diffusely scattered electrons. This generates diffraction cones of electron beams at each plane in the crystal due to Bragg diffraction. However, in projection these cones will appear as two parallel lines on either side of the diffracting plane. A set of lines contains one deficient (dark) and one excess (bright) line and is often referred to collectively as a Kikuchi band. In a highly diffracting zone several Kikuchi bands will meet at a Kikuchi node and two zones containing the same plane will be connected by the corresponding Kikuchi band. This is very useful when it comes to orienting the sample studied in a specific viewing direction (Figure 2.2) or even going from one node to another (as in Paper I). The thickness of the sample determines the degree of Kikuchi diffraction and in the ideal case both the normal diffraction pattern and the Kikuchi bands can be observed. For nanowires the beam has to be condensed in order for the Kikuchi patterns to appear since this enhances the number of electrons entering the sample at lower angles Double diffraction and Moiré patterns Another specific case of diffraction observed in this work is double diffraction. This process occurs when the electron beam is rediffracted by a second crystal of different orientation and/or structure than the first crystal. This generates satellite spots in the diffraction pattern since the resultant diffraction vector depends on the combination of vectors from the two crystals. The relative position of the two crystals can be determined based on the appearance of the diffraction pattern. In so-called crystal-2 patterns the upper crystal gives the principle diffraction spots while the lower crystal corresponds to the satellite spots [10]. But the opposite relationship has also been found [11]. The latter case is referred to as the top-bottom effect and can be attributed to dynamical diffraction effects, where the size of the deviation parameter causes the strongest diffracting spots to be arranged around the spot of the lower crystal. This was found to be valid at certain relative thickness ratios of epitaxial films of hematite on sapphire and vice versa [11]. The principle of crystal-2 patterns is used in Paper V to determine the relative position of the InP nanowire leaves growing topotaxially on the GaP nanowire trunk. Double diffraction is very often accompanied by Moiré patterns in the corresponding TEMimage as a consequence of interference between two different periodically spaced structures. In other words, due to the same process causing double diffraction. Depending on 20

21 Entering the world of electron microscopy Figure 2.2: The zones of a crystal is connected by Kikuchi bands even when the diffraction spots are faint. This gives a road-map of the structure and can be used to orient the sample in the microscope. Here, some of the nodes used in this work and the relation between them is presented. Particularly tilting between 11 2 and 110 zones where performed by following the ±(111) Kikuchi band. the relative orientation of the spacings different Moiré pattern types are observed. Parallel fringes of two overlapping structures cause translational Moire patterns where the new spacing, d tm is related to the respective spacings d 1 and d 2 of the two structures (eq. 2.1) where d 2 > d 1. d tm = (1 d (2.1) 2 d 1 ) Should the fringe patterns be rotated in relation to one-another a rotational Moiré pattern is generated and the angular relation needs to be considered. When two or more fringes appear in the respective crystals crossed Moiré patterns are generated. The appearance of the crossed pattern corresponds to that of the double diffraction spots and is occurring due to interference of the two original sets of fringes. In the early days of TEM this was used as a method to indirectly study structures with spacings not resolvable by the microscope [12]. The observation of translational and crossed Moiré patterns in Paper V was used to determine the relative misfit of the two structures using eq d HRTEM So far the processes in the TEM have been presented in a rather idealised way. However, as an operator you will become painfully aware that the TEM does not necessarily behave in an ideal way. The capabilities of the microscope largely depend on the hardware and its condition, and it s all in your hands. An alternative view of the TEM is to consider it as an optical device transferring most of the information from the sample to the image. There will be losses and restrictions on the way that prohibit all of the information from being collected, and to make matters worse some of the information will be distorted. Hence, a point in the specimen will be imaged as a disc; this smearing effect is often referred to as the point spread function (PSF). This can be described based on the transfer of spatial frequencies, u in Fourier space as follows (eq. 2.2) where G(u) corresponds to the Fourier transform of the disk in the 21

22 Chapter 2 image, F(u) the Fourier transform of the point in the sample and H(u) the Fourier transform of the PSF. G(u) =H(u)F (u) (2.2) The PSF can in turn be expressed as the product of the aperture function, A(u), the envelope function, E(u) and the aberration function, B(u) (eq. 2.3). An aperture effectively reduces the size of the beam and prevents part of it from being fully transferred. The envelope function is an intrinsic property of the lenses similar to A(u) asthe beam is attenuated when passing through the lenses. The aberration function corresponds to the distortion of the beam caused by the imperfect lenses and can be expressed as in eq H(u) =A(u)E(u)B(u) (2.3) B(u) =e iχ(u) (2.4) The function χ(u) (eq. 2.5) is in turn dependent on defocus, f, wavelength, λ, and the spherical aberration constant, C s. When expressed as sin χ(u) vsu it is referred to as the contrast transfer function (CTF) and can be used to study the degree of useful information transferred by the microscope (Figure 2.3). χ(u) =π fλu πc sλ 3 u 4 (2.5) The phase contrast in the formed image follows the fluctuations of the CTF and the position of the first cross-over corresponds to the point resolution of the acquired image. Up to this point the CTF has the same phase and the contributing frequencies are easily interpretable. The point resolution of a TEM-instrument is often determined at so-called optimum focus where a maximum cross-over with acceptable loss in contrast is obtained [13]. For the instrument used in this study the point resolution was determined to be 0.17nm. After the cross-over, oscillations in the CTF make the information at high spatial frequencies difficult to interpret. However, if the CTF is fully known for the instrument used, image reconstructions from focal or tilt series can make use of these frequencies [14]. All spatial frequencies are then sampled and transferred to the same phase in the CTF to form a reconstructed image. The resolution limit in such an image is in theory the information limit of the microscope as determined by the envelope damping function. The information limit resolution can be expressed as in eq. 2.6 where depends on the chromatic aberration constant, C c and the fractional change in voltage, δv/v, lens current, δi/i and the energy spread of the electron beam, δe/e (eq. 2.7) [13]. d L = πλ /2 (2.6) = C c (δv/v ) 2 +(2δI/I) 2 +(δe/e) 2 (2.7) These factors are some of the famous obstacles of the TEM-manufacturers and have led to the development of the field-emission gun (FEG), the aberration corrector and the monochromator. With the FEG the stability of the electron gun was greatly enhanced and in combination with a monochromator reducing the energy spread, the information limit would be pushed even further out. The solution for the aberrations of the lenses was to add an extra lens package counter-acting the distortion caused by the former lens. This has been done both for the condenser and objective lenses [15]. However, adding a monochromator also effectively reduces the intensity of the beam and an instrument equipped with all of these extra packages becomes, if possible, even more operator intense. Normally HRTEM-images are supported by image simulations to verify the origin of the experimentally observed structures. This becomes even more crucial when operating an aberration corrected and/or monochromated 22

23 Entering the world of electron microscopy Figure 2.3: The contrast transfer function (CTF) at Scherzer focus (-34nm) of a 300kV FEG-TEM with C s = 0.6mm plotted as sin χ(u) vs the reciprocal spacing u. The undamped function is shown by the dotted line, the symmetrical envelope damping function by dashed lines and the resulting damped CTF by the full line. instrument as the operating conditions becomes more variable. The operators for the microscopes of tomorrow might have more tools available but the question still remains: What do Ireally see?! Multi-slice simulations The most common approach used for HRTEM-image simulations is the multi-slice method. The principle behind this method is to divide a model of the sample in thin slices normal to the incident beam and allow the beam to pass the slices one by one (Figure 2.4). Three components are considered: the electron wave (Ψ), the phase grating (Q) and the propagator (P ). The electron wave is diffracted by each slice acting as a phase grating, then the diffracted wave is propagated to the next slice where the process is repeated. The interaction between Ψ and the Q is calculated based on the weak-phase object approximation (WPOA) where the slice is assumed to generate kinematical scattering only with a linear dependence between the amplitude of the scattered wave and the projected potential of the slice. The calculations can be performed using either of the following approaches: reciprocal space, fast Fourier Transform (see subsection 2.2.8), real space or Bloch-wave. The first two are based on diffraction in reciprocal space, considering diffraction in all directions where the FFT approach gives faster computation. The real space approach uses the approximation that P is strongly peaked in the forward direction and the Bloch wave method considers the diffraction from a wave-property point of view. In Paper II the FFT-approach is used in the image simulation software JEMS [16, 17] Image processing To improve the appearance of and/or to extract information from the acquired HRTEMimages different image processing techniques can be used. For example, the fast Fourier Transform (FFT) is often used to measure occurring lattice spacings and their intermediate angles as it condenses the information in the corresponding real HRTEM-image. In essence it 23

24 Chapter 2 Figure 2.4: Multi-slice simulations of thick samples are performed by slicing a model of the sample into thin cross-sections orthogonal to the incident beam. The thickness of the slices should be chosen to fulfil the weak-phase object approximation (WPOA). The calculation is performed in steps where the wave of the incident beam (Ψ)isscattered by each slice acting as a phase grating (Q) and propagated (P ) through vacuum in between each slice. gives the reciprocal lattice of the studied structure and is a good approximation of the corresponding diffraction pattern of the transformed image. By back-transforming masked areas in the FFT specific spacings can be high-lighted in the corresponding HRTEM-image. In this way, regions of different crystal orientations can be mapped out, so called FFT-mapping, as performed in Paper II and V. Another procedure would be to remove certain spatial frequencies in the FFT, so called Fourier filtering. A specific Fourier filtering technique often used to improve signal-to-noise ratios is Wiener filtering [18]. In this case, an estimated noise is subtracted from the FFT and subsequently back-transformed to generate a less noisy HRTEM-image. This technique was used before FFT-mapping in Paper II. 2.3 X-ray energy dispersive spectroscopy (XEDS) The generation of X-rays in the TEM column results from the interaction between the electron beam and the sample itself (Figure 2.5). Electrons entering deep into the electron cloud of an atom can excite the atom by knocking out one of its inner shell electrons. To fill the gap in the lower shell an upper shell electron takes its place, and the energy difference between the respective shells is released as a characteristic X-ray. Another possibility is for the atom to release an electron corresponding to the excess energy of the excited state. These electrons are known as Auger electrons and are characteristic of each element. However, the Auger electron signal is weaker than the X-ray signal and the technique is less widely used than XEDS in TEM. In order to detect the X-ray signal a Si(Li)-detector is used. When an X-ray hits the detector a number of electron-hole pairs is formed, the number being directly related to the energy of the X-ray. Hence, the detector can be calibrated using samples of known composition. The detector is mounted onto the column above the sample and will be protected by an atmospheric window that can withstand the pressure difference between the column (10 5 Pa) and normal atmosphere (10 5 Pa). The window has to be transparent to X-rays in order not to affect the signal and also protects the N 2 (l)-cooled detector crystal from condensation of hydrocarbons or ice. Today, Al/polymer windows are used which can detect X-rays down to Be (Z=4). The number of X-rays that the detector can process is limited and 24

25 Entering the world of electron microscopy Figure 2.5: Ionisation (1) of an inner shell electron by interaction with the incoming high energy electrons puts the atom in an excited state. To release the excess energy an outer shell electron can fill the formed hole, releasing the corresponding energy difference as a characteristic X-ray (2). Another possibility is the release of an electron (3) of the atoms excess energy, these electrons are called Auger electrons. there will be occasions when no signal is actively collected as processing needs to be done. This is referred to as dead-time and the set time for data collection is often referred to in liveseconds, corresponding to the active sampling time. Normally it is not recommended that the dead-time is higher than 30% when collecting data, as this means that the processing is less efficient. There are a few common artefacts known to occur with XEDS set-ups that should be considered when applying this technique. For example, Si escape peaks can be found at 1.74eV as a result of fluorescence instead of electron-hole pair formation. Also, internal fluorescent peaks of Si can appear if the p-type region (dead-layer) is thick. Sum peaks are an artefact of processing and appears when the electronics is too slow. In other words, when the count rates or dead-times are high. These peaks are a result of coincidence, where two X-rays hitting the detector simultaneously are interpreted as one X-ray of the total energy. The combination of XEDS and STEM is a particularly efficient probing tool where very localised areas can be qualitatively analysed. For example, an XEDS-spectra could be acquired from a specific point, along a line or in a randomly shaped area. The distribution of the present elements can also be obtained using specific peaks to map the contribution in an area or along a line. The line-scan analysis is for example used in Paper III to monitor the distribution of Ga in the Au seed nanoparticle. For quantitative EDS-analysis the Cliff-Lorimer ratio approach (eq. 2.8) is used where the ratio of the concentrations, C of element A and B is related to the ratio of the intensities, I of A and B respectively by the Cliff-Lorimer factor, k AB (also known as the k-factor). C A I A = k AB (2.8) C B I B The k-factor depend on the peaks used but are also sensitive to the instrument set-up and should be determined by experimental standards or simulated from first principles calcula- 25

26 Chapter 2 Figure 2.6: The EEL-spectrum shows the energy distribution in the transmitted beam based on energy loss. Elastically transmitted electrons contribute to the zero-loss peak (ZLP). Low-loss electrons that have generated plasmons give the so called plasmon peak. Finally core-loss electrons give edges of specific appearance and energy-losses. This spectrum is taken for GaAs and the core-losses correspond to Ga L 2,3 (1115eV) and As L 2,3 (1325eV), respectively. tions. The quantification procedure includes background subtraction and peak integration to get the result in either weight or atomic percent. To certify that the obtained spectrum is reliable for quantification the peak height should be clearly distinguishable from the background and the sample should be aligned with the detector. In Paper III EDS-quantification is used to determine the Ga content in Au seed nanoparticles of GaAs nanowires. 2.4 Electron energy loss spectroscopy (EELS) The inelastically scattered electrons will loose some energy from interacting with the sample. The loss is specific to the interaction process and can be used for further characterisation or even energy filtering of the obtained image. In order to separate the transmitted electrons based on energy a magnetic prism is used to deflect the electrons. Electrons of high-loss are more easily deflected than low-loss electrons and the signal is effectively separated. By studying the full range of energy-losses an EEL-spectrum can be obtained, using the spectroscopy mode. The EEL-spectrum (Figure 2.6) contains information from all of the active inelastic processes and is a good basis for describing them. The first intense peak around zero is simply called the zero-loss peak. However, it also includes very small losses up to about 0.3eV. The next broad peak comes from plasmon (oscillation of electron density) losses and occurs in most materials but predominantly in free-electron structures. Losses due to single electron interactions are seen next and often superimpose the plasmon peak. These peaks and the plasmon peak are often collectively referred to as low-losses, and identification of samples is done in a finger-print fashion against databases with spectra of known samples. The highloss region of the spectrum is generated by interaction with the shells closest to the atomic core. Such ionisation losses are seen as edges in the spectra and have specific energies depending on the shell type. 26

27 Entering the world of electron microscopy Another operation mode is to generate images based on specific energy windows of the spectrum, using identified edges to map out areas containing certain elements. This technique is called energy-filtered TEM (EFTEM) and results in elemental maps by parallel acquisition. Also, the thickness of the sample can be determined since the scattering is directly thickness dependent. Normally this is taken as the ratio between the zero-loss peak and the total intensity of the spectrum. However, as the spectrum intensity is dominated by the low-loss region the total intensity is approximated to this region. If pressed on further, even the plasmon alone could suffice as representative for the total intensity. However, this is only reliable if single scattering is dominating. If operated in EFTEM mode, thickness maps can be obtained by taking the ratio of the low-loss region and the zero-loss peak. This technique has been tested on GaP 111 B nanowires to study the appearance of the side facets (see section 5.1). 27

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29 Chapter 3 Crystallography and twin defects of III-V semiconductors A crystal is an ordered structure with atoms arranged at specific positions with given relationship to one another. In theory a crystal is infinite but in practice the internal ordering can express itself as well-defined crystals with given facets. Although, the facets are directly related to the atomic structure of the crystal, much of the field of crystallography was developed without considering the exact atomic structure. Instead, the idea of a unit cell as a principle building block of a crystal was discussed among mineralogists [19]. The crystal systems were deduced from symmetry alone and developed a surprisingly consistent field of science. To be able to describe given directions and planes in crystals the Miller index (hkl) was introduced [20] which related them to the defined crystal axes. In principle each index correspond to the reciprocal intercept of these axes with correction for multiples. This means that a plane is normal to the corresponding reciprocal lattice vector. To denote the difference between a plane and a vector different sets of parentheses are used. In a cubic crystal three equidistant crystal axes a = b = c are related to one another by intermediate angles of 90.Inthat case, the three crystal axes a, b and c correspond to the directions [100], [010] and [001], respectively. Stacking of solid spheres is often used during introductory courses in crystallography to illustrate the concept of symmetry. Close-packing of spheres can be obtained by stacking of three different close-packed layers of spheres - A, B and C. When the spheres are stacked in a (ABCABC..) sequence a cubic close-packed structure is obtained and when stacked in a (ABAB..) sequence the hexagonal close-packed structure is achieved. However, alternative stacking sequences are also found, mixing the three possible layer types in longer sequences creating so called polytype structures. For example, another possible way to stack spheres is (ABC BCA CAB..) resulting in a rhombohedral structure called 9R, as it has 9 layers in its repeated sequence. This notation was introduced by Ramsdell to categorise observed polytypes of SiC [21]. Using this notation the close-packed hexagonal structure would be denoted as 2H and the close-packed cubic as 3C. As seen for SiC, the concept of stacking is not limited to single atomic structures. 3.1 Crystal structures Tworeoccurring structures for stacking of atomic bilayers are zinc blende (or sphalerite) and wurtzite, corresponding to the cubic and hexagonal crystal system respectively (Figure 3.1). Zinc blende can be described as two interpenetrating systems of close-packed cubic struc- Single planes (hkl), a set of planes {hkl}, a single direction [hkl] and a set of directions hkl. 29