Ion channeling in ultra thin crystals 2

Chapter Impact of narrow {111} planes in planar channeling This chapter presents channeling patterns that are clearly resolved effects of the narrow {111} planes in planar alignments for MeV protons passing through a 55 nm [001] silicon membrane. As a consequence of the shallow potential well at the narrow planes, incident protons suffer dechanneled trajectories which are excluded from channeling within the wide planes, resulting in an anomalously large scattered beam at {111} alignment. Ion trajectory simulations and phase space analysis revealed the dechanneling of protons entering narrow {111} planes for incidence angles less than the critical angles. The demonstration of a larger angular spread from {111} patterns due to narrow {111} channels compared to {110} channeling at high energies (GeV, TeV) is presented using MC simulations. Beam extraction and bending experiments mainly use {111} planar channeling due to its largest width of the channel giving the highest critical angle among all the planar channels in Si. However, they not consider the narrow {111} planar channel and encounter a high amount of dechanneling. We have observed detailed narrow {111} planar channeling angular distributions which were previously unresolvable. 5.1 Introduction: The planar channeled ion trajectory can be completely described in terms of the motion in the transverse direction using the continuum model [14], the planar channeling critical angle,  c and the planar oscillation wavelength “” as given by [37, 99] 93 c    4Z1 Z e Nd p CaTF pv Ed p 2Z1 Z e NaTF (5.1) (5.2) where Z1 and Z2 are the atomic numbers of the incident and lattice nuclei, N is the atomic density, dp is the planar spacing, C  , aTF is the ThomasFermi screening distance and p, v are the ion momentum and velocity. The planar channeled trajectories oscillate back and forth in the regions of lower electron density between channel walls. Hence the channeled spatial flux distribution is strongly depth dependent due to coherent oscillations of all ion trajectories. The ion oscillation wavelength, λ is a function of its impact parameter at the entrance side with the channel walls. For channeled ions the smaller the oscillation amplitude the longer the wavelength. In the incident ion beam, each ion has its own impact parameter. However the variation in wavelengths of all the ions is small enough to have “coherence” among all the ions. Due to the maintenance of coherence among all the individual channeled ions, there are several oscillations along their trajectories up to some depth into the crystal before they become dechanneled. 5.2 FLUX Simulated Planar Channeled ion trajectories: Channeled ion trajectory plots give a clear understanding of angular patterns observed in experiments or simulations. A visual presentation of the ion trajectories inside the planar channels using simulations is given in this section. Figure 5.1 shows the FLUX simulated planar channeled MeV proton trajectories along the {011} plane for 10,000 protons in 400 nm thick silicon at planar alignment. The red/blue colour signifies the high/low intensity flux 94 distribution. The FLUX simulation provides the X-Z coordinate data of the ions for nm depth intervals and the bin size chosen in the plot is 0.5 nm depth interval, which is why the plot has several vertical blank rows with a size of one bin. The ions are steered away from the planar walls and get super-focused* (see the session 8.1 for super-focusing) into the center of the planar channel at a quarter wavelength (λ/4) oscillation which is the red colour region marked with a dashed white line in Figure 5.1. They move apart (de-focused) after being focused towards the opposite channel walls and reach the walls at half wavelength (λ/2) oscillation depth, and are again focused back into the channel center at a depth of 3λ/4. This cycle repeats with increasing depth. This oscillatory motion of ions causes a change in ion flux distribution in the transverse plane at different depth. The fading of the sharp focused region at deeper regions can be observed in Figure 5.1, with the focused regions becoming spread out with increasing depth. Coherency among all the ions breaks down with increasing depth due to the spread in wavelengths as well as multiple scattering effects. At larger depths (at micron depths of this case) the ion flux distribution becomes independent of depth, where statistical equilibrium is reached [14], with the accessible area being populated with ions of uniform transverse energy . The majority of ions enters in the middle of the unit cell where the potential is small so that the channeled oscillation amplitude is also small and all the features in the experiments correspond to this kind of trajectory. 95 Figure 5. 1: FLUX simulated {011} planar channeled MeV proton trajectory distributions for 10,000 ions to a depth of 400 nm Si over two adjacent planes. A depth of 65 nm is indicated by the dashed white vertical line. The horizontal axis, Z, represents the depth in nm while the vertical axis, Y, represents the space of 1.92 Å between {110} planes. Red/blue colour scales show the high/low flux density regions. The oscillation amplitudes and wavelengths directly depend on the channel transverse potential and several groups have enabled determination of the channel potential by studying the exit planar ion channeled angular distributions or/and their energy losses. As the theoretical treatment of planar channeling is simple, it was studied more intensively than the axial channeling. The channel potential can be obtained directly if details of the particle trajectory could be determined. There are several procedures discussed in [5, 100] to evaluate the planar channeling potentials by several groups, however the underlying model is the same for all the methods. One method was from the stopping power measurements of channeled protons; the advantage of this method is that it is insensitive to the mosaic spreads and variation in the thicknesses of the membranes used. Another method was by measuring the population of different energy loss groups of channeled ions as a function of exit angle; the advantage of this method is that the potential determination does not depend on the stopping 96 power functions; however these measurements are very sensitive to the mosaic spreads and thickness variations of the crystals. Breese et.al, [67] experimentally observed the channeled planar oscillations by capturing the transmitted angular distributions from thin crystals using focused beams from nuclear microprobe, and interpreted observed results with MC FLUX simulations, while all the others were using broad beams, where the spot sizes are in millimetres [5]. Multiple scattering and planar dechanneling of MeV protons using thin silicon and germanium wafers were studied by [101]. In all those reported measurements the minimum achievable crystal thickness was ~275 nm. The fabrication procedure we adopted helped us in preparing ultra-thin 55nm crystals with a uniform thickness over the entire surface and use of a nuclear microprobe helped to perform experiments on such membranes. 97 5.3 Experimental results: 5.3.1 Comparison of {111} planar channel atomic projections near different axes: Figure 5. 2: Atomic projections of axes which contain {111} plane running in vertical direction. Before going into a detailed experimental study of planar channeling, it is worthwhile to note the atomic projections of the {111} plane and their projections at different axes. A planar channel consists of two parallel closely packed lattice planes and most of the planes are the same, but in diamond-type of crystals the {11n}, where n = odd number, family of planes have two set of planes adjacent to each other, instead of one. This is an inherent property of the crystallography of diamondtype crystals and it is important to note each set of planes has a different planar spacing, so that the atomic and electron density varies quite dramatically for the two channels. In the present thesis most of the work is devoted to the case of n=1, 98 that is, {111} plane of Si. They are called wide and narrow planes, with planar spacings of 2.4 Å and 0.71 Å respectively. Figure 5.2 illustrates the crystallographic atomic projections at axes which are along {111} plane. Even though the planar lattice spacing’s are the same for all the axes, the relative orientations in the opposite side walls of the narrow {111} planes are quite different at every axis. The consequences of this asymmetry in the atomic projections will be discussed in chapter 6. 5.3.2 Experimental planar channeling studies of MeV protons: Figure 5.3 shows experimentally recorded {110} and {111} planar channeling patterns for MeV protons incident at small tilts across the horizontally-running {110} direction and vertically-running {111} direction of a 55 nm [001] silicon membrane, at an angular location chosen as free from interference by any intersecting minor axes near the [112] axis respectively. The effective thickness of the membrane is ~65 nm of this angular location, the thickness matches the first quarter-wavelength channel oscillation depth for MeV protons along {110} planes from Figure 5.1. For a layer thickness of a quarter of a wavelength, or a multiple thereof, the angular spread of the transmitted beam is the largest. As the channeled protons are spatially focused on the exit side of the membrane along {110} planes, they get angularly defocused and the width of the angular distribution is ψp as shown in Figure 5.3(I, a). By tilting across the plane, the exit angular distribution appears in the opposite direction to the incident tilt angle. This is because the spatially focused protons fall on one of the planar walls, so they are repelled back and get deflected in the opposite direction as shown in Figure 5.3(I, c-e). For further increasing the tilt angle, protons overcome the potential barrier and come in the same direction along the incident direction from Figure 5.3(I, f-h). The edges of all the planar 99 channeled patterns which are across the channel exhibit larger transverse spread than the other patterns. This is because the protons were incident near to planar walls at the entrance side where the electron clouds are denser than the other place in the channel which thereafter gives rise to a larger spread in the other direction. Figure 5. 3: Experimental (I) {110} (II) {111} planar channeling patterns near [112] axis for MeV protons from a 55 nm [001] Si membrane for increasing tilt angle across the plane (a-i). 100 Figure 5.3(II) shows {111} planar channeling patterns, which show spectacularly different features compared to {110} planes in the transverse direction. There is a special feature in the middle of the patterns, which is shifting faster compared to other protons in the same pattern with the same incident beam tilt angle from Figure 5.3 (II, a-f), also it has large transverse angular spread. This feature is not observed in patterns along any other major planar directions such as {001} and {011} which comprise only a single plane width. This special bunch of protons arises from the narrow {111} planar channeling confirmed with the FLUX simulations shown in Figure 5.10. 5.4 Discussion: Figure 5.4 shows the calculated static continuum ZBL universal inter-atomic potentials for the protons channeled in the (a) {110} (b) {111} planes of silicon. The wide, narrow {111} channels have deep, shallow potential wells and their corresponding spacing’s are 2.4 Å and 0.71 Å respectively, giving a ratio of 0.54 between the values of wide and narrow planes, of  and , with w = 0.15°, n =0.08°, and w = 240 nm, n = 110 nm respectively for low amplitude trajectories for MeV protons. Since only ~23% of the beam is incident on the narrower planes, together with their small critical angle, their effects are rapidly lost in thicker layers for MeV beam energies, so most previous channeling measurements involving the {111} direction have only considered the wide planes determining the channeling behaviour, in which case the measured critical angle agreed with this assumption [5, 101]. 101 Figure 5. 4: Static continuum inter-atomic potentials for the ions channeled in (a) {110} (b) {111} planes of silicon for ZBL universal potential. Figure 5.5 shows FLUX simulated planar channeled 2MeV proton trajectories along {111} plane for 10,000 ions in 400nm thick silicon at an aligned case, in which the separate channeling depth oscillations in the narrow {111} planes are observed. These narrow planar channeled protons lose coherence quite rapidly compared to wide channel ions with increasing depth because of its large transverse potential and mainly due to multiple scattering from the dense electron clouds. At about ~65 nm depth in Figure 5.5 the wide {111} planar channeled ions are closer to the quarter wavelength oscillation condition ( w = 240 nm) where all the protons are focused spatially so the angular distribution has a wide distribution at the exit side and the narrow {111} channeled protons are close to the half wavelength oscillation condition (n = 110 nm) has a narrow distribution at the exit. This is why the experimentally observed channeling pattern shows two distinctive features from both wide & narrow planes at both aligned case and tilted cases up to the critical angle of n =0.08°. The large transverse spread observed in the middle of the experimental pattern shown in Figure 5.3(II, a-f) is 102 Figure 8. 9: The calculated Rainbow lines in the scattering angle plane in 55 nm thick [001] Si for 0.7 MeV protons using (a) ZBL and (b) Molière potential models compared with the experimental rainbow lines. The experimentally observed 0.7 MeV energy pattern shown in Figure 8.8 (a) is analysed using Rainbow code calculations in Figure 8.9 (a, b) for ZBL and Molière potential models respectively. The black colour star symbols denote the experimentally observed highest intense peak angular locations, which are compared with the calculated rainbow lines, the red colour lines in Figure 8.8 (a) are far from experiments, the peripheral four cusps are a having larger angular extent to the experiment and the calculated ZBL inner rainbow line shape is near to cross symbol, whereas there are four isolated cusp shaped regions in the experimental pattern. The Molière model calculated rainbow lines shown in Figure 8.8 (b) is also not matching with the experiment, the inner rainbow lines (four cusp shapes) are having larger angular extents, however the outer rainbow lines are matched with the experiment. The outer rainbow lines are from the protons which are incident near the atomic strings, whereby the potential is larger and the inner rainbow lines are due to the 180 protons entered in the middle of the unit cell experiences a relatively low potential repulsion from axial atomic strings. 8.4 Modification of inter-atomic potential: The important starting point in most of the analytical calculations on channeling is to assume accurate inter-atomic potential and most frequently used ones are Lindhard standard potential, Molière potential, ZBL universal potential and Hartree-Fock potential. Ref [152] pointed out the consideration of the Inter atomic potentials for Channeling Calculations, the use of these potential models in various limits is probably justified only to the extent that they are merely mathematical approximations but in order to justify their suitability as inter-atomic potential for use in channeling problems other than they have been postulated for, they should be first tested and properly modified on a physical basis. All potentials based on statistical ideas should be tested as regards the behaviour of the screening function at different impact parameters. To correct those inter-atomic potential models we interchanged the screening radii of ZBL and Molière potential models and compared the calculated rainbow lines with the experimental results shown in Figure 8.9. Figure 8.10 (a, b) shows the comparison of 0.7 MeV energy pattern experimental bright angular locations with the modified ZBL (ZBL*) and modified Molière (Molière*) models calculated rainbow lines respectively. The modification is done just by interchanging their screening radiuses in the calculations, i. e. aZBL = aMolière and aMolière = aZBL in ZBL, Molière potential model rainbow lines calculations respectively for the first trails. Now 181 dramatically, the both modified potentials calculated inner rainbow lines coincide well with the experimental data shown in Figure 8.10 (a, b), but the outer rainbow lines are not matching, they attain larger angular extents, which suggests further more work is necessary. The empirical formula given by both the Refs [53, 54] for ZBL, Molière potential models are derived from huge data sets for many ion-lattice pair combinations our plan is to use the ZBL, Molière potential models screening functions based on specific ion-lattice data. Figure 8. 10: The calculated Rainbow lines in the scattering angle plane in 55 nm thick [001] Si for 0.7 MeV protons using (a) modified ZBL and (b) modified Molière potential models compared with the experimental rainbow lines. 182 Figure 8. 11: (a-e) The calculated Rainbow lines in the scattering angle plane in 55 nm thick [001] Si from 0.85 to 0.65 MeV protons using modified Molière potential in scattering angle and impact parameter planes for direct comparison. To understand the origin of these focused angular ridges in the angular distributions is studied using Rainbow lines in the scattering angle and impact parameter planes at each condition and 0.85 to 0.65 MeV energy rainbow lines are displayed in Figure 8.11 (a-e) respectively with a step of 0.05 MeV decrement in energy for 55 nm thick [001] Si using modified Molière mentioned in the Figure 8.10. The protons incident in between the atomic strings are (marked with the blue colour dashed arrow in impact parameter plane) the ones which give inner rainbow lines in the scattering angle planes, as the energy of the beam is decreasing then the axial oscillation wavelength is decreasing, this change in wavelength split the cross like shape at 0.85 MeV into four separated cusp shaped rainbow lines at 0.65 MeV, and their corresponding incident protons maps are shown in the impact parameter planes in Figure 8.11. The protons incident towards the atomic strings are scattered larger angles and are the outer rainbow lines at the corners in the scattering angle planes (marked with a black colour dashed arrow). 183 The experimental observation of separate angular focused regions is due to the spatial focusing effect, as the channeled protons are spatially focusing to ~pm spots, when they exit suddenly from the crystal just after focused inside the crystal, they immediately get defocused angularly, but in a complex manner, that’s what we see in 0.7 MeV pattern in Figure 8.5 (a), 8.6. 8.5 Conclusions: Star to square shaped angular distribution is observed with the decrease in energy of the ion beam for the same thickness and crystallographic orientation of the [001] Si. FLUX, RAINBOW simulation studies have been done using ZBL, Molière and Hartree-Fock inter-atomic potential models, neither of them reproduced the experimental patterns due to their imperfections in the screening functions. Slight increase in ZBL at decrease in Molière’s screening radii lead to better agreement with the experimental patterns. This work motivated us to refine the most fundamental parameter to deal in the ion beam science “inter-atomic potential” accurately, as our results are not encountered with great multiple scattering and any other detector resolution issues. 184 Chapter Summary and Future Work 55 nm thick ~2 x mm2 area free standing [001] Si membranes were fabricated using a polymer based mask for KOH etching for the first time and achieved low roughness surfaces on both the sides of the membranes and defect free crystals. As the thickness is very small for such large area membranes, they are bent, and the measured bend angle typically varies by 0.05° for a 25 µm lateral distance, however, they are sufficiently flat to perform ion channeling experiments using a focused MeV proton beam and RBS-Channeling spectroscopy revealed the excellent crystalline quality of the membranes. This new fabrication process opens a route to a better understanding of ion channeling phenomena under highly non-equilibrium conditions. The star like channeling patterns used to observe from thicker crystals showed unique shapes from 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 proved several predictions made by Ref [26, 88-91] for the first time. This study has also revealed the separate ion channeling behaviour in narrow and wide {111} planes of silicon for the first time using transmission channeling. These separate channeling angular distributions can only be seen experimentally from ultra-thin crystals (minimum of at least 75nm thick for 185 2MeV protons), and not with thicker crystals. As the narrow channel critical angle is smaller than the wider channel, protons incident in the narrow channel became dechanneled within the critical angle incident angles with respect to wide {111} channel. This dechanneling fraction cannot be avoided and we suggest the {110} channel may be more relevant than the previously considered {111} for beam extraction and bending schemes. The doughnut patterns exhibited unique geometric shapes which, in most cases, are a reflection of either that formed by their widest intersecting planes or a direct atomic crystallographic projection, unlike ring shaped patterns from thicker crystals. These geometric shapes also showed the impact of atomic arrangement on the surface. We proved that doughnuts are rainbows with tilted crystals, by doing a detailed morphological study. The study has been performed using the theory of crystal rainbows, which includes a precise analysis of the mapping of the impact parameter plane to the transmission angle plane. The results of our study clearly demonstrate that the theory of crystal rainbows is the proper theory of ion channeling in very thin crystals. It ensures excellent agreement between results of calculations and high-resolution ion channeling measurements with such crystals. Star to square shaped angular distribution is observed with the decrease in energy of the ion beam for the same thickness and crystallographic orientation of the [001] Si. FLUX, RAINBOW simulation studies have been done using ZBL, Molière and Hartree-Fock inter-atomic potential models, neither of them reproduced the experimental patterns due to their imperfections in their screening functions, however it provides indirect proof for the Super-focusing effect for the first time. Slightly larger and smaller 186 screening radiuses are matching with the experimental patterns for ZBL and Molière’s models respectively. We developed the methodology to improve approximations to interatomic potentials. This work motivated us to refine accurately the fundamental “interatomic potential” in future, which is the crucial parameter in the entire ionbeam related science. There is a needed to find the best accurate potential for at least Proton-Silicon and Alpha-Silicon ion-atom pairs, as most of the IBA techniques rely on those two pairs. 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K181K185. 195 [...]... been several Rainbow channeling simulation studies of MeV ions passing through 20 0 to 300 nm thick silicon membranes and ultra- thin silicon membranes of about 100 nm [26 , 118, 119] for small tilts away from a major crystal axes, mainly with the aim of understanding rainbow channeling behaviour However, in all such experimental studies of ion channeling patterns in thin crystals the minimum achievable... preserved during the passage of ions, so doughnuts display unique structures depending on the crystallographic geometry By increasing the tilt angle, the transverse energy of each ion with respect to an axial projection will be increased from E in2 relative to axial projection (just after entering the crystal) to E in2 + U(rin), the additional term depending upon its entry into the crystal rin Here rin is... separate ion channeling information from narrow {111} planes alone This is why there are no previous observations of separate narrow {111} planar oscillations using proton channeling patterns due to the unavailability of ultra- thin crystals If we measure the energy loss of protons at different angular locations in the transverse direction in the 65nm thick {111} planar channeled patterns, we can find the... dechanneling of ion beam The backscattering signal gets increases at quarter oscillation depth locations marked in red circle in Figure 5.8(b) 107 5.6 FLUX Simulation analysis of {111} planar channeled angular distributions: Figure 5 9: Simulated FLUX channeling patterns for the angular distribution in (a) the combined (c,d) in the wide and narrow {111} planar channeling patterns near [1 12] axis for 2 MeV protons... explained in more detail using phase space analysis in the section 5.11 Confirmation of these experimental results using simulations is mentioned in section 5.10 Figure 5 10: Experimental {111} planar channeling patterns near [1 12] axis for 2 MeV protons from a 300 nm [001] Si membrane for increasing tilt angle across the {111} plane (a) high (b) low exposure times 110 5.8 FLUX simulations of {111} channeling. .. channeled ions as a function of atomic density directly, which is valuable information for several channeling application studies [5] The 400nm thick angular pattern shown in Figure 5.11 also shows the blocking of narrow {111} planes as in the experiments shown in Figure 5.10, which confirms the experimental observation The channeling oscillation wavelength λ is a function of incident energy of the ion beam... 5.11: Conclusions: This study has revealed the separate ion channeling behaviour in narrow and wide {111} planes of silicon The separate channeling angular distributions can only be seen experimentally from ultra- thin crystals (minimum of at least 75nm thick for 2MeV protons), and not with thicker crystals As the narrow channel critical angle is smaller than the wider channel, protons incident in the narrow... the incident ions are deflected more strongly compared to the ions incident in the middle part of the unit cell Due to the oscillation behaviour of channeled ions and rotational symmetry of axial potential, the close impact parameter ions will cross from one unit cell to the next along its trajectory 6.3 Dechanneling: Even though the conservation of ET is a usefull approximation in channeling modelling,... intersecting planar channels at an axis is presented to gain insight into the origin of the geometric shapes observed in such patterns and how they evolve into the ‘doughnut’ distributions in thicker crystals 6.1 Introduction: When the incident ion beam is tilted away from a crystallographic direction, the angular distribution of the channeled ions exhibits a “ring-like” shape This effect, named the doughnut... if the angle of incidence in is less than the critical angle ψc for axial channeling There are however some exceptions - S.K Anderson et.al., reported in CERN-EP 79/99 that the doughnut shape angular distributions of 120 electron beam appear even with the incident angles far beyond the critical angle for channeling The situation with thin crystals is different, the multiple scattering is very small . with increasing depth. This oscillatory motion of ions causes a change in ion flux distribution in the transverse plane at different depth. The fading of the sharp focused region at deeper regions. in thicker layers for MeV beam energies, so most previous channeling measurements involving the {111} direction have only considered the wide planes determining the channeling behaviour, in. distributions: Figure 5. 9: Simulated FLUX channeling patterns for the angular distribution in (a) the combined (c,d) in the wide and narrow {111} planar channeling patterns near [1 12] axis for 2