POLITECNICO DI MILANO. Study of thin films and mesoporous materials by means of Positron Annihilation Spectroscopy for applied and fundamental Physics

Transcription

1 POLITECNICO DI MILANO Department of Physics Doctoral Program in Physics Study of thin films and mesoporous materials by means of Positron Annihilation Spectroscopy for applied and fundamental Physics Stefano Aghion Supervisor Prof. Rafael Ferragut Coordinator of the Research Doctorate Course Prof. Paola Taroni XXVII Doctoral Cycle

2 Contents Summary 1 1 Positron Annihilation Spectroscopy Techniques Introduction Positrons in condensed matter Backscattering Positron thermalization and diffusion The epithermal positrons Bulk annihilation Annihilation in defects Positronium in condensed matter Surface Ps formation Positronium formation in cavities Positron Spectroscopy Techniques Positron Lifetime Spectroscopy Doppler broadening spectroscopy Positron Annihilation Spectroscopy: case studies Hybrid solar cells Problem statement Samples PAS experimental results Conclusions Metal Oxide Semiconductors - IGZO Problem statement Samples

3 Contents PAS experimental results Conclusions Polymers - PMMA Problem statement Samples PAS - experimental results Conclusions The AEgIS experiment Introduction The Antiproton Decelerator (AD) Hall AEgIS scientific motivations The experiment g measurement Experimental setup Positron apparatus Achievements Antiproton catching and cooling Moiré deflectometer Positronium formation in AEgIS Mesoporous Silica for cold Ps formation Ps production in mesoporous silica Ps emission in vacuum Ps cooling Time of Fligth (TOF) Monte Carlo simulations Ps in transmission geometry Case study Future perspectives Conclusions List of publications 160 Acknowledgements 163

4 Summary This thesis consists of two parts: the first two chapters are devoted to Positron Annihilation Spectroscopy (PAS) techniques, and the studies performed at L-NESS by their means, the last two chapters are devoted to the Antimatter Experiment: gravity Interferometry Spectroscopy - AEgIS - and the design of an innovative positron/positronium converter for the AEgIS experiment. In the first chapter, the history of positron physics and its fundamental theory are introduced, the behavior of positrons and of positronium in condensed matter is illustrated, and PAS techniques are then exemplified. This leads to the second chapter, where the practical application of PAS techniques to the characterization of hybrid solar cells, of Metal Oxide Semiconductors - IGZO in particular - and of Polymers is illustrated and discussed. PAS techniques have been historically applied to the study of defects in metals, alloys and semicondutcors as well as to the measurement of free volumes in polymers. The results obtained and discussed show that PAS represents also a suitable techinque for the analysis of cavities, voids and free volumes of contemporary thin film based devices and allows disclosing new sets of information on them. The third chapter introduces the AEgIS experiment, its setup within the broader CERN context, and its scientific goal and significance. In particular, the design, construction, and operation of the apparatus are illustrated, as they were carried out by the international collaboration over the years , achieving the trapping and cooling of antiprotons in 2012 and successfully testing the moiré deflectometer with antiprotons in Within the collaboration, the main task of the Author was the setup and tuning of the AEgIS positron pulsed beam, which is illustrated in detail. The fourth and last chapter is devoted to the production of cold Positronium and to the study of its yield in transmission geometry by using mesoporous silica thin films.

5 Chapter 1 Positron Annihilation Spectroscopy Techniques 1.1 Introduction The positron (e + ) is the antiparticle of the electron. Its existence was postulated by Paul Dirac in 1928 [1] and was proven experimentally a few years later by Carl D. Anderson whilst performing experiments with the Wilson chamber (Figure 1.1) [2]. According to the Charge Parity Time (CPT) theorem 1 [3] the positron has the same mass of the electron m e + = m e = m 0, the same spin s = 1, but opposite charge 2 q e + = q e and opposite magnetic moment µ e + = µ e. When the positron interacts with the electron an annihilation event occurs and two or more γ-rays are generated. If the positron annihilates with a free electron two γ-rays are emitted according to the relation e + + e 2γ. Under the hypothesis that the center of mass of the couple e + e is at rest in respect to an inertial frame of reference, the two γ are emitted on the same line but in opposite directions, with an angle θ = π, following the momentum conservation law. The energy of a particle at rest is E = m 0 c 2, where m 0 is the rest mass of the particle and c is the velocity of light. Thus, according to the energy conservation law, the energy of each γ-ray is equal to E γ = m 0 c 2 = 511 kev (the total energy is 1 The CPT theorem states that every particle has its own antiparticle with equal spin and mass but opposite charge and magnetic moment.

6 Introduction 3 Figure 1.1: First positron track in a Wilson chamber, Source: [2]. E 2γ = 2m 0 c 2 = 1022 kev). If the electron-positron pair is considered having a momentum different from zero in respect to an inertial frame of reference, when annihilation occurs, an inertial observer sees that the two γ-rays lose the collinearity and their energy differs due to the Doppler effect. However the total energy given by the contribution of the two photons must remain equal to 1022 kev. The phenomena described above were observed for the first time in the late 1940 and represented the beginning of positron spectroscopy applied to condensed matter. In 1949, De Benedettti et al. [4] discovered that the angle between two γ-rays emitted from the same e + e annihilation event was θ = π ± α, with α an angular deviation of the order of some mrad. In the same year, DuMond, Linf and Watson detected a difference in energy in the emitted photons [5]. Since the positrons undergo a process of thermalization before annihilating inside a material and the velocity of any electron in the material is far higher than the velocity of a thermalized positron, v e >> v e +, the γ-ray annihilation bears information about the momentum distribution of the electrons. Therefore, in the middle of the XX th century, it was already clear that the detection of γ-rays emitted by positron annihilation would have led to the study of material condensate properties. At present, by means of positron annihilation techniques, it is possible to conduct the following studies in a non-destructive way: concentration and characterization of defects in semiconductors, metals and alloys;

7 Introduction 4 characterization of porosity in mesoporous materials, amorphous oxides and free volumes in polymers; production of positronium (Ps) in materials; Fermi surfaces mapping. The positronium atom The positronium atom (Ps) consists in the instable bound state of a positron and an electron. The positronium Schrödinger equation is hydrogen-like with a reduced mass equal to µ = m e + m e m e + +m e = m 0 2. Although the precise calculation of the energetic levels of the Ps atom requires the Bethe-Salpeter treatment [6], a good estimation is also obtained applying the equation of the energetic levels for the Bohr hydrogen atom: E n = µq4 e 8h 2 ɛ n = 6.8 ev, (1.1) 2 n2 where q e is the charge of the electron, h the Planck constant, ɛ 0 the vacuum dielectric constant, µ the reduced mass and n the principal quantum number. The bound energy of the fundamental state (n = 1) is E 1 = 6.8 ev. The positronium atom can be formed in two different states, corresponding to spin S = 0 or S = 1, which influence both its energetic levels and the lifetime. The singlet state (S = 0) is when the electron and the positron spin are antiparallel, and is called para-positronium (para-ps), while the triplet state (S = 1) is called ortho-positronium (ortho-ps). The mean lifetimes of the two spin states are very different: the para-ps mean lifetime is τ p P s = 125 ps and the orho-ps mean lifetime is τ o P s = 142 ns [7]. A diagram of the Ps energetic levels for the fundamental state and for the first three excited levels is shown in Figure 1.2 [7]. The angular momentum conservation law and the CP invariance lead a Ps atom, in the spin S and orbital angular momentum L state, to annihilate in n γ γ-rays according to the following rule: ( 1) nγ = ( 1) L+S. (1.2)

8 Introduction 5 Figure 1.2: Ps atom:diagram of the energetic levels of the fundamental state and of the first three excited levels. Source: [7]. The singlet ground state (L = 0), 1 1 S 0, annihilates in an even number of photons, whereas the triple ground state, 1 3 S 1, annihilates in an odd and complanar number of photons. Because the annihilation probability decreases very rapidly with the increase of the number of emitted photons, either two or three photons per annihilation are usually observed. The ratio of the production of ortho-ps and para-ps in vacuum is 3:1 (three states available for the ortho-ps and one for the para-ps: each state has the same probability). Of course, the sum of the energy of the three γ-rays emitted by an ortho-ps annihilation must be equal to 1022 kev. Thus, if the energy of one γ-ray is about 511 kev, the sum of the energy of the other two must be equal to 511 kev. Figure 1.3 (a) illustrates the energy spectrum of the γ-rays emitted by an ortho- Ps annihilation and Figure 1.3 (b) shows two spectra, normalized in peak height and measured with a Ge detector, relative to a case of 0 % Ps production and to a case of 100 % Ps production. The 100 % Ps production is achieved at nearly zero positron implantation energy on a metal or single crystal germanium surface at 1000 K (in this case, all the positrons transform into Ps [8]); the 0 % Ps production instead is obtained by implanting positrons at high energy inside metals or semiconductors. The valley in the 100 % Ps spectrum is also populated with the

9 Positrons in condensed matter 6 ortho-ps γ rays. This effect explains the difference in the two spectra and allows the measure of the ortho-ps production in a system. Figure 1.3: (a) γ-ray energy spectrum relative to the ortho-ps decay. (b) γ-ray spectrum in the case of 0 % positronium production (lower spectrum) and in the case of 100% positronium production (upper spectrum). Source: [7]. 1.2 Positrons in condensed matter This section introduces a scheme of the various phenomena involved in the interaction between positrons and matter. With the support of Figure 1.4 a brief physical description of each phenomenon is given Backscattering A fraction of the positrons implanted in a material is backscattered in vacuum without entering inside the sample. This is due to the elastic scattering of the positron with the nuclei of the material in a similar way to what happens with electrons, but here the scattering cross section is smaller [9]. The fraction of backscattered positrons depends on the positron kinetic energies, the incident angle and the atomic number Z of the atoms of the sample material. The higher the atomic number Z, the higher the fraction of backscattered positrons. Figure 1.5 shows the

10 Positrons in condensed matter 7 Figure 1.4: Scheme of the interactions between positrons and matter. (A) High energy positron backscattering. (B) Stopping, thermalization and diffusion of implanted positron. (C) Partial thermalization and emission of epithermal positron. (D) Annihilation of a delocalized positron in bulk. (E) Positron trapping inside a defect and annihilation. (F) Positronium (Ps) formation in an open volume having nanometric dimensions. (G) Ps formation in a defect connected with the vacuum and Ps escape from a pore-channel. (H) Ps formation in bulk and emission from the surface. (I) Positron backdiffusion towards the surface and positron (or Ps) emission or positron trapping in a surface state. positron backscattering probabilities, for some selected materials, as a function of the positrons incident energy [9] Positron thermalization and diffusion When a positron is implanted inside the sample it undergoes a thermalization process: the positron loses its kinetic energy through scattering events. This kind of activated stopping mechanism depends on the kinetic energy of the positron. At high kinetic energies, the Coulombian positron-electron scattering is dominant.

11 Positrons in condensed matter 8 Figure 1.5: Backscattering probabilities for positrons, as a function of the implantation energy, for: graphite, Si, Ge and Au. On the left: experimental results; on the right: Monte Carlo simulations. Source: [9]. Inside insulators, core electrons are excited by the scattering with positrons and atomic ionization can happen; inside semiconductors if the energy of the positron is high enough (higher than the semiconductor energy gap) an electron from the valence band is promoted to the conduction band creating an exciton. Inside metals the principal interaction occurs with plasmons and, independently of the material, when the positron loses most of the initial kinetic energy, the phonon scattering becomes dominant. The stopping power S p = de/dx, i.e. the energy loss as a function of the depth, is treated under the so called "continuous approximation" [10] where the slowing down of the positron is treated as continuous in time through several small scattering events. The fast positrons, regardless of the positron implantation energy, are immediately subjected to a strong deceleration: in a time t e1, of the order of a fraction of a picosecond, the positrons reach an energy of the order of 100 ev. Then, through Coulomb scattering, the positrons continue for a time t e2 the thermalization process till a threshold energy E ph (a fraction of ev) is reached; then the scattering with the material phonons becomes dominant. The time t e2, 5 t e2 83 ps, is comparable with the time t ph necessary to reach the thermal equilibrium energy 3k 2 BT (T, material temperature and k B Boltzmann constant)

12 Positrons in condensed matter 9 with the material lattice. The thermalization time, t therm, is the sum of t 1e, t 2e e t ph. According to W. Brandt [10], the estimation of t therm is given by the following formula: t therm = r 2 s 560 u 2 0c r2 s 3 ps u 2 0c T T 0, [ ( 8 u ) ( ) ] T c T 0 1 ps u 2 0c > T T 0, (1.3) where u 0c = E k /k B T 0, E k the positron kinetic energy, r s is the radius per electron fo the material (Bohr radius unit) and T 0 = 316 K. Thermalization times are, for example, 45 ps in Pb and 13 ps in Al. Note that if a positron lives inside a homogeneous material for long enough, it surely reaches the thermalization energy, since the low level states for a positron are free and the Pauli exclusion principle does not apply. Once the thermalization process ends, the positron is affected by the potential of the host material. Inside a material, the positron is described by a probability wave function, the extension of which is characterized by the de Broglie wavelength λ B = h/p, with h being Planck constant and p the positron momentum. According to the energy equipartition theorem, the kinetic energy E k of a thermalized positron is E k = 1 2 m 0v 2 = 3 2 k BT, and λ B is equal to: λ B = 61( 316 T ) 1 2 Å, (1.4) which is always bigger than the interatomic distances a, with a (3 5) Å. For temperatures around 300 K, λ B 60 Å, and the wave function fills a volume which hosts about lattice cells. For crystalline materials the lattice potential is periodic and the positron wave function is a wave packet of Bloch functions, eigenfunctions of the quantum hamiltonian. Since the positron is repulsed by the nuclei (positively charged) the density probability function has its local maxima in the interstitial spaces among the atoms. The wave packet diffuses till the annihilation event and covers a large region of the material; the diffusion process is described by the semiclassical theory of the random walk [9]. The equation that rules the diffusion is: n(z, t) t = P (z, t) + D + 2 n(z, t) 2 z kn(z, t), (1.5)

13 Positrons in condensed matter 10 where n(z, t) represents the stochastic population of the positrons at a time t and at a depth z, D + is the constant diffusion and k is the loss rate due to the absorption of positrons in potential wells or to their annihilation in the material. P (z, t) is the positron implantation profile, i.e. the positron fraction implanted with energy E and which thermalizes at a z +dz depth. The positron implantation profile follows a parameterized Makhovian distribution [11]: ( z z 0 ) m P (z, t) = d dz = mzm 1 [ ( ) m ] z, e z0 m z 0 (1.6) where m is an adimensional parameter and z 0 is a function of the positron implantation energy: z 0 = z Γ[(1/m) + 1]. (1.7) Γ is the Euler Gamma function 2 and z is the mean positron implantation depth: z = A ρ En, (1.8) where ρ is the material density. The value of A, m and n have been determined by the comparison of Monte Carlo simulations with experimental results. The value of m is 2 (Γ( 3 2 ) = 2 π ), A is equal to 40 nm g cm 3 kev 1.6 [12], while n = 1.6 [13]. Figure 1.6 shows an example of implantation profiles inside a silicon sample. From eq. (1.5) it is possible to calculate that the positron mean free path between two scattering events is given by: < l >= 3D + < ν2 > with < ν2 > = 3k BT m, (1.9) where ν is the positron thermal velocity, k B the Boltzmann constant, T the temperature and m the positron s effective mass. Note that the positron s effective mass is higher than the rest mass, m = m because of the phonon scattering and of the potential of the material. 2 Γ(n) = 0 t n 1 e t dt

14 Positrons in condensed matter 11 Figure 1.6: Makhov implantation profiles, at different positron implantation energies, inside crystal Si. Source: [14]. The mean positron diffusion length inside a material is: L + = k B τ b D + with D + = τ r T, (1.10) m where τ b = λ 1 b is the bulk mean positron lifetime while τ r is the relaxing time for the dominant scattering mechanism. For example, at room temperature the positron mean diffusion length is about 200 nm in a metal and a semiconductor (nearly defect free) and a few nanometers in amorphous materials The epithermal positrons If the positron implantation energy is lower than 1 kev, a fraction of the implanted positrons are emitted in vacuum after being partially thermalized. The positrons which follow these trajectories are called epithermal [15] Bulk annihilation Bulk annihilation is the case in which the positron stays delocalized in the bulk material and annihilates after a time characteristic of the material. The annihila-

15 Positrons in condensed matter 12 tion rate Γ is given by [16, 17]: Γ = πr0c 2 d 3 rρ + (r)ρ (r)γ(ρ (r)), (1.11) where ρ + (r) is the positron density, ρ (r) is the electron density, r 0 = 1 4πε 0 e 2 m 0 c 2 is the classical electron radius and γ(r) is a density dependent enhancement factor caused by the strong electron-positron correlation which increases the electron density of the site of the positron. For materials with high electron density the annihilation rates are higher and the positron lifetimes τ = Γ 1 are shorter. In metals, the positron lifetimes are τ 200 ps. The lifetimes in a material depend on its atomic volume unit [17] and are usually much longer in respect to the thermalization time in it, therefore the positron annihilates with a velocity v e + electron the positron annihilates with. much lower than the velocity of the Annihilation in defects The presence of a vacancy or a dislocation represents a deep potential well for a positron. The positrons are a good probe for defects since the wave function of a thermalized positron can reach up to lattice cells during the positron lifetime (this estimation is done considering a de Broglie wavelength of λ B = 60 Å, a positron mean diffusion length of 100 nm and an interatomic distance of a = 3 5 Å). The trapping rate k (see eq. (1.5)) is calculated from the Fermi golden rule [13]: k = 2π h P i Mifδ(E 2 i E f ) (1.12) i,f where P i is the occupation probability of the initial state i, M if is the matrix element of the transition from the initial state i (delocalized wave) to the final state f (localized state), and E i, E f are the energies of the initial and final states. The trapping rate can be written in a simplified form proportional to the defect concentration C: k = µc, (1.13)

16 Positronium in condensed matter 13 where µ is a coefficient related to the kind of defect which is the product of the positron thermal velocity ν and the positron trapping cross section σ (µ = νσ). When a positron is trapped, its kinetic energy is enhanced by the quantum confinement effect as well as the positron mean lifetime. This is because the trapped positron sees a lower electron density. When the bound energy is of the order of the thermal energy, positron detrapping is possible. 1.3 Positronium in condensed matter Positronium (Ps) inside homogeneous materials has been observed only in molecular or ionic insulators, like alkali solids or amorphous materials, e.g. silica SiO 2. There is no experimental evidence of the Ps formation inside metals and semiconductors. Inside metals Ps can not be formed because of the high electron density: the positron remains bounded to the electron for a too short time, of the order of the inverse of the plasma frequency ( s). Instead, with regards to semiconductors, the most accepted hypothesis [18] is that there is Ps formation but its radius, due to electric fields, is much larger than the radius of Ps formed in vacuum 2 Å. Therefore, the annihilation of the positron occurs with another electron of the material and the distinction between para-ps and ortho-ps is lost. For that reason it is not possible to measure the Ps presence inside semiconductors. In order to have an idea of how to model the Ps atom inside a crystalline insulator, the models thought for the excitons, electron-hole couples, can be used as reference [10]. As for the excitons, for Ps there exist two limit cases: a) the analogous of the Wannier exciton, a Ps characterized by a radius r (distance between e + e ) much bigger than the interatomic distances; b) the analogous of the Frenkel-Mott exciton, a Ps atom characterized by a radius r of the order of the interatomic distances. For the a) case the effective mass approximation is valid for the electron and the positron. The model, that is applied when the interaction between e + and e is weak in respect to the interaction with the crystalline potential, leads to the following conclusions: the system travels like a free atom having mass 2m e +; the internal structure is represented by a hydrogen-like wave function with radius a = a 0 ɛm e+ /µ, where a 0 is the Bohr radius, ɛ the static dielectric

17 Positronium in condensed matter 14 constant and µ the effective reduced mass. For instance, this model well describes the behavior of Ps in semiconductors, where the dielectric constant values are high. The second case is more interesting from an experimental point of view since the annihilation occurs between the positron and the electron that form the Ps atom. According to this model, the Ps atom dimension is comparable to the interatomic distances and the semiclassical approach (the effective mass approximation) is no longer valid. The model suggests that the wave function of the Ps fundamental state inside a material is represented by a sum of Ps eigenstates, with the eigenstate n=0 having the highest weighting. This model allows to calculate the Ps features within the material: for example, the response to electrical fields, magnetic fields and annihilation rates. There are mainly two Ps formation processes: 1. the Ore process; 2. the spur process. The Ore process corresponds to the reaction: e + hot + e P s hot P s th, (1.14) where e + hot and P s hot are the positron and the Ps atom not yet thermalized. The required energy E P s for the formation of hot Ps is: E P s = E + (W + E gap ) > E 0 P s = (E P s b + W P s ), (1.15) where E + is the positron energy, E gap the energy gap of the material, W the work function of the electron, EP 0 s the energy of the delocalized Ps fundamental state inside the crystal ( EP 0 s = 6.8eV + W P s, W P s Ps work function in the crystal) and Eb P s the Ps energy in vacuum (Eb P s = 6.8 ev). The Ps thermalization, through phonon scattering, is a process that can lead to the Ps dissociation when energetically allowed. The production of stable Ps occurs only if: E P s = E + (W + E gap ) < W W +, (1.16)

18 Positronium in condensed matter 15 where W + is the positron work function. Considering both eq. (1.15) and (1.16) the gap within the Ps formation is allowed can be calculated as: W + E gap (E P s b + W P s ) E + E gap W +. (1.17) The eq. (1.17) defines the Ore gap for the various materials. The second process, the spur process, involves cold positrons which can form Ps with the electrons they have previously excited toward the conduction band during the thermalization process. The reaction which describes this kind of event is: e + hot + e v e + th + e c P s th, (1.18) where e + hot is the not yet thermalized positron, e v is a valence electron, e + th is the thermalized positron which has exchanged energy with the valence electrons and e c is the conduction electron which the positron forms the Ps atom with. The probability to form Ps by means of spur, p(e), can be described using an empirical expression [19]: p(e) = p max + (p 0 p max )e 1 2 ( E E 1 ) β (1.19) where p 0 and p max represent the Ps formation probability at 50 ev and in bulk respectively, E 1 and β are two parameters that depend of the material, while E is the positron implantation energy. As discussed before, in vacuum a 3:1 ratio of ortho-ps/para-ps formation is expected. Inside a material that proportion is no longer valid. It is difficult to experimentally determine the initial ratio because there is a process, called pick-off, that transforms ortho-ps atoms in para-ps atoms. There is a pick-off event when the positron of an ortho-ps catches an electron of the material having antiparallel spin and annihilates with it, shortening the Ps lifetime, in two 511 kev γ-rays Surface Ps formation If a Ps atom is formed inside the bulk material it is possible that the Ps diffuses towards the material surface from which it can be emitted in vacuum. The Ps work

19 Positronium in condensed matter 16 function W P s is defined as: W P s = µ P s + E B 1 2 R inf (1.20) where E B is the Ps bound energy inside the material, R inf is the Ps energy in vacuum and µ P s is the chemical potential given by the sum of the electron and positron chemical potentials, µ P s = µ + + µ = W + W. The Ps is emitted in vacuum only if the Ps work function is less than zero. The work function W P s can be seen as the energy necessary to separate the positron from the electron inside the material (E B ) plus the energy required to remove both the positron and the electron (µ P s ), subtracted from the energy gained in the Ps formation in vacuum. If there is no Ps bulk formation it is however possible that a thermalized positron, Figure 1.7: Monodimensional potential for a thermalized positron nearby a metallic surface. Source: [7]. emitted from the surface material, can acquire a surface electron and form positronium. Figure 1.7 reports, as an example, a schematic representation of the positron interaction with a metal surface [7]. It is shown that the electron density forms a dipole layer which acts as a potential barrier for the electrons. The electron work function is thus enhanced (W > 0) but the positron work function is decreased

20 Positronium in condensed matter 17 (W + < 0). The dipole layer leads the positron outside the material that can catch an electron and form positronium. In general, the positronium bound energy (6.8 ev) is higher than the energy required to take the electron (W ). Figure 1.7 also shows the presence of a potential well for positrons at the metal surface. That potential well for great distances, is due to the forces associated with the positron charge image, while for short distances it is due to the correlation energy with the electron gas at low density Positronium formation in cavities Positronium can be formed inside cavities in materials with nanometric dimensions. Polymers and amorphous materials have free-volumes, or cavities, where Ps can be formed. There exists a class of materials, defined as mesoporous, for which the cavity dimension ranges from the nanometer to hundreds of nanometers. Mesoporous materials are crystalline or amorphous; their internal structure is characterized by pores which can allow the reversible passage of molecules of a dimension that can be compared to that of the pores. From the point of view of Ps formation and study, SiO 2 mesoporous material like Aerogel and MCM-41 are very interesting since the Ps formation inside such materials can be up to % and when the pores are interconnected Ps yield in vacuum is allowed. The Ps in SiO 2 is mostly formed in bulk (conversion yield 72% [20]) and both the Ore and spur process contribute to its formation. A minor contribution to the Ps formation comes from a Ps surface process (conversion yield 12% [20]). The study of such materials is presented in chapter IV of the present thesis.

21 Positron Spectroscopy Techniques Positron Spectroscopy Techniques This section describes the two positron annihilation spectroscopy techniques present at VEPAS laboratory (Variable Energy Positron Annihilation Spectroscopy) in Como [21]: the Positron Annihilation Lifetime Spectroscopy (PALS) and the Positron Annihilation doppler broadening Spectroscopy (PAS) Positron Lifetime Spectroscopy Positron lifetime spectroscopy is a technique mainly used in the study of internal defects of metal alloys and semiconductors. The lifetime of a positron which enters into a perfect crystalline material is described by Poisson s probability distribution. Average lifetime differs according to the material and is proportional to its electronic density. In the presence of defects, such as vacancies or cavities, the temporal spectrum is the result of a superposition of exponentials decreasing over time, characterized by different intensity and different average lifetimes. The presence of various components is due to the fact that positrons annihilating in cavities or defects interact with a lower electronic density compared with the electronic density of bulks, therefore they tend to annihilate over longer periods of time. The duration of the average lifetime is related to the nature of the defect (the more space, the longer the lifetime) and the intensity is related to spatial concentration of defects. Besides the analysis of defect, PALS is used in the morphological study of pores in mesoporous materials and voids in polymers. The lifetime spectrum of a mesoporous material shows a long component, due to the formation of ortho-ps (in the order of s for mesporous materials while 10 9 s for polymers) the analysis of which allows to estimate the average dimension of the pores or voids [22]. Experimental setup Figure 1.8 shows a scheme of the set-up of a lifetime spectrometer for bulk measurements. The nuclear decay in the radioactive source ( 22 Na) creates the positron implanted in the material under study and produces, almost instantaneously, a MeV gamma ray. The positron source is placed in between two identical

22 Positron Spectroscopy Techniques 19 Figure 1.8: Scheme of the Lifetime Experimental set-up in fast-fast coincidence. Source: [23]. samples in the so called sandwich configuration. Gamma radiation is detected by means of two scintillators, one dedicated to the start signal and the second to the stop signal (in the fast-fast scheme). The start signal is a MeV gamma ray, while the stop is one of the annihilation gamma rays coming from the implanted positrons. Scintillators are coupled with photomultipliers which produce a current signal fed to two constant fraction discriminators (CFD). Discriminators signal the arrival of current pulses by generating fast logic signals fed to a time to amplitude converter (TAC). The stop signal is delayed by some ns in order to avoid non linearities in the TAC at low time intervals. The amplitude of the TAC output signal is proportional to the time interval elapsed between the arrival of the start and the stop signals (if we neglect the additional time delay). An analog to digital converter (ADC), coupled with a multi channel analyzer (MCA) is used to store the time information in a digital form. Positron source Positrons are generated through the use of a radioactive source, the sodium isotope 22 Na. Its half-life is 2.6 years and it decays in 22 Ne, generating a positron, a γ photon and a neutrino, with the probability of an electronic capture event, as shown in Figure 1.9. The emission of positrons from a radioactive sodium source has a wide energy spectrum, from 0 to 542 kev, as shown on the upper part of Figure 1.9. Since each energy corresponds to a different average implantation

23 Positron Spectroscopy Techniques 20 Figure 1.9: Above left: positron emission spectrum of a 22 Na. The rectangle centered at 3 ev represents the positron energy distribution after a process of moderation by means of W foil. Above right: scheme of a lifetime sandwich configuration. Below: radioactive decay scheme for a 22 Na source. Source: [14]. depth of the positron in the material, that is, of the depth at which the positron thermalizes and starts moving in diffusive motion, sources without any kind of moderation are used only to study bulk properties of homogeneous materials. The implantation profile depends on the material density, but generally the average implantation depth obtained is in the order of µm. In a lifetime experiment, 22 Na is supplied in the form of an aqueous solution of sodium chloride (NaCl). A drop of the solution is deposited and dried between two thin (7.5 µm) foils of kapton, a polyammide film with high performances in terms of mechanic and thermal resistance. The source, thus prepared, is placed in contact with the material in a configuration called sandwich, as shown in Figure 1.9, and placed in a vacuum chamber.

24 Positron Spectroscopy Techniques 21 The detection of start and stop signals The physical phenomenon that needs to be detected is the start signal, and consequently the stop signal, which accompanies the production and the annihilation of a positron. These two signals are, respectively, the γ quantum at MeV, almost contemporary to the β + decay of the 22 Na source, and quantum γ of 511 kev, contemporary to the annihilation of the positron (if the event observed is the annihilation of ortho-ps, the stop γ is a distribution between zero and 511 kev energy). The first element of the measurement process is a couple of scintillators, each combined with a photomultiplier (Figure 1.10). Figure 1.10: Scintillator-photomultiplier coupling. Source: [24]. A scintillator is a crystal that, by receiving γ photons, produces a radiation in the visible or ultraviolet range through fluorescence processes. When the γ radiation penetrates into a scintillator, three phenomena can take place: 1. Photoelectric absorption by core electrons [25]. The energy of the excited electron, equal to E = hν E b, where hν is the energy of the incident photon and E b is the bound energy of the electron, is entirely transmitted to other electrons by the material, through radioactive and non-radioactive relaxation mechanisms. The probability of a photoelectric absorption phenomenon is proportional to the Z atomic number of the material, according to a potential law between 4 and 5. This kind of process is typical of inorganic scintillators, while it is absent in plastic ones. 2. Compton scattering. The photon elastically collides with an electron of the

25 Positron Spectroscopy Techniques 22 material. The energy of the hν photon after the collision is equal to [26]: hν = hν 1 + hν m 0 (1 cos(θ)), (1.21) c 2 with θ, 0 θ 180, scattering angle, hν the energy of the photon before the collision and m 0 c 2 the energy of the photon at rest. By observing the eq. (1.21) one can easily obtain the maximum energy transferrable to the electron by Compton effect and therefore to the scintillator, since the probability of a second collision is generally very low. By defining α = hν/m 0 c 2, the maximum transfer energy is: Emax e α(1 cos(θ)) = hν 1 + α(1 cos(θ)), (1.22) this energy defines the so-called Compton edge (see Figure 1.11). 3. Production of electron-photon couples. This process is rather unlikely since it requires photons with an energy equal to or over 1022 kev. The ideal scintillator should have the following characteristics: 1. it should convert the kinetic energy of charged particles into detectable light with a high conversion efficiency; 2. conversion should be linear; 3. the decay time of the induced luminescence should be short, in order to avoid signal superposition; 4. the refraction index of the material should be close to that of glass ( 1.5) to allow the efficient combination of the scintillator with the photomultiplier (which converts the light signal into an electric signal). Scintillators used at L-NESS consists of two types: the inorganic scintillator BaF 2, for the stop signal, and the organic (plastic) scintillator PILOT U, for the start signal. Inorganic scintillators tend to have the best light output and linear response but are also rather slow in terms of time response; however organic scintillators are generally faster, but produce less light [25].

26 Positron Spectroscopy Techniques 23 The crystal BaF 2 is a good scintillator since, besides the mentioned properties of inorganic scintillators guaranteed by a high density (4.88 g/cm 3 ) and by the high Z atomic number of barium (56), it also has a good response in terms of time; that is because it has a strong population of an optic level with a fast decay component [25]. However, due to the high atomic number, there is a high probability that, in a 180 disposition such as in Figure 1.9, a backscattering event will take place, that is, that photons enter in the scintillator in back-diffusion from above. Since the configuration at 180 has been maintained, in order to have the maximum count number (maximum coverage of the solid angle), to avoid the backscattering event probability an organic and an inorganic scintillator have been combined. An organic scintillator, such as PILOT U, is less prone to diffuse γ rays, compared with BaF 2. At the same time, the choice of BaF 2 as the stop signal detector is due to its high efficiency to detect the 511 kev gamma rays (because of the presence of a photo-peak associated with photoelectric absorption ). The light impulse reaches the photocathode -a semitransparent glass layer Sb-K- Cs- of the photomultiplier. The photomultiplier consists of a photocathode able to emit electrons thanks to the photoelectric effect and an amplification system made of a series of dynodes. The dynodes, which emit secondary electrons by impact, are placed at increasing potential differences, in order to keep the electrons accelerated until they reach the anode (tension difference between anode and cathode V= V). The essential parameters that describe the properties of a photomultiplier are: 1. the quantum efficiency of the photocathode; 2. the efficiency of photoelectron gathering at the entrance of the amplification zone; 3. the time spread, that is, the dependence of the transit time on the initial emission energy and direction of photoelectrons; 4. the time variation, that is, the dependence of the transit time on the point of the photocathode where primary electrons are emitted. The anodic signal is temporally well defined, which means it indicates well the moment of the arrival of the radiation, while it is not well defined in terms of

27 Positron Spectroscopy Techniques 24 energy, as it shows a less precise correspondence between the area below the peak, and the charge initially deposited in the scintillator by the incident radiation. For this reason, it can be usefully employed to determine the moment of detection of γ, but not its energy. Calibration of a lifetime spectrometer Before performing a lifetime measurement, it is necessary to accurately perform the following operations: 1. set the window for the start and stop signals coming from the photomultiplier; 2. determine the resolution of the instrument and of the time-channel conversion. The setting of a window for the start and stop signals is an operation of primary importance for the success of the experiment. On the accuracy of this setting depends the resolution of the instrument and the number of counts per second, which determines the duration of the measurement. The last two characteristics are in competition one against the other because on the one hand, a fine filtering of the energies, in order to increase resolution, may result in a low number of counts. On the other hand, an excessive opening of the windows may determine distortions in the measured spectrum, due to detection errors. The main detection error situations are [27]: 1. a gamma at 511 kev is signaled at the star or a gamma at 1274 kev is signaled at the stop; 2. a start gamma detected in the corresponding scintillator is deflected to the other scintillator and detected again; 3. as in number 2, but with a stop gamma. Errors 2 and 3, which involve the backscattering phenomenon, can be limited by choosing a plastic scintillator in the measurement chain; error number 1, instead, depends solely on a poor window.

28 Positron Spectroscopy Techniques 25 From a functional point of view, to select the desired energy interval, a photomultiplier dynode signal (more sensitive to the photon energy than the anode signal) is adequately pre-amplified and then sent to an oscilloscope. Therefore, the tension signal from the oscilloscope will be proportional to the energy of the incident photon on the scintillator. The anodic signal must be placed in coincidence with the logic impulse coming from the constant fraction (CF), in turn connected with the exit of the anode of the same photomultiplier. Indeed, the role of the CF is to produce a logic signal when it receives an incoming signal with a width falling within the interval predetermined by the user. By the observation of signals placed in coincidence in the oscilloscope, it is possible to tune the tension interval within which to accept the signal. The criteria used to choose the broadness of the energy windows depend on the choice of the type of scintillators. In our case the start we use a plastic scintillator, and for the stop a BaF 2 crystal, the lower threshold of the start at about 65% of the value of the energy of the Compton edge of the photon at MeV, and for the stop we center the peak at 511 kev. If interested in detecting ortho-positronium, it will be necessary to decrease the lower threshold of the stop to the Compton edge at 511 kev, in order to detect the distribution of 3γ-rays. Figure 1.11 shows the spectra measured with the two detectors from a source of 22 Na. Note that, due to the properties discussed above, the Pilot U scintillator does not allow to observe the 511 kev and 1274 kev peaks.

29 Positron Spectroscopy Techniques Backscattering distribution Compton edge 511 kev Counts 1000 Compton edge 1274 kev Energy (kev) kev 511 kev peak Compton edge 1274 kev peak Compton edge Counts kev Energy (kev) Figure 1.11: Above: Energy spectrum of the emitted photons by a 22 Na source measured by BaF 2 scintilator (stop signal). Below: Energy spectrum of the emitted photons by a 22 Na source measured by plastic Pilot U (start signal). The areas correspond to the energy windows.

30 Positron Spectroscopy Techniques 27 Resolution For correct data analysis it is essential to determine the resolution of the instrument and the conversion of the channel-time. Resolution can be obtained from the study of the response of the system to the impulse. In lifetime terms, an impulse is time lapsing between two γ photons, when this time is much less than the spectrometer resolution. The response to the impulse is general, for a PALS system, a sum of Gaussians. For a lifetime systems, the main mechanisms that tend to increase resolution are [27]: 1. oscillations of the decay times of the optic status of the scintillator; 2. variations in the time interval between the light emission in the scintillator and the detection at the photocathode; 3. efficiency in the photon-electron conversion process at the photocathode and absolute number of primary electrons emitted; 4. oscillation of the transit time of electrons through the photomultiplier and variations in the process of multiplication; 5. method of treatment of the impulse coming out from the photomultiplier. To estimate the instrumental resolution a source of 60 Co is used. 60 Co decays to 60 Ni according to the following relation: 60 Co 60 Ni + β + ν e. (1.23) Consequently, the isometric status 60 Ni decays in the stable status 60 Ni with the emission of two photons γ with an energy of 1173 kev and 1332 kev, separated by an interval of about 2 ps, according to the relation: 60 Ni 60 Ni + 2γ. (1.24) Using this methodology with the windows previously prepared with a 22 Na source, it is possible to measure two signals by the emission of a 1173 kev photon (within the starts window) and a 1332 kev photon degraded after a Compton effect (within the stop window). The time difference between this pulses is about 2 ps and the

31 Positron Spectroscopy Techniques 28 prompt curve appears centered in the t 0 channel. With our measurement system it is possible to obtain resolutions in the range of ps. Figure 1.12 shows a peak due to the source of 60 Co interpolated with a Gaussian curve Co Gaussian fit Counts ps FWHM Time (ns) Equation = Adj. R-square 0.99 ( ) 2 Value Standard error A [ ] [ ] Figure 1.12: Above: Peak from 60 Co interpolated with a gaussian function. Below: Table with the fitting results.

32 Positron Spectroscopy Techniques 29 Data analysis The analysis of the spectrum is performed thanks to specific software suites, such as PATFIT-88 [28], which includes the program POSITRON-FIT. PATFIT-88 is used to determine the characteristics of the resolution curve of the instrument, to be used in the next phase of spectrum analysis performed with POSITRONFIT. When observing a couple of essentially simultaneous events, such as the emission of the two photons in the decay of 60 Co, the measurement system, due to the effects mentioned in the preceding section, does not produce a Dirac δ, but a sum of Gaussian curves. The model used by POSITRONFIT is the sum of exponential decays (each one associated to different states of the positron) convoluted with the resolution function of the lifetime spectrometer, added to the constant background 3. We will assume k 0 the number of components, a j the decay function for the j-th component, R the resolution function and B the background. The spectrum has this form: k 0 f(t) = (a j R)(t) + B, (1.25) j=1 where A j e t/τ j, t > 0, a j = 0, t < 0. (1.26) In eq. (1.26) τ j is the average lifetime of the j-th component and A j = I j τ j is a pre-exponential factor and I j is the lifetime intensity of the j component. The R resolution function, sum of the Gaussian k p, has this form: R(t) = k g p=1 w p 2πσp exp ( (t t 0 t p ) 2 2σ 2 p ), (1.27) 3 It is presented in chapter 3 a polymer (PMMA) PALS study for which LT [29, 30] program has been used. As it is described in sec the main difference between LT and POSITRONFIT program is that LT allows an analysis of a continuous distribution of lifetime components instead of a discrete distribution.

33 Positron Spectroscopy Techniques 30 where t 0 corresponds to the zero time channel, t p a displacement, and σ p is the standard deviation of the Gaussian curve. If, like in our case, the resolution curve consists in a single one Gaussian curve, its observation will allow to derive both the values of σ and of t 0 + T 1, which indeed will correspond to the maximum channel of the resolution function, while the standard deviation is correlated to the width at mid height of the curve, through: F W HM = 2(2ln2) 1/2 σ. (1.28) The software estimates the time constants τ j and the component A j of each of the j components and thus the intensities I j. They are determined by using the minimum square criteria. That is, by trying to minimize the expression: φ = n w i y i f i (b) 2, (1.29) i=1 where b is the vector of the parameters, f i (b) is the approximation value of the i-th channel, and w i is the reciprocal of the variance (relative to the error distribution, σ 2 i = 1/w i ). The program requires the input of the number of lives necessary for analysis and produces as an output the lifetimes and intensities inferred. The statistical accuracy of the result is measured through the significance of the imperfect model (χ 2 divided by the number of freedom degrees, that is minimum φ calculated on the total number of points, minus the number of free parameters) Doppler broadening spectroscopy The Doppler broadening spectroscopy technique is based on the detection of the momentum of the annihilation of the electron-positron couple, and allows the study of the electronic structure of a solid body and the nature of its defects. A measurement of this kind can be performed with the same source or, as in our case, with a beam of slow positrons. The slow positrons beam allows to obtain a Doppler spectrum with different depths and perform a study in function of the implantation profile of the positrons inside the examined sample. A second application of this technique is the study of the production of positronium, which is a good probe for cavities and voids, in materials.

34 Positron Spectroscopy Techniques 31 Physics principle Figure 1.13: Momentum scheme of an annihilation event. In an annihilation event within a material where a positron is implanted the energy of each of the photons emitted is about 511 kev and the Doppler shifts are due to the kinetic energy of the electron, since the kinetic energy of a thermalized positron is negligible. Figure 1.13 shows a schematic representation of an annihilation event. p 1 and p 2 are the γ-ray momenta and p is the electron momentum. The total energy E of the two gamma is (the kinetic energy of annihilating particles is neglected): E 2m 0 c 2 = cp 1 + cp 2 = E 1 + E 2, (1.30) where m 0 is the electron rest mass. The quantity of motion is preserved, therefore, according to Figure 1.13: p cos(φ) = p 1 p 2 cos(θ), (1.31) p sin(φ) = p 2 sin(θ). (1.32) Considering only the longitudinal momentum in respect to the two revelators placed 180 one in respect to the other along the longitudinal direction, and being θ very small, some milli-radiant (sin θ θ), the motion conservation law becomes: pcos(φ) = p 1 p 2 = p L, (1.33) where p L is the quantity of the motion of the electron in the longitudinal direction.

35 Positron Spectroscopy Techniques 32 As a consequence the energies of the photons are given by: E 1 E 2 m 0 c 2 + p Lc 2 (1.34) m 0 c 2 p Lc 2 (1.35) and the Doppler shift for each photon: E = 1 2 m 0vc = c 2 p L (1.36) The energy difference between the two γ, which bears information on the distribution of the momenta of the material s electrons, can be measured with solid state detectors very precise in respect to energy; indeed, strict conditions are required on resolution, which must be in the kev order. The 511 kev peak is, therefore, broadened and bears information on the distribution of the momenta of electrons in correspondence with the annihilation site. Experimental setup Figure 1.14: Positron Doppler Broadening experimental setup. Source: [31]. The energy broadening described in the preceding section is measured with the detection system described in Figure High efficiency ultrapure germanium crystals are used (about 50%), cooled with liquid nitrogen. The signal coming from the crystal, proportional to the energy of the detected photon, is preamplified and then memorized in a multichannel analyzer (MCA). Background noise can be drastically reduced by using the Doppler broadening technique in coincidence, able to detect both the light quanta emitted. A second setup which allows to perform a more precise analysis is shown in Figure This technique is

36 Positron Spectroscopy Techniques 33 particularly important in the measurement of the high momentum part, starting from 9 kev from the center of the spectrum [14]. The measurement of the high part with high momentum is important because it refers to core electrons, typical of the atomic species. Figure 1.15: Coincidence positron Doppler Broadening experimental setup. Source: [31]. The experimental setup for this technique is shown in Figure It must be noted that the possibility to work in coincidence is guaranteed by the nearly co-linearity of the emission. This technique offers two main advantages: 1. the improvement of a factor equal to 2 of the resolution [32]; 2. the reduction by at least two orders of magnitude of the background noise, obtaining a relation peak/background of about The mono-dimensional momentum spectrum shown in Figure 1.16 has been obtained by adding up the counts of the bi-dimensional spectrum S(E 1, E 2 ) shown in Figure 1.16 along the line p x = E 1 E 2 c within the interval 1022 kev E < E 1 + E 2 < 1022 kev+ E, where E = 21 kev. The momentum resolution is evaluated starting from the mono-dimensional energy spectrum free from the Doppler effect, obtained by adding S(E 1, E 2 ) along the lines E 1 +E 2 = constant.

37 Positron Spectroscopy Techniques 34 Figure 1.16: Doppler measurement performed in coincidence mode with two detectors. Above: counts matrix; Below: measured spectrum (down) obtained summing the counts of both the detectors along the second diagonal of the count matrix.

38 Positron Spectroscopy Techniques 35 Positron beam The positron beam at the Positron Lab Facility (VEPAS) at L-NESS allows the tuning of the implantation energy of positrons between 0.1 and 17 kev. The positrons used in the beam are produced by a 22 Na radioactive source and filtered by a moderator. The role of the moderator is to decelerate the high energetic positrons emitted by the source, so that they can be accelerated in a controlled way by an electronic optic. The moderator is a pure crystalline foil, of a material which has a negative work function for positrons: it absorbs positrons from the source and reemits a small percentage of them at a predetermined energy. The moderator consists of a crystalline tungsten foil, with a diameter of about 1 cm and a thickness of 1 µm, able to emit positrons perpendicularly to its own surface, with an energy equal to 3 ev (see Figure 1.9). The exact determination of this energy is totally negligible, since the positrons being accelerated have energies in the order of 1 kev. Since the efficiency depends on the purity of the crystal, it is necessary to perform periodically an annealing procedure in vacuum, lasting a couple of hours, to reach for two minutes the temperature of 2000 K, between two ramps of ascent and descent. This way, surface impurities are removed and the monocrystalline structure, damaged by the impact with positrons, is restored. At the Positrons Lab Facility, we have recently performed the annealing of a moderator, obtaining a positron production 10 times greater [33]. With regard to Figure 1.17, the beam consists of two perpendicular tracks, where electrostatic tubular lenses have been placed at specifically determined potentials. The electrostatic tubular lenses consist of a series of electrodes placed at different potentials. There are two tubes lenses, consisting of two electrodes with diameter D, far one from the other by one tenth of D, and three tubes lenses, which can be symmetrical or asymmetrical according to the potentials applied to the first and third electrode (if the potentials are the same, the lenses are symmetrical). The positrons emitted by the moderator are initially gathered through a series of electrodes, optimized in order to bring to the first anode the highest number of positrons, according to the modified design of a Soa gun [14]. The first track has to accelerate the beam and make it parallel. Figure 1.17 shows that next to the fifth electrostatic lens there is a deflection unity (bender), similar to an analyzer

39 Positron Spectroscopy Techniques 36 Figure 1.17: Design of the electrostatic optic of the VEPAS slow positron beam. with parallel flat faces [34], which bends the beam by 90. This curve is necessary to avoid that the sample comes directly into contact with the positrons and γ rays emitted by the source. After the bending, there are three lenses. The first lens refocuses the beam, the second lens accelerates and finalizes the beam, and the third, consisting of three electrodes, focuses the beam on the sample. The final kinetic energy of positrons is the potential difference between the sample and the moderator. Between the moderator and the last electrode, there has to be a potential difference of at least 1000 V, to obtain a sufficient track efficiency. To obtain implantation energies between 1 kev and 17 kev, the tension of the whole apparatus must be increased until the eighth tube. To obtain a potential difference inferior to 1 kev, a tension of the sample between 0 and 900 V is required. Germanium detectors For the detection of γ rays, we use two high purity germanium detectors (HPGe), with an impurity concentration of about atoms/cm 3 cooled with liquid ni-

40 Positron Spectroscopy Techniques 37 trogen. Intrinsic germanium at low temperatures has an empty conduction band, and therefore offers a high resistance. When a γ photon is absorbed by germanium, it induces an inter-band transaction of a number of electrons proportional to the energy of the photon. Excited electrons are carried and stored thanks to a potential, in the order of kiloelectronvolts, applied to the germanium heads. The main characteristic of the germanium detectors is their excellent energy resolution when used in gamma rays spectroscopy. The width of a peak at half height is in average 1.7 kev that is reduced to 1.3 kev for the 511 kev peak [25]. Figure 1.18 shows a spectrum, comparing the image obtained with a NaI(T1) scintillator and the one obtained with a germanium detector. The difference in energy resolution is remarkable [25]. Figure 1.18: Comparison between the detection of a 108 Ag and 110 Ag spectra obtained with a NaI scintillator and Ge HPe detector. Source: [25].

41 Positron Spectroscopy Techniques 38 Analysis and interpretation of data In order to evaluate the form of the annihilation peak, we introduce two parameters, S and W. The S parameter, in reference to Figure 1.19, is defined as the relation between counts registered in the central zone of the peak and the total counts of the peak, while the W parameter is the relation between the sum of the counts in the two lateral regions of the peak and the total counts of the peak. The Figure 1.19: 511 kev positron annihilation peak. energy interval we chose for the S parameter in our lab is E 511 kev< 0.85 kev, while for the W parameter 2.75 kev < E 511 kev< 4 kev (Figure 1.19). The S parameter is sensitive to the low momentum electronic distribution (valence or conduction band electrons) and to the annihilation of para-ps annihilation while the W parameter is sensitive to high momentum electronic distribution (core electrons). Let us observe that a positron in a vacancy, for example, will tend to bond more easily to a valence electron, and will therefore contribute to the increase of the peak (the peak is normailzed in area). Once the energy of the beam is fixed, the positron will be implanted according to a Makhovian profile, to be then diffused according to the eq. (1.5). The S parameter can be expressed as the result of the following linear combination: S n (E) = f surf (E)S surf + f bulk (E)S bulk + i f def i (E)S def i (1.37)

42 Positron Spectroscopy Techniques 39 where f surf, f bulk, f def i represent the probabilities for annihilations in the surface, in the bulk and in defects; S surf, S bulk, S def i instead are the values of the S parameters typical of the annihilation site. The equations are: [ ] dn(z, E f surf = D + (1.38) dz z=0 f defi = ν i C(z) ν i n(z, E)dz (1.39) 0 f bulk = λ b n(z, E)dz (1.40) 0 where λ b is the annihilation rate in the bulk, D + is the annihilation coefficient of the positron, C(z) ν i is the concentration of type i defects, and ν i is the trapping coefficient. Also, the normalization condition must be met: f sur + i f def i (E) + f bulk (E) = 1 (1.41) Physic information coming from the calculation of the S(E) parameter are obtained thanks to fit programs which work with experimental values of the S parameter at different implantation energies. VEPFIT [15] is the most used program, based on the numeric resolution of the stationary diffusion equation, it allows to detect the presence of layers having different characteristics (different material, different porous structure, etc.), allowing, therefore, to obtain information on their boundaries and on the diffusion length of the L + positron inside them. Further information can be obtained by creating the graphic rendering of the S W couples. Each of these two parameters could contain information independent from the information contained in the other. In this instance, each state is completely characterized by a specific couple (S, W ). If we consider the positron having a certain number of possible annihilation channels inside a material, each characterized by a probability, f i, the measured value of S will come from: S = i f is i i f i (1.42)

43 Positron Spectroscopy Techniques 40 and similarly: W = i f iw i i f i (1.43) where S i and W i represent the values of W and S in the various channels. When in a material there are only two distinct annihilation processes, characterized by the couples S 1, W 1, and S 2, W 2, this kind of representation causes some rectilinear paths where extreme point are representative of the two states. Ortho positronium detection By using the instruments described in the preceding section, it is possible to detect the production of ortho-ps through a method called method of the 3-γ [35]. As stated in the preceding chapter (Figure 1.3(a)) ortho positronium annihilates in 3-γ. Figure 1.20 shows two areas: A v, the valley area where the γ coming from the annihilation of ortho-ps are accumulated and A p, the peak area of the para-ps annihilations and of a fraction of ortho-ps annihilation (usualy one of the three ortho-ps γ rays has an energy near to 511 kev). The measure of the peak area is: Figure 1.20: Annihilation spectrum in which are shown the valley and peak regions used for the definition of the F 3γ fraction. P = P 0 + F 3γ (P 1 P 0 ), (1.44)

44 Positron Spectroscopy Techniques 41 where P 0 and P 1 are the area of the peak when respectively the 0% and 100% of positronium is formed, and F 3γ the fraction of positronium formed. Similarly, in the valley: V = V 0 + F 3γ (V 1 V 0 ). (1.45) Defining R the relationship valley-peak, R = V/P, the F 3γ positronium fraction is: F 3γ = [ 1 + P ] 1 1 R 1 R. (1.46) P 0 R R 0 A Ge single crystal (100) or a metal may be used to calibrate Ps production in the vacuum, since they can yield 0% and 100% of Ps. In particular, R 1 is obtained by extrapolation at zero implantation energy of the R(E) curve, measured in the sample at 1000 K (all the positrons transform into Positronium); R 0 is the R(E) value at the highest positron implantation energy (no Positronium is produced) [36]. The fraction F 3γ obtained takes into account both the annihilation of ortho- Ps and of para-ps and is the parameter we have taken into account for all the experimental results presented in this thesis. In order to measure only the ortho-ps fraction a PALS measurement is needed too for the measure of the pick-off phenomenon. The pick-off phenomenon reduces the probability of annihilation in 3-γ by a factor equal to: ɛ = λ 3γ λ 3γ + λ p.o. (1.47) where λ 3γ is the annihilation rate of ortho-ps in void, and λ p.o. is the rate of pickoff annihilation. Therefore, the expression for the measure of the ortho-ps fraction becomes: F (E) = ɛ F 3γ(E). (1.48)

45 Chapter 2 Positron Annihilation Spectroscopy: case studies. 2.1 Hybrid solar cells The development of clean power generation methods based on solar energy conversion is of pivotal importance to guarantee a sustainable economic growth. In particular, those recent technologies which promise low costs and a high level of daily life integration have become extremely appealing. Among the photovoltaic systems developed with this intent, hybrid solar cells are emerging, where nanostructured metal oxide scaffolds are interfaced to conjugated polymers. They could in principle combine the success of dye-sensitised solar cells (DSC) with that of fully organic solar cells. A conjugated polymer behaves both as a light antenna system and as a hole transporting layer while electrons are injected in the high mobility metal oxide, thus reducing the complexity of the DSC in a solid state device. As a consequence, the technological impact of these devices may prove to be highly significant. This possible outcome combined with the fact that hybrid solar cells had never been the object of Positron Annihilation Spectroscopy (PAS) analyses before, led us to apply positron spectroscopy techniques to a particular type of hybrid cells.

46 Hybrid solar cells 43 In cooperation with the Istituto Italiano di Tecnologia (IIT), which has designed, produced and electrically characterized the devices, hybrid solar cells consisting in a mesoporous titanium dioxide structure filled with a photoactive polymer were analysed. The purpose of these PAS analyses has been the study of the interaction between oxide and polymer in function of the depth of the device Problem statement Figure 2.1: TiO 2 /P3HT hybrid solar cell scheme. The scheme of a complete prototype of hybrid solar cell is represented in Figure 2.1 [37]. The polymer hole transporter, poly(3-hexylthiophene-2.5-diyl) (P3HT), is infiltrated by spin coating inside a mesoporous titanium dioxide (TiO 2 ) scaffold covered with a monolayer of 4-mercaptopyridine (4-MP). A P3HT capping layer is formed on the top of the mesoporous structure and put in contact with an Ag cathode. On the opposite side of the cell, the compact TiO 2 is in contact with a conductive transparent glass, a fluorine doped tin oxide (FTO) coated glass substrate, that works as anode. The working mechanisms of excitonic solar cells are strongly dominated by interface processes as well as by the degree of polymer infiltration inside the device, which influence the final device efficiency. The current-voltage curves for devices tested under AM 1.5 (AM= air mass 1 ) con- 1 The air mass coefficient defines the optical path of the solar rays that reach the ground through

47 Hybrid solar cells 44 Figure 2.2: Current density-voltage (J,V) characteristics of the TiO 2 /P3HT, TiO 2 /4-MP/P3HT pristine and annealed devices under illumination with simulated solar light. Source: [37]. ditions are shown in Figure 2.2. The TiO 2 /P3HT device shows state-of the-art figures of merit and a power conversion efficiency (η) of about 0.4 % but, when the molecular interlayer is added, the photocurrent (J sc ) is doubled and the open circuit voltage (V oc ) is enhanced [37]. In the best case, the photocurrent is pushed from 1.4 ma cm 2 to 3.26 ma/cm 2, together with an enhancement of the V oc from 0.51 to 0.62 V, bringing the power conversion efficiency from 0.37 % to 0.95 %. Further improvement is observed upon annealing, with an increase in the shortcircuit photocurrent to 3.75 ma/cm 2 and a rise of the efficiency to 1.13 % (see Table 2.1 for a summary of the devices figures of merit). The reason for the improvement, i.e. the role of the 4-MP interlayer effect, was investigated with PAS. In the next sections I will show that PAS results contributed to demonstrate that a suitable chemical structure of the interlayer molecule induces selective intermolecular interactions and, therefore, a preferential surface energetic landscape and morphological order at the interface [37]. These phenomena consequently drive a strong improvement in charge generation and a decrease in recombination losses. the atmosphere. It is expressed as the ratio between the optical path at a given solar position and the optical path when the solar is in the zenith position. [38]

48 Hybrid solar cells 45 Table 2.1: Summary of device parameters of TiO 2 /P3HT with and without the 4-MP interlayer and after annealing treatment. The values reported refer to the best results achieved. Source: [37] Samples Figure 2.3: TiO 2 /P3HT hybrid solar cell simplified scheme studied by PAS. The samples studied in the VEPAS laboratory at L-NESS, Figure 2.3, are a simplified version in respect to the real solar cell prototype (Figure 2.1, sec ). They were specially prepared for PAS studies because only the cell core, formed by the TiO 2 mesoporous structure and by the photoactive polymer, was in fact of our interest. Consequently the samples characterized are composed only by the titania scaffold with/without 4-MP and/or with/without P3HT deposited on a glass substrate. A set of samples was prepared in order to study the influence of the 4-MP monolayer on the P3HT-oxide interface. That set is composed of 1±0.1 µm mesoporous TiO 2 on a glass substrate. The TiO 2 porosity is about 60%. The details are listed in Table 2.2.

49 Hybrid solar cells 46 # P3HT 4-MP Annealing Scope 1 X X X TiO 2 reference 2 X X TiO 2 /4-MP reference 3 X X P3HT influence 4 X 4-MP influence 5 annealing influence Table 2.2: Solar cell TiO 2 /P3HT sample list. The procedure used to prepare the samples is the following [37]. The glass substrates were covered with a compact TiO 2 layer of a thickness comprised between 150 and 200 nm. Deposition of the compact layer was carried out by spray pyrolysis at 500 C with oxygen as the carrier gas, starting from a 1:10 by volume titanium diisopropoxide bis(acetylacetonate): ethanol solution. The commercial Dyesol TiO 2 paste (DSL 18NR-T), previously diluted in ethanol and ultrasonicated until complete mixing, was doctor-bladed by hand onto the TiO 2 compact layer substrates to obtain a mesoporous TiO 2 film of an average thickness of 1 µm. The substrates were then slowly heated to 550 C (ramped over 1 hour) and baked at this temperature for 300 min in air. After cooling, the substrates were soaked in TiCl 4 solution (15 mm in water) and oven-baked for 1 hour at 70 C. After oven-baking, the substrates were rinsed with bidistilled water, dried in air and baked again at 550 C for 450 min. In the case of devices provided with a 4- MP interlayer, after being cooled down to 70 C, the substrates were immersed in a saturated solution of 4-MP in chlorobenzene for several hours (20 h). Immersion was followed by rinsing with pure chlorobenzene. P3HT (M w = 77500, PD=2 and RR = 96.3, purchased by Merck and used without further purification) was then spin coated onto the substrates at 1000 rpm for 60 sec from a 30 mg/ml chlorobenzene solution. Spin coater rotation was activated 15 seconds after dispensing the solution onto the substrate in order to promote effective polymer infiltration inside the mesoporous TiO 2 layer. In the case of samples without a 4-MP interlayer, the substrates were re-heated at 200 C and then cooled down to 70 C right before spin coating the P3HT, to allow the mesoporous TiO 2 layer to expel residual water.

50 Hybrid solar cells PAS experimental results In order to investigate if the infiltration of the mesoporous TiO 2 with P3HT is influenced by the 4-MP interfacial modification, Positron Annihilation Spectroscopy (PAS) has been employed for the first time in this field. Since positronium (Ps) is sensitive to the presence of free volume and to the extension of inner pore surface, PAS can directly detect buried, isolated pores of a size of nm that are not accessible to conventional probes (TEM, SEM, etc.). Moreover, an analysis of the resulting gamma-rays allows an inference on the nature of the annihilation sites (TiO 2 pores, polymer, etc.). This enables a nanometer scale mapping of the pore composition over the entire thickness of the device in a non-destructive way. In order to resolve the polymer distribution inside the porous metal oxide, the S-parameter was measured. The S-profiles reported in Figure 2.4 display an evolution from the high S-value characteristic of P3HT toward lower values expected for porous TiO 2 with or without 4-MP (reference values for the single P3HT and for porous TiO 2 and TiO 2 /4-MP are shown in Figure 2.4). The curves through the experimental points are the result of a fitting procedure (VEPFIT [15]) which identifies four layers in the explored structure: a solid P3HT cap, a thin porous TiO 2 layer of about nm heavily infiltrated with P3HT, a second thick porous TiO 2 region of about 700 nm containing less P3HT and the glass substrate. Following the decrease of the S-parameter we can conclude that there is a P3HT concentration gradient within the oxide in both samples, with and without the interlayer; however, in the presence of 4-MP the degree of P3HT infiltration is reduced in the first layer and enhanced in the deeper region, while the annealing treatment does not induce any change. A quantitative evaluation of this action in the deep region is given by the analysis of coincidence Doppler broadening (CDB) taken at fixed implantation energy, 5 kev (Figure 2.5). At this energy more than 87% of the positrons annihilate in the porous film containing P3HT and about 13% in the capping layer as shown in Figure kev is the maximum implantation energy that allows to avoid the glass substrate contribution (<0.5%). The CDB momentum distributions ρ of the reference samples are used as well differentiated fingerprints to characterize each material inside the prototype cells. These distributions depend on the electron structure of P3HT and TiO 2 [39, 40]. In Figure 2.5 the CDB spectra are presented in terms of relative change with respect

51 Hybrid solar cells 48 S-parameter 0.58 P3HT Positron implantation energy (kev) capping layer TiO 2 /4-MP TiO 2 1 st layer TiO 2 \P3HT TiO 2 \4-MP\P3HT TiO 2 \4-MP\P3HT + annealing 2 nd layer Positron mean implantation depth (nm) glass Figure 2.4: S-parameter as a function of the positron mean implantation depth for P3HT embedded in porous TiO 2 without and with 4-MP together with the reference values for P3HT and for TiO 2 with and without 4-MP. Horizontal and vertical dashed lines represent the thicknesses and the S-parameters for each layer. Source: [37]. to the reference spectrum of the porous TiO 2. The CDB results for TiO 2 /P3HT and TiO 2 /4-MP/P3HT samples, taken at a fixed positron implantation energy (5 kev), are fitted using synthetic spectra created as linear combinations of the spectra taken separately for P3HT, for TiO 2 and for TiO 2 /4-MP. It is possible to observe two effects in the CDB distributions presented in Figure 2.5 for TiO 2 /P3HT with and without 4-MP in terms of the relative difference Γ = (ρ ρ T io2 )/ρ T io2 : a) lowering of the valence electron density, which leads to a narrowing of the central part of the momentum distribution (Γ > 0); b) reduction of the positron wave function overlap with atomic cores, which reduces the relative intensity of the CDB spectrum at high momentum (Γ < 0).

52 Hybrid solar cells 49 TiO P3HT P L / m 0 c ( - ) / TiO TiO 2 \P3HT P L (atomic units) TiO 2 \4-MP TiO 2 \4-MP\P3HT Figure 2.5: CDB spectra of TiO 2 /P3HT and TiO 2 /4-MP/P3HT taken at a fixed implantation energy (5 kev) together with the spectra of three references: P3HT, porous TiO 2 (the line through zero) and TiO 2 /4-MP are shown. The lines through the experimental data are calculated using a linear combination of the reference spectra. Source: [37]. The continuous lines through the experimental points in Figure 2.5 represent a linear combination fit following equation: ρ = wρ P 3HT + (1 w)ρ T io 2 (2.1) where w is the weight of the P3HT contribution, ρ P 3HT and ρ T io 2 are the momentum distributions of P3HT and of porous TiO 2 oxide respectively. Note that ρ T io 2 was different for TiO 2 /P3HT and TiO 2 /4-MP/P3HT. In each case the reference oxide with and without 4-MP was used, as the sample contains or does not contain mercaptopyridine. The fitting procedure reproduces the experimental results at low and high momentum and gives w values of 0.37 ± 0.02 and 0.44 ± 0.02 in TiO 2 /P3HT and TiO 2 /4-MP/ P3HT samples respectively. w is univocally related to the filling factor f, i.e. the fraction of the empty spaces filled by the polymer, but an experimental calibration is not available. Thus, we make an estimation based on the hypothesis that the probability of annihilation in P3HT and in the oxide is proportional to the mass fraction times the decay rate of the free positron

53 Hybrid solar cells 50 Positron implantation fraction % surface P3HT capping layer TiO 2 \4-MP\P3HT 1 st layer TiO 2 \4-MP\P3HT (CDB - 5 kev) 2 nd layer TiO 2 \4-MP\P3HT Positron implantation energy (kev) glass substrate Figure 2.6: Positron implantation fraction as a function of the implantation energy obtained in ptio 2 4-MP P3HT by means of the VEPFIT model6 [15]. The curves indicate the percentage of positrons that are implanted and thermalized at each energy. The vertical dashed line represents the implantation energy used. The continuous blue line is the sum of the contribution of the two oxide layers infiltrated with P3HT, where the main contribution is given by the second layer. Source: [37]. population λ freei as obtained from annihilation lifetime spectra: w = λ freep 3HT m P 3HT λ freep 3HT m P 3HT + λ freet io2 m T io2 (2.2) where m P 3HT and m T io2 are respectively the masses of P3HT and TiO 2 inside the porous composite. The free positron annihilation rate for a porous TiO 2 layer with the same characteristics of those studied here (nanoparticles of 20 nm in diameter of the anatase phase) was recently determined as λ freet io2 = s 1 [41]. In the case of P3HT it was possible to estimate λ freep 3HT by assuming that part of the implanted positrons were trapped into defect sites in the polymeric matrix.

54 Hybrid solar cells 51 Following the standard trapping model [42]: λ freep 3HT ( ) 2 LP 3HT = λ P 3HT (2.3) L DP 3HT where λ P 3HT is the characteristic decay rate in P3HT (λ i = λ P 3HT = s 1 [43]). L P 3HT and L DP 3HT are respectively the positron diffusion lengths measured in P3HT without defects (L P 3HT = 79 ± 3 nm) and in the defected thin capping layer studied here after spin-coating (L DP 3HT = 20 ± 5 nm). Therefore, is about s 1. Considering that the porosity p of the studied λ freep 3HT TiO 2 oxide is 60% (p = V E /V T, initial free volume in respect to the total volume) and using eq. 2.2, it was possible to estimate the filling factor f (f = V P 3HT /V E, volume of P3HT inside the pores in respect to the initial free volume). f = ρ T io 2 ρ P 3HT λ free T io2 λ freep 3HT w 1 p w 1 p (2.4) where ρ T io2 = 3.84 g cm 3 and ρ P 3HT = 1.33 g cm 3 are the mass densities. The calculated filling factors are: f = 16.5±3% and f = 22±3% for TiO 2 /P3HT and for TiO 2 /4-MP/P3HT respectively. The difference observed in terms of f indicates that the presence of 4-MP does not sizably affect the polymer filling factor in such a way as to justify the enhancement in photocurrent observed. This suggests that the pore filling by itself is not the limiting factor controlling the device performances shown in Figure 2.2. Remarkable differences in terms of positronium (Ps) fraction are found when the 4-MP interlayer is introduced. In fact, the Ps depth profile of Figure 2.7 drops drastically when TiO 2 is infiltrated with P3HT, especially in the presence of 4-MP (a monolayer of 4-MP in bare TiO 2 does not reduce the Ps yield - full red and open orange symbols in Figure 2.7). In particular, the bump in the TiO 2 /P3HT sample (black open symbols) which appears in the deeper region ( nm) is washed out in the presence of 4-MP. The Ps yield reduction can be the consequence of: (i) a better pore filling that favors 2-γ annihilation and/or (ii) a larger P3HT covering of the free inner titania surface where Ps is formed. In both cases, the polymer induces Ps inhibition and ortho-ps quenching [44, 45]. The small difference in the filling factors measured in the deeper region by CDB in samples with and without 4-MP cannot explain the large reduction in Ps yield. Moreover looking at

55 Hybrid solar cells 52 Positron implantation energy (kev) / 5 \ Positronium fraction (%) TiO 2 TiO 2 \4-MP TiO 2 \P3HT TiO 2 \4-MP\P3HT TiO 2 \4-MP\P3HT + annealing Results Positron mean implantation depth (nm) Figure 2.7: Positronium fraction profile in the studied samples. The zero of the depth scale is fixed at the surface of the porous TiO 2. Two color ticks are presented in the upper frame (positron implantation energy): red and black correspond to the devices without and with a capping layer of P3HT, respectively. Source: [37]. 4/11 Interlayer (4-MP) effect on the infiltration of P3HT in porous TiO the shallowest region, the S-parameter shows a lower concentration of the P3HT phase in the presence of the 4-MP layer, while the Ps yield is again reduced. P3HT 4-MP P3HT Figure 2.8: Schematic representation of the 4-MP effect: the inner pores of the TiO 2 are better covered with P3HT.

56 Hybrid solar cells 53 Therefore it is possible to conclude that the Ps fraction reduction is due to a reduction of free TiO 2 surface, which means a better contact between the oxide and P3HT phases and a closer polymer packing at the interface (see a schematic representation in Figure 2.8). In the light of this, it is interesting to notice here that there is also a small difference in the Ps-profiles between pristine and annealed samples, which is the signature for a reordering of the polymeric chains and closer packing with a reduction of free oxide surface also after annealing. This presented information, inaccessible by optical and electron microscopy techniques previously used, is in perfect agreement with an improvement of charge generation and device photocurrent and, most importantly, moves the focus of the investigation to the most critical point in the system, the nature of the hybrid interface. To further understand the interaction between the 4-MP and the titania surface, Figure 2.9: Side and top views of (a) P3HT/TiO 2 interface as obtained by MPMD simulations at room temperature. Panels (b) shows the modification of the interface as due to the presence of 4-MP and 2-MP interlayers, respectively Source: [37]. atomistic simulations were performed based on a combination of model potential and first-principles methods [37]. It was found that a single 4-MP molecule efficiently binds to the (101) anatase surface through the active lone pair of the ni-

57 Hybrid solar cells 54 trogen atom. In the presence of an ideal surface, an N-Ti bond is formed with the titanium atoms of the substrate. In the lowest energy configuration, the molecule is roughly normal to the surface with a N-Ti distance of about 0.2 nm (see Figure 2.9 b)), and it is bound to the surface with an energy as large as 1.5 ev. By successively depositing molecules on titania we predict the formation of a 4-MP monolayer exposing a flat surface formed by rows of thiol groups (see Figure 2.9 a)). Each Ti atom of the metal oxide binds to the 4-MP nitrogen atom so that the TiO 2 surface is fully covered. Notably, as a result of the π π intermolecular interaction, the monolayer spontaneously forms an ordered zigzag pattern stable at room temperature. This arrangement has fundamental effects on the surface thermodynamics. The first remarkable effect of 4-MP coating is to enhance the mobility of the polymer on the TiO 2 /4-MP substrate. In particular, we find that, at room temperature, the polymer diffusivity on TiO 2 /4-MP is about one order of magnitude larger than on bare TiO 2, the first being 3.0 ± cm 2 s 1 and the latter 4.0± cm 2 s 1 respectively. The energy barrier for the polymer migration is smaller in the case of TiO 2 /4-MP since the local charges are smaller and the corresponding electrostatic energy landscape is smoother. Accordingly, the polymer easily migrates on the TiO 2 /4-MP surface, yielding a larger polymer/substrate interface area. This is nicely consistent with the results shown by PAS and is perfectly in line with the enhancement in coverage area found upon annealing which provides extra energy to the polymer chains. The higher polymer chain mobility on the substrate surface can of course affect its final morphology, due to higher chances of getting its lower energy configuration Conclusions The Positron Annihilation Spectroscopy (PAS) has been demonstrated a useful non-destructive technique for the study of the filling degree of mesoporous thin films with polymers. The S parameter and the F 3γ fraction allow to distinguish different filled layers within the structure. Moreover the presence of a monolayer coating, 4-MP, on the mesoporous structure and its effects on the P3HT polymer were successfully studied with PAS. Summarising the overall characterization we can assert that the presence of an oriented molecular layer, triggered by selective interactions with the TiO 2 surface,

58 Hybrid solar cells 55 drives local ordering smoothing the otherwise abrupt interface. These results point out the importance of molecular interactions and local morphology in hybrid interfaces and the implications they have on charge separation and recombination. PAS results gave experimental evidence of that: the first remarkable effect of 4-MP coating is to enhance the mobility of the polymer on the TiO 2 /4-MP substrate. The polymer easily migrates on thetio 2 /4-MP surface, yielding a larger polymer/substrate interface area. Besides, considering that the porosity p of the studied TiO 2 oxide is 60% using PAS results it was possible to estimate the filling factor f. The calculated filling factors are: f = 16.5 ± 3% and f = 22 ± 3% for TiO 2 /P3HT and for TiO 2 /4-MP/P3HT, respectively.

59 Metal Oxide Semiconductors - IGZO Metal Oxide Semiconductors - IGZO Metal Oxide (MO) semiconductors have emerged as enabling materials for nextgeneration thin-film electronics owing to their high carrier mobility even in the amorphous state, large-area uniformity, low cost and optical transparency. They are applicable to flat-panel displays, sensor arrays, flexible circuitry and photovoltaic cells [46, 47, 48]. Indium Gallium Zinc Oxide (IGZO) is a metal oxide semiconductor synthetized for the first time in 1985 [49]. Later, in 2003, IGZO thin film transistor (TFT) was developed by Nomura et al. research group [50, 51, 52] led by Hideo Hosono at the Tokyo Institute of Technology. IGZO-TFT technology is at the present used for new generation Liquid Crystals Displays (LCDs) and for Organic Light Emitting Diode displays (OLED) that is recently commercialized by important companies such as Samsung Electronics and Sharp Problem statement Metal-oxide (MO) semiconductors represent an appealing family of materials for next-generation electronics. In fabricating high performance electronics with acceptable fidelity, conventional fabrication processes require capital intensive physical or chemical vapor deposition techniques which are not readily compatible with high-throughput, large-area roll-to-roll (R2R) manufacture. Capitalizing on the solubility of MO precursors in common solvents, solution methods have been utilized to fabricate semiconducting MO layers for TFTs. However, the fabrication process and field-effect mobilities of these TFTs are not yet competitive with the corresponding vapor-deposited (e.g., sputtered) devices. Developing solution phase technologies for MO TFTs having performances comparable to state-of-art vapor-deposited devices is viewed as a critical milestone for MO electronics. So far, independently of the solution processing methodology, significant quantities of gaseous H 2 O, N 2, NO x, HCl, and CO 2, are evolved, disrupting film continuity and yielding porous films when thick film growth is attempted in a single coating step [53, 54, 55, 56]. A research group led by Antonio Facchetti at Northwestern University has recently discovered a new low-temperature, nanometer-thickness controlled solution route to high performance MO electronics via spray-combustion synthesis (SCS) [57]. Owing to the reduced trapping of gaseous byproducts during thin film

60 Metal Oxide Semiconductors - IGZO 57 growth, high-quality, dense, macroscopically continuous films can be produced for both crystalline and amorphous metal oxides, including the most technologically relevant MO and excellent thin-film transistor (TFT) responses [57]. Figure 2.10 illustrates the SCS deposition processes as well as the present TFT structure. The attraction of SCS is illustrated by comparing single-layer IGZO films fabri- Figure 2.10: Schematic of the Spray Combustion Synthesis (SCS) process used for growing metal oxide films under ambient conditions, and the corresponding bottom gate top contact TFT structure. Inset: combustion for a generic metal nitrate acting as the oxidizer and acetylacetone as the fuel. Source: [57]. cated by SCS with other methods. These methods are: spin Combustion Synthesis (spin-cs), sol-gel, and sputtering. Spin-SC is a technique previously developed by Kim M.-G. et al. [47] which uses the same reaction as SCS but the solution is spin-coated on the dielectric instead of being sprayed. Sol-gel processing techniques are used extensively to fabricate MO films [58] [59], enabling rapid production of coatings, including those for high-performance TFTs; sputtering, or metal organic vapor deposition (MOCVD) [52], is an almost standard growth technique which on one hand guarantees large area high quality thin films but on the other hand requires a costly set-up and is time consuming. IGZO, indium-gallium-zinc oxide, is an amorphous MO, as it is shown by XRD (X-ray diffraction) analysis in Figure By comparison of the TFTs grown with different techniques it is shown that SCS IGZO/SiO 2 f TFTs exhibit carrier mobilities times greater than those achieved with sol-gel and spin-cs, and rival those of magnetron-sputtered, FAB-quality IGZO devices [57]. In order to study the physical differences between the samples obtained with different deposition methods, many characterization techniques have been used [57]. Among those, PAS techniques were chosen in order to study the influence of the

61 Metal Oxide Semiconductors - IGZO 58 Figure 2.11: X-ray (XRD) diffraction patterns of IGZO films deposited on SiO 2 using SCS technique. Source: [57]. porosity in the IGZO devices, strictly related to densification and therefore to electrical properties. Indeed, since IGZO is an amorphous oxide, its electrical properties strongly depend on the material porosity that is not easily characterized by conventional techniques Samples The studied samples are composed of a layer of IGZO (In:Ga:Zn=1:1:1) (MO) of about nm, deposited on 300 nm of SiO 2 and a p-si substrate (p doped silicon). Four different deposition methods were taken into account: sol-gel; spin-combustion synthesis (spin-cs); spray-combustion synthesis (SCS) sputtering. For the SCS method, two different concentrations were chosen: SCS-IGZO (In:Ga:Zn=1:0.11:0.29), high In content ; SCS-IGZO (In:Ga:Zn=1:1:1), balance. Acetylacetone fuel-based In 2 O 3, ZnO, and Ga 2 O 3 combustion precursor solutions were prepared with 2M In(NO 3 ) 3 xh 2 O, Zn(NO 3 ) 2 xh 2 O, and Ga(NO 3 ) 3 xh 2 O

62 Metal Oxide Semiconductors - IGZO 59 in 2-methoxyethanol with acetylacetone and NH 4 OH to yield M solutions. In case of spin coating precursor solutions with concentrations of 0.5 M were spin-coated at 2000 rpm for 60 s, and then annealed for 30 min at the desired temperature. They were then stirred overnight at 25 C. In case of spray-coating: substrates were maintained at C on a hot plate while 0.05 M precursor solutions were loaded into a spray gun and sprayed intermittently onto the substrates by airbrush. The nozzle-substrate distance was cm, depending on the temperature. After 5 to 10 s, the spray-process was interrupted for 60 s to allow combustion to proceed, and the cycle was then repeated until the desired thickness (20 or 50 nm) was obtained. Prior to spin or spray-coating, the precursor solutions were combined in the desired molar ratios and stirred for 2 h. MO Deposition Method Thickness [nm] IGZO (1:1:1) sol-gel 32 ± 1 IGZO (1:1:1) spin-cs 27 ± 1 IGZO (1:1:1) SCS 50 ± 1 IGZO (1:0.11:0.29) SCS 27 ± 1 IGZO (1:1:1) sputter 55 ± 1 Table 2.3: Lists of IGZO samples studied with PAS techniques. IGZO thicknesses measured by XRR. Source: [57]. Table 2.3 shows the sample list with the relative thicknesses measured by means of X-Ray Reflectivity (XRR) technique [57]. The mobility and the electrical response of TFTs samples were also evaluated (Figure 2.12 and Table 2.4). The sol-gel TFT performance is poor since a temperature of 350 C, an annealing condition identical to typical commercial sputtering protocols, is inadequate for densification. Reflecting the low combustion efficiency of thicker films, the single-layer spin-cs IGZO TFTs also exhibit poor performance for 350 C processing. In contrast, for IGZO (1:1:1) and for IGZO (1:0.11:0.29), much greater mobilities than for the sol-gel and spin-cs devices, and approaching that of sputtered 1:1:1 IGZO devices, are obtained. XPS further supports these trends [57] (Figure 2.13), indicating greater densification of the SCS films versus the spin-cs/sol-gel films. XPS analysis of the O bonding states in these films indicates three different oxygen environments: M- O-M lattice species at ± 0.1 ev; bulk and surface metal hydroxide (M-OH)

63 I DS (A) I DS (A) Frequency I DS (A) Metal Oxide Semiconductors - IGZO 60 c. a b. IGZO (1:1:1) IGZO IGZO (1:1:1) (1:0.11:0.29) Sol-gel Sol-gel Spin-CS Spin-CS SCS SCS b. IGZO (1:0.11:0.29) Sol-gel SCS Sputter Spin-SC 300 C SCS/ SCS ZrO x ZrO x IGZO (1:0.11 Sol-gel Spin-SC SCS Sp SC Zr a V GS (V) V GS (V) V GS (V) IGZO IGZO (1:0.11:0.29) (1:0.11:0.29) IGZO (1:1:1) IGZO IGZO (1:0.11:0.29) (1:1:1) Sol-gel Spin-CS Sol-gel SCS Spin-CS SCS Sputter SCS Sol-gel Sputter Sputter C Spin-SC SCS/ 10-4 ZrO x 6 SCS ZrO x V GS (V) c. c V GS (V) V GS (V) GS VV GS GS (V) (V) b. d. d Mobility (cm 2 V -1 s -1 ) Figure 2.12: IGZO Transfer (1:1:1) characteristics, bias stress experiments, for IGZO single(1:1:1) layer Sol-gel IGZO TFTs Spin-CS fabricated by SCS different deposition Sputtermethods. The IGZO composition (1:0.11:0.29) on p-si/sio2 substrates is annealed at 300 C. The IGZO composition (1:1:1) on Si/SiO 2 substrates is annealed at 350 C. Source: [57]. d. IGZO (1:1: MO Method Mobility [cm 2 /Vs] IGZO (1:1:1) sol-gel ± IGZO (1:1:1) spin-cs ± IGZO (1:1:1) SCS 1.8 ± 0.24 IGZO (1:0.11:0.29) SCS 6.8 ± 1.8 IGZO (1:1:1) sputter 10.9 ± 0.12 Table 2.4: Performance metrics of single layer IGZO TFTs on 300 nm SiO 2 /p-si substrates wih Al source/drain electrodes. Source: [57].

64 Metal Oxide Semiconductors - IGZO 61 Figure 2.13: X-ray photoelectron spectra of IGZO films by various deposition methods. Source: [57]. species at ± 0.1 ev; and weakly bound adsorbate species, e. g. H 2 O or CO 2 at ± 0.1 ev. For both the SCS-derived 1:1:1 and 1:0.11:0.29 IGZO samples the M-O-M lattice content (41% and 56% respectively) is greater than that of both the spin-cs and sol-gel ones ( 30% and 50% respectively). Furthermore, the SCS M-O-M content of the 1:0.11:0.29 IGZO composition (56%) approaches that of the sputtered 1:1:1 film (58%). These results indicate that more In-rich IGZO compositions have increased M-O-M content in these solution-processed films. Thus, the role of In in enhancing TFT transport is not only by forming more O vacancies, but also by reducing porosity and structural defects, as supported quantitatively by PAS data (see section 2.2.3). This result probably reflects, among other factors, the lower lattice formation enthalpy of In 2 O 3 vs. Ga 2 O 3 by almost 1700 kj mol 1, which enables In-rich compositions to more readily reorganize

65 Metal Oxide Semiconductors - IGZO 62 and densify during low-temperature solution-phase MO precursor decomposition [57] PAS experimental results PAS was applied to quantify the IGZO film porosity. This technique is sensitive to voids and can detect isolated, buried pores as small as 0.3 nm, not accessible to conventional probes [60, 61]. In amorphous porous IGZO films, the implanted positrons interact with electrons to form positronium (Ps) atoms which enable nmscale porosity mapping over the entire film thickness. Figure 2.14 shows results for the fraction of 3-γ ortho-ps annihilations (F 3γ ) and the shape or S r -parameter (relative to the S-parameter value of p-si, the substrate) as a function of mean positron implantation depth for all the five samples (Table 2.3). As the positron implantation fraction (dashed lines) in the top panel of Figure 2.14 shows, almost 95% of the 1-2 kev positrons are implanted in the film. Ps is formed at the surface of materials, as in the case studied for a positron mean implantation depth lower than 10 nm, but is not found inside the silicon substrate (at great depths). F 3γ evolution between 10 to 50 nm, encompassing the IGZO film and the IGZO/SiO 2 interface, identifies large Ps fractions for the 1:1:1 sol-gel and spin- CS films, where the process is far less efficient (F 3γ 0), for 1:1:1 sputtered and 1:0.11:0.29 SCS films, and an intermediate case for 1:1:1 SCS films. Three-γ annihilations in the sol-gel and spin-cs samples indicate that ortho-ps occupies empty cavities large enough to maintain the pick-off annihilation rate λ po at a level not significantly larger than the self-annihilation rate λ 3γ [62]. The lower limit of cavity diameter to observe 3-γ annihilation is about 1 nm [62]. This effect is observed in the amorphous SiO 2 of all samples (see bump centered at 170 nm in Figure 2.14, upper panel). Generally, the PAS S r -parameter depends on the chemical environment of the annihilation site and on the defects concentration (vacancies, voids, pores). The direct correlation between this parameter and the ortho-ps fraction F 3γ in Figure 2.14 clearly indicates that in the present amorphous films, S r values depend mainly on porosity. Thus, higher S r values in the IGZO films correspond to higher Ps formation (para-ps and ortho-ps pick-off that annihilate in two-γ rays) [36]. The F 3γ and S r results confirm that the 1:0.11:0.29 SCS and 1:1:1 sputtered IGZO

66 Metal Oxide Semiconductors - IGZO 63 Positronium fraction F 3 % S r parameter Positron implantation energy (kev) IGZO SiO 2 Si sub Surface 1.00 SCCS (1:1:1) SCCS (1:0.1:0.29) Sol-gel (1:1:1) Spin-CS (1:1:1) Sputtering (1:1:1) Implantation fraction Positron mean implantation depth (nm) Figure 2.14: Positron annihilation spectroscopy S r and F 3γ parameters for IGZO films deposited on SiO 2 (300 nm)/si as a function of the positron mean implantation depth. Source: [57]. films are the least porous. For a quantitative estimation a fitting procedure was implemented (VEPFIT [15]) represented by the continuous curves through the experimental points of the S r evolutions in Figure 2.14, lower panel. The results are presented in Table 2.5. The fitting procedure is based on a model that schematically divides the explored regions in three layers: IGZO, SiO 2 and the silicon substrate, separated by three interfaces (vacuum/igzo -surface-, IGZO/SiO 2 and SiO 2 /Si). The interfaces were chosen very thin 1 nm and

67 Metal Oxide Semiconductors - IGZO 64 L + diff [nm] Z [nm] S r F 3γ % sol gel (1:1:1) 6(2) 32(1) 0.933(1) 5.2(6) spin-cs (1:1:1) 5(2) 27(1) 0.932(1) 5.0(6) SCS (1:1:1) 10(2) 50(1) 0.904(1) 2.1(5) SCS (1:0.1:0.29) 11(2) 27(1) 0.881(1) 0.9(5) sputtering (1:1:1) 12(2) 55(1) 0.878(1) 0.7(5) Table 2.5: Lists of IGZO samples studied with PAS techniques. IGZO thicknesses measured by XRR. completely absorbing, i.e. inside of them the positron diffusion length is < 1 nm [62]. The positron diffusion lengths L + diff into the IGZO films are about 10 nm (see Table 2.5), while the positronium diffusion lengths were 2(1) nm. The thicknesses of the IGZO films were measured accurately by means of XRR within an absolute error of about 1 nm (see Table 2.3). Based on these thickness values, the mass density of the films were estimated minimizing the reduced chi-square statistic of the model fits χ 2 R. 2.5 Sputtering (1:1:1) SCS (1:0.1:0.29) 2 R Mass density (g cm -3 ) Figure 2.15: Reduced chi-square statistic of the S r -parameter (calculated for thicknesses lower than 100 nm) as a function of the mass density of the IGZO films. Source: [57].

68 Metal Oxide Semiconductors - IGZO 65 Figure 2.15 shows, as an example, the χ 2 R plots for IGZO 1:0.11:0.29 SCS and 1:1:1 sputtering. The values obtained, that minimize the fits are: ρ sputt = 5.8(2) g cm 3 and ρ SCS = 6.4(2) g cm 3. The IGZO films 1:1:1: spin-cs, sol-gel and SCS were also fitted and the values of the number densities are: < 5.2 g cm 3, < 5.4 g cm 3 and 5.6(2) g cm 3, respectively. In the case of spin-cs and solgel films the S r -parameter is under saturation regime (an important amount of positronium - para-ps and ortho-ps pick-off - annihilates in two- gamma rays into the amorphous film) and, in these cases, the obtained diffusion lengths into the films are highly influenced by Ps diffusion. For this reason the number densities in spin-cs and sol-gel films were considered upper limits. Figure 2.16: Electron densities profiles of the IGZO films calculated from the XRR measurements. Source:[57]. The densities estimated by PALS are in good agreement with the densities estimated by XRR [57]. XRR analysis asses film electron density, and is used to calculate the mass density (Figure 2.16). For 1:1:1 IGZO films the density monotonically increases as ρ spin CS (3.57 g cm 3 ) < ρ sol gel (3.78 g cm 3 ) << ρ SCS1:1:1 (5.20 g cm 3 ) < ρ sputtering (5.66 g cm 3 ), tracking the TFTs performances and confirming that SCS achieves greater densification. The balanced SCS 1:1:1 density versus the SCS 1:0.11:0.29, ρ SCS1:0.11:0.29 (6.13 g cm 3 ), primarily reflects the lower high-z indium content. The porosities of the 1:1:1 films (sol-gel, combustion, SCS and sputtering) were estimated by PAS considering the density of a single IGZO crystal (ρ IGZO 6.2

69 Metal Oxide Semiconductors - IGZO 66 g cm 3 )[63]: p sol gel > 15%; p comb > 16%; p SCS = 10(2)% and p sputt = 6(2)% (Figure 2.15). By comparison between the PAS results of sputtering 1:1:1 and SCS 1:0.1:0.29, we conclude that the porosity of the last film rich in indium would be approximately the same of the sputtering film, i.e. 6%. In order to determine the mean cavity size of the IGZO samples, preliminary results obtained by pulsed positron annihilation lifetime spectroscopy for balanced IGZO (sol-gel, spin CS and sputtering) and high In content (SCS) are also discussed. The measurements were carried out at the NEutron induce POsitron source MUniCh facility (NEPOMUC) inside the FRM II reactor (TUM University, Munich), where it is installed the Pulsed Low Energy Positron System with PLEPS [64]. The PLEPS allows to obtain a positron lifetime annihilation at a chosen positron implantation energy so as to select a region of interest of the sample under study. The positron implantation energy chosen was 1.5 kev since, at this energy, most of the positron are implanted inside the IGZO layer (see Figure 2.14). Preliminary results of the o-ps mean lifetime inside the IGZO has allowed to calculate the mean cavity sizes d reported in Table 2.6 using the extended Tao-Eldrup model [22, 19]. MO Method Φ [nm] IGZO (1:1:1) sol-gel 1.7 ± 0.1 IGZO (1:1:1) spin-cs 1.7 ± 0.1 IGZO (1:0.11:0.29) SCS 0.4 ± 0.1 IGZO (1:1:1) sputter 0.4 ± 0.1 Table 2.6: Preliminary IGZO mean cavity sizes results obtained by means of pulsed positron annihilation lifetime spectroscopy at NEPOMUC facility [64]. Two porous film families were considered: 1. The most porous films (sol-gel, spin-sc and SCS 1:1:1). According to XRR estimations the porosity p of the sol-gel and spin-sc films is about 40 ± 2% (p = (1 ρ m /ρ SC ) = V E /V T = v E ), where ρ m and ρ SC are the mass densities measured in the film and of the single crystal respectively, V E and V T are the free and total volume respectively, and v E is the free volume for volume unit. The average pore size Φ is 1.7 ± 0.1 nm. Considering that the porosity (or v E ) is equal to the number density of cavities η multiplied by the unitary average free volume V U (v E = ηv U = η 4π( Φ 3 2 )3 ), η is equal to

70 Metal Oxide Semiconductors - IGZO ± cm 3. IGZO 1:1:1 SCS has a porosity 10 ± 2%, and even in lack of experimental values of the mean pore size, it is reasonable to indicate 1.5 ± 5 nm as a likely range. Therefore the corresponding number density of cavities is 6 ± cm The most compact films (sputtering 1:1:1 and SCS 1:0.1:0.29). From the F 3γ measurements it was possible to obtain an upper-limit of the pore dimension of 1 nm (where F 3γ 0) [62]. The average pore size of film is 0.4 ± 0.1 nm for IGZO sputtering 1:1:1 and SCS 1:0.1:0.29 respectively. The porosity of this films was estimated in 6 ± 2 % by PAS and XRR measurements. Thus, the number density results are 1.8 ± cm 3 for both samples. These results emphasize the great importance of porosity, along with composition, for optimizing solution-processed IGZO film properties. In particular, for the case of most porous films, the porosity (40 ± 2 %) and the average cavity sizes (1.7 ± 0.1 nm) fall within the range of interconnectivity pores [60], i.e. inside the material the pores are often interconnected and create larger voids which reduce the electron mobility (see Table 2.4); for the most compact case, instead, the porosity (6±2 %) and the average sizes (0.4±0.1 nm) fall in the range of isolated pores, as the typical voids distribution of a polymer [45]. A voids study in PMMA polymer is presented in section and the values reported in Table 2.9 relative to the polymers voids distributions are similar to the values found for the second family of IGZO thin films Conclusions Positron Annihilation Spectroscopy (PAS) was applied as a characterization technique to the innovative and technologically relevant typology of transparent thin film metal oxide (MO) semiconductors. By means of PAS it was possible to estimate, in a non-destructive way, the density of amorphous IGZO thin films grown with different techniques. Besides the IGZO average pore sizes were estimated, giving a detailed picture of the thin film porosities. Among the grown techniques employed, a new low cost and low temperature methodology for large area IGZO (MO in general) thin film, the Spray Combustion Synthesis (SCS), demonstrated to produce high quality IGZO layers, having

71 Metal Oxide Semiconductors - IGZO 68 the same electrical properties of the IGZO layer grown with standard sputtering process. For the first time PAS gave a quantification of the density and the size of the voids that, due to gas formation during the fabrication process, are created inside IGZO films. It was found that the SCS technique is able to create compact thin films, with porosity of about 6 %, having isolated voids with dimensions of 0.5 nm; other methodologies instead, like sol-gel and Spin Combustion Synthesis, create porous thin films, about 40 % of porosity, with larger and interconnected pores having dimension of 1.7 nm. Concluding it is possible to state that both the difference in porosity and in morphology (interconnected or isolated pores) is crucial for the electron mobility of the thin films.

72 Polymers - PMMA Polymers - PMMA Poly(methyl methacrylate) (PMMA) (C 5 O 2 H 8 ) n is one of the most common transparent thermoplastics [65]. It is often used as an alternative to glass and to optically transparent materials with a large-area, in the manufacture of light diffusers and solar concentrators. Figure 2.17 shows a monomer of PMMA. Figure 2.17: Repeating unit of a PMMA chain Problem statement For the first time, the optical properties of one of the most common polymers, poly(methylmethacrylate), are correlated with the microstructural characterization obtained by Positron annihilation spectroscopy [66]. PAS measurements detect finer microscopic differences that can be correlated with the optical properties themselves. A research group led by Professor Roberto Simonutti at Bicocca Milan University searched for a route, suitable for the industrial process, for the synthesis of large sheets of PMMA having an optical transparency similar to that of the PMMA plates sold by Evonik [67], which are the best available on the market. Researchers from Bicocca Milan University produced and chemically and optically characterized the samples. It was found out that annealing is fundamental in order to improve optical transparency. Indeed, after annealing a PMMA sheet, optical properties improve as a consequence of the reorganization of the large-size heterogeneities (about nm) of the polymer. On the other hand,

73 Polymers - PMMA 70 optical measurements reveal a small scattering excess respect to the intrinsic scattering loss estimated on the basis of the thermal fluctuation theory by Einstein [66]. The PALS technique allowed to understand the origin of the discrepancy between theory and experimental data, providing quantitative information relative to the presence of nanometric voids, their volume concentration of them from the surface up to the bulk and, as a consequence, the material density Samples Bulk polymerization was performed from a pre-polymerized syrup, synthesized with the monomer MMA (99%, Aldrich), purified with basic activated alumina (Sigma-Aldrich), and a first initiator: 2.2-Azobis(2-methylpropionitrile) (98%, Aldrich). A second initiator: lauroyl peroxide (98%, Aldrich) was used in the actual polymerization. The preparation of PMMA plates was performed by bulk polymerization using the industrial cell casting process. The process consists of two steps. At the beginning, a so-called syrup is prepared, in which the purified monomer and the first initiator (100 ppm) react in a beaker at 80 C, where a prepolymerization step takes place. The aim of the prepolymerization step is to mix the reactants and to heat the reaction mixture until polymerization reaction conditions are reached. When the monomer boils the syrup is quenched. Normally, in this step, only % of the monomer is converted. In a second step, the prepolymer is mixed with a solution of MMA (10% in weight) and the second initiator (400 ppm) is dissolved in it. The viscous liquid is introduced into the casting mold, where the polymerization reaction proceeds until most of the remaining monomer is consumed. Casting mold is assembled with two flat sheets made with toughened glass sealed with a PVC gasket and clamped together. The clamps are fitted with springs in order to accommodate the shrinkage of the polymer plate during the polymerization process. Initially, when the reaction heat produced at low conversion is slow (because of the very low polymerization rate at these conditions), heat is provided to the molds by inserting them into a hot water bath at 55 C. The process is finalized by curing the plate in an oven. In this case, two different curing temperatures were tried: a first set of samples (L1 1, L1 2 ) was cured at 95 C, just below the polymer s transition glass temperature (T g ) that is in the range of C[66]; while a second set (L 2 ) was cured at 115 C, just

74 Polymers - PMMA 71 over the polymer s transition glass temperature. The reference is the commercial Evonik GS (GS), that has one of the highest optical transparencies in the market [67]. Chemical properties The chemical properties of the studied samples as a function of the preparation conditions are summarized in Table 2.7 and compared with the commercial GS PMMA by Evonik. This product has been chosen as reference because of its recognized high optical quality among cast PMMA plates; in its case, the conditions of polymerization are obviously unknown and - as a consequence - omitted in the table. Table 2.7 shows that by raising the curing temperature above T g, the Sample Polymerization temperature ( C) Curing temperature ( C) M w, 10 5 PDI (M w / M n ) Residual monomer, wt % Tacticity % syn :% ata :% iso L1_ : 32 : 13 L1_ : 32 : 12 L : 33 : 13 GS / / : 33 : 11 Table 2.7: Chemical properties of PMMA plates, including the tacticity of PMMA, the amount of monomer residual, the molecular weight (M w ) and the distribution of molecular weights (Polydispersity Index PDI = M w /M n ). Source: [66]. weight-average molecular weight M w increases from about to about , and the residual monomer decreases from about 2.1 wt % to 0.4 wt %; on the other hand, the polymers tacticity in the triad expression doesn t change, approaching the molar ratio reported in literature. From this point of view, the curing temperature does not modify the chemical structure of the polymer, apart from small differences in the amount of monomer residual and the final molecular

75 Polymers - PMMA 72 weight. Moreover, the chemical properties of the PMMA thermally treated above T g are more similar to the reference. Optical properties In pure PMMA the absorption coefficient in the nm range is well below 10 4 cm 1 [68], and it is therefore not straightforward to measure attenuation directly even on large samples of tens of cm in length. However, it is well known that absorption in this spectral range originates from either intrinsic or extrinsic diffusion of light, at least for pure samples [69]. Therefore, by measuring quantitatively the intensity of diffused light it is possible to estimate optical attenuation. Extrinsic diffusion originates from inclusion in the PMMA matrix of micro or nanoparticles having different indexes of refraction, such as dust particles. Extrinsic diffusion may have a different wavelength, depending on the particles being larger compared to the wavelength of light in PMMA or not. However, large particles quickly precipitate in MMA (which is not very viscous), and preparation of large quantities of PMMA allows to reach high levels of purity, such that we expect extrinsic diffusion from particles to be negligible compared to intrinsic diffusion. Intrinsic diffusion of light originates from small fluctuations in the density of the material, which in turn result into small fluctuations of the index of refraction. When the correlation lengths of these fluctuations are well below the wavelength of light, intrinsic diffusion is of the Rayleigh type. Koike et al. [68, 69] in a series of works characterized the diffusion of light from pure PMMA sample. In particular, they used polarized light and measured the angular dependence of the diffused intensity on a wide range of angles around 90. It was found that before annealing PMMA above the glass transition temperature, the correlation length of the density fluctuations is large, well above 50 nm, and up to 100 nm, while after annealing, the correlation length is drastically reduced, and diffusion becomes of the Rayleigh type. The measure of the intensity of diffused light at 90 for unpolarized only is shown in Figure This intensity is a measure of the light scattered inside the sample. Based on the previous works by Koike et al. [69] it is assumed that, for samples annealed above T g, diffusion of light is of the Rayleigh type (elastic scattering). The measured irradiance along the collimated

76 Polymers - PMMA I [ W/cm 2 ] GS L2 L1_1 L1_ x II [cm] Figure 2.18: Intensity of diffused light at 90 C from the PMMA plate along the collimated LED beam. Source: [66]. LED beam is reported in Figure Diffusion in L1_1 and L1_2 is so strong that the beam waist rapidly increases in the first 10 cm of propagation, resulting in a remarkable attenuation of the irradiance at its center. In L2 and GS cases the beam waist remains practically constant all along the 20 cm of propagation, i. e. the transparency of GS is similar to the transparency of the L2 sample. That is the result the researchers were looking for. The variations of the beam waist could be both detected visually, and measured by scanning with the detector across the collimated beam. The optical attenuation was estimated from the measured intensity of diffused light [66]. Bulk scattering of the Rayleigh type in the PMMA plate was considered. Results are reported in Table 2.8: the absorption coefficient for L2 and GS is comparable and lower, of about one order of magnitude than the absorption coefficient of L2 and GS. This difference is due to a different organization of the polymer as the values of M w and residual monomer in Table 2.7 suggest. To further investigate the reasons improvement in the optical properties of the PMMA plates, PALS measurements were performed.

77 Polymers - PMMA 74 Sample L1_1 L1_2 L2 GS a [10-4 cm - 1 ] Table 2.8: Absorption coefficient for PMMA plates. Source: [66] PAS - experimental results Positron annihilation spectroscopy has been demonstrated as a suitable characterization technique of polymers. In particular, free volume concentrations and average free volume sizes are important quantities detectable by using this technique. Positron lifetime measurements (PALS) were carried out in the four PMMA samples analysed. Figure 2.19 represents an example of a lifetime spectrum taken for the GS sample. A first attempt to analyze the data of the PMMA samples was Figure 2.19: Positron lifetime spectrum measured in GS samples. performed with a model of three discrete components, but the results were not very good. The variance of the fits was about 1.3. When the model used for the analysis of the data considered the two first components as discrete and the third one as continuous (Eq. (2.5) an important improvement with the fit of the data was obtained. The variance in this case was around 1 for all samples (Table 2.9).

78 Polymers - PMMA 75 The model equation is: S (t) = I 1 e t τ 1 + I 2 e τ 1 τ 2 t τ 2 + I 3 L n (λ) λe λt dλ (2.5) 0 where λ = τ 1 s 1 and τ 1, τ 2, I 1 and I 2 are the mean lifetime and intensity of the first two components. In all the samples the average of the shorter lifetime component τ 1 is 0.18 ns with an associated intensity I 1 of about 24% and is ascribed to free positrons, which annihilate in the microstructure of the polymer, as well as to p-ps whose component having faint intensity (0.125 ns), cannot be distinguished. The second component τ 2 with an intermediate average lifetime 0.39 ns and an intensity I 2 of about 44% is attributed to annihilation in the outer cores of polymeric chains and small free volume holes between PMMA microregions. The information on these two components is mainly contained in the first two nanoseconds of the lifetime distribution. For the study of the third component, the values of τ 1, I 1, τ 2, I 2 were fixed for the best fit procedure. The third component is the most interesting one (located in the zone of the red slope in Figure 2.19), since it is used to estimate the free volume size in accordance to well-accepted criteria (Tao-Eldrup model [70]). This component is attributed to o-ps annihilation by pick-off in the free volume sites: the o-ps lifetime is shortened due to the positron of the o-ps annihilates with an electron of the porous surface, rather than the o-ps electron, in a relative singlet state with emission of two gamma rays instead of three. The o-ps lifetime is interpreted as a sum of discrete decay components (Eq. (2.5)) weighted by a log-normal distribution L n (λ), that is a Gaussian distribution in a logarithmic scale of lifetimes [29, 30]: L n (λ) = 1 (2π) (σλ) 1 exp { [ln (λ) ln (1/τ 0 )] 2 /2σ 2}, (2.6) where σ and τ 0 are free parameters of the fit. A continuous distribution of decay components was chosen because the lifetime of o-ps in a polymer increases with increasing pore size. Therefore, the lifetime spectrum reflects the free volume size distribution in the continuous lifetime distribution. The mean lifetime τ 3 and the standard deviation from the mean lifetime σ 3 are to be intended as the log-normal

79 Polymers - PMMA 76 L n (λ) distribution mean and standard deviation: τ 3 = σ 2 3 = 0 0 λ 1 L n (λ) dλ, (2.7a) ( λ 1 τ 3 ) 2 Ln (λ) dλ. (2.7b) According to a semi-empirical model proposed by Nakanishi et al. [71], under the hypothesis of spherical free volumes, the mean pore radius R(Å) and the free volume fraction f v (%) were calculated [70]. The model is based on the assumption of spherical potential wells with infinite depth and radius R that trap the positronium. The relation between τ 3 and the radius R of the free volume (Tao-Eldrup) [72] and the relation between τ 3 and I 3 and the free volume fraction f v are given by: [ τ3 1 = 2 1 R + 1 ( )] 2πR R + R 0 2π sin R + R 0 (ns) 1, (2.8a) f v (%) = ci 3 (%) < 4 3 πr3 >. (2.8b) where < 4 3 πr3 > is the mean free hole volume of the porosities, c and R 0 are semiempirical parameters, c = Å 3 and R 0 = 1.66 Å [45]. The free-volume hole radius probability density function, Rpdf (R), was calculated as [73]: Rpdf (R) = L n (λ) dλ dr K (R) ( ) 2πR = 2R 0 [cos R + R 0 ] 1 L n (λ) (R + R 0 ) 2 K (R) (2.9) K(R) is the correcting factor for the Ps trapping rate in different hole radii and is defined as K(R) = R [73]. Table 2.9 shows the samples density, estimated from the ratio between their mass and volume within an error of about 0.01 %, and the parameters of the third component as well. The mean radius showed in the table - therefore the free volume fraction - has been calculated as the mean value of the distribution in Eq. (2.9). PALS results are consistent with those of Gel Permeation Chromatography (GPC), where two groups among the samples, characterized by two different molecular

80 Polymers - PMMA 77 Sample Density Mean life time Intensity Standard deviation Mean radius Free volume fraction Variance ρ (g cm -3 ) τ 3 (ns) I 3 (%) σ 3 (ns) R (Å) f v (%) L1_ (1) 1.96 (1) 32.1 (1) 0.39 (1) 2.74 (1) 4.98 (6) 0.98 L1_ (1) 1.94 (1) 31.5 (2) 0.38(1) 2.73 (1) 4.83 (6) 0.97 GS (1) 1.88 (1) 32.0 (1) 0.35 (1) 2.68 (1) 4.64 (6) 1.01 L (1) 1.87 (1) 31.8 (1) 0.30 (1) 2.67 (1) 4.56 (6) 0.95 Table 2.9: Parameters of the third lifetime component (τ 3 and I 3 ), variance of the fit, pore radius and free volume fraction as a function of the number density of the samples. Source: [66]. weights and residual monomer concentrations, were identified. The mean lifetime τ 3 for L1_1 and L1_2 samples is higher than those of samples L2 and GS and, consequently, a higher mean pore radius and free volume fraction is found. Furthermore, according to the results in Table 2.7, L1_1 and L1_2 are characterized by a higher residual monomer and a lower molecular weight in respect to, L2 and GS. Figure 2.20 shows the two extreme distributions of the free volume radius, corresponding to L1_1 and L2 samples, according to the lifetime analysis mentioned before. Sample L2 has the sharpest distribution centered in the lowest average radius and possesses the lowest free volume (Table 2.9). These parameters indicate that L2 is a sample of good quality if compared with the high quality of the commercial Evonik sample (GS). In Figure 2.21 the free volume fraction and mean free volume were plotted as a function of density for each sample and the presence of two families is confirmed. When the polymerization temperature is lower than the T g the polymer chains almost loose energy of motion and the free spaces generated by volume shrinkage during further polymerization remain empty. According to Koike et al. [68] this process is responsible for large heterogeneities in the density that drastically enhance the light attenuation. The fact that these heterogeneous structures disappear after a heat treatment above or near to T g, explains the remarkable optical difference between the L1 group and

81 Polymers - PMMA 78 Figure 2.20: Size distribution of the free volume in samples L2 and L1_1. These distributions represent the two extreme cases. The other distributions are in between the presented cases. Source: [66]. those that contain L2. Indeed the curing temperature for the first group is lower than T g and the free volume and the residual monomer fractions are higher in respect to L2 and GS. Instead the best sample is the one treated above T g (L2) that possesses both higher light transmission properties and lower mean free volume (similar to GS). These results indicate that if the polymer is treated below the T g the movement of the polymer chains is weakened, leaving the free radicals and unreacted monomers trapped between the chains promoting the existence of free volumes. These results are consistent with the idea that if a slight amount of monomer trapped inside the PMMA glass is polymerized in-situ that generates localized voids and that increases the scattering losses as well [69].

82 Polymers - PMMA L1_1 L1_2 Mean volume (A 3 ) GS L Density (g cm -3 ) L1_1 Free volume (%) L1_2 GS L Density (g cm -3 ) Figure 2.21: Mean free volume and free volume fraction as a function of number density of the PMMA samples. Source: [66].

83 Polymers - PMMA Conclusions Positron Annihilation Lifetime Spectroscopy (PALS) was applied to the study of voids inside PMMA transparent sheets. The samples were prepared varying the curing temperature below or above the transition glass temperature. A correlation between the free volume fraction and the mean free volume size with the optical properties was found and would suggest that the voids represent a scattering center for the light in the visible region. PALS measurements allowed to exclude further growth of the voids when annealing above the transition glass temperature (T g ), despite a further substantial re- duction of the MMA residual fraction. Instead, a slight reduction of their volume was observed, possibly related to the long-range re-arrangement in the polymer matrix. Interestingly, despite an average distance of only 1.2 nm, the voids are not diffusing and fusing in the above T g treatment, which would also result in a large increase of the optical scattering.

84 Chapter 3 The AEgIS experiment This chapter presents the Antimatter Experiment: gravity Interferometry Spectroscopy (AEgIS). I joined the AEgIS collaboration in 2012 and I partecipated to the antiproton run and to the setup of the AEgIS pulse positron beam. After an historical overview on antimatter, the presentation of the experiment is given. Then the AEgIS positron system will be described in detail and finally the collaboration main achievements along will be briefly discussed. 3.1 Introduction The history of anti-matter begun when Paul Dirac, in 1928, predicted the existence of the anti-particle of the electron: the positron (e + ). Later, in 1932, Carl Anderson observed the track of positrons in a cloud chamber giving experimental proof of Dirac s theoretical prediction. Anderson s discovery, as illustrated in the first part of the present thesis, immediately opened the path to positron physics, which embrace the study of the positron s properties, positronium (Ps) physics and positron annihilation spectroscopy. Of course, antimatter physics is not limited to positron (and positronium) physics: in principle, every particle has its own antiparticle 1. But it took more than 20 years from the discovery of e + for the scientific community to be able to produce heavier antiparticles: indeed while positrons are naturally emitted by radioactive 1 For particles whose additive quantum numbers are all zero, like photons and neural pions, the particle itself represents its own anti-particle.

85 Introduction 82 isotopes that undergo β + decay 2, the method to create massive antiparticles, like anti-protons (p), is to bunch protons clouds with an energy of the order of several GeV towards a metal block, where the anti-particles are generated by pairs production. In 1955 [74] at the Bevatron, the world s largest particle accelerator at the time which had just come into operation at the Lawrence Berkeley Laboratory the year before, Owen Chamberlain and Emilio Segrè led a team that observed for the first time an antiproton. Chamberlain and Segrè shared the 1959 Nobel Prize for this remarkable achievement, and soon also the antineutron was observed at the Bevatron [75]. Once the three particles that make up atoms were known to have each an antiparticle, the question became: can antimatter particles form antiatoms like matter does? The answer arrived in 1965 from A. Zichichi, using the Proton Synchrotron at CERN [76], and L. Lederman, using the Alternating Gradient Synchrotron (AGS) accelerator at the Brookhaven National Laboratory [77]. Almost contemporarily they observed the antideuteron, an anti-nucleus consisting of an antiproton and an antineutron. The possibility to produce antiatoms appeared then feasible, and the scientific community focused its effort on the production of anti-hydrogen (H), the antiatom composed by a positron plus an antiproton. In 1995, Walter Oelert led a team that for the first time managed to create antihydrogen atoms in the Low Energy Antiproton Ring (LEAR) at CERN. Nine of these atoms, produced by collisions between antiprotons and xenon atoms over a period of three weeks, remained in existence for about 40 billionths of a second, travelled at a velocity close to the speed of light covering a length of 10 m, finally annihilating with ordinary matter. Despite the relevant result, the production rate was too small and the atom energy too high to allow the measurement of antimatter properties at an interesting level of accuracy. Antimatter represents a perfect subject for the study of charge conjugation (C), parity (P), and time reversal (T) symmetries. CPT symmetry is a fundamental symmetry of physics laws: its theorem states that every particle has an antiparticle with the opposite electric charge, the opposite internal quantum numbers, the opposite magnetic moment, the same lifetime and the same inertial mass [3]. 2 The most common isotope used in laboratories is Na 22, easily produced and handed. See section 1.4.

86 Introduction 83 Every theory in the framework of the modern quantum mechanics, like the Particle Standard Model [78], should be invariant under CPT transformations. Given the importance of research on CPT violations, it is not surprising that in 1997 CERN approved the Antiproton Decelerator AD project, with the aim of producing bunches of 10 7 cold antiprotons with energies of about 5 MeV and bunch lengths down to 200 ns. The availability of cold antiprotons has allowed the production and study of cold antihydrogen which is the best physical system to test the consistency of CPT invariance. Hydrogen (H) is indeed the most studied atom and the comparison between H and H energy spectroscopy mat give evidence of CPT violations. The progress in the field of antimatter illustrated so far referrers to a time before the construction of the AD at CERN. The following sections of this chapter present the AD facility and the main results achieved in the last decade by the experiments hosted in the AD hall The Antiproton Decelerator (AD) Hall The Antiproton Decelerator (AD) facility at CERN began operating in 1999 and is currently the world s only source of low energy (E = 5.3 MeV) antiprotons (p). The AD facility was built in order to perform high precision laser spectroscopy of antihydrogen (H) and of antiprotonic Helium (phe + ). The results of the former experiments have to be compared with the ones obtained from ordinary matter spectroscopy, while the results of the latter have to be compared with quantum electrodynamics calculations (QED). Since the experimental precision of hydrogen spectroscopy frequencies is of the order of 10 15, one needs the coldest atoms (< 10 K), where the Doppler effect on the measured atomic frequencies caused by thermal motion is minimized [79]. Therefore the first technological issue faced by the experiments hosted in the AD hall has been to cool to sub-ev energies the p delivered by the AD. The AD hall (Figure 3.1) at the moment hosts five international experiments: AL-

87 Introduction 84 PHA 3, ATRAP 4, ASACUSA 5, ACE 6 and AEgIS 7. Figure 3.1: Inside of the Antiproton Decelerator Hall at CERN. The Antiproton Decelerator Figure 3.2 shows the design of the antiproton decelerator AD: the AD is an ovalshaped, 188 m circumference synchrotron [80]. The antiprotons (p) come from the collisions of p, accelerated by the Proton Synchrotron (PS), with an Ir target. The reaction involved in the p production is: p(beam) + p(target) p + p + p + p (3.1) The proton (beam) energy threshold for the reaction in reaction (3.1) is around E 6 GeV and the p and p emerging from the target have energies of about E 1 GeV. The efficiency of the process is energy dependent so, to increase the yield of p, the PS uses p with energies of E = 26 GeV. In this condition, the efficiency (number of p on number of p(beam)) is about 10 6 and the p have an energy of E 3.6 GeV. Into the AD is injected a beam containing > p of momentum p 3.6 GeV/c, transverse emittance ε 200π mm mrad and momentum spread of p/p 6%. After an entire AD cycle, which last about 100 s, the p beam ejected

88 Introduction 85 Figure 3.2: Schematic diagram of Antiproton Decelerator. Source: [80]. from AD contains p and has the following features [80]: momentum p = 100 MeV/c; emittance ε = 0.3π mm mrad; momentum spread p/p = 0.01%; time length t = ns; energy E = 5.3 MeV. The mechanisms involved in the p cooling are: 1. radiofrequency (RF) bunch rotation: inside RF cavities the pulse length L of the bunch is stretched. Since the longitudinal emittance L p/p is preserved during this procedure, the momentum spread is reduced; 2. stochasting cooling and deceleration: along the AD circumference, deviation from the mean values of the momentum and transverse position of

89 Introduction 86 subgroups of p are detected. This detection allows to steer the orbit of those subgroups by the application of electric pulses at steering electrodes. After several cycles the emittance and the momentum spread as well as the beam energy, are reduced. The p are decelerated to 2 GeV; 3. electron cooling: the p cloud is bathed in an electron cloud. The velocities of electrons are matched to the p velocities so that in the center-of-mass frame, the p see a stationary (low temperature) electron cloud. The cooling mechanism is Coulombian and very efficient: the antiprotons are decelerated to a momentum p = 100 MeV/c. Figure 3.3 represents an entire cycle of the AD. It is possible to observe the different cooling steps with their timing. Over the time of a cycle about 100 s p are cooled by three orders of magnitude in energy: from 3.6 GeV to 5.3 MeV. Figure 3.3: Cycle of the Antiproton Decelerator. The p is represented as a function of the time elapsed. The times and duration of the stochastic and electron cooling are indicated in the lower part of the figure. Source: [80].

90 Introduction 87 Milestones at the AD As foreseen, the availability of low energy antiprotons (p) at CERN opened the possibility to produce and confine massive antiparticles: anti-hydrogen (H) and antiprotonic helium (phe + ). In order to perform laser spectroscopy experiments on antimatter, the first great achievement of the collaborations working at the AD was to cool down and confine antiparticles. The p energy delivered by the AD (5.3 MeV) is indeed too high to perform laser spectroscopy experiments: the p has to be cooled to thermal energies corresponding to at most 10 K or - in ev unit - to 1.3 mev, nine order of magnitude lower than the energy of the p from the AD. The first progress in the trapping of H came in 2002 from the ATHENA (AnTi- HydrogEN Apparatus) collaboration [81]: cold H was formed in nested Penning traps by overlapping clouds of p and e +. In the same year, also the ATRAP collaboration successfully produced cold H [82]. But the first material progress arrived in 2010, when the ALPHA collaboration produced H at cryogenic temperatures [83]. One year later, the same collaboration confined 300 cold H for more than one thousand seconds [84]. Once H was trapped and cooled, the first microwave excitations between the ground state hyperfine substates of H have been performed [85]. The p were also used to conduct studies on phe + : its transition frequencies were measured by laser spectroscopy reaching a fractional precision of 10 9 by the ASACUSA collaboration [86]. From the comparison between QED calculation and experimental results, the antiproton to electron mass ratio was estimated as M p /m e = (23) [86]. Furthermore, microwave spectroscopy led to the estimation of the p magnetic moment with a precision of 3% [87]. Finally, the ATRAP collaboration in 2013 measured the magnetic momentum of a single p trapped in a Penning trap with fractional precision, in respect to the known value of the proton magnetic moment, of [88]. The future goals in the field of cold antimatter at CERN are related to the spectroscopy experiments on H and phe + but not limited to them: other antimatter intrinsic properties, like mass, angular and spin momenta, are going to be measured with great accuracy.

91 AEgIS scientific motivations AEgIS scientific motivations The principal aim of the AEgIS (Antimatter Experiment: gravity Interferometry Spectroscopy) [89] experiment is the measurement of the antihydronen (H) gravitational acceleration (g) in the earth s gravitational field. AEgIS was approved by CERN in 2008 and, after years of commissioning, the AEgIS collaboration is now about to produce, in an innovative way, a pulsed cold H beam. The first goal is to measure g with a 1 % relative precision: even if that precision is far from the accuracy achieved in matter experiments, it would represent a progress of note, and the basis for further improvements. A second step of the collaboration is to perform spectroscopy measurement with H in order to test the Charge Parity Time (CPT) invariance[3]. Among the four fundamental interactions - gravitational, electromagnetic, strong nuclear, and weak nuclear - only the gravitational is not yet described by a quantum theory. Indeed, gravity is described by Einstein s General Relativity, a classical theory which has a geometric framework: the bodies travel along geodesics in a four-dimensional space-time which is modified by the presence of massive objects. One of the cornerstones of the General Relativity is the Weak Equivalence Principle (WEP). This principle states that the trajectory of a free falling body in a gravitational field depends only on its initial position and velocity and is independent from the composition of the body. From a Newtonian point of view this means that the acceleration of the body is independent on the mass and this happens only when the inertial mass is equal to the gravitational mass of the body. The WEP has been tested very carefully, with a precision of 10 13, by Eotvos-type experiments [90] for matter-matter systems, but never for antimatter-matter systems. A precise measurement of g could give information about which is the best quantum mechanical model to describe gravity. The fact that no quantum effects have been observed yet with matter-matter systems does not exclude the possibility to observe them in antimatter-matter systems. Indeed, theories on supergravity [91] predict that H could fall differently from H in the Earth s gravitational field. The attraction or repulsion between two bodies is mediated by the exchange of virtual bosons and their characteristics (spin and mass) determine the properties of the force. Three gravitons are considered [92]: the ordinary Newtonian gravity corresponds to the exchange of massless tensor (spin-2) gravitons while additionally,

92 The experiment 89 vector (spin-1) and scalar (spin-0) gravitons may exist. Simplifying the classical potential between two point masses 1 and 2, the static potential in the case of one vector and one scalar partner of the graviton takes the form: V = G r m 1m 2 ( 1 ve r/λ v + se r/λs) (3.2) where G is the gravitational constant, m 1 and m 2 the rest masses, v and s the coupling strengths and λ v, λ s the distance range of the vector and scalar potentials, respectively. The sign of the gravivector is negative in a matter-matter system but is positive in antimatter-matter systems, therefore the former experiments would be sensitive to s v but the latter to s + v. This difference would make possible, in principle, to measure a quantum effect associated with gravity. Note that even if a violation of the WEP was verified, it would be consistent with the CPT theorem: the CPT theorem predicts the behavior of an anti-apple falling on an anti-earth but it does not predict the behavior of anti-apple on the earth. The CPT invariance will be tested in a second phase of the AEgIS experiment: H spectroscopy is planned after the g measurement. 3.3 The experiment In order to perform the gravity measurement (g), an electrical neutral system like H is necessary, otherwise the electromagnetic forces due to residual electric or magnetic fields would surely overwhelm the gravitational interaction. H will be produced by charge exchange reaction [93] in a pulsed mode. The reaction will be activated by a plasma of cold antiprotons (p) held at cryogenic temperature (100 mk) and by a cloud of cold and laser excited positronium (P s ) atoms. In formula: p + P s H + e. (3.3) Once formed, the H will be accelerated by means of inhomogeneous electric fields (Stark effect) towards a classical moiré deflectometer coupled with a position sensitive detector. The annihilation position of the H that travels through the deflectometer with a controlled velocity will be recorded, allowing the measure-

93 The experiment 90 ment of the acceleration experienced by antiatoms. Note that the measurement of g is model free: no assumptions or hypothesis except the validity of Newtonian laws, are made in order to calculate the g value. Thus the result will be independent from any classical or quantum model. Figure 3.4 represents the scheme of the measurement. The procedure will be per- Figure 3.4: AEgIS antihydrogen formation scheme. formed along the following steps: 1. the antiprotons are delivered by the AD in bunches of 10 7 every 100 s with an energy of 5.3 MeV, and are trapped and cooled to sub-ev energies by the AEgIS trap system; 2. every 200 s bunches of 10 8 positrons accelerated to some kev are implanted inside a positron/positronium converter where Ps atoms are produced and emitted in vacuum at a velocity of the order of 10 4 m s 1 [36] (the p delivery frequency is double in respect to e + delivery frequency therefore, for each pulse of P s atoms, two pulses of antiprotons are cooled and stored); Ps atoms are laser excited to Rydberg levels, n P s = 20 25, where n P s is the principal quantum number [89]; 4. the Ps cloud overlaps the p plasma, the H is produced by charge exchange reaction and finally accelerated toward the moiré deflectometer where the g measurement is performed. The method proposed for H production is innovative in respect to the other experiments for two reasons: i) instead of positrons, Ps atoms are involved and the

94 The experiment 91 charge exchange reaction is employed; ii) the H beam will be pulsed and not continuous. The second feature allows to determine a start signal, fundamental to perform time of flight measurements. Every experimental condition is crucial for the accuracy of the measurement. Cold p implies cold H and is important in order to minimize the transversal velocity of the antihydrogen atoms. In an ideal experiment, transversal velocity v t should be zero or much lower than the horizontal velocity v h (v h >> v t ) in order to minimize the H losses during the flight. Besides, also the initial horizontal velocity spread has to be minimized in order to reduce the uncertainty on the v h of the beam. The excitation of Ps atoms is planned for two reasons: the first is that the cross section σ of the charge exchange reaction (eq. (3.3)) goes with the fourth power of the Ps principal quantum number σ n 4 P s ; the second reason is that by using Ps excited atoms, antihydrogen will be excited as well and it will be easier to accelerate the antihydrogen beam by means of inhomogeneous electrical field thanks to the larger H electrical dipole. According to Monte Carlo simulation results [89], with n P s = 20 40, v P s 10 4 m/s and p cooled to 100 mk the cross section of the reaction will be σ 10 8 cm g measurement The AEgIS experiment is aimed at measuring the free fall trajectories of a H beam horizontally accelerated, with controlled velocity, that travels 1 m. The technique that will be used, the Stark acceleration, has already been tested for Rydberg hydrogen atoms [94]: the H atoms formed will reach a velocity up to 500 m/s. The beam will be divergent in fact even if the p were thermalized at T = 100 mk, the transversal velocity would be: v2 = 3kB T m 50 m s (3.4) where k B is the Boltzmann constant and m the antiproton mass. The spatial broadness would be: d 50 m s 1m 500 m s 10 cm. (3.5)

95 The experiment 92 In order to select trajectories, the H beam will go through a classical moiré deflectometer represented in Figure 3.5, consisting of two identical gratings, perpendicular to the beam direction, having periodicity 40 µm, transmittance 30% and placed at a distance L=50 cm from each other [95]. The device works in classical regime: the de Broglie wavelength of an H at 500 m s 1 is λ B = h/p m << 40µ m. The antiatoms passing through the two gratings reach a Figure 3.5: The moiré deflectometer. The trajectories of undisturbed particles (grey lines) are modified by the presence of a force (blue lines) and a shift of the fringe pattern occurs. third plane, where the position sensitive detector is located, at a distance L from the second grating. The antiatoms will form on the third plane a fringe pattern having the same periodicity of the gratings. The antiatoms final position pattern is shifted in the presence of a force; in the case of (anti)gravity the shift δ depends on both the flight time and g: δ = ḡt 2. Therefore, g can be obtained by fitting the shift versus the time of flight on an event-by-event basis. The attainable precision in the measurement of g is strongly related to the spatial resolution: with a spatial resolution of 1 µm to get g with 1% uncertainty less than 1000 events are required. Despite the expected flux of few H atoms per second [89], even considering 1 H every 10 seconds, the measurement could be performed in a few hours.

96 Experimental setup Experimental setup The AEgIS experimental setup is composed by: positron source and accumulator; two superconducting magnets allocating the Penning- Malmberg traps (main traps); a magnetic transfer line to transfer positrons from the accumulator to the main traps; several detectors mounted inside and outside the vacuum chambers; laser system; the moiré deflectometer for the g measurement. Every part of the apparatus is installed in the AD except for the moiré deflectometer, the design of which is under study. Figure 3.6 shows the drawing of the central PART II EXP. LAYOUT region EXPERIMENTAL of the AEgIS apparatus. LAYOUT The main part of the AEgIS set-up consists of a Transfer line 5 T magnet + 1 T magnet 10 8 e + /200s 10 7!! 5.3 MeV/100 s Malbert-Penning trap Moirè deflectometer Figure 3.6: A section of the central region of the AEgIS apparatus. positron system and a cryogenic system in ultra high vacuum composed by two magnets (5 T and 1T), where a system of traps is located.

97 Experimental setup 94 Antiproton traps The traps in the main magnet consist of a series of 105 cylindrical electrodes of varying length [96]; part of them are located in the cold bore of the a 5T magnetic field (trapping region) and the rest in the bore of the 1 Tesla (antihydrogen formation region) field. All the electrodes are individually biased to shape Penning or Malmberg traps of variable length for trapping and manipulation of antiprotons, electrons and positrons. Some electrodes are radially split in 4 sectors allowing the application of the radio-frequency voltages necessary to compress the trapped plasma (Rotating Wall). Antiprotons from the AD are routinely trapped and cooled by collisions with electrons (trapped together with antiprotons) in the trapping region. Anti-hydrogen formation region The design of the electrodes located in the 1 Tesla field is not standard (Figure 3.7): in particular there is a large radius trap (2.2 cm radius while the electrodes of trapping region have 1.5 cm radius) connected with two series of electrodes (0.5 cm radius) mounted along two horizontal parallel axes [96]. They are called on-axis trap and off-axis trap. The on-axis trap is mounted along the axis of the Figure 3.7: AEgIS trap region inside 1 T. Source: [97]. magnetic field and it is used to collect the antiprotons and cool them in the final region mounted below the positron/ps converter (nanoporous target). The electrodes facing the nanoporous target are equipped with a grid on the top to allow the passage of positronium. The grid is designed to optimize its transparency and

98 Experimental setup 95 minimize at the same time the distortion of the electric field due to the lack of rotational symmetry. Detectors Positrons and antiprotons are detected by several scintillators located around the apparatus. A double stage MCP coupled to a phosphor screen and a CCD camera is mounted in the fringe field of the 5 T magnet along the path from the AD to the main traps (see an image of a cold p dump in Figure 3.8). This MCP is operating with a quite high magnetic field (about 3.1 T) in a cryogenic environment and it is mounted on a movable support. A second MCP with a phosphor screen is mounted in front of the last electrode of the on-axis trap. A Faraday cup not sectorized is mounted in front of the first electrode of the main trap also on a movable support. A radially sectorized Faraday cup is located in the middle of the two magnets with sectors collecting the plasma dumped from the 1 Tesla trap or from the 5 Tesla. Another movable support allows to place in position this Faraday cup or an electrode used during the transfer of the particles. Figure 3.8: CCD image (left) and intensity plot (right) of a cold p dump. Laser system The photo-excitation of positronium to Rydberg states entails the use of photon energies close to 6.8 ev (Ps binding energy). Corresponding wavelengths (close to 180 nm) are not delivered by commercially available laser systems. We are

99 Experimental setup 96 therefore planning to perform a two-step excitation, from the ground state to the n = 3 state, and then to the n = 35 Rydberg band [98]. Two pulsed-laser systems, both of which are pumped by the same Nd:YAG laser, are mounted close to the 5 T magnet. The whole system relies on a 650 mj Q-switched Nd:YAG pump laser delivering a 4 ns pulse. The wavelenghts are produced by a secondorder polarization process inside optical crystal. The 205 nm radiation for the first transistion is produced by summing inside a non-linear BBO crystal the 266 nm fourth-harmonic of the 1064 nm Nd:YAG pulse and the 894 nm radiation (amplified by an optical parameter amplifier, OPA) generated in an optical parametric generator (OPG) by means of down-conversion of the second harmonic of the same laser. The wavelenght for the second transistion ( 1670 nm) is produced in one step by an OPG starting from the same pump laser and then amplified by a second OPA system [89].

100 Experimental setup Positron apparatus Figure 3.9: Positron apparatus scheme. Source: [99]. The positron apparatus consists of a two stage Surko type device [100] (Figure 3.9) in which the accumulation and the trapping stage are separated [99] [101]. The positrons are emitted by a 22 Na radioactive source, moderated by a solid neon target and then trapped in the first section of the device where a suitable pressure of the background gas allows their deceleration. Pulses of positrons are then extracted every few hundreds ms and trapped in the section of the apparatus called accumulator. The set-up combines elements procured from the First Point Scientific company with and a high-quality ( B/B = 10 4 ) solenoidal magnet used in the accumulator and developed by the AEgIS collaboration. The positrons are confined radially by axial magnetic fields and electrostatic potentials are imposed to cylindrical electrodes in order to trap, accumulate and bunch positrons. Bunches of 10 8 with a duration of some nanoseconds can be obtained from a 50 mci 22 Na source. Positron source and trap Positrons are moderated with a solid neon moderator having the shape of a parabolic cone (Figure 3.10). The neon is deposited on the cone surface kept at 7 K by a two-stage refrigerator. The moderation efficiency is about 0.1 % and the mean energy of the positrons emitted is 2 ev with a spread of 1 ev. Figure 3.11 shows

101 Experimental setup 98 Figure 3.10: Positron source and solid neon moderator. Source: [102]. the scheme of the trap electrodes with the potential applied. The solid lines correspond to the trapping of positrons and the dashed line to the releasing of positrons toward the accumulator. It is a three-stage trap. The positrons are cooled through inelastic collisions with proper gases introduced in the Malmberg-Penning trap. A buffer gas, N 2, is introduced in the first stage with a pressure of about 10 3 mbar (base pressure is mbar); the high pressure allows a high probability of collision between positrons and gas molecules in a single pass, with therefore a high trapping efficiency. The differences potential are set in order to maximize the probability of an electronic excitation of nitrogen close to the threshold energy ( 8.8 ev)[99]. The pressure decreases along the stage 2a and 2b due to the larger trap radius. Working pressures are about 10 4 mbar and mbar, for stage 2a and 2b respectively. The stage 2b is where the positrons are finally compressed and cooled. The positrons are radially compressed with a Rotating Wall technique (RW) [100] with frequencies of about 5-6 MHz. In order to cool the positron a SF 6 was introduced. SF 6 has a cooling time much lower than N 2 but also a lower annihilation time [103]. The positron lifetime inside the 2b stage is about 2 s and the working frequency used is 6 Hz. Before installing the accumulator, the positron beam characteristics at the end of the trap were measured by means of a CsI scintillator coupled with a photomultiplier (PMT), and of a phosphor screen coupled with a CCD camera. In order to annihilate the positrons on the phosphor screen, the CsI scintillator, previously calibrated, was set at a known distance from the point of annihilation. First we estimated the number of positrons at the end of the trap in continuous mode without the buffer and cooling gases: the positrons were only accelerated with a constant voltage difference

102 Experimental setup 99 Figure 3.11: Positron trap scheme and voltages. Source: [99]. towards the phosphor screen. The efficiency under continuous mode declared by the First Solar is ε = ε mod ε tr where ε mod is the moderation efficiency and ε tr the transport efficiency. The CsI detector placed at 15 cm from the phosphor screen detected an average of 931 counts/s (Figure 3.12) that corresponds, considering the solid angle and the steel the γ rays have to pass through, to positrons/s. The source activity was 21 mci, that is Bq, and therefore the efficiency was , very close to the value declared by the First Point. In the upper part of Figure 3.13 are shown an image of the beam Figure 3.12: Counts of CsI scintillator coupled with a PMT of γ-ray at the end of the trap in continuos mode. 931 counts/sec corresponds to positron/sec. in continuous mode taken with the CCD camera and its relative intensity profile. The phosphor screen, charged at -6 kv, shows a bright ring, with a diameter of

103 Experimental setup mm, due to the implanted positrons. The ring shape is due to the geometry of the moderator (see Figure 3.10): the design of the trap is thought so as to lose the fastest positrons which are emitted from the center of the moderator. Later, the positron beam under the pulse mode was characterized. In the lower part of Figure 3.13 are shown an image of the beam in dumped mode taken with the CCD camera and its relative intensity profile. The spot dimension is about 2 mm and the FWHM about 1 mm. From the comparison with the intensity of the continuous beam, it has been possible to estimate the number of positrons for each pulse, positrons for dump, and also the trap efficiency ε trap = 14% (the trap efficiency declared by the First Point is 17%).!! Figure 3.13: On top: image of the positron beam at the end of the trap in a continuous mode with the relative intensity. On bottom: image of the positron beam at the end of the trap in pulsed mode with the relative intensity.

104 Experimental setup 101 Positron accumulator The positron accumulator represents the third and last stage of the positron apparatus. Positrons are dumped from the trap with a frequency of 6 Hz and stored in the accumulator. The accumulator is designed to deliver up to 10 8 positrons every 200 s in length of 10 ns, few mm FWHM and with a mean energy of 100 ev. Figure 3.14 shows the scheme of the accumulator trap with the potential pro- Figure 3.14: Positron accumulator scheme and voltages. Source: [99]. files. The inlet potential allows the positrons to get inside the accumulator when dumped by the trap. In Stage 1, 2 and 3 the positrons are cooled by the scattering with CF 6 gas. The pressure inside the trap is kept at 10 8 mbar in order to maintain a long positron lifetime (the base pressure is /10 11 mbar). Positrons are finally cooled and stored in the Stage 3 where an harmonic potential well is created by means of a multiring electrode trap. The electrode number 4 in Figure 3.14 is divided into four electrodes for the Rotating Wall procedure. The rotating wall radially compresses the plasma but at the same time the plasma is heated: that is the main reason for the presence of a cooling gas (the magnetic field imposed is about 1000 G, too low for an efficient cyclotron radiation cooling). We did not have the possibility to measure the trapped plasma temperature but typical temperatures for this condition are ev [99]. At the end of the accumulator a calibrated CSI scintillator coupled with a photodiode was placed in order to characterize the number of positrons accumulated and dumped. This kind of detectors are relative slow (µs response) but the signal

105 Experimental setup 102 Dump amplitude (a.u.) Frequency 3 MHz Cooling gas pressure 3 10^-7 mbar Dump amplitude (a.u.) Amplitude 0.1 Cooling gas pressure 3 10^-7 mbar RW amplitude (V) RW frequency (MHz) Figure 3.15: CsI amplitude signal at the end of the positron accumulator as a function of the rotating walll amplitude (left) anf of the rotating wall frequency (right). amplitude is linear with the number of γ-ray detected, i.e. with the number of positrons dumped. In Figure 3.15 are shown the CsI amplitude signal as a function of the RW amplitude and RW frequency, and the best performances were obtained at 0.1 V and 3 MHz. Figure 3.16 shows the curve of the number of positrons dumped as a function of the storage time and of the number of pulses from the trap. The data points has been fitted with an exponential curve (see table in Figure 3.16) and the mean lifetime of the positrons inside the accumulator is 118 ± 5 s. The number of positrons has been measured by means of a CsI scintillator coupled with a photodiode and in 1500 s the number of positrons stored is

106 Experimental setup 103 Number of pulses 660 5x Number of positrons e + 4x10 7 3x10 7 2x10 7 1x Time (s) Equation = 1 / Adj. R-square 0.99 Value Standard error A 5.03E E+06 τ (s) Figure 3.16: Graph: Number of positrons stored in the accumulator as a function of the time and number of trap pulses. Table: fitting equation and results.

107 Achievements Achievements This section presents a brief introduction to the achievements by AEgIS between 2012 and The first great achievement consists in the set up of the apparatus in only two years. This was made with great effort by the whole collaboration and now the apparatus is ready to produce H. This result will be accomplished in The images of Figure 3.17 can give an idea of the work done in such a short time. One of the main issues of the experiment concerns the detection of H both in the trap where is supposed to be formed and in the region of the moiré deflectometer. Several articles have been published on this topic, here is a list by subject: nuclear emulsions as a position sensitive detector for the moiré deflectometer [104, 105, 106]; segmented silicon detector as a position sensitive detector for the moiré deflectometer [107, 108, 109] :'%"R4Dc/"f+(%" silicon detector for the trap region [110]. Figure 3.17: AEgIS zone in early 2011 (left) and in late 2012 (right).

108 Achievements 105 The next two paragraphs are dedicated to the two main results of the collaboration: the antiproton catching and cooling and a test of the moiré deflectometer performed with antimatter Antiproton catching and cooling Antiprotons coming from the antiproton decelerator with an energy of 5.3 MeV are slowed down in a set of Al micrometric foils placed at the entrance of the 5 T magnet. The p are trapped raising high voltages at the entrance and at the end of the 5T trap and cooled by electron cooling: an electron cloud, cooled by emission of cyclotron radiation, is loaded inside the trap before the entrance of p. The mean energy of the p cloud is lowered till sub-ev values and then transferred towards the 1T trap. Figure 3.18 shows the number of p trapped as a function of the high Figure 3.18: Number of p trapped as a function of trapping voltage. Source: [111]. voltage of the potential well inside the trap. Annihilations of antiprotons were detected by means of a set of plastic scintillators coupled with photomultiplier tubes (shielded with µ-metal from the 5T B field) in contact with the 5 T cryostat vessel. The detection efficiency for a single annihilation has been calculated using GEANT3 MC with real AEgIS geometry and is in the range of 6-11 % [111]. At 9 kv the p stored were per AD bunch with a trapping efficiency of

109 Achievements %. The p were held in the trap for times up to 300 s without significant losses. Figure 3.19 shows the fraction of hot and cold p as a function of time electrons were loaded into a 120 V potential well and cooled by cyclotron radiation. After being trapped, the cooled p particles remain in the 120 V well along with the e. The red dots in Figure 3.19 are obtained by lowering the Figure 3.19: Fraction of cold (blue dots) and hot (red fots) antiprotons trapped. Source: [111]. 9 kv barrier towards the Al foil and detecting the annihilation there; the blue dots, instead, are the measure of the number of annihilations of the cold p launched toward the Al foils. About 90 % of antiprotons were cooled to ev-range within 20 s [111].

110 Achievements Moiré deflectometer Figure 3.20: a) Scheme of the moiré deflectometer for antiprotons; b) scheme of the p fringe pattern shifted by a force; c) light reference for measure of the shift. Source: [112]. A moiré deflectometer used with slow antiprotons has been successfully tested [112] (the moiré deflectometer and the measure principles are described in section of this present chapter). The position sensitive detector chosen is the emulsion detector developed for neutrino experiments [113]. Figure 3.20 represents the layout ot the experiment. A beam of cold antiprotons coming from the AD at 5.3 MeV and decelerated through the degrader foils (225 µm thickness) entered the deflectometer. According to simulations [112] the p energy distribution mean value is 106 kev with the root mean square value of 150 kev. Incoherent light with λ = 640 nm was used in a Talbot Lau regime in order to measure the shift of the p fringe pattern in respect to a beam not subjected to any forces, like a beam of photons. The contact grating represented in Figure 3.20 is used as experimental reference. Figure 3.21 shows the results: 241 p annihilation events have been recorded with a spatial resolution of 2 µm. A shift of 9.8 µm was measured and corresponds to a force of 530 ± 50 an [112], due to residual electrical or magnetic fields. This measurement is the first step towards the g measurement and this is

111 Achievements 108 Figure 3.21: a) Detected p compared with the recorded light; b) antiproton annihilation positions and light pattern for the moiré deflectometer (left) and for a moiré deflectometr plus contat grating (right); c) shift between light pattern and antiproton fringe pattern. Source: [112]. also the first time that a moiré deflectometer was used to measure an antiparticle beam deviation. It can be considered as a a crucial step towards the direct detection of gravitational acceleration of antihydrogen with the AEgIS experiment. It is important to note that the expected absolute shift of the antihydrogen pattern due to gravity is comparable to the one observed in the current experiment. Although the gravitational force acting on antihydrogen is 10 orders of magnitude smaller than the sensitivity level reached with the presented small prototype deflectometer, the resolution of the setup can be improved simply by scaling up the deflectometer and the detector. The main improvement may be achieved by increasing the transit time. Using a beam of antihydrogen atoms with a significantly lower velocity of 500 m s 1 and a distance of 1 m between the gratings (in this experiment v p = m s 1 and L=25 mm) will improve the sensitivity by 11 orders of magnitude [112] (eight orders of magnitude due to slower velocity and three orders of magnitude due to increased length of the device), thus allowing the application of this technique to direct measurements of the gravitational force with antihydrogen.

112 Chapter 4 Positronium formation in AEgIS A high yield of cold positronium atoms (Ps 1 ) is fundamental for an efficient anti-hydrogen (H) production. In the AEgIS experiment H will be produced by charge exchange reaction (see section 3.3) between a cloud of cold Rydberg Ps atoms and a cloud of cold antiprotons (p) where Ps atoms are emitted by a positron/positronium converter in reflection geometry (see Figure 4.1 and 4.2). So far the common method to produce a large amount of Ps atoms has been to use macroscopic samples of engineered mesoporous silica employed as targets of positron beams in backscattering geometry [36]. Among the mesoporous silica samples studied at the VEPAS laboratory, the focus was put on hydrophobic MCM-41 (Mobil Composition of Matter No. 41) and Aerogel 85 samples that have showed a particularly high Ps production and long Ps lifetime both independent of temperature (in the limits of our experimantal results). The choice of reflection geometry in AEgIS was also suggested by the fact that, at the time the experiment was thought, silica mesoporous thin film converters suitable for transmission geometry did not exist. Backscattering geometry in fact implies a poor overlap between the Ps cloud and the antiproton cloud, as well as the design of non conventional trap system (Figure 4.1). The recent introduction of thin film silica aerogel grown on a nanometer carbon foil [114] offers the possibility of using transmission geometry for Ps production. The possibility to make H in transmission geometry would lead to a better overlap of the Ps cloud with the p cloud as well as to an easier trap design, enhancing the 1 In this chapter, when there is no distinction between ortho-ps and para-ps, Ps is normally referred to ortho-ps.

113 110 Figure 4.1: AEgIS anti-hydrogen formation scheme. H production efficiency. Moreover, transmission geometry would allow, as it is shown in the present chapter, an enhancement of the Ps emission in vacuum. This chapter first presents the macroscopic mesoporous silica samples studied in backscattering geometry at the VEPAS laboratory; then Ps emission yield, cooling and diffusion are described by means of a classical diffusion model proposed by Cassidy et al. [115] and of Monte Carlo simulations. In conclusion Ps emission from a mesoporous silica thin film (with similar characteristics to Aerogel 85) is simulated and future perspectives related to the production and experimental characterization of silica mesoporous thin films are discussed.

114 Figure 4.2: Above: picture of the AEgIS anti-hydrogen trap system. Below: detail of the positron/positronium target. 111

115 Mesoporous Silica for cold Ps formation Mesoporous Silica for cold Ps formation Implanting positrons inside mesoporous silica samples represents the most common method for the production of cold positronium atoms [36]. Even if positronium is formed also at the surface of metals and semiconductors, the use of mesoporous silica is more preferable because of the cooling the Ps atoms undergo inside the porous scaffold. Ps is formed both in the SiO 2 bulk (conversion yield of 72%) and in the porous surface (conversion yield 12%) and is emitted with a high kinetic energy, from 1 ev to 3 ev inside the porous structure (see section 1.3) [116, 20]. Then the cooling process with the pore walls begins and, if the pores are interconnected, Ps atom can be emitted in vacuum from the sample surface with a kinetic energy that can reach the order of mev. According to the quantum confinement effect, the minimum energy of a Ps confined in a pore with diameter d is E c = h 2 /4m P s d 2, where h is the Planck constant and m P s is the Ps mass. Therefore, Ps cannot thermalize at room temperature if d < 3 nm since E c 42 mev, while the thermalization energy at 300 K is E th = 3k 2 BT 38.7 mev. Besides if the pores have nanometric sizes the Ps lifetime is reduced in respect to its mean value in vacuum due to the pick-off process [45] and thus the emission probability is reduced. Since in several experiments, like the AEgIS, the mesoporous silica converter is supposed to be placed in cryogenic environments, pores sizes need to be bigger than 3 nm in order to allow the Ps thermalization process. Besides, the silica surface has to be hydrophobic to prevent the formation of ice, which can trap Ps inside the mesoporous channels. Below are presented the production methods for two mesoporous silica, Aerogel and MCM-41 (Mobil Composition of Matter No. 41), that well match the requirements for a good Ps production and cooling. Aerogel Silica aerogel samples (Figure 4.3) were produced using a procedure developed for the particle capture collectors of the NASA Stardust project [117]. The first step for preparing ultra-low density aerogels involves the formation of a silica sol, where the hydrolysis and condensation of a silicon alkoxide forms a suspension of micro-particles. The aerogel precursor mixture was prepared by combining

116 Mesoporous Silica for cold Ps formation 113 Figure 4.3: A picture of an Aerogel (left), a sketch of its composition and morphology (center) and a SEM image (10µm x 10µm) (right). acetonitrile, sol, water, methyl triethoxy silane and ammonium hydroxide. The density of the final aerogel is controlled by varying the ratio of the acetonitrile to that of the sol. The methyl triethoxy silane was added to make the aerogel hydrophobic. The resulting wet gel was dried in an autoclave, where the temperature was ramped up to 568 K at approximately 36 K/h, after pressurizing the system to 54 bar with argon. The vessel was then depressurized at a rate of 2.25 bar/h. Once the temperature had reached ambient pressure, the system was opened and allowed to cool before removing the aerogels. This process of supercritical solvent extraction allows the solvent to be removed while the silica network remains in a highly expanded state in the form of a three dimensional array of filaments. The aerogel samples had densities of 85 mg cm 3 (Aerogel 85) and 150 mg cm 3 (Aerogel 150) with a porosity of 96 % and 93%, respectively. MCM-41 Swollen Mobile Composition of Matter No. 41, MCM-41 (Figure 4.4) [118], was prepared in autoclave at 388 K by using cetyltrimethylammonium bromide (CTAB), 1,3,5-trimethylbenzene (TMB) as swelling agent, pyrogenic silica (Aerosil 200 Degussa), sodium hydroxide, and deionized water in molar ratios 1 SiO 2 /0.26 NaOH/0.035 NaAlO 2 /0.1 CTAB/20 H 2 O/1.3 TMB. The resulting samples were dried at 353 K and calcinated in air at 773 K for 8 h. The MCM-41 samples were compressed to form pellets with a thickness of 5-6 mm and a diameter of

117 Ps production in mesoporous silica 114 Figure 4.4: Sketch of a MCM-41 structure with a SEM images. 13 mm. The pressure used to form the pellets is critical for the stability of the material. The mechanical stability of MCM-41 depends on its pore size and the thickness of the silica walls between the pores. In the case of swollen MCM-41, it has been shown that, while the pore size is retained for pressure as high as 160 MPa, 20% of the pore volume is already lost after a compression to 80 MPa. The swollen MCM-41 samples were compressed at 7 and 30 MPa and the densities of the samples were 0.39 g cm 3 with mesoporous volume of 1.84 cm 3 g 1. MCM- 41 possesses hydrophobic patches due to the presence of siloxane groups at the corner of the pores and swollen MCM-41 (obtained by addition of trimethybenzene in the micelles) possesses additional hydrophobic patches on the surface of the pores. 4.2 Ps production in mesoporous silica Investigation of positronium formed in the pores near the surface of Aerogel 85 and MCM-41 was carried out by sending a beam of monoenergetic positrons on each sample [119, 120]; positron implantation energy was variable between 1 and 18 kev. The upper curves of Figure 4.5 (uncapped) show the Ps yield as a function of the positron implantation energy in Aerogel 85 mg cm 3 and MCM-41 at room temperature and at cryogenic temperature. The Ps yield is very high