Ion channeling in ultra thin crystals 1

Chapter Introduction 1.1 Ion scattering experiments: The passage of energetic ions through a solid material has been extensively studied for the last ~110 years. The interaction of ions with atoms in a solid depends on the impact parameter of the ion with the atomic nuclei, energy and the charge to mass (e/m) ratio of the incident ions. Several types of analytical spectroscopy methods have been established, depending on the impact parameters of ion-solid collisions and on the nature of elastic/inelastic types of collisions. Nevertheless, the cross section for all scattering processes depends on the impact parameter “b” involved in collisions with individual target atoms. Incident ions with impact parameters between b and db will be deflected through an annular region of area 2π(R sinθc )(R dθc), see Figure 1.1, ‘b’ is defined as the perpendicular distance between the ion straight trajectory to the target atom, when there is no Coulomb interaction between them. If the target material is amorphous or polycrystalline, the atomic arrangement is homogeneous and isotropic, and so the impact-parameter distribution is independent of the relative orientations of the incident beam to the target. Figure 1. 1: Schematic illustration of classical ion-atom scattering in the centre of mass frame [1]. 1.2 Ion Beam Analysis: Ion Beam Analysis (IBA) [2, 3] is based on the interaction of accelerated charged particles with the target material at both the atomic and the nuclear levels. IBA typically uses light ion beams of a few MeV energy directed into solid targets to probe elemental compositions non-destructively as a function of depth to several microns, with a typical depth resolution of a few nanometers to a few tens of nanometers. Atomic depth resolution can also be achieved but requires more specialized equipment. The typical energy of the ion beam is in the range of 0.5 to MeV and the light ions are mainly H+ and He+. Figure 1.2 shows an overview of the available IBA techniques. The generalized principles involved are the same; the incident energetic charged particles get slowed down in the target by colliding with the electrons and nuclei of the atoms in the target, and are deflected from their initial trajectory. This can lead to the emission of either particles or electromagnetic radiation whose energy is characteristic of the target elements in the sample. Analytical techniques based on elastic scattering are Rutherford Backscattering Spectroscopy (RBS) [4], Elastic (non-Rutherford) Backscattering Spectroscopy (EBS), Channeling [5], Elastic Recoil Detection Analysis (ERDA) [6] , whereas those based on inelastic scattering are Particle Induced X-ray Emission (PIXE) [7] and Nuclear Reaction Analysis (NRA) [6]. The same incident beams also usually damage the samples, as encountered in Ion Beam Implantation [8] and made use of in Ion Beam writing [9]. Figure 1. 2: A Schematic illustration of ion beam analysis techniques. Among all the ion beam analysis (IBA) [2, 3] techniques RBS is the most commonly used one, for quantitative, non-destructive, and depth-profiling in materials science. It uses energetic ions, typically ranging from 100 keV to several MeV per nucleon light ions (He+, H+). RBS is based on nuclear scattering and the energy distribution of backscattered ions from the target at a fixed scattering angle θ is measured, see Figure 1.3. The yield of backscattered ions from any given element is proportional to its concentration in the target, therefore thickness and depth profiles of individual elements can be obtained without the need for reference samples to quantify the absolute atomic ratios in the target. Importantly, it is insensitive to the chemical environment. It can also determine the film thickness in terms of areal atomic density by assuming the mass density precisely, and energy distribution of backscattered ions quantifies the depth distribution for a given element. RBS is sensitive to heavy elements in a light matrix, but if one wants to quantify the light elements in the heavy matrix, EBS can be used which is sensitive to lighter elements. Figure 1. 3: Experimental set up for ion beam analysis techniques (RBS spectra shown). Figure 1.3 shows the typical RBS experimental set up in most accelerator laboratories. The accelerated MeV ion beam is incident on the target which is placed in the target chamber and the backscattered ions are collected by a detector, typically a surface barrier detector. The data is collected by a multi-channel analyser which displays the ion energy versus counts. The four basic fundamental concepts underlying the capability of RBS spectroscopy are kinematic factor, scattering cross section, stopping cross section and energy straggling (broadening), which determine the mass resolution, relative atomic composition, depth perception and ultimate mass, depth resolutions respectively. The process underlying the collection of RBS spectra can be seen in the schematic in Figure 1.3, where the backscattered energy will be higher for the heavy elements and lower for lighter elements. The high energy ions (2 MeV H+ and He+) can overcome the Coulomb barrier shown in Figure 1.4, and interact with the nucleus of the target atom. When this occurs, new reaction products can be generated through nuclear reactions (NRA) [6] and also nuclear resonance reactions may occur at specific energies. Under these circumstances the ions cannot be treated by Rutherford’s approximation of a point charge, and the scattering mechanism can only be solved by Schrodinger’s equation using quantum mechanics. Such backscattering spectroscopy is also called Elastic (non-Rutherford) Backscattering Spectroscopy (EBS). EBS is useful for quantifying the light elements in a heavy matrix. Figure 1. 4: The calculated Coulomb barrier energies of the different element/ion pairs. Figure 1.4 shows the Coulomb barrier energies for protons, deuterons, He and 4He in all target atoms. Figure 1.5 (a) shows the ratio of the non-RBS to RBS cross-section as a function of He+ beam energy, and the maxima is at 3.037 MeV. Using such energetic ion beam one can enhance the oxygen EBS signal and Figure 1.5 (b) shows the experimentally measured spectra. Another advacntage of these nuclear reactions is to precicely determine the precise value of terminal voltage of the accelerators, for example in our case 3.043 MeV terminal voltage is giving the maximum EBS signal of oxygen. We can clearly see the oxygen signal in the EBS spectra is so large compared to the normal Rutherford scattering cross section simulation (black colour line), where the oxygen signal is smaller and flat. Figure 1. 5: (a) The ratio of non-Rutherford cross section to Rutherford cross section as a function of energy for oxygen atom in the target to the incident He+ ion, (b) measured RBS-Channeling spectra for SrTiO3 single crystal substrate using the oxygen resonance energy of 3.043 MeV He+ ions, the random spectra is fitted with the pure Rutherford scattering cross section simulation. Figure 1. 6: (a) The phenomenological model of axial channel trajectory seen by incident ion inside the crystal, the yellow colour atomic strings are steering the ion inside the channel, (b) the rough diagram of goniometer rotation set up in the RBS experiment to collect the spectra at aligned (channeled) case. Figure 1. 7: (a) Schematic ion flux distribution at aligned case after passing one monolayer of atoms, marked the shadow cone formation of ions, and the trajectories of different impact parameter ions are shown in the crystal, (b) the comparison of aligned and random RBS spectra, surface peak in the aligned case is highlighted. In addition to thickness and elemental compositional information, RBS can also provide the structure of single crystal targets and epitaxially grown films, using the Channeling technique. The regular atomic arrangement of a crystalline material influences the ion’s passage, and this is called Channeling; the beam is gently steered by atomic strings or planes into the empty channels so that small impact-parameter and large-angle scattering events with atoms are suppressed. The red colour line spectra showed in Figure 1.5(b) is collected at the channeled alignment, by aligning the sample normal ň to the crystallographic axial direction using goniometer with (ψ, φ) angular rotations (see Figure 1.6 (b)). The RBS signal drops nearly two orders of magnitude, with most ions escaping close encounter collisions with the nuclei of the crystal. The phenomenological atomic view of an axial trajectory is shown in Figure 1.6(a). At channeled alignment, the ions escape backscattering events as they move in the middle of the unit cell, however some of the ions cannot escape from these close encounter events, particularly those which are incident exactly upon the atomic strings. This is why the RBS spectrum has a finite peak size at the surface and then reduces at greater depths. This is marked as a surface peak in Figure 1.7 (b) and the remaining ions get steered by the Coulomb forces along the channel into the middle of the unit cell shown in Figure 1.7 (a). Surface atoms provide a shadowing effect to the ions behind them, the incident ions are deflected by the surface atomic layer, forming a “shadow cone” which shields the rest of the atoms lining the channel from head-on and low impact parameter approach by the ions, which reduces the backscattering yield, i.e. the backscattering yield at surface peak is higher than the shadowed ions. Subsequent encounters of channeled ions with lattice atoms make the small-angled collisions with large impact parameters, with an oscillatory ion trajectory within the channel in near-surface regions. The channeling minimum yield, χmin , is defined as the fraction of the nonchanneled ions relative to the total number of incident ions; this can be found experimentally by dividing the yields from aligned to random spectra. It can be found for different element signals, and by knowing this one can get a measure of the crystallinity of the near surface region. PIXE can determine elemental concentrations down to ~ppm levels in the sample. Typically a - MeV energy ion beam is used in this technique. The incident ion ionizes the core shell electrons of the atoms in the sample, and the higher shell electrons de-excite and generate a characteristic X-ray. A schematic of this process of knocking out inner shell electron by protons and the subsequent emission of an X-ray is shown in Figure 1.8. Using PIXE, the relative composition of the target can be quantified, and it can distinguish similar mass elements which cannot be quantified in RBS, however it cannot provide any depth resolution. A related technique, particle-induced gamma-ray emission (PIGE) can also be used to detect some light elements and provides excellent sensitivity (~ppm) and/or depth resolution (~50 Å) for certain light isotopes such as 1H, 15N, and 19F. Figure 1. 8: A schematic diagram of knock out of electron in the atom by incident MeV proton and the generation of X-ray are shown for PIXE spectroscopy. 10 ERDA detects the sputtered (knocked-out) target atoms by the incident ions. In general, ERDA is used to analyse light target atoms, from hydrogen to oxygen, while RBS is used to analyse heavier atoms, from carbon to uranium. The advantage of both techniques is that they are quantitative, without any need for calibration samples. Since both techniques use nuclear scattering, the chemical makeup and electronic binding configurations have little effect on the measurements. All the above IBA spectroscopy techniques have yields which become strongly orientation dependent due to steering of the ion beam away from the nuclei of crystalline targets in channeling alignment. The first evidence of the channeling effect was in backscattering yields [10], in nuclear reaction yields [11], and in characteristic X-rays [12], when ion beams were directed parallel to the crystal axes. The following chapters are all related to the channeling phenomena in thin crystals, with a comprehensive introduction given in Chapter 2. Figure 1. 9: Random, planar and axial crystallographic projections in a silicon lattice. 11 4.7.2 FLUX simulated energy loss studies of [001] channeled ions for MeV protons in 55nm thick silicon: The energy loss of [001] channeled MeV protons from 55nm thick Si is very low, and the average energy loss is just ~1.5 keV as predicted by FLUX, so that it is difficult to measure it directly by experiments. The first column of Figure 4.10 shows FLUX simulated energy loss maps portrayed in spatial and angular coordinates, and the corresponding channeled spatial, angular ion distributions in the second column. Figure 4.10 (a) displays the energy loss map in the entrance spatial coordinates, which shows that the protons entering near the atomic strings lose more energy, than those protons entering the middle part of unit cell and the remaining protons lose medium energy. Figure 4.10 (b,c) shows the energy loss maps in exit spatial, angular coordinates, the high intense distribution beam loses less energy as they move in the middle of the unit cell and the high energy loss is corresponding to the beam spread into the neighbour unit cells while the beam deflected with large angles has a higher energy loss. 77 Figure 4. 10: Simulated FLUX energy loss maps of channeled MeV protons from a 55 nm [001] Si crystal in first column (a,b) portrayed in entrance, exit spatial coordinates (c) angular distribution style. Second column shows corresponding spatial and angular maps. The case of the largest angular scattered protons at the [111] axis case formed slightly curved shapes in Figure 4.6(c). The origin of such shapes is studied using FLUX simulations by an option CFILE [18]. CFILE is an option in the FLUX programme, which helps to simulate the programme in the specific entrance spatial coordinates. Figure 4.11 (a,b) shows the simulated exit angular and spatial distributions respectively from for MeV 78 protons as a function of depth in the crystal for the protons incident with a maximum impact parameter of 0.2Å to the atomic string. Figure 4. 11: FLUX simulated CFILE exit (a) angular (b) spatial distributions for the maximum impact parameter chosen for 0.2Å to the atomic string of axis for MeV protons as a function of depth into the crystal. 79 At a depth of 20nm inside the crystal, the protons are distributed uniformly around the incident atomic string location, but as they penetrate deeper, they start to be blocked by the surrounding atomic strings. We clearly see the division of the uniform distribution at 20nm to different branches of distribution at a depth of 60 nm, and at about 80 nm depth, they are again blocked by the second nearest neighbour atomic strings, and the corresponding angular distributions also showed such blocking in angular space, however these protons spatially experience the blocking effect by the atomic strings and keep changing their trajectories. An important point to note here is that even at a depth of 350nm the protons are still steered by the atomic strings, and we can see several atomic string blocking centers. 80 4.8: Experimental axial channeled distributions at major and minor axes: Figure 4. 12: Collage of experimental channeled angular distributions at different axial angular locations along (001), (011), (111) planar directions for MeV protons from a 55 nm [001] Si membrane. All pictures are for high exposures to differentiate the features. Figure 4.12 shows a collection of axial channeling patterns recorded for MeV protons through a 55 nm [001] silicon membrane for the same axes 81 shown in Figure 4.5. These patterns are recorded with high exposure camera times for similar beam currents. The maximum tilt angle was 54.7 ° to reach the [111] axis, where the effective thickness is ~84 nm, well below the axial channeling oscillation quarter wavelength depth. As we know, protons entering nearer to the atomic strings get deflected with larger angles. By observing the distributions of protons with significant deflection angles in the streaks at each pattern, can give axial atomic orientation information. In this figure we can clearly see the variation in the channeling patterns with the axial projections which cannot be observed in thicker crystals. Each axial pattern shape is unique and represents its crystallographic geometry. Figure 4. 13: Stereographic projection of planes near the Si (100) pole in a linear projection with the width of each plane drawn proportional to the probability of channeling. Negative signs are omitted in the labels of indices of the planes. This picture is from Ref. [51] 82 The major axial patterns were discussed in section 4.6, here we mainly focus on the minor axial patterns in between major axes. If we look closely near at [001] axis, there are many higher order planes intersecting with the {001}, {011} planes, forming higher order axes shown in Figure 4.13. We can clearly see that [014] axis consists of no lower order planes intersecting with the horizontal {001} plane, that’s why its channeled pattern in Figure 4.12 shown only bright intense region in the middle of the pattern located along {001} plane with four higher order planar intersections to it, where all the large angle scattered protons are captured by planar walls and we can see the blocking of those planes quite clearly. [013] axis have a similar atomic arrangement to [011] axis can be seen from Figure 4.5 but the diagonal intersecting planes are {113}, {133} at [013] and {111}, {113} at [011] axis which can be seen all of them in Figures 4.5, 4.13 respectively. The channeled patterns showed the blocking of these planes quite clearly in Figure 4.12. Axis [012] has a hexagonal atomic arrangement see Figure 4.5 and the channeled pattern shows sided arms in Figure 4.13. From Figure 4.5 there are two sets of {112} family of planes diagonally intersecting with horizontally running plane at [113] axis and the axial pattern in Figure 4.12 shows the blocking of those diagonal planes. [112] axis has a rectangular in shape atomic arrangement with two atoms at each corner and it has vertically running {111} plane, diagonally intersecting {113} planes and horizontally running plane from Figure 4.5. The channeled pattern shown in Figure 4.12 is rectangular in shape in the middle and the peripheral region of the channeled pattern contained streaks which signifies the intersection of {113}, {111}, {011} planes. The planes of symmetry in 83 each pattern correspond to that within the relevant atomic potential map, with none for the and axes which exhibit a bright, symmetric, horizontal band, with an asymmetric component to either side, differently oriented for the two axes. The asymmetry is reflected about the horizontal plane in the patterns recorded from the and axes as well. This asymmetry is due to the asymmetry in the atomic arrangement in narrow {111} planes; the origin of these patterns will be discussed in details in chapter 5. 4.9 FLUX simulated axial channeled distributions at major and minor axes: Figure 4.14 shows the FLUX simulated emergent angular distributions for 500,000 MeV protons for the corresponding axes through a 55 nm [001] Si shown in Figure 4.12. In all such FLUX simulations, blue/red regions correspond to low/high intensity. The experimental patterns are in good agreement with the simulations at all axis and also confirm the strong asymmetry observed at , axial patterns in Figure 4.12 exhibited in the location of the two bright dots. The channeling patterns change their shapes by changing the incident energy (or) the thickness of the crystal and the ion type at any axial projection. This study will be discussed in detail in chapter 8. 84 Figure 4. 14: Collage of FLUX simulated channeled angular distributions at different axial angular locations along (001), (011), (111) planar directions for MeV protons from a 55 nm [001] Si membrane arranged in a same fashion as in Figure 4.12. Figures 4.15 show the experimental major and minor axial channeling patterns along the {011} plane as a function of camera exposure times. This 85 set of data provides detailed information on the evolution of such complex shapes at each axes. Figure 4. 15: Experimental channeling patterns at axes along {011} plane: for MeV protons from a 55 nm [001] Si membrane in the aligned cases at (a) [001], (b) [114] (c) [112] and (d) [111] axes. Downwards direction shows the effect of increasing camera exposure. 86 Figure 4. 16: Schematic of the planes around [114] axial projection in silicon. The highest exposure [114] axial pattern shows a peculiar feature shown in Figure 4.15 (b). There is a narrow width dark region surrounded by two bright intense streaks appear below and above the axial pattern, marked with a blue colour arrow. This narrow blocking region is due to the higher order plane which cannot be observed in thicker crystals (shown in Figure 4.2) or with the RBS experiments [51]. Figure 4.16 shows the schematic diagram of the planes at [114] axis, where two sets of {113} planes are intersecting diagonally (with 49.5° inclination to each other) with the horizontally running {011} plane and there is a higher order (narrow planar width) plane in vertical direction. The wide angle scattered protons are still captured by this narrow planar channels near the axis allowing the observation of blocking of the narrow channel from ultra-thin crystals. There are a few important observations of the [112] axis which require comment, where the red colour dashed and white colour solid lines 87 highlighted at the highest intensity [112] pattern in the Figure 4.15(c). The channeled proton intensity within the red, dashed region appears beyond the horizontally-running {011} planar channel and is directed along the widest planar channel, i.e. the {111} planes at this axis. This specific part of the angular distribution is due to the protons entering in the centre of the narrow {111} planar channel at [112] and closer to their atomic strings, where the potential energy is highest, so that the protons acquire relatively large ET compared to other protons. This was confirmed with the FLUX simulations shown in Figure 4.18, where the data plotted is from the protons entering near the atomic strings at narrow {111} plane. The protons entering in the narrow {111} planar channel behave as a separate axial channeled fraction, this can be seen by their spatial distributions in the Figure 4.17 (I,III c). Because of the large potential in this specific area of the unit cell, we can see this behaviour in more details regarding narrow {111} plane are discussed in Chapter 5. 88 Figure 4. 17: Simulated FLUX channeling patterns for the angular distribution in (a) the combined (c,d) in the wide and narrow {111} planar channel regions in the [112] axis for MeV protons from a 65 nm [001] Si membrane, (I) angular (II,III) entrance, exit spatial coordinates. White circles denote the atomic string locations. Figure 4. 18: Simulated FLUX channeling patterns from the selected data near the atomic string locations at narrow {111} planes of [112] axis (a) angular distribution (b, c) entrance, exit spatial distributions White circles denote the atomic string locations. 89 Figure 4. 19: Experimental channeling patterns at axes along {001} plane: for MeV protons from a 55 nm [001] Si membrane in the aligned cases at (a) [001], (b) [013] (c) [012] and (d) [011] axes. Downwards direction shows the effect of increasing camera exposure. Figures 4.19 show the experimental major and minor axial channeling patterns along {001} plane as a function of camera exposure times as in Figure 4.15. [001], [011] axial patterns are discussed in section 4.6. The highest exposure picture shown in Figure 4.18 (c) display the planar intersections of a diagonal plane {121} and horizontal {001} plane, the stereographic projection at this axis can be seen in Figure 4.4. The minor axes along the {111} plane are shown in Figure 4.20. The atoms in the narrow {111} plane are at different depths and so change their 90 locations with respect to each other, resulting in asymmetries in the adjacent plane walls. This is reflected in the local channel potential and the resulting fine-scale angular structure as can be seen in Figure 4.20 (b,c) where asymmetrically deflected channeled protons with respect to vertical direction are highlighted in red colour dots. Figure 4. 20: Experimental channeling patterns at axes along {111} plane: for MeV protons from a 55 nm [001] Si membrane in the aligned cases at (a) [112], (b) [213] and (c) [314] axes. Downwards direction shows the effect of increasing camera exposure. 91 4.10 Conclusions: The star like channeling patterns observed in thicker crystals show unique shapes in ultra-thin crystals at all the major and minor axes, which directly correlate with the respective crystallographic orientation. The best high resolution rainbow (or) early evolution channeled angular distributions from ultra-thin crystals at major and minor axes are captured and confirmed with the FLUX Monte-Carlo simulations and simultaneously we proved several predictions made by Ref [26, 88-91] for the first time. 92 [...]... with indices (h1, k1, l1,) and (h2, k2, 12 ) is given in Formula 3.2 35 ANGLE (10 0) (11 0) ( 010 ) (0 01) (10 1) (10 0) 0.00 o 45.0 o 90.0 o 90.0 o 45.0 o ( 011 ) 90.0 o 60.0 o 45.0 o 45.0 o 60.0 o (11 1) 54.7 o 35.3 o 54.7 o 54.7 o 35.3 o ( 211 ) 35.2 o 30.0 o 65.9 o 65.9 o 30.0 o ( 311 ) 25.2 o 31. 4 o 72.4 o 72.4 o 31. 4 o ( 511 ) 15 .8 o 35.2 o 78.9 o 78.9 o 35.2 o ( 711 ) 11 .4 o 37.6 o 81. 9 o 81. 9 o 37.6 o Table 3 1: ... extraction experiments [13 ] Lindhard [14 ] , Barrett [15 ] and many others [16 - 21] developed analytical and numerical methods for channeling phenomena, but none of the models explain axial channeling in ultra- thin crystals (at the very early stages of the channeling trajectories) The angular distributions of an axially channeled ion beam through an ultra- thin crystal shows finite ridges and strings at... RC distributions are presented in Chapter 4 This study takes advantage of the diversity of new channeling phenomena observed at planar alignments, especially different channeling effects at narrow and wide {11 1} planes of Si The early evolution of {11 1} planar ion channeling patterns and the observed separate ion channeling and dechanneling behaviours of narrow {11 1} planes is discussed in Chapter 5... protons in < 011 > and channels is proportional to Zρ2/E, with the depth “ρ2” denotes the mean square atomic vibration amplitude and “Z” denote the depth in the sample But for the planar case, the dechanneling varies exponentially with increasing depth The extent of dechanneling is characterized by a half thickness “Z1/2” Ref [45] found that, Z1/2 values for 3 MeV protons along {11 1}, {11 0} and {10 0}... doesn’t assume the channeling effects initially, because the calculations are based on binary collisions of the incoming particle and the target atoms only, which are described by a screened ion- atom potential 30 Figure 2 6: Projections of the diamond lattice along the , < 011 > and axes, illustrating some of the ideas used in the simulation program The FLUX calculation confines only to a rectangular... LAROSE [15 ] in 19 71, which provided the information on the channeled beam flux in the crystal and nuclear encounter probability which can be useful for ion- atom scattering experiments 2 10 Inter-atomic potentials: In channeling, the regular atomic structure of a solid is the crucial factor in determining the motion of ions and the properties of the beam The continuum model shows, how this governed motion... depth 10 3 Å whereas they would penetrate into amorphous Ge only to a depth ~44 Å according to SRIM [ 31] calculations Robinson and Oen reported computer studies of the slowing down of atoms in solids [32] though it had been predicted much earlier in 19 12 [33] However, MeV ion channeling was observed experimentally only in 19 60’s [34-36] Detailed descriptions of the channeling process are given in a famous... potential For this reason, channeling phenomenon is described by a so-called “continuum” model, and the same model can be used to calculate the parameters involved in channeling There is a corresponding maximum incident angle, the channeling 19 “critical angle” ψc, for which incident ions can be steered by the channel according to continuum model By averaging the ion atomic interaction potential along the... transmission mode, based on recording transverse momentum distributions in experiments with thin target crystals Figure 1. 10 shows the typical transmission channeling set up, with transmitted ion energies and transverse momentum distributions collected either by a position sensitive detector or a fluorescent screen at aligned or tilted cases Figure 1 10: Geometry of a typical transmission channeling set... transfers occur ~10 0 keV in billiard ball type collisions resulting in the large angle scattering of the incident particle which cannot be channeled anymore 2.7 Dechanneling: The ions can be divided into a channeled fraction and a non-channeled fraction at any point of time of their trajectory inside the channels Even though the channeled fraction is 97-98% for 3 MeV protons along [ 011 ] axis in Si at the . separate ion channeling and dechanneling behaviours of narrow {11 1} planes is discussed in Chapter 5. This is the first report on the observation of such channeling effects from narrow {11 1} planes. phenomena in thin crystals, with a comprehensive introduction given in Chapter 2. Figure 1. 9: Random, planar and axial crystallographic projections in a silicon lattice. 12 1. 3 Transmission. transmission mode, based on recording transverse momentum distributions in experiments with thin target crystals. Figure 1. 10 shows the typical transmission channeling set up, with transmitted ion