Analysis of light elements in solids by elastic recoil detection analysis

Transcription

1 University of Ljubljana Faculty of mathematics and physics Department of physics Analysis of light elements in solids by elastic recoil detection analysis 2nd seminar, 4th year of graduate physics studies Jožef Visočnik pedagogic course Advisor: doc. dr. Matjaž Žitnik Ljubljana, February 27, 2008

2 CONTENTS Abstract Elastic recoil detection analysis (ERDA) is an ion beam technique for depth profiling of light elements in solid state materials. The present work describes the fundamentals of this technique and the physical processes that occurs by interactions between ions and atoms. In the second part we focus on hydrogen detection in metal and present an example of ERDA measurements which was recently made at the Jožef Stefan Institute with 4.2MeV 7 Li 2+ ion beam emerging from the Tandetron accelerator. Contents 1 Introduction 3 2 Collision between two particles 3 3 Scattering cross section 5 4 Energy loss of moving particles in matter 6 5 Depth resolution 8 6 Example of H measurement in metal 9 7 Conclusion 14 List of Figures 1 ERDA and RBS technique setup Collision between incident ion and target atom Sample of ERDA spectrum Real trajectory of ion in matter and his idealization Stopping power of material Propagation of energy straggling distribution through matter Calculating the depth of particle collision Processes of H interaction on metal surface Hydrogen exposure cell Spectra and concentration of H in Ti Energy spectra of H measurement in W H and D energy spectrum in W Time evolution of H 2 and D 2 in W

3 1. Introduction 1 Introduction Ion beam analysis is a well developed approach for determination of elemental concentrations in materials. The stable, positive charged ions are usually used as projectiles. One of the very useful ion beam analysis techniques is Elastic Recoil Detection Analysis (ERDA) [1], which is quite similar to Rutherford Backscattering Spectrometry (RBS). In the first case the ions are observed which are ejected from the target by the projectile while in the second case the object of detection are the projectiles backscattered from the target ions (figure 1). Since both methods stand on the same physical footing they are usually introduced together although they find quite different use in the practice. Figure 1: By ERDA the recoiled target atoms are the subject of interest, while by RBS the backscattering projectiles are measured. Both methods stand on the same physical footing, but in practice they use is quite different. Source: [2]. 2 Collision between two particles The collision between the projectile (accelerated ion) and the atomic nucleus in the target (a sample of material) is governed only by the Coulomb repulsive force and can be described simply as an elastic collision. This is a good approximation since usually the kinetic energy of the projectile is much greater than the binding energy of electrons. Let us observe the collision in the laboratory system [1 4]. The projectile with mass M 1 and velocity v 0 hits the target atom with mass M 2 (figure 2), which, initially at rest, recoils with velocity v 2 at recoil angle ϕ with respect to the incident projectile direction. The projectile is backscattered with velocity v 1 at scattering angle ϑ. Because the collision is elastic, the conservation of (kinetic) energy 1 2 M 1v 2 0 = 1 2 M 1v M 2v 2 2 (1) 3

4 2. Collision between two particles and the conservation of momentum apply: M 1 v 0 = M 1 v 1 + M 2 v 2 { M1 v 0 = M 1 v 1 cos ϑ + M 2 v 2 cos ϕ 0 = M 1 v 1 sin ϑ M 2 v 2 sin ϕ (2) Figure 2: The collision between incident ion and target atom is elastic and so conservation of energy and momentum apply. Since we are interested in recoiled atoms, the energy of them after the collision should be as large as possible. Source: [2]. Another important quantities in Elastic recoil detection analysis (ERDA) and Rutherford backscattering spectrometry (RBS) are the kinematic factors. These are the ratios between particle energies after the collision and the energy of the incident ion: K 1,2 = E 1,2 /E 0. The ratios are readily expressed from the conservation equations (1) and (2) to give M 1 cos ϑ ± M 2 2 M2 1 sin2 ϑ K 1 = M 1 + M 2 K 2 = 4M 2 /M 1 (1 + M 2 /M 1 ) 2 cos2 ϕ. (4) The complementary nature of both techniques is demonstrated by the fact that to get the scattered projectiles out of the sample in the perpendicular projectile incidence, ϑ should be larger than π/2 and therefore M 1 < M 2. On the other hand, since sin ϕ max = M 2 /M 1 the recoil angle can never be larger than π/2 and reaches this limiting value only when M 1 = M 2. RBS/ERDA technique basically consists of measuring the energy spectra of the projectile/recoiled ion at a given detector angle and a peak in this spectrum corresponds to the corresponding kinematic factor (figure 3). To increase the sensitivity of the method it is important to chose experimental parameters in such a way to make as large as possible the difference 4 2 (3)

5 3. Scattering cross section between the kinematic factors K 1 which describe a spectral contributions of the projectile backscattered from different kinds (masses) of a target atoms, or K 2 describing spectral components of different kinds (masses) of recoiled target atoms. It comes out that the sensitivity of RBS method is increased when the projectile energy and/or mass is larger and when ϑ approaches 180 degrees. Similarly, the sensitivity of Elastic recoil detection analysis (ERDA) is increased at smaller recoil angles and it is advantageous to select M 1 M 2. Figure 3: Typical ERDA spectrum has one peak, which corresponds to the kinematic factor K 1. If two or more lighter elements are in the target (in this case vitreous graphite sample), their peak is found at different energies due different kinematic factors. Source: [1]. 3 Scattering cross section We saw how the experimental parameters should be chosen to maximize the sensitivity of the method but to estimate the spectral intensities, i.e. the probabilities for the projectile scattering/target recoil, we must evaluate the scattering cross section. This is given by the ratio of the number of ions scattered through angles ϑ and ϑ + dϑ per time unit and the total number of particles crossing a unit target area per unit time. The cross section is determined by the type of interaction potential V(R) which governs the collision [1 4]. In our case this is a repulsive Coulomb potential V(r) = e i e t /(4πε 0 r), where e t = Z t e 0 and e i = Z i e 0 is the charge of target and projectile, respectively. In center mass system (index C ) the cross section of ion beam scattering on target atom at angle ξ is given by the well-known Rutherford cross section ( ) ( ) 2 dσ zi z t 1 = (5) dω C 4πε 0 4E c sin 2 (ξ/2) 5

6 4. Energy loss of moving particles in matter where E c is the energy of projectile before scattering. With appropriate transformation of angles between the laboratory and center-of-mass system (2ϕ = π ξ) and with considering the energy transformation between the two systems the differential recoil cross section in the laboratory system can be written as: ( ) ( ) dσ zi z t 1 2 ( = 1 + M ) dω ϕ 4πε 0 2E 0 M 2 cos 3 ϕ. (6) As we see, the differential recoil cross section reaches a minimum value for ϕ = 0 and goes to infinity for ϕ π/2. At smaller incident energy E 0 the recoil probability for a given recoil angle ϕ is increased and when the mass ratio M 1 /M 2 is larger, the corresponding differential recoil cross section is larger. Also, at given projectile energy and mass ratio the yield of recoil ions is larger when the recoil angle ϕ is larger. The scattering cross section was presented and calculated considering ion beam collision with a single atom. In a matter of fact an ion usually travels through a dense medium of different atoms and ions and in some fraction of events it suffers a double, a triple, a multiple Coulomb scattering with target nucleus. This correction modifies the RBS/ERDA spectrum and is known as multiple scattering. It is not yet fully analytically described. The largest effect of multiple scattering is due to a double scattering and can be estimated by a Monte Carlo simulation. (More about multiple scattering is written in [1].) Figure 4: Trajectories of ions in matter are unpredictable, a straight line is just an approximation. Incident ions can be scattered several times in the target, the same process happens for recoiled ions. Source: [1]. 4 Energy loss of moving particles in matter Energy loss of penetrating projectile in matter is described by a stopping power of a dense medium which is defined as an energy loss per unit path: S de/dx. In the 6

7 4. Energy loss of moving particles in matter past, stopping power for many kinds of projectile ions was determined by different experimental methods [1]. Bohr s work was the first to describe the energy loss in a media and his theory was improved with years. There are several different processes important for the stopping power of a matter (figure 5): at low kinetic energies, where projectiles are much slower than the Thomas-Fermi velocity (v 0, where v B = m/s 1 Bohr s velocity is) the nuclear interaction between ion and target nucleus is predominating (nuclear stopping power). At high non relativistic energies (v 0 v TF ), which is an ion beam analysis domain, ions loose their energy mostly by interaction with free electrons in the target (electron stopping power). v TF = v B Z 2/3 t Figure 5: At different velocities of an ion the stopping power of material is different and different processes must be considered. At ion beam analyses the energy loss of moving particles is due interactions with free electrons in target. Source: [1]. The stopping power in this region is described by the Bethe-Bloch equation [1 5] S = de dx = e 2 [ ( ) 4πr2 em e c 2 i 2me c 2 β 2 γ 2 n t ln β 2 δ ] C(v, I ), (7) β 2 I 2 Z t where r e = 1 e 2 0 4πε 0 m e c = m (8) the classical electron radius (alias Compton radius alias Thomson scattering length) is and e t n t = ρn A (9) A the atomic density of absorbing material (target), m e represents the electron mass, I the mean excitation potential (ionization energy) and for incident particle: absorbing material: z i = Z i e 0, charge, e t = Z t e 0 charge, β = v/c, velocity ratio, A t : atomic weight, γ = (1 β 2 ) 1/2, ρ: density. 7

8 5. Depth resolution By calculating the stopping power of a target usually the Bethe-Bloch equation is improved with shell (C) and density (δ) correction (equation (7)). Ion collisions with target nuclei are statistical in nature because after a large number of collisions the primary focused incident ion beam with very narrow energy and direction distribution is dispersed around the mean value due to energy loss fluctuation coming from the interaction with the atomic electron clouds (figure 6). This process of changing the ion beam energy distribution is known as the energy straggling (spreading) [1 4]. The simplest model was presented by Bohr and is based on the assumption, that energy transfers take place between ion and free electrons of the target. It predicts a Gaussian energy distribution with standard deviation σ 2 B = 4πe2 i Z tn t l (10) along the travelled path length l. Figure 6: Energy straggling of proton beam through thin Al absorber foil. In thin films the energy distribution is asymmetric because of large energy transfers. Source: [1]. 5 Depth resolution Incident projectiles collide with atoms in the target at different depths. Recoiled particles with different energies will be therefore detected. From the setup of experiment (figure 7) we can calculate [6] a relation between energies of detected particles and their original depth. 8

9 6. Example of H measurement in metal Figure 7: Recoiled particles, hit on the target surface, have the largest energies. Incident projectiles and recoiled particles looses their energy when traveling in target. From energies of detected particles their depth of collision can be calculated. Source: [6]. The incident projectile with known energy E 0 looses his energy to the place of collision at depth x. Before the collision his energy can be approximated as E(x) = E 0 x cos θ 1 S 1, (11) where S 1 is the stopping power of incident ion at mean energy E 1 = (E(x)+E 0 )/2. We know the energy of recoiled nucleus after the collision from equation (4). Energy of recoiled (detected) ion can be calculated similarly as the energy of incident projectile before the collision x E 2 = E 20 S 2 (12) cos θ 2 where S 2 is the stopping power of recoiled particle at mean energy E 2 = (E 2 +E 20 )/2. Difference between detected energy of a recoiled ion on a surface (that is the largest detected energy) and that from depth x is [ ] K 2 E = K 2 E 0 E 2 = S 1 + cos θ 2 S 2 x = Sx (13) cos θ 1 We notice, that deeper is the collision lower are the detected energies. The energy difference is an indicator of the depth at which collision took place. Energy resolution is therefore connected with the depth resolution of the method. According to (13) they are related to each other by where S represents the energy loss factor. δx = δẽ S, (14) 6 Example of H measurement in metal After we have explained the basic processes of elastic recoil detection analysis, let us examine an example of hydrogen concentration measurement by ERDA 9

10 6. Example of H measurement in metal [2, 7]. At Jožef Stefan Institute the processes in metals which involve hydrogen are recently studied. They are interested in interactions between neutral hydrogen and deuterium particles (H, D, H 2, D 2 ) with different materials, we will present the case of titanium (Ti) and tungsten (W). The main interest on research of such processes on metals is due its importance for fundamental research and practical applications. Absorbed hydrogen that remains in the metal can change his properties. Hydrogen interact with metal surfaces differently (figure 8): adsorption: hydrogen molecules tend to dissociate on metal surfaces and the resulting atoms chemically adsorb to the surface. desorption: interaction of two hydrogen atoms on the surface leads to their recombination and desorption from it as a vibrationally excited H 2 molecule. direct interaction where hydrogen atom hits the surface and interacts (immediately or during thermal accommodation) with another hydrogen atom and desorbs via H 2 molecule. Figure 8: There are several different interaction processes of H on metal surfaces. Most recent are adsorption and desorption, but the probability for direct interaction of H atom by hitting the surface with another H atom on the surface is high too. Source: [6]. For sample exposure to neutral hydrogen atmosphere a special hydrogen exposure cell was made (figure 9). It has a shape of half cylinder, where the sample is mounted on the flat side. For incoming beam and observation of recoiled particles two windows are cut on the round part of cell at angles ±15 due to the flat side. Angle of detection is ϕ = 30, with respect to the direction of incident particles. To prevent hydrogen leaking the windows are closed with 0.8µm on the incident ion beam side and 6µm thin Al foil on the recoiled particles detection side. In front of detector another 6µm thin foil is mounted for stopping the scattered incident He ions. On the other hand 12 µm foil is thin enough to let the recoiled H and D ions through with high probability. Processes were observed under controlled conditions: the 10

11 6. Example of H measurement in metal sample was heated to specific temperature and the rest of the cell was held at lower temperature with water cooling. For hydrogen molecules dissociation a thin tungsten filament (0.2 mm diameter) was mounted on the top of the cell. When needed, it was heated to a fixed high temperature (above 1200 C), where hydrogen (or deuterium) molecules are readily dissociated. Figure 9: Hydrogen exposure cell has a half cylinder shape with inner radius r = 35mm and a height of h = 50mm. The conditions in the cell are controlled, what allows us processes evolution observing with parameters changing. Source: [7]. Spectrum of ERDA is shown in form of histogram (pulse height analysis mode) [6]. Each detected particle contributed one pulse in the spectrum to a channel i where energy of particle E p is E i E p (E i + E). Intensity of spectrum is determined from concentration of target atoms at appointed depth in a sample using previously described procedure. Because the collision with light particles occur in this experiment the Rutherford cross section is a poor approximation it is better to use experimental cross sections for 7 Li 2+ on hydrogen. For collisions between lithium and deuterium there are not yet any experimental cross sections reported and we were therefore forced as our best approximation to use Rutherford s cross section. The experiment started with hydrogen H 2 concentration measurements in Ti sample placed into the background vacuum: first at room temperature and then the sample temperature was gradually raised to approximately 130 C (figure 10A). With temperature raise in a sample hydrogen concentration decrease can be seen. As mentioned before, hydrogen atoms recombine on the surface and desorb as hydrogen molecules. The peak around 700 kev is from the target surface and the tail at lower energies comes from the target bulk. It is seen that the bulk component decrease with increasing the temperature of the sample. Upon heating hydrogen is leaving the sample. The concentration profiles are presented in 10B. They were obtained from the measured spectra by a fitting procedure with layer concentrations as free parameters. Measurements on W in a background vacuum (figure 11 left) shows, that hydrogen concentration is higher on the surface and is lower, almost zero in the metal bulk. The difference in hydrogen concentration depends on the material. We must know that metals, concerning hydrogen diffusion, can be roughly divided into two 11

12 6. Example of H measurement in metal Figure 10: With temperature raise the energy spectra in Ti sample decrease, therefore H concentration decrease with T raise can be seen (figure A). If we observe the concentration of H in Ti bulk (figure B), H passing to surface with T raise is observed. Source: [7]. groups. In the first group are metals (V,Ti,Pd,... ) where hydrogen can easily enter the bulk. When such material is exposed to hydrogen the hydrogen bulk concentration becomes high. In the second group of materials (Fe,Ni,W... ) a diffusion coefficient is small and hydrogen mostly stays on the surface and this is seen in the first part of the experiment. At measurements the data is handled by SIMNRA code. That is a commonly used and powerful code for simulating backward or forward scattering and recoil spectra in IBA. It includes a large database with (corrected) Rutherford scattering cross sections for different targets and projectiles with MeV energies. A succesful SIMNRA modelling of the W spectrum is shown in figure 11. Figure 11: A sample of H measurement in W (left) is by ERDA commonly handled with SIMNRA (right). Source: [6, 7]. Experiments on W sample were made also in the presence of D 2 and D atmosphere. When examine the spectral regions of H 2, D 2 and partly dissociated D (figure 12) large differences between the concentrations are seen which depend on 12

13 6. Example of H measurement in metal the atmosphere type and the sample temperature. The peak around 800 kev is due to hydrogen at the surface and the peak around 1500 kev is due to deuterium on the surface. There is a nice separation of peaks due to considerably different kinematic factors. Figure 12: Concentration of elements depends also from the atmosphere around the target. On figure different concentrations of H and D in W can be observed due different atmosphere conditions (exposure in vacuum or in D 2 or D 2 +D atmosphere). Source: [7]. A sequence of ERDA spectra was recorded at different conditions to observe time evolution of hydrogen and deuterium concentrations in W sample. We are mainly interested in concentration of these elements in our target as a function of temperature. To the purpose a total amount of detected particles (integral of the surface signal peak) H or D was calculated at each temperature and this is presented in 13. From point a to g the W sample was only in the background vacuum and from h to n it was exposed to deuterium D 2. As seen there is just a slight increase in surface hydrogen concentration with time when sample temperature is increased. Similarly occurs in the second group of spectra: when sample was exposed to D 2 the deuterium concentration starts to increase gradually due to a constant rate deuterium adsorption on W surface. It can be seen, that with temperature rise the concentration of both elements in is rising. After these session of experiments the metal sample was exposed only to deuterium. From d2 point on the target tungsten filament was heated and sample was exposed to deuterium atoms. Upon switching on the filament the surface concentration of D was promptly increased and simultaneously a fast hydrogen concentration decrease was observed. Deuterium atoms therefore replaced hydrogen on the W surface. A subsequent deuterium decrease is attributed to further temperature rise of the sample and possibly, an absence of hydrogen on the surface. 13

14 7. Conclusion Figure 13: If the controlled conditions are with time slightly changed, we can observe due successive ERDA spectra recordings time evolution of H 2 and D 2 concentration on W surface. Here the temperature (and the exposure gas: vacuum (a-g), D 2 (h-n) and dissociated D - label d ) after each ERDA recording was changed. Source: [7]. 7 Conclusion Elastic recoil detection analysis is a powerful tool for concentration measuring of light elements in materials. In this seminar the basics of ERDA was presented and a recent example of its application was presented. The technique is relativelly simple and applicable on cyclotrons, tandem accelerators and on other ion beam producing machines. Moreover, as shown by the example, the method can be made efficient so that it allows a real time studies of processes with a characteristic times of the order of a few minutes. 14

15 REFERENCES References [1] J. Tirira, Y. Serruys, P. Trocellier, Forward Recoil Spectrometry, Application to Hydrogen Determination in Solids (Plenum Press, New York, 1996). [2] A. Razpet, Spektrometrija odrinjenih ionov z merjenjem časa preleta (doctoral thesis, 2002). [3] Ž. Šmit, Spektroskopske metode s pospešenimi ioni (DMFA, Ljubljana, 2003). [4] J. Zlatič, Analiza tankih plasti z Rutherfordovim povratnim sipanjem (2nd seminar, 2004). [5] W. R. Leo, Tehniques for nuclear and particle physics experiment (Springer-Verlag, Berlin, 1992). [6] S. Markelj, Studies of hydrogen interaction with solid by real-time ERDA (postgraduate seminar, 2006). [7] S. Markelj, I. Čadež, P. Pelicon, Z. Rupnik, Nucl. Instr. and Meth. in Phys. Res. B 259, 989 (2007). 15