HIGH RESOLUTION RUTHERFORD BACKSCATTERING SPECTROSCOPY: HAFNIUM BASED HIGH-K DIELECTRIC THIN FILMS AND SIMULATION OF 2-D FOCAL PLANE DETECTOR

Transcription

1 HIGH RESOLUTION RUTHERFORD BACKSCATTERING SPECTROSCOPY: HAFNIUM BASED HIGH-K DIELECTRIC THIN FILMS AND SIMULATION OF 2-D FOCAL PLANE DETECTOR TAY XIU WEN A THESIS PRESENTED FOR THE DEGREE OF BACHELOR OF SCIENCE DEPARTMENT OF PHYSICS NATIONAL UNIVERSITY OF SINGAPORE 2014

2 Table of Contents Table of Contents Acknowledgements...iv Summary...v List of Figures...vi Chapter 1 : Introduction High Resolution Rutherford Backscattering Spectrometry New generation of two dimensional position detector Swift Heavy Ion irradiaton of HfO2/Si ultra thin film Outline of thesis Chapter 2 : Physical Concepts Kinematic Factor Rutherford Scattering Cross Section Deviation from Rutherford Scattering Stopping cross section Energy Straggling Rutherford Backscattering Spectrometry Ion Channeling Thin film on substrate SIMNRA Numerical Simulation of RBS spectrum Chapter 3 : HRBS Set-up HRBS Endstation Main chamber, load lock and vacuum system Goniometer Micro-channel Plates Electrostatic plates D Focal Plane Detector and HRBS electronics D Focal Plane Detector...28 ii

3 Table of Contents Chapter 4 : Study of Swift Heavy Ion Irradiation effects on Hafnium based high k-dielectric thin films deposited on Silicon Swift Heavy Ion Ion beam Mixing HfO2/SiO2/Si Samples HRBS experimental parameters HRBS Depth profiling results Conclusion Chapter 5 : Simulation and characterisation of new 2-D focal plane detector using SIMion D Focal Plane Detector Overall layout of the HRBS detection system Spectrometer ion optics Beam entry parameters Drawing the magnet Maxwell s and Laplace s equations Refining the magnet array Finite Difference Method Calculation of ion trajectories SIMion simulation details SIMion simulation results Splat profiles Height and Width of splat profiles Variations in starting x-position of backscattered ions Simulation Conclusion Bibliography...57 Appendices...59 iii

4 Acknowledgements Acknowledgement I would first like to thank my supervisor Associate Professor Thomas Osipowicz who has been a great mentor and with his careful guidance, has made this thesis possible. I am also thankful of his patience and the time he spent to guide my work despite his busy schedule. I am also very grateful to Dr TK Chan who taught me almost everything I know about RBS and HRBS as well as various laboratory techniques. I would also like to thank my life mentors, Sumithra and Lionel for their love and trust for which without them, this thesis would not be possible. Last but not least, I would like to thank my family for their unwavering support and my deceased father whose memory will always live on in my heart. iv

5 Abstract Abstract Due to advancement in the miniaturization of microelectronic components, conventional Rutherford Backscattering Spectrometry (RBS) can no longer provide sufficient depth resolution for ultra-thin films. The High-resolution RBS (HRBS) system in CIBA allows thin film depth profiling of such films with a modified RBS system where the differentiation of energy of the backscattered ions is achieved by spectrometer magnet and a Micro- Channel Plate-Focal Plane Detector (MCP-FPD) detection system. The backscattered ions travel through the spectrometer magnet with different ion trajectories according to their energy are subsequently incident on the MCP-FPD at the focal plane. The energy of the backscattered ion is then determined by the MCP-FPD and subsequent HRBS electronics In modern microelectronics, thickness of SiO 2 gates dielectrics reach the subnanometer range with the increasing miniaturization of Metal-Oxide Field Emission Transistors (MOSFETs). Thicker dielectric materials with higher dielectric constants (high-k dielectrics) must be used to reduce the leakage current, retaining the same capactitative density of a thinner layer of SiO 2. In recent years, other high-k material such as HfO 2 have been used and studied for their properties as gate dielectrics. In the first part of the thesis, ultra-thin HfO 2 /SiO 2 /Si samples of increasing irradiated fluence of Au Swift Heavy Ions films were characterized using HRBS depth profiling. HRBS measurements suggest that the interlayer is a mixed HfSiO/SiO layer instead of a pure SiO 2 layer as intended. A systematic increase in thickness of the interlayer as a function of increasing fluence of Au swift heavy ions. In current HRBS analysis, a 1-D focal plane detector is used to profile the detected backscattered ions according to backscattered ion energy. However, in preparation of future hardware upgrade, a 2-D FPD is proposed to profile splat profiles of the end of the ion trajectories in both directions of the FPD; along the height as well as length of the FPD. Hence, in the last part of the thesis, SIMion simulations were done to characterize the 2-D splat profiles on the FPD. The simulations shows that height of splat profiles for 2mm collimeter is below 8mm and for 1mm collimeter, it is below 4mm. Hence, the splat profiles are able to fit into the 15mm height of the 2-D FPD. It is also observed that at least 50 splat profiles of 50 different ion energies (2mm collimeter) or at least 100 splat profiles of 100 different ion energies (1mm collimeter) can be fitted into the 100mm length of the FPD. v

6 List of Figures List of Figures Fig. 2.1 Elastic collision diagrams as seen in the (a) lab reference frame (b) CM reference frame. [7]...5 Fig. 2.2 Fig. 2.2 Plot of F (, E c ) vs. Correction magnitude increases rapidly at small and decreases with increasing E 0 at large. Source [8]...11 Fig. 2.3 Plot of Chu correction factors H vs Z2 for various E/M1 values. Dots are original data from Chu and the lines are extrapolations by Szilágyi [9]. Source [7]...14 Fig. 2.4 Diagram of RBS measurement...15 Fig. 2.5 Schematic of ion channeling. Source [10]...15 Fig. 2.6 (a) Schematic of the formation of the shadow cone at the surface and the trajectories of channeled particles. The horizontal scale on the right is compressed in relation to the vertical scale to show the trajectory oscillations. (b) The comparison between the channeled and the non-aligned RBS spectrum. The channeled spectrum shows a drastically reduced substrate signal. Source [10]...17 Fig. 2.7 (a) Scattering geometry and (b) spectrum of an RBS measurement of a thin compound target Source [11]...17 Fig. 2.8 Diagram of the target divided into thin layers. Source [11]...19 Fig. 3.1 (a) Main chamber, goniometer and load lock. (b) Load lock with a sample holder (c) View of sample holder on the goniometer in the main chamber through the main viewport. Source [11]...22 Fig. 3.2 Schematic of the vacuum pump and valve network. Source [11]...23 Fig. 3.3 Schematic of the HRBS goniometer. Source [12]...24 Fig. 3.4 Diagram of Micro-channel plates...25 Fig. 3.5 Schematic and layout of the installation of the electrostatic plates. Source [11]...26 Fig. 3.6 Schematic of 1-D Focal Plane Detector and HRBS electronics. Source [11]...27 Fig. 4.1 Sample structure of Pristine-H1A...31 vi

7 List of Figures Fig. 4.2 Aligned(Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation of Pristine- H1A sample...32 Fig. 4.3 Aligned(Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation H1B-1E13 Au sample...32 Fig. 4.4 Aligned(Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation H1C-5E13 Au sample...33 Fig. 4.5 Aligned(Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation H1C-1E14 Au sample...33 Fig. 4.6 Aligned(Channeled) HRBS spectra of Hafnium peak for all four samples (H1A, H1B, H1C, H1D)..34 Fig. 4.7 Elemental depth profile for H1A, H1B, H1C, H1D...35 Fig 5.1 Diagram of 2-D FPD with true counts (red dotted ovals) and counts derived from HRBS (black ovals)...37 Fig. 5.2 Schematic of simulation done using SIMion...38 Fig. 5.3 Schematic of Spectrometer magnet, MCP-FPD in HRBS. Source [11]...39 Fig. 5.4 Schematic of the incident and backscattered beam profiles...41 Fig. 5.5 Finite backscattered beam profile and point source approximation...41 Fig D isometric view of the workbench with a magnified view of the spectrometer magnet. Source [11]...43 Fig 5.7 Diagram depicting Finite Difference Method (FDM)"...45 Fig. 5.8 The potential distribution plot along the x-y plane at a fixed value of z. The darkened flat top represents the region with uniform magnetic field, while the smooth slopes at the sides represent the non-uniform fringe fields. Source [11]...45 Fig. 5.9 The overview of the workbench in the x-y plane looking down towards the negative z-direction. Source [11]...47 Fig Splat profile for a point spot and beam spot of E = 427keV collimated by a 1mm collimeter...48 vii

8 List of Figures Fig Splat profiles of a point spot of energy, E from 400 kev to 421 kev simulated through 1mm collimeter Fig Splat profiles of a point spot of energy, E from 421 kev to 442 kev collimated by 1mm collimeter...50 Fig Height of the splat profiles for point and beam spots collimated by 2mm collimeter...51 Fig Width of the splat profiles for point and beam spots collimated by 2mm collimete...52 Fig Height of the splat profile of the double focusing point at different starting x-position of the backscattered ion (2mm collimeter)...53 Fig Width of the splat profile of the double focusing point at different starting x-position of the backscattered ion (2mm collimeter)...54 Fig Centre position of the splat profile of the double focusing point at different starting x-position of the backscattered ion (2mm collimeter)...54 Fig. A.1 Figure Splat profiles of a point spot of energy, E from 400 kev to 421 kev simulated through 2mm collimeter...59 Fig. A.2 Splat profiles of a point spot of energy, E from 421 kev to 442 kev collimated by 1mm collimeter...60 Fig. A.3 Height of the splat profiles for point and beam spots collimated by 2mm collimeter...60 Fig. A.4 Width of the splat profiles for point and beam spots collimated by 2mm collimeter...61 Fig. A.5 Height of the splat profile of the double focusing point at different starting x-position of the backscattered ion (1mm collimeter)...62 Fig. A.6 Width of the splat profile of the double focusing point at different starting x-position of the backscattered ion (1mm collimeter)...62 Fig. A.7 Centre position of the splat profile of the double focusing point at different starting x-position of the backscattered ion (1mm collimeter )...63 viii

9 Introduction Chapter 1 Chapter 1 Introduction 1.1 High Resolution Rutherford Backscattering Spectrometry Rutherford Backscattering Spectroscopy is a non-destructive method which is mainly used for depth profiling of thin films. The PIPS detector used in conventional RBS to detect backscattered ions is only able to provide a depth resolution of up to 5nm at glancing geometry. However with ultra-thin films with order of tens of angstrom, conventional Rutherford backscattering is not able to provide adequate depth profiling. In order to quantify the depth profile of ultra thin films, a high resolution Rutherford backscattering spectrometry (HRBS) system is used [21]. In HRBS, the PIPS detector is replaced by a spectrometer-focal plane detector. This provides a better resolution (circa 1KeV) and subnanometer depth resolution. HRBS is useful for depth profiling of thin films eg. Gate dielectric films in semiconductor devices. Combined with channeling technique, it can also provide information on dopant position in crystal lattices, lattice strain and stress. 1.2 New generation of two dimensional position detector In the current HRBS facility, a one dimensional focal plane detector is used to detect the backscattered ions and measure their backscattered ion energy. 1-D FPD measures only the position of the incident ions in the dispersion plane of the magnet, all the ions incident perpendicular to this direction are summed over and this may lead to spectral distortion 1

10 Introduction Chapter 1 effects. In preparation of a future hardware upgrade, a 2-D FPD is proposed, which allows the measurement of the incidence positions in both direction of a 2-D FPD; along the height as well as along the length of the FPD. This will allow rejecting by software ions at extreme positions on the FPD and more accurate HRBS spectra can be obtained. 1.3 Swift Heavy Ion Irradiaton of HfO 2 /Si ultra thin film As integrated circuit technology progress is paving the way for further miniaturization of microelectronic components, the thickness of the gate dielectric (SiO 2 ) in transistors decreases to maintain capacitance at a desired level. This reduction of thickness results in high leakage current due to quantum tunneling. In recent years, other high-k material such as HfO 2 have been used and studied for their properties as gate dielectrics. However, due to their thermodynamic instability on Si, deposition of HfO 2 on Si wafers would result in high concentration of interface defects [17]. By introducing a thin interface layer of Silicon oxide / nitrides between Si and HfO 2 the interface quality is expected to improve [17]. Therefore it is crucial to investigate the composition, thickness and intermixing effects to optimize the fabrication of Hf based Metal-Oxide-Semiconductor (MOS) devices. The increase in RF-power during sputter deposition of HfO 2 on Si substrate was shown to lead to the formation of Hfsilicates [1, 2] which belong to a new class of alternate high-k dielectric materials with tunable electrical and thermal properties [3, 4, 5, and 6]. Swift Heavy Ion (SHI) irradiation is expected to be an important in the synthesis and modification of many materials [18]. There are only a few reports on SHI induced mixing of Hf/Si or HfO2/Si interfaces, even though some work has been done on ion beam studies of Hf based high-k dielectric materials [17, 19,20]. Hence it is of paramount interest to investigate the ion beam mixing effects of HfO 2 on Si substrate, it is important to understand defect creation and mixing at the interface due to ion irradiation. Ion irradiation effects on the material 2

11 Introduction Chapter 1 properties are of great significance when HfO 2 based devices for terrestrial / space application is used. 1.4 Outline of thesis This thesis consists of two parts. In the first part, we have the HRBS analysis of Hf based high-k dielectric thin films while the second part consist of the SIMion simulation of 2-D splat profiles for 2-D FPD. In chapter 2, the physical concepts of RBS and the method of simulation of RBS spectra is described. The HRBS end station and experimental set-up in CIBA are described in chapter 3. In chapter 4, the HRBS analysis of Hf based high-k dielectric thin films is discussed before going on to chapter 5 where the simulation of 2-D splat profiles for 2-D FPD is looked into. 3

12 Physical Concepts Chapter 2 Chapter 2 Physical Concepts Summary RBS concept - Kinematic factor o Kinematic factor is defined as the ratio of the ion energy after scattering, E 1 to that before the scattering event, E 0 happening on the surface of the target with a scattering angle θ. - Rutherford scattering cross section o probability at which the ion scatters at a certain angle θ - Ion scattering cross section o The ion scattering cross section S describes the ion stopping within the target. It is closely dependent on the interatomic potential. - Energy straggling 2.1 Kinematic Factor For typical ion energies used in RBS, the mean free path between collisions are much larger than the atomic spacing, hence all scattering events are effectively binary elastic collisions. The dynamics of the binary collisions between two particles determine the energy of an ion after it 4

13 Physical Concepts Chapter 2 scatters from a target atom. The dynamics of binary collision can be view as a centre of mass system where the binary collision can be modeled as a single particle moving in a central force field potential centered about the origin of the centre of mass frame. This would eliminate the difficulty of describing the system in the lab reference frame. Fig. 2.1 Elastic collision diagrams as seen in the (a) lab reference frame (b) CM reference frame. Source [7] In the lab reference frame, an incident ion with mass M 1 with moving with speed ν 0 and energy E 0 collides and scatters with a stationary target ion with mass M 2. The incident ion then scatters off with speed ν 1, energy of E 1 and scattering angle θ. The target atom scatters off with speed ν 2, energy of E 2 with angle φ. This collision can also be described using a centre of mass system. In this system frame, the incident and the target ion approach the origin of the centre of mass frame with speed (ν 0 ν c ) and ν c respectively. The speed of both the incident ion and the target ion remain unchanged after the scattering event due to the conversation of total linear momentum of the frame. 5

14 Physical Concepts Chapter 2 M 1 (ν 0 ν c ) = M 2 ( ν c ) where The velocity vectors of the centre of mass frame compared with the lab frame The kinematic factor K, is defined as the ratio of energy of the ion after scattering, E 1 to the energy just before scattering, E 0 where,. From Fig.0 Hence, In conclusion, 6

15 Physical Concepts Chapter Rutherford Scattering Cross Section For a quantitative analysis of the RBS spectra, the probability that an ion will backscatter and be detected by the detector at a given geometry must be known. In the previous section, the binary elastic collision in the CM reference frame involves asymptotic values of momentum and energy far away from the collision site. However, in this case, we have to consider the ion under the influence of the Coulomb force as it approaches the scattering center in CM reference frame. The impact parameter is defined as the perpendicular distance between the target atom and the ion trajectory in the scenario where there is no interaction between them, i.e. at infinite distances apart. During the collision of the incoming ion and the target atom, the ion will be deflected at an angle θ c. The total cross section σ(θ c ) is the cross sectional area πb 2 about the target nucleus, normal to the incident ion beam. Incident ions within these areas will be deflected with angles greater than θ c. The Angular Differential Cross-section is defined as the probability of incident ions scattering into angular region between θ c and θ c + dθ c per unit solid angle Ω of the detector, per areal density of target. Incident ions with impact parameter between b and db are deflected through the annular area about the target. Hence. The angular differential cross section is then (1) 7

16 Physical Concepts Chapter 2 As noted from the equation above, the relationship between b and is needed to evaluate the angular differential cross section. This relationship can be derived from the Classical Scattering Integral in the CM reference frame Where r is the distance of separation between the ion and the target atom, r min is the distance of closest approach, V(r) is the interaction potential and E c is the ion energy in the CM frame. For most case in backscattering spectroscopy, the distance of the closest approach during the collision is smaller than the orbit of electrons, so that the interaction between the ion and the target atoms can be described as an unscreened Coulomb repulsion of two charged nuclei with charge of Z 1 e and Z 2 e, where Z 1 and Z 2 are the atomic numbers of the projectile and the target atom and e is the magnitude of charge of an electron. The screening of the charge of the nuclei by electrons gives an only small correction. The potential V at a distance r between the projectile and the target atom is given in the cgs units by. Making substitutions and, so that, 8

17 Physical Concepts Chapter 2 Evaluating, consider the CM energy at the point of closest approach, Hence, since at The angular momentum has a value of at. Both quantities and are conserved throughout the motion. Therefore, Substituting (3) into (2) Hence, 9

18 Physical Concepts Chapter 2 From equation (4) and (1), the Rutherford Scattering Cross section in the CM reference frame, The Rutherford Scattering Cross section in the lab frame, 2.3 Deviation from Rutherford Scattering In the previous section, the Rutherford Scattering Cross section is derived from the Coulomb potential between the incident ion and the target atom. This is a good approximation when the energy of the incident ion is sufficiently large such that it penetrates into the electron shells of the target atom. However in small-angle scattering, low incident ion energy, the incoming ion does no completely penetrate through the electron shells and the charge of the nucleus is partially screened by the electrons of the inner shell of the target atoms. This screening effect can be accounted for in the Rutherford Scattering Cross section by introducing a correct factor. This correction factor assumes that the incoming ion gains additional kinetic energy due to the attraction of the ion charge and the electrons of the target atom, during the time when the ion has not penetrated fully through the electron shells. A widely used correction is developed from Andersen et al where the potential V(r) is corrected for the increase in kinetic energy of the ion. The correction factor was derived, 10

19 Physical Concepts Chapter 2 The correct factor is significant at large. For, approaches unity as increase with correction of for and for. Fig. 2.2 Plot of F (, E c ) vs. Correction magnitude increases rapidly at small and decreases with increasing E 0 at large. Source [8] 2.4 Stopping cross section Only a small fraction of the incident ions backscatter from the target surface due to the relatively low probability of the ions coming in close encounter with a target nucleus. Ions which do not backscatter from the target surface proceed to travel beneath the target surface and are backscattered at a certain depth or stop within the sample as all of their kinetic energy is lost. As the ions travel within the target, the ions lose energy as they collide with the target nuclei. The backscattered ions also lose energy as they travel into the target before a backscattering event as well as out of the target after a backscattering even. Hence, energy loss of the backscattered ion is larger as the depth of the backscattering target beneath the surface increases. This measure of energy loss provides information of the elemental profile as well as the depth profile of the elements in the target sample. 11

20 Physical Concepts Chapter 2 Stopping cross-section is used to discuss on the energy loss. The stopping cross section is where N is the atomic density and is the energy loss per unit path length within the target. The stopping cross-section can be contributed by two components, the stopping cross-section due to collision with nuclei and electrons, S n and S e respectively. Nuclear stopping are due to elastic collisions that can give rise to large scattering angles and discrete energy losses of the ion per collision event, while electronic stopping are mainly due to inelastic collisions involving much smaller energy losses per collision as well as negligible angular deflection of the ion trajectory. At higher ion energies, only S e is significant as S n is nonnegligible at energy, E 10 kev/amu. Since in RBS or HRBS, measurements are usually done with He + ions with incident energy, E kev and the energy of the backscattered ion, E kev, nuclear stopping is negligible. There are theoretical models to describe electronic stopping at both low (E 30 kev/amu) and high (E 1 MeV/amu) ion energies. However, most RBS measurements are carried out an intermediate ion energy range. For He ions, there are two commonly used functions to describe the ion's stopping cross-section, the Ander-Ziegler stopping data and the Ziegler Biersack stopping data, where different function are used to fit the Stopping cross-section for high and low ion energies, S high and S low. The Andersen-Ziegler stopping for He is and where A 1 to A 5 are tabulated parameters. The Zierler-Biersack stopping for hydrogen stopping data is and 12

21 Physical Concepts Chapter 2 where C 1 to C 8 are fitted parameters. The stopping cross-sections are then scaled using effective charge γhe 2, where 2.5 Energy Straggling Light particles such as H or He lose energy due to the statistical fluctuations in the electronic and nuclear energy processes as they travel within the target sample. These statistical fluctuations causes a broadening of the ion energy distribution which is known as energy loss straggling. The distribution of energy loss ΔE for the particles after passing through a foil gives a distribution that is approximately Gaussian when ΔE is small compared with the incident energy E0. Thus the probability of finding an energy loss between ΔE and ΔE + dδe is expressed as where is the mean energy loss and is the variance if electronic energy. Based on classical considerations of collisions between a charged particle such as proton or α particle and free target electrons, is given as where is the path length in the target sample. This expression is also referred to as the Bohr's value of energy loss straggling. Bohr's straggling theory is valid when ion velocity is high, where the straggling value is almost independent of ion energy. For lower ion energy E, Chu's straggling theory can be used, 13

22 Physical Concepts Chapter 2 where H is the Chu correction factors, which are tabulated for 100 E/M (kev/amu) by Szilágyi [9] are plotted for several values of E/M 1 as a function of Z 2 in Figure 2.3. For 500 kev He ions, the deviation from Bohr's straggling is around 60% to 80%. Fig. 2.3 Plot of Chu correction factors H vs Z 2 for various E/M 1 values. Dots are original data from Chu and the lines are extrapolations by Szilágyi [9]. Source [7] Ions with different charge states will also transfer different amounts of energy to electrons during a backscattering event. For He ions, the charge state varies as they travel within the target sample due to the excitation and capture of electrons within the target sample. These fluctuations in charge state contributes to additional energy straggling effects and be described by a semi-empirical formula with fitted parameters C 1 to C 4 where and 14

23 Physical Concepts Chapter 2 For 500 kev He ions, the additional energy straggling factor is estimated to be around The total energy straggling is the sum of Chu and Yang straggling components, 2.6 Rutherford Backscattering Spectrometry The various quantities describe earlier are now used to provide a picture of RBS analysis of thin film on a substrate which is one of the focus of this thesis. In a RBS measurement, the incident ions of energy E 0 is backscattered with a scattering angle θ with energy E 1 and its detected by a detector placed at certain position along the ion trajectory. A spectrum of the distribution of the energies E 1 of the backscattered ions is then obtained which is used to determined the elemental composition of the target using numerical simulations of the energy spectra with the software package SIMNRA. Fig. 2.4 Diagram of RBS measurement 15

24 Physical Concepts Chapter Ion Channeling Ions incident onto a target with a lattice structure along a major crystalline axis may be steered into channels (i.e. channeled ) where they undergo a series of correlated, small angle collisions with the nuclei that line the channels. Fig. 2.5 Schematic of ion channeling. Source: [10] The incident ions will be deflected by the first atom on the surface atomic layer, forming a shadow cone which shields the rest of the atoms lining the channel from head-on and closeencounter (low impact factor) approach by the ions (Fig. 6.5(a)).Subsequent encounters of channeled ions with lattice atoms will be small-angled collisions with large impact factors, with the ion trajectory exhibiting oscillatory behavior within the channel (Fig. 6.5(b)) in near-surface regions. The backscattering cross-section of channeled ions are therefore greatly reduced, the RBS signal from the crystalline (Si) substrate may fall by up to 98% of the random yield for pure crystals with clean surfaces along major axes. 16

25 Physical Concepts Chapter 2 Fig. 2.6 (a) Schematic of the formation of the shadow cone at the surface and the trajectories of channeled particles. The horizontal scale on the right is compressed in relation to the vertical scale to show the trajectory oscillations. (b) The comparison between the channeled and the non-aligned RBS spectrum. The channeled spectrum shows a drastically reduced substrate signal. Source [10] 2.8 Thin film on substrate In this thesis, the focus on the thin film deposited on a substrate is focused on depth profiling and stoichometry of elements in the thin oxide film at the interface region of the sample. Fig. 2.7 (a) Scattering geometry and (b) spectrum of an RBS measurement of a thin compound target. Source [11] 17

26 Physical Concepts Chapter 2 Fig. 2.7 illustrates the scattering trajectory and the RBS spectrum of a thin film A y B 1-y on a thick substrate S. In high k gate dielectric, A is usually a heavy element, B is either O or N, and S is usually Si. The signals from elements A and B in the spectrum have high energy edges at K A E 0 and K B E 0 respectively. The substrate signal S pushed back to lower energy by ΔE s, due to the ions losing energy within the thin film. The signal from B rests on top of the substrate signal S, due to K B E 0 < K S E 0 ΔE s. Ions will lose the same amount of energy per unit length along the way in, but may lose a different amount along the way out depending on which atom they backscatter from, due to the difference in K values. The energy widths of the respective signals in the spectrum are: and where and, is the areal density of the thin film, is the stopping cross section of the ion as in enters the sample while and is the stopping cross section of the ion as after it backscatters from ion A and B. Apply the Bragg's rule of additivity which states that the stopping cross section of the compound can be estimated by the linear combination of the stopping cross section of the individual atoms The area of the spectrum attributed to element A and B are 18

27 Physical Concepts Chapter 2 Using the areas, the stochiometric ration of the two elements A and B can be determined. 2.9 SIMNRA Numerical Simulation of RBS spectrum SIMNRA is a computer software that carries out numerical simulations of an RBS spectrum. In the numerical simulation by dividing the target sample into i thin sub-layers as shown below in figure 2.8. Each sub-layers is thin enough such that the variation of the stopping cross section is assumed to be negligible within each layer. In the i th sublayer the energy of the ion that enters the layer of thickness δx is E i-1 and the energy the ion that exits the layer is E i. Fig. 2.8 Diagram of the target divided into thin layers. Source [11] The energy loss within the layer i is ΔE and the mean energy of the ion in layer i is the incident ion energy E 0 subtracting the energy loss within layer 1 to layer i-1 and half the energy loss within layer i which are given by 19

28 Physical Concepts Chapter 2 The integral in is numerically computed using the Runge-Kutta method. The ion energy along the outward is computed in the same way, using for the backscattering at the back of layer i. Beam straggling within the i th layer for the inward is calculated using where the first term in the equation above is the non-statistical beam straggling due to varying stopping cross-section and is the total (Chu and Yang) energy straggling within layer i. Scattering from within each layer will result in a signal in the spectrum called the "brick". Each brick has an area The stopping cross-section is evaluated at the mean energy in the layer and is assumed to be constant. The final simulated spectrum is formed by the summation of the "bricks" from different elements and different depths (layers). 20

29 HRBS Set-up Chapter 3 Chapter 3 HRBS Set-up 3.1 HRBS Endstation The HRBS end station was fabricated by the Machinery Company of Kobe Steel Ltd and installed at CIBA in The general setup consists of a Main chamber with a load lock chamber, Ultrahigh Vacuum (UHV) system (pumps, valves and interlocks), 5-axis Goniometer, Spectrometer magnet and Micro-Channel Plate Focal Plane Detector stack (MCP-FPD) Both the main and the MCP-FPD chambers are constantly maintained under UHV with two turbo-molecular pumps, which are located beneath the main chamber and the MCP-FPD chamber. Sample exchange is carried out by a transfer rod which transfers a target holder onto the goniometer attachment in the main chamber from a load-lock chamber through a gate valve. A controller program in the control cabinet oversees the vacuum interlocks system. This allows for programmed or manual control of all valves as well as the goniometer rotation axes. During measurements, the divergence of the ion beam is defined using the motorized slits located ~ 1 m before the main chamber. Backscattered ions from the sample target enter the detection system, which consists of a spectrometer magnet and a Micro-Channel Plate Focal Plane Detector (MCP-FPD) stack. The output signal from the FPD is then processed by a system of electronics in the control cabinet to provide information of the position of incidence along the length of the FPD. The output spectrum is sorted by a MCA before the final spectrum is obtained in the computer 21

30 HRBS Set-up Chapter Main chamber, load lock and vacuum system The sample is placed in a specially designed sample holder which is held on the goniometer attachment in the main chamber during RBS measurements. Insertion and removal of the sample holder is carried out using a transfer rod within the load lock chamber. Fig. 3.1 (a) Main chamber, goniometer and load lock. (b) Load lock with a sample holder (c) View of sample holder on the goniometer in the main chamber through the main viewport. Source [11] A UHV vacuum of smaller than 5 ᵡ10 9 mbar is maintained by a Mitsubishi FT-800WH turbomolecular pump (TMP) in main chamber (TMP 1) and a Mitsubishi PT-50 TMP in the MCP-FPD chamber (TMP 2). Both TMPs are being backed by a Mitsubishi DS-251L scroll pump with valve V2 perpetually open. Valve V3 allows the load-lock to be pumped (also by the scroll pump), V4 controls the venting with N2 during sample change and V1 isolates the load lock from the main chamber. 22

31 HRBS Set-up Chapter 3 The network of valve is monitored by an interlocks system at the control cabinet which prevents sudden change in vacuum pressure due to accidental activation of valves. Fig. 3.2 Schematic of the vacuum pump and valve network. Source[11] During sample change, the interface from control cabinet activates sequential steps which activates the appropriate valves. During insertion of the sample into the main chamber, the sample holder is placed on the transfer rod within the load lock with the all valves except V2 closed. V3 is opened to allow the load lock to be pumped to a pressure of ~ 10-2 mbar, after which V1 is opened to allow the sample to be transfer into the main chamber. Lastly the inserting rod is retracted into the load lock and both V1 and V3 are closed. On the other hand, in sample removal, V3 is first open to pump the load lock down before V1 is opened. After the sample is removed and the transfer rod id retracted into the load lock, V1 and V3 are closed. Finally, V4 is opened to allow N 2 to flood the load lock back to atmospheric pressure and the load lock chamber can be opened to remove the sample. 23

32 HRBS Set-up Chapter Goniometer A Kitano Seiki 5-axis goniometer controls the sample orientation in the main chamber by enabling translation in the x, y and z axes, as well as rotation about the θ and ϕ axes. The translation resolution is 0.01 mm with a repeatability of 0.05 mm along all directions, while rotations have resolution of 0.05 and are repeatable to within ± An electric potential of ~ +480 V is applied to the attachment which holds the sample holder during measurements, suppressing secondary electron emissions to allow for accurate beam current readings. Fig. 3.3 Schematic of the HRBS goniometer. Source: [12] 24

33 HRBS Set-up Chapter Micro-channel Plates The 2-D FPD is used to detect the position of the backscattered ions along its length and breadth. The position is then analyzed to determine the energy of the corresponding backscattered ions. However, the charge of the backscattered ion is too small to result in an electrical pulse significant enough to be processed by the electronic equipment. With the implementation of the MCP, the electrical signal by the backscattered ion can be amplified by an electron multiplication process through the channel plates. The walls of the plate have a low electron emission work function and a voltage bias of 1kV is applied across each channel plate using an ORTEC 660 High Voltage Bias. This would cause the incident backscattered ion to initiate an electron cascade down the channel plate. The electron multiplication process will saturate and an electrical pulse would be recorded. There are residual gases in the channels which might be ionized during the cascade process which will accelerate upwards within the channel. This ionized gas will gain kinetic energy as it accelerates upwards and might initiate another cascade, creating dark counts. The orientation of the plates at an angle relative to each other prevents this initiation by ensuring that the gas ions at the bottom stack will be stopped at the junction between the two plates. Fig. 3.4 Diagram of Micro-channel plates 25

34 HRBS Set-up Chapter Electrostatic plates Work has been done by C. S. Ho [22] to install a pair of electrostatic plates as shown in figure 3.5 between the spectrometer magnet and the MCP chamber. Fig. 3.5 Schematic and layout of the installation of the electrostatic plates. Source [11] The plates were carefully adjusted to be horizontal, so that all ions are deflected only in the vertical direction. The electrostatic field serves to eliminate low-energy stray ions that have scattered off the collimator, floor, walls or ceiling of the conduit along any part of the ion trajectory between the target and the MCP. Without the electrostatic plates, the low-energy stray ions will produce a background counts in the actual HRBS spectra. The addition of the electrostatic plates would then remove a large part of the background counts and increasing the accuracy of the HRBS measurement. 26

35 HRBS Set-up Chapter D Focal Plane Detector and HRBS electronics The FPD is a 100 mm long resistive strip of uniform resistance per unit length. As the electron cascade from the MCP deposits a charge pulse on the FPD, the position of the charged pulse can be determined by a system of electronics. A charged pulse detected on point X, would cause a current flowing to the right and to the left of the FPD, I L and I R respectively. The charged collected on the left and right of the FPD, Q L and Q R are measured over a time interval t and compared to the total charge collected to determined distance X from the edges of the FPD. The length of the FPD is Land since the FPD has uniform resistance per unit length, we have Fig. 3.6 Schematic of 1-D Focal Plane Detector and HRBS electronics. Source[11] 27

36 HRBS Set-up Chapter 3 The charge division to determine the position of the electron cascade is calculated by a system of analog processors. The charge pulses QL and QR are each processed first by ORTEC 113 Preamplifier and then by ORTEC 571 Amplifier [11]. The resultant pulses were then added using ORTEC 533 Dual Sum and Invert card while the Seiko EG&G PSDA card is used to divide an amplified signal with the summed signal to obtain the position output [11]. The summed signal output is also processed. The output is then processed by a Canberra 8706 ADC which is subsequently sorted using a Labo NT2400 Multichannel Analyzer and finally displayed on the PC[11] D Focal Plane Detector For a 2-D FPD, there are added long resistive strips of uniform resistance in another dimension. Similar to the 1-D system, the electron cascade from the MCP deposits a charge pulse on the FPD, the 2-D position of the charged pulse can be determined. A charged pulse detected on point X in the x-direction and point Y in the y-direction, would cause a current flowing to the right and to the left of the FPD, I L and I R respectively as well as to the top and the bottom of the FPD, I T and I B respectively. Similar to the charged collected on the left and right of the FPD, Q L and Q R, the charged collected at the top and bottom of the FPD Q T and Q B are measured over a time interval t and compared to the total charge collected to determined distance Y from the top and bottom edges of the FPD. With height, H of the FPD and taking account the uniform resistance per unit length of the FPD, we have With the knowledge of the x and y positions of the incident charge pulse, the 2-D position of the incident charge pulse can be determined. 28

37 Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon Chapter 4 Chapter 4 Study of Swift Heavy Ion Irradiation effects on Hafnium based high k- dielectric thin films deposited on Silicon 4.1 Swift Heavy Ion The energetic ions through a material loose energy via two processes along their trajectories. The two processes are known as nuclear energy loss and electronic energy loss. In nuclear energy loss process, dominant in low energies, the energy is lost by elastic collisions of incident ions with the atoms in the material. However at dominant at high ion energies (>1 MeV/nucleon), electronic energy loss is dominant. In electronic energy loss process, the energy is lost by inelastic collisions of the ion with the electrons of the atoms, leading to excitation or ionisation of the atoms. At such high energies, the velocity of the ion is comparable to or higher than the velocity of Bohr electron. Heavy ions with such high energies are also referred to as Swift Heavy Ions (SHI). 4.2 Ion beam Mixing Ion beam mixing (IBM) is a process, in which the atoms of two different species across an interface are mingled together under the influence of the passage of ion beam. Conventionally it is achieved by low energy ion up to a few MeV[12]. In IBM, elastic collisions and subsequent collision cascades, recoil implantation and radiation-enhanced diffusion is observed. Collision cascade is initiated only in the case when the recoils have sufficient energy to displace the 29

38 Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon Chapter 4 lattice atoms. The heavier ions will have large number of collision cascades as compared to that of lighter ions. IBM was considered to be a phenomenon associated with low energy ion irradiation. However since early 1990s, the ion beam mixing by SHI irradiation was observed. In all the above studies, SHI induced mixing at the interface has been identified as diffusion in melt phase created by transient temperature spike [13,14]. It is proposed that each ion produces a transient molten cylindrical zone in the material for typical time duration in the regime of picoseconds. The inter-diffusion across the interface takes place during the molten phase resulting in mixing. Quantitatively, it has been shown that the diffusivity of the atomic species across the interface during the transient melt phase as obtained in these experiments [13,14], is of the order of 10-6 to 10-9 m 2 s -1. Such a high diffusivity is possible only for the liquids, which supports the hypothesis that the ion beam mixing is a consequence of inter-diffusion across the interface during transient melt phase. 4.3 HfO2/SiO2/Si Samples HRBS analysis was done for four HfO2/SiO2/Si samples obtained from SEMATECH, USA which were grown by Atomic Layer Deposition (ALD). The sample in the absence of Swift Heavy Ion Irradiation is labeled as Pristine-H1A where its sample structure is shown in figure 4.1. The other three samples are irradiated at IUAC, New Delhi using 120 MeV Au ions with different fluence and labeled as H1B, H1C and H1D. The four samples are described below: i) Pristine-H1A ii) 1E13 ions/cm MeV Au irradiated-h1b iii) 5E13 ions/cm MeV Au irradiated-h1c iv) 1E14 ions/cm MeV Au irradiated-h1d 30

39 Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon Chapter 4 Fig. 4.1 Sample structure of Pristine-H1A 4.4 HRBS experimental parameters The samples were measured using a 500 kev He + beam incident on the sample and ions scattered at 65 with incident and exit angle 54.7 and 60.3 respectively. The backscattered ions were then analyzed by the spectrometer and were collected by the MCP-FPD. Two experimental data for each sample is obtained. The first data obtained is the aligned HRBS spectra (along <111> axis of Si) in order to minimize background scattering from Si and analyze amorphous layers (SiO 2 /HfO 2 ) on Si surface. Prominent surface peaks corresponding to Si and O from amorphous layers on surface are observed due to a reduction of about 80% in the back scattering yield of Si (χ min = ~ 20%) in <111> aligned spectrum. A non-aligned or random HRBS spectrum is also obtained where angle φ is slightly rotated under IBM geometry which was then simulated using SIMNRA to obtain an elemental depth profile. 4.5 HRBS Depth profiling results The non-aligned and channeled spectra of all four (H1A, H1B, H1C, H1D) samples are shown the figures 4.2 to 4.5: 31

40 Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon Chapter 4 Fig. 4.2 Aligned (Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation of Pristine- H1A sample Fig. 4.3 Aligned (Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation H1B-1E13 Au sample 32

41 Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon Chapter 4 Fig. 4.4 Aligned (Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation H1C-5E13 Au sample Fig. 4.5 Aligned (Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation H1C-1E14 Au sample 33

42 Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon Chapter 4 In figure 4.5 below, an overlay of Hf peaks from the previous four graphs for is illustrated. A widening of the Hf peaks as the irradiation fluence increase from sample H1A to H1D. This supports the proposition that ion beam mixing is present which results in the inter-diffusion of Hf into the sample and that the increase in fluence of Au ion irradiation corresponds to an increase in the degree of inter-diffusion of Hf into the sample. Fig. 4.6 Aligned (Channeled) HRBS spectra of Hafnium peak for all four samples (H1A, H1B, H1C, H1D) 34

43 Concentration Concentration Concentration Concentration Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon Chapter 4 H1A (Pristine) H1B (1E13 Au) 1 Hf 0.9 Si 0.8 O Depth ( atoms/cm 2 ) Depth ( atoms/cm 2 ) H1C (5E13 Au) H1D (1E14 Au) 1 Hf 0.9 Si 0.8 O Hf 0.8 Si 0.7 O Hf 0.9 Si 0.8 O Depth ( atoms/cm 2 ) Depth ( atoms/cm 2 ) Fig. 4.7 Elemental depth profile for H1A, H1B, H1C, H1D Using SIMNRA, the concentration of the Si, O, Hf in various depth layers is simulated. A total of five different depth layers are fitted to the non-aligned spectra of each of the four samples. The top layer of all four samples consists of HfO where the stoichiometric ratio of Hf : O for all four samples is roughly 1 : 2. The subsequent interface layers consist of a HfSiO layer and three different SiO layers with different stoichiometric ratios. The bottom layer is the Si substrate which is for clarity reasons, not depicted in figure 4.7. As observed from figure 4.7, there is a systematic increase in the thickness of the interface layers as the irradiation fluence increase from sample H1A to H1D (thickness of interface layers for H1A ~ atoms/cm 2, H1B ~ atoms/cm 2, H1C ~ atoms/cm 2, H1C ~ atoms/cm 2 ). 35

44 Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon Chapter Conclusion HRBS measurements suggest that the interlayer is a mixed HfSiO/SiO layer instead of a pure SiO 2 layer as intended. It is well known that SiO 2 is very much stable on Si surface. Hence this mixed layer might have formed either during or after the deposition of HfO 2 layer. Inter diffusion of Hf into SiO 2 and Si into HfO 2 at SiO 2 /HfO 2 interface is likely to be responsible for the observed mixed layer. An interdiffusion of O into the Si substrate. This information is expected to be useful for understanding the kinetics of growth during atomic layer deposition. A systematic increase in thickness of the interlayer as a function of increasing fluence is also observed as seen in figure 4.7. These observations confirm that SHI using high energy Au atoms can induce ion beam mixing where inter-diffusion of Hf and O across HfSiO/HfO 2 interface is observed. Such inter-diffusion is also more pronounced as irradiation fluence increases. 36

45 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 Chapter 5 Simulation and characterisation of new 2-D focal plane detector using SIMion D Focal Plane Detector Fig 5.1 Diagram of 2-D FPD with true counts (red dotted ovals) and counts derived from HRBS (black ovals) A 2-D FPD allows the profiling of splat profiles of the end of the ion trajectories in both directions of the FPD; along the height as well as length of the FPD. If the true counts, the red dotted oval seen in figure 5.1 is known, the dark counts can be discerned from the original experimental data or the black ovals as seen in figure 5.1. Hence, any counts that originate from the shaded area seen in figure 5.1 would be considered as dark counts and can be screened out to obtain a more accurate HRBS spectrum. It is also important to characterize the height as well as the width of the splat profiles to determine whether the dimensions of the splat profile would fit well into the 2-D FPD. 37

46 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 In this part of the thesis, we look into the 2 dimensional splat profile onto the median (x-y) plane along the FPD of the exit beam. Since the FPD determines the energy of ion according to ion's position along the length of the FPD. A simulation is performed using SIMION to sweep the ion incidence position across the length of FPD. The length and height of the FPD is approximately 100mm and 15mm respectively. The 2-D splat profile (height and width) of the ions of different energies at the end of their trajectories incident on the FPD is characterized and then investigated. An example of simulation is shown in figure 5.2 as a point ion spot is created at S and its trajectory is simulated through a circular collimeter (1mm or 2mm in diameter) and a subsequent splat profile is obtained at the end of its trajectory. Fig. 5.2 Schematic of simulation done using SIMion 38

47 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter Overall layout of the HRBS detection system Fig 5.3 Schematic of Spectrometer magnet, MCP-FPD in HRBS. Source [11] In CIBA, HRBS spectrometer magnet used in a double-focusing 90 sector magnet with a straight edge rotated by 26.6 and a circular exit edge with radius m as shown in the diagram in figure 5.3. Assuming a static magnetic field, every ion energy, E has a unique central trajectory with radius r given by: 39

48 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 where m = Mass of the ion, B = Magnetic flux density and q = Ion charge. A 90 sector magnet of radius r 0 with flat entrance and exit edges that are both rotated at 26.6 is expected to produce a stigmatic image of a point source at both object and image distances of 2r 0 = 0.350m. The HRBS spectrometer and detection setup is designed to produce a stigmatic image according to this principle. As seen from the diagram from figure 5.3, the incident beam backscatters from the sample at S, passes through the collimeter which defines the beam divergence before entering the magnet at P, When the ions travels along a trajectory of radius of r 0 = m, they will exit the spectrometer magnet at Q before they ending up at the MCP- FPD stack at Q. Assumptions were made that no fringe fields were present in the spectrometer magnet. 5.3 Spectrometer ion optics Beam entry parameters In the SIMION simulation, the ion beam was assumed to have incident on a target tilted at 45 with IBM geometry (Fig. 4.4). The incident finite beam spot size on the target is 1 1 mm as seen along the target normal. Particles backscattered at a scattering angle of α will form a beam of half- - width, ω = sin β (metres) that will subsequently be collimated by a 2 mm or 1mm circular collimeter placed between the target in the scattering chamber and the magnet entrance. The simulation was repeated thrice with scattering angle α at 90, 110 and 130 with corresponding β at 45, 65 and 85 respectively. A point beam spot is also simulated as a reference to the finite beam spot. 40

49 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 Fig 5.4 Schematic of the incident and backscattered beam profiles Fig. 5.5 Finite backscattered beam profile and point source approximation As seen in figure 4.5, the total distance between the beam spot on the target and the magnet entrance is m, and the collimator is m from the magnet entrance. The maximum divergence of the backscattered beam through the collimeter can be modeled by the beam envelopes created by the ion trajectories at the extreme ends of the beam spot. The combination of the beam envelopes point source at point S ' at a distance d would model the 41

50 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 maximum divergence envelope of angle θ 0 (red dotted lines in figure 5.5) of the beam spot that contain all envelopes formed by the finite incident beam. The point beam at S ' was therefore used as an equivalent of the finite beam. By similar triangles, we have Hence, for a 90, 110 and 130 scattering angle, d is 295 mm, 292 mm and 288 mm respectively Drawing the magnet The program simulates a 3-dimensional universe called workbench that is divided into grids. The centre of each grid cube is known as a grid point, while the separation between 2 adjacent grid points is known as a grid unit. Grid points are divided into 2 types: electrode points and non-electrode points. The size of the workbench was first defined, followed by the drawing out of the exact shape of the magnetic pole pieces (known as electrodes within SIMION). Drawing a pole piece is done by deciding the set of grid points to be defined as electrode points, while the rest of the grid points are designated to be non-electrode points. The exact shape of the HRBS spectrometer magnet was drawn using a geometry file where exact geometrical shapes were drawn using its in-built definition language by TK Chan [11]. The pole pieces were separated by 18 mm, while their thicknesses were drawn out to be 40 mm. The exact thickness along the z-direction was not simulated because only the shape and the magnetic potential at their boundaries define the magnetic field between them. The inner boundary edges are filed at an angle of 45 at both the magnet entrance and exit. 42

51 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 Fig D isometric view of the workbench with a magnified view of the spectrometer magnet. Source [11] Maxwell s and Laplace s equations The Maxwell s equations for electric and magnetic fields in vacuum for static magnetic fields not containing any electric charges: Since both curls and divergence are zero, we can write the Laplace's equation in terms of the scalar potential where and 43

52 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 However, since only magnetic field is involved in our set-up, the subscripts are dropped and the scalar potential now refers the scalar magnetic potentials Refining the magnet array All electrode points within a single magnetic pole piece share the same magnetic potential. A non-zero potential was chosen for the top magnetic pole piece and a zero potential is chosen for the bottom magnetic pole piece. All non-electrode points are set to zero potential. The electrode potentials form the Dirchlet boundary condition which ensures the uniqueness of the harmonic solutions to Laplace s equation Finite Difference Method The next step was to solve the Laplace s equation numerically to determine the magnetic potentials for all non-electrode points within the workbench that will reflect the correct magnetic field, this is known as refining the array in SIMION. SIMION solves the Laplace equation using the numerical method called the Finite Difference Method (FDM)" which is rather straightforward which is essentially a process of assigning a potential to each nonelectrode point that is equal to the average value among those of the neighbouring points. SIMION does this sequentially and over a number of iterations. During each iteration, the program sequentially calculates for every non-electrode point within the array the average potential of the 6 neighboring points (Figure 5.7). A potential distribution is then obtained after the iterations are completed (Figure 5.8). This also implies that the potential energy map from a static electric field can contain no local minimum or maximum. 44

53 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 Fig. 5.7 Diagram depicting Finite Difference Method (FDM)" Fig. 5.8 The potential distribution plot along the x-y plane at a fixed value of z. The darkened flat top represents the region with uniform magnetic field, while the smooth slopes at the sides represent the non-uniform fringe fields. Source [11] Calculation of ion trajectories Ions of mass M were created at point S and given an initial energy E. The program divides the flight duration of the ion through into time steps in which the size of the time steps is dependent on the rate of change of magnetic potential gradient at that point. At regions of 45

54 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 constant gradients, the time steps are larger as compared to the regions with greater gradient variations. At each time step, the program also employ linear interpolation between the potential V at the ion's position with the potentials at 6 adjacent grid points, V i (i = 1,2,3,4,5,6) to determine the potentials at the surrounding 6 intermediate points half a grid unit (gu) from the current ion position which is half the addition of the V and V i. These potentials were then used to obtain the component of the magnetic field as well as the acceleration in the x, y and z direction using to B =. The acceleration components derived from, which leads to the components in the velocity change during every time step: 46

55 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter SIMion simulation details d Fig. 5.9 The overview of the workbench in the x-y plane looking down towards the negative z-direction. Source [11] He + ion spot with a finite width were created at point S ' and given an initial energy E. The ion then follows a trajectory as determined by the spectrometer magnet with a fixed magnetic field between the pole pieces. The half-width of the beam spots 0.42mm, 0.45mm and 0.5mm which simulates the ion backscattering at different scattering angles (90, 110 and 130 scattering angle are respectively). Ions of different backscattered energy were then created at point S ' to sweep the ion incidence position across the FPD of length approximately 100mm. A point He + ion spot was also created to contrast the splat profile for the finite beam spot. 47

56 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter SIMion simulation results Splat profiles Fig Splat profile for a point spot and beam spot of E = 427keV collimated by a 1mm collimeter For each ion energy and beam spot size, we obtained a splat profile at the end of its trajectory at the FPD. Here, a new parameter is defined, ε which is ratio of the E to E 0 where E is the fixed energy of the backscattered ion incident on a fixed position on the FPD, while E 0 is the energy of the backscattered ion at which the end trajectory is incident on the centre of the FPD. The splat profile of ions with energy, E from 400 kev to 571 kev (range of ion energy to sweep the ion incidence position across the FPD of length) was plotted out and studied. An example of a 48

57 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 plotted splat profile is illustrated in figure 5.10 which depicts the splat profile for a point spot of as well as a beam spot of half-width 0.42mm of E = 427keV collimated by a 1mm collimeter. In figure 5.11, the various splat profiles corresponding to different energy, E (400 kev to 421 kev) for a point spot simulated through 1mm collimeter are plotted out. It can be observed that the height of the splat profiles (dimension of the splat profile in the z-position) decreases as energy of the point spot increases from 400 kev to 421 kev. Fig Splat profiles of a point spot of energy, E from 400 kev to 421 kev simulated through 1mm collimeter However, as the energy of the point spot, E continues to increase from 421 kev to 442 kev, the height of the splat profile increases (figure 5.12). The point at which the splat profile is 49

58 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 minimum can be deduced to be double focusing point of the spectrometer magnet which is at ε 0.87, at the right end of the FPD. Hence, it can be seen that the height of the splat profile increases as the end trajectory incident the FPD moves to the left of the FPD. The splat profiles for the point spot through a 2mm collimeter were also plotted out (see figure A.1 and A.2) and the splat profiles follow the same trend as that of the 1mm collimeter. Fig Splat profiles of a point spot of energy, E from 421 kev to 442 kev collimated by 1mm collimeter Height and Width of splat profiles 50

59 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 In figure 5.11 and 5.12, the height variation of the splat profile along the length of the FPD is observed. However, the width variation is too small to be observed. Hence, an overall height and width of the splat profile along the FPD is plotted out for point spot and various beam spot sizes collimated by 2mm collimeter (figure 5.13 and figure 5.14). As depicted in figure 5.13, the height of the splat profiles decreases as ε increases until it reaches a minimum point at the double focusing point after which it continues to increase. The height of the splat profiles are shown to be all smaller than 8mm. The height of the splat profile along the FPD through a 1mm collimeter was also plotted out (see figure A.3) and the splat profiles follow the same trend as that of the 2mm collimeter. The height of the splat profiles for that of a 1mm collimeter are smaller than 4mm. Fig Height of the splat profiles for point and beam spots collimated by 2mm collimeter 51

60 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 As depicted in figure 5.14, the width of the splat profiles for the beam spots increases as ε increases. However, for the point spot, the width of the splat profiles decreases until it reaches a minimum point before it starts to increase. The trend for the beam spot is expected to follow the trend of the point spot as ε continues to decrease. The width of the splat profiles are shown to be all smaller than 2mm. The width of the splat profile along the FPD through a 1mm collimeter was also plotted out (see figure A.4) and the splat profiles follow the same trend as that of the 2mm collimeter. The height of the splat profiles for that of a 1mm collimeter are smaller than 1mm. Fig Width of the splat profiles for point and beam spots collimated by 2mm collimeter Variations in starting x-position of backscattered ions 52

61 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 The starting position of the point spot was varied in the x-direction from the original position at 675 grid unit (gu) on SIMion workbench and the corresponding height, width as well as the centre position variation of the splat profile at double focusing point was then studied. This was to model for the position uncertainty in the x-direction of the backscattered ion in HRBS. Here, 674 gu is 1mm in the x-direction closer to the spectrometer magnet and 676 gu is 1mm in the x- direction further from the spectrometer magnet. In figure 5.15, 5.16 and 5.17, the height, width and centre position of the splat profile at double focusing point with different starting points of the backscattered ion trajectory, collimated by a 2mm collimeter are plotted out respectively. Fig Height of the splat profile of the double focusing point at different starting x-position of the backscattered ion (2mm collimeter) 53

62 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 Fig Width of the splat profile of the double focusing point at different starting x-position of the backscattered ion (2mm collimeter) Fig Centre position of the splat profile of the double focusing point at different starting x-position of the backscattered ion (2mm collimeter) 54

63 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 The variations of height of the splat profile due to variations in starting x-position of backscattered ions is around 0.01mm and variation of width is around 0.015mm which is also the height and width resolution at double focusing point for a starting position uncertainty of 1mm. The variation of the centre position of the splat profile at double focusing point is smaller than mm, which is relatively quite small. For 1mm collimeter, see figures A.6, A.7 and A.8, the corresponding variations of height and width is around 0.003mm and 0.007mm respectively. The variation of the centre position is smaller than mm which is also relatively quite minute. 5.6 Simulation Conclusion A SIMION Simulation of height and width of the Splat profile of beam spot of different scattering angle and different half width for different backscattered ion energy was done. For a 2-D focal plane detector, it important to consider of height of the splat profile; if the height of the splat profile is larger than the height of the detector, some of the counts will not be recorded which would distort the HRBS spectra. The 2-D FPD that is available has a height of 15 mm and length of 100 mm. The simulations shows that height of splat profiles for 2mm collimeter is below 8mm and for 1mm collimeter, it is below 4mm. Hence, we can safely assume that the splat profiles will fit into the height of the 2-D FPD and all the counts on the FPD can be recorded. The width of the splat profiles for 2mm collimeter is smaller than 2mm while that of the 1mm collimeter is smaller than 1mm. Hence, it can deduced that at least 50 splat profiles of 50 different ion energies (2mm collimeter) or at least 100 splat profiles of 100 different ion energies (1mm collimeter) can be fitted into the length of the FPD. The height and width resolution at double focusing point for variations in starting x-position of backscattered ions of uncertainty of 1mm through a 2mm collimeter is around 0.01mm and 55

64 Simulation and characterization of new 2-D focal plane detector using SIMion Chapter 5 variation of width is around 0.015mm. The corresponding height and width resolution for 1mm collimeter is around.003mm and 0.007mm respectively. The variation of the centre position of the splat profile at double focusing point is relatively quite small. Hence, the uncertainty of the starting position does not cause a large variation of the position of the double focusing point of the FPD. 56

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66 Bibliography [14] Santos, D.L.; de Souza, J. P.; Amaral, L. & Boudinov, H. Ion beam mixing of Fe thin film and Si substrate, Nucl. Instr. and Meth, 103, (1995) [15] Srivastava, S.K.; Avasthi, D. K.; Assaman, W.; Wang, Z. G.; Kucal, H.; Jacquet, E.; Carstanjen, H. D. & Toulemonde, M.; Test of the hypothesis of transient molten state diffusion for swift-heavy-ion induced mixing, Phys. Rev, 71, (2005). [16] Diva, K.; Kabiraj, D.; Chakraborty, B. R.; Shivaprasad, S. M. & Avasthi, D. K. Investigation of V/Si mixing induced by swift heavy ions, Nucl. Instr. And Meth, 222, (2004) [17] N. Manikanthababu, Chan Taw Kuei, A. P. Pathak, G. Devaraju, N. Srinivasa RaoYang Ping, M. B. H. Breese, T. Osipowicz and S. V. S. Nageswara Rao, Ion beam studies of Hafnium based alternate high-k dielectric films deposited on silicon, Nucl. Instr. And Meth in Phys. Res. B, (2014). [18] D. K. Avasthi, G.K. Mehta, Swift Heavy Ions for Materials Engineering and Nanostructuring Springer Series in Materials Science, 145, (2011) 1. [19] Xiangkun Yu, Lin Shao, Q.Y. Chen, L. Trombetta, Chunyu Wang, Bhanu Dharmaiahgari, Xuemei Wang, Hui Chen, K.B. Ma, Jiarui Liu, Wei-Kan Chu, Nucl. Instr. Meth. Phys. Res., B 249 (2006) 414. [20] A. Benyagoub, Nucl. Instr. Meth. Phys. Res., B 245 (2006) 225. [21] T. Osipowicz, H.L. Seng, T.K. Chan, B. Ho, The CIBA high resolution RBS facility, Nucl. Instr. Meth. Phys. Res., B 249, (2006) [22] C.S. Ho, The Study of Ultra-thin Diffusion Barriers in Copper Interconnect System, Dissertation, NUS,

67 Appendices Appendices Fig. A.1 Figure Splat profiles of a point spot of energy, E from 400 kev to 421 kev simulated through 2mm collimeter 59

68 Appendices Fig. A.2 Splat profiles of a point spot of energy, E from 421 kev to 442 kev collimated by 1mm collimeter 60

69 Appendices Fig. A.3 Height of the splat profiles for point and beam spots collimated by 2mm collimeter Fig. A.4 Width of the splat profiles for point and beam spots collimated by 2mm collimeter 61

70 Appendices Fig. A.5 Height of the splat profile of the double focusing point at different starting x-position of the backscattered ion (1mm collimeter) Fig. A.6 Width of the splat profile of the double focusing point at different starting x-position of the backscattered ion (1mm collimeter) 62

71 Appendices Fig. A.7 Centre position of the splat profile of the double focusing point at different starting x-position of the backscattered ion (1mm collimeter) 63