Development of silicon sensors for dosimetry and microdosimetry

UNIVERSIDADE DE SANTIAGO DE COMPOSTELA FACULTADE DE F´ ISICA DEPARTAMENTO DE F´ ISICA DE PART´ ICULAS Grupo de Imagen Molecular y F´ısica M´edica PhD THESIS Development of silicon sensors for dosimetry and microdosimetry. Author: Juan Prieto Pena PhD supervisor: Faustino G´omez Rodr´ıguez Santiago de Compostela, October 2019 Dr. Faustino G´omez Rodr´ıguez, Profesor Titular do Departamento de F´ısica de Part´ıculas da Universidade de Santiago de Compostela, CERTIFICA Que a presente memoria titulada Development of silicon sensors for dosimetry and microdosimetryfoi realizada por D. Juan Prieto Pena baixo a s´ua direcci´on no Departamento de F´ısica de Part´ıculas da Universidade de Santiago de Compostela e constit´ue a Tese que presenta para optar ao t´ıtulo de Doutor pola Universidade de Santiago de Compostela. Santiago de Compostela, outubro de 2019 Faustino G´omez Rodr´ıguez Director da tese Juan Prieto Pena Autor da tese A mis padres, a mi hermano y a Mar´ıa. Acknowledgments I think some acknowledgment for the support and help that some people have provided is in order, or in words of my wise mother, “De bien nacido es ser agradecido”. This dissertation would be so much different (or even non-existent) without their support and input. The first person I want to express my sincere gratitude and acknowledge all the support that he provided me all this years is my supervisor, Faustino G´omez Rodr´ıguez for all his help along this path. His advice not only in scientific matters, but also all kind of problems we had to deal throughout the research and writing process. His kind words when I thought that I was not going to make it helped me to carry on and if you, reader, have this document in your hands is probably thanks to him. Almost all I learned about research and medical physics is thanks to him. Also, I would like to offer my most sincere gratitude to the rest of the people from our research group, Diego Gonz´alez and Nicol´as G´omez, for their support and help with some of the experiments we performed on the microdosimeters. I would like to also thank them for all the coffee breaks and happy times during the conferences we have been together. I hope the future will bring more people like you near me, as I felt humbled of working alongside you and learning all the knowledge you shared with me. Antonio Pazos, our technician, was the backbone of all the experiments and deserves some acknowledgement here and my gratitude, viii Contents 2.6.1 FLUKA Monte Carlo code . . . . . . . . . . . . . . . . . . 53 3 Description of the silicon detectors and experimental device 57 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.2 Description of the silicon detectors . . . . . . . . . . . . . . . . . . 60 3.2.1 U3DTHIN detectors . . . . . . . . . . . . . . . . . . . . . . 60 3.2.2 3D Cylindrical Microdosimeters . . . . . . . . . . . . . . . . 66 3.3 Detector readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.3.1 U3DTHIN detector . . . . . . . . . . . . . . . . . . . . . . . 73 3.3.2 3D Cylindrical microdosimeters . . . . . . . . . . . . . . . . 73 3.3.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.4 Charge collection efficiency . . . . . . . . . . . . . . . . . . . . . . 80 3.4.1 Materials and methods . . . . . . . . . . . . . . . . . . . . . 82 3.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4 Experimental validation of the microstructured 3D thin silicon sensors 99 4.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.1.1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . 101 4.1.2 FLUKA Monte Carlo . . . . . . . . . . . . . . . . . . . . . 103 4.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.2.1 Results and discussion . . . . . . . . . . . . . . . . . . . . . 106 4.2.2 RBE Calculations with 3D cylindrical microdosimeters . . . 112 4.2.3 Study of the uncertainty of RBE . . . . . . . . . . . . . . . 118 5 Future work and conclusions 125 Contents ix 5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Appendix A Proton test at CNAO ion beam 135 A.1 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 135 A.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Appendix B FLUKA Monte Carlo code for boundary crossing particle tracking 141 Appendix Resumen en castellano 149 Bibliography 168 List of Figures and Tables 183 List of publications by J Prieto-Pena 191 xContents Chapter 1 Introduction Cancer is a broad term that defines a very large number of different diseases that are characterized by certain common traits [1,2]: Self-stimulation of growth, insensitivity to growth inhibitory signals, evasion of apoptosis, limitless replicative potential, sustained angiogenesis, tissue invasion and metastasis, reprogramming of the body’s energy metabolism and mechanisms to avoid immune response from the host’s body. The IARC (International Agency for Research on Cancer, an UN-dependent Agency) in its 2014 Cancer report [3] shows that cancer is one of the biggest causes of mortality worldwide, with around 14 million cases reported and 8 million direct attributable deaths only in the year 2012. Reports show [4] that the number of cases projected for developed countries will increase by 20-60% in 2030, depending on the type of cancer studied due to the continuous increase in the living expectancy and the increase in healthcare quality. Traditionally, the main avenues for cancer treatment were three, often combined between them: Surgery, chemotherapy and radiation therapy (RT). Currently, novel treatments are being developed, such as hormonal therapy or immunotherapy. Choice of method is dependent on the size and localisation of the tumour site, stage and other several factors. 1 2Chapter 1. Introduction The most common treatment for cancer, either as a main treatment or a coadjuvant one, is radiotherapy. It is estimated that around the 50% of all cancer treatments use any type of radiotherapy [5, 6]. This type of treatment has been demonstrated to be an efficient tool for a successful tumour control [7]. In radiotherapy, a certain quantity of radiation is prescribed by a physician to reach the tumour volume. The goal of radiotherapy is delivering to the tumour volume a prescribed dose of radiation, avoiding damage to healthy tissue if possible. Dosimeters are used to verify that dose prescribed by a physician in the tumour volume is delivered to the patient correctly. Quality assurance programs describe how to measure dose appropriately [8, 9]. These devices work by reading the response to the radiation of a material by different means of processes (physical, chemical...) of a known size. By knowing the processes endured by the detector material to the radiation one can translate the measured affected property to a measurement of the dose imparted in the material. Since tumour tissue is generally less radioresistant than healthy tissue, radiotherapy can provide a way to damage more the tumour region while not affecting significantly the healthy tissues surrounding the tumour area. Ionising radiation cannot distinguish between healthy and tumour tissue, except for some unusual types of radiotherapy, as Boron Neutron Capture Therapy, in which a tumourbinding drug with 10B is injected and then the patient is irradiated with neutrons. Since 10B has a high cross section for neutrons the radiation interacts more in the tumour area. Extreme care should be taken in order to avoid unnecessary damage that could compromise the correct healing of the patient. There are several ways to accomplish this depending on the particularities of the disease. As stated before, cancer is a very broad term, and the tumour can take several forms (different types of cells, solid or liquid tumours, definition of the tumour area, etc.). Dose can be provided externally (as in linear accelerators) or internally (brachytherapy). The particles employed can be also different (electrons, photons, neutrons or even heavier particles as atomic nuclei). In this work we will focus on the effects of protons and atomic nuclei in tumour tissues, 3 called particle therapy (PT) or hadrontherapy. External radiotherapy will always damage the healthy tissue around the tumour, delivering dose all over its propagation trajectory but several technological developments heavily reliant on imaging techniques can minimise the probability of complications. Also, traditionally, the treatments are fractionated, in order to allow the healthy tissue to repair the damage done by ionizing radiation and to attack the tumour cells in different stages of their cellular cycle. A way to minimise damage to healthy tissue is to superpose several beams entering from different parts of the patient’s body and make them converge in the region of interest, delivering the prescribed dose in the tumour volume. The shape of the beam can be adjusted to conform to the cross-section of the tumour to further minimise the damage to healthy tissue. This technique is called beam conformation. The most common flavour of radiotherapy employs photons to irradiate the tumour volume. Nowadays, this form of radiotherapy is highly advanced [7], using Image-Guided Radiotherapy (IGRT) techniques, such as Intensity-modulated RT (IMRT) or stereotactic body RT (SBRT), allowing a very high dose conformation to the tumour volume. Combining these techniques with hypo-fractionation in some specific types of tumours, the treatment time can be greatly reduced, even to a unique fraction, allowing RT to compete directly with surgery in some cases. Due to the nature of the interaction between radiation and matter, specially the exponential decay of the intensity with depth in the case of X-Ray radiation, it is necessary to irradiate the healthy tissue surrounding the tumour area, increasing the probability of further complications in the patient. A different approach was proposed by Robert Wilson in 1946. In his seminal paper [10] Wilson proposed the use of heavier charged particles for therapy, citing several advantages of using protons (and heavier particles) instead of X-rays, giving birth to the field of Particle Therapy. The rationale behind it is that nuclei provoke a higher damage both at cellular and sub-cellular level than traditional radiotherapy using photons and electrons and a better dose conformation. By using heavier charged particles, additional 4Chapter 1. Introduction advantages can be obtained due to the higher deposition of energy per unit length (Linear Energy Transfer or LET) and the different behaviour of cells to different types of radiation. Using protons or ions, healthy tissue is irradiated with lowLET radiation, slightly similar to X-Rays, while the tumour region is irradiated with high-LET particles. Charged particles traverse the media in a very straight line, and its particle range is heavily dependent on the kinetic energy they have in the entrance of the body and the mean ionization potential of the medium. Charged particles deposit most of their energy at the end of their range and a very little amount of energy in the body entrance. By using a different mixture of energies, the whole tumour volume can be covered. Figure 1.1 shows the dose profiles in depth of photons compared to protons and carbon ions. Depth in water (mm) 0 20 40 60 80 100 120 140 160 Relative dose 0 1 2 3 4 5 6 7 Photons 21 MeV Protons 148 MeV 12C 270 MeV A-1 Figure 1.1: Different depth dose distributions for 21 MeV photons, 148 MeV protons and 270 MeV A−1 12C ions. Data taken from [11] The number of proton and ion radiotherapy facilities has been growing steadily during the past decade [12]. In the case of Europe, particle therapy started its 5 course in Uppsala, Sweden in the year 1953. According to PTCOG [13], there are currently 80 facilities in operation (as of January 2019) and 67 particle therapy centres (either in planning phase or under construction). Currently, in Spain, two private hospitals are building proton therapy centres in Madrid with opening planned in 2019 and 2020. Although there is no significant evidence in favour of using protons and heavier charged particles for the treatment of tumours [14] there is evidence that for some types of tumours the use of particle therapy results in less secondary complications [15]. This suggests that further research on the topic to assess the validity of these new techniques and its effectiveness against cancer is of clinical interest. To study the biological processes and energy deposition in small masses related to radiation-matter interaction a new approach to the dosimetry, called microdosimetry, is employed [16,17]. From the microdosimetric behaviour of the radiation in the energy transfer to cells, radiation weighting factors can be obtained. Lineal energy distributions can be benchmarked to a Monte Carlo model to aid experimental methods and perform beam characterization [18,19]. The contents of this dissertation are the results from research in the field of microdosimetry and silicon detectors for hadrontherapy done at the Molecular Imaging and Medical Physics group of the University of Santiago de Compostela (USC) from 2014 to 2019. Chapter two consists of a brief introduction to describe the basic terms employed through the dissertation and the theory in which the following chapters are sustained, with a description of radiation physics, different physical quantities employed in the dissertation, an introduction to dosimetry and microdosimetry, radiobiology, radiation detectors, and Monte Carlo simulation. Next, chapter three describes the different silicon devices employed for measuring the particle beams, with an electrical characterisation of the different silicon detectors, their layout, the electrical circuits used to obtain the signal, all the associated ’hardware’ employed to get the data for this thesis, and a study on the limitations of these particular detection systems. Chapter four is focused on the data obtained, with a description of the 6Chapter 1. Introduction Monte Carlo methods used to compare the experimental data with the theoretical results, a description of the monoenergetic fields used, the results for carbon nuclei. Finally, chapter five discusses future work on the microdosimeters, some of the possible improvements that could be done to the system in order to increase accuracy with respect to physical characteristics of the silicon detectors, the possible changes to the data acquisition system and changes to charge collection efficiency, and also states the conclusions from this work. Chapter 2 Background and state of the art 7 14 Chapter 2. Background and state of the art when the kinetic energy is at its lowest known as Bragg peak and shown in figure 1.1. For particles with 0.1≤βγ ≤1000 this equation can describe the energy loss of the particle with an accuracy of a few percent. In the upper limit, radiative losses become more important and corrections to account for that are needed. Additional corrections to the formula can be added for low-energy incident particles that can extend the validity of 0.05 ≤βγ, around 1 MeV in the case of protons. If the energy loss of the particle is assumed as continuous and equal to the Bethe-Bloch equation 2.7 and any kind of energy loss fluctuation (energy straggling) is neglected, a particle range can be found by integrating the energy loss between the initial energy (Ei) and zero. This is called continuous slowing down approximation (CSDA) range, shown in equation 2.8. RCSDA(Ei) = ZEi 0 1 ρ*−dE dx +!−1 dE (2.8) On the other hand, the projected range is defined as the average value of the depth to which a charged particle will penetrate in the course of slowing down to rest. It takes into account energy and position straggling (as any interaction could cause the initial trajectory of the incident particle to vary). Depth is measured along the initial direction of the particle. The projected range will always be less than the CSDA range. The ratio between projected an CSDA range is known as the detour factor, which is bigger than 0.99 for particles with residual ranges over 10−3cm in the clinical hadrontherapy beams [26]. Straggling As stated before, Bethe-Bloch formula calculates the mean stopping power. There will be some deviations from this value arising from the stochastic nature of the radiation-matter interaction. As the incident radiation starts to lose energy by traversing the media it will broaden its energy, position and angle distribution. 2.1. Radiation-matter interaction 15 This statistic fluctuation resulting in a different range of values for energy or range associated to each individual particle is called straggling. In the case of hadrontherapy, these distributions can be considered Gaussian. The summation of multiple scattering events yielding a Gaussian energy loss can be described [27] by equation 2.9 to account for the energy straggling: N(E) dE 1 N=1 απ1/2exp"−(E−¯ E)2 α2#(2.9) This equation represents the density of probability of particles having energies in the interval (E,E+dE) after traversing a thickness x0of absorber from an initially monoenergetic beam. After the transport through a thickness x0the particles have a mean energy ¯ Ebeing αthe straggling parameter representing the half-width at the (1/e)-th height of the energy distribution and given by [28]: α= 4πz2e4nZx0"1 + KI mv2ln 2mv2 I!# (2.10) With nthe electron density in the medium, Ka constant depending on the electron shell structure varying from 2/3 to 4/3 and vthe initial velocity of the heavy ion. Range straggling can also be described in a similar manner as equation 2.9: N(R) dR 1 N=1 απ1/2exp"−(R−¯ R)2 α2#(2.11) Where ¯ Ris the mean range. Figure 2.2 shows some range (also called longitudinal straggling) and lateral straggling values for protons and carbon ions as a function of the incident energy. Another consequence of incident particles traversing matter is the deflection due to atomic nuclei collisions. Those angular deflections, individually, will be almost negligible, but the sheer number of them will provoke a significant deviation from the expected particle position by the end of the range. They can be 16 Chapter 2. Background and state of the art Energy per nucleon (MeV A-1) 0 10 20 30 40 50 60 70 80 90 Straggling (mm) 0 0.2 0.4 0.6 0.8 1 1.2 12C, longitudinal 12 C, lateral p, longitudinal p, lateral Figure 2.2: Range (longitudinal) and lateral straggling for protons and carbon ions in water as a function of the energy per nucleon of the incident particle. Data taken from SRIM [29]. thought of as a lateral straggling effect that adds to the other two mentioned before in this section. This phenomenon is called multiple Coulomb scattering (MCS). The MCS distribution will be very close to a Gaussian one, since it is the result of a big number of small interactions that follow the Central Limit Theorem, but there also be some non-Gaussian contribution from big scatters, although with the energies used in clinical practice those contributions are almost negligible. The main models employed to describe MCS are the Highland’s formula [30,31], that only considers the Gaussian contribution, and the widely used but also algebraically complicated Moli`ere’s Theory [32,33]. A thorough discussion on Moli`ere’s theory is out of the scope of this thesis, and the author would refer any interested reader to the aforementioned literature. Highland’s formula only depends on the incident energy of the particle and the material traversed and can be described in the following way: 2.1. Radiation-matter interaction 17 θ0=14.1MeV pv rL LR"1 + 1 9log10 L LR!# (2.12) Where θ0represents the standard deviation of the angular distribution (approximately Gaussian) expressed in radians. Lrefers to the thickness of the absorber, LRis a material dependent parameter called radiation length that can be found in tables and pv is a term called kinematic factor and described as pv =τ+ 2 τ+ 1E(2.13) with τbeing the reduced kinematic energy of the particle: τ≡E mc2(2.14) 2.1.2 Interaction of neutral particles with matter Photons There are three main mechanisms by which the photons interact with matter. Those mechanisms are the photoelectric effect, the Compton scattering and the pair production. Figure 2.3 shows the predominance of these effects as a function of the photon energy and atomic number of the absorber. In the photoelectric effect, an incident photon transfers all its energy to an atomic electron that will escape the nucleus influence with a kinetic energy equal to the photon energy minus the atomic binding energy. In addition to the electron emission, the atom will have a vacancy in one of its shells that will be quickly filled by a re-ordination of the remaining bound electrons or the capture of a free electron. This process will emit fluorescence X-Rays. Photoelectric effect is the dominant mechanism for low energy photons and materials with high atomic number. The Compton scattering is the interaction between a photon and an electron, 18 Chapter 2. Background and state of the art Figure 2.3: Regions of relative predominance of the three main photon-matter interactions as a function of the photon energy and the atomic number, Z, of the absorber. The left line shows where the probabilities of photoelectric effect and Compton scattering are equal. Right line shows where the probabilities of Compton scattering and pair production are equal. Figure taken from [34] in which the photon transfers some of its energy to the electron and is deflected. This process is dominant in the keV range. The transferred energy (E=hc/λ) and the scattering angle can be found by the Compton relation: ∆λ=λ0−λ=h mec(1 −cosθ) = λC(1 −cosθ) (2.15) Where ∆λis the wavelength shift and λC=h/mecis the Compton wavelength. 2.1. Radiation-matter interaction 19 In pair production the photon gives up all its energy to create an electronpositron pair. For pair production in the nuclear field there is an energy threshold for it to occur equal to the sum of an electron and a positron rest mass (1.022 MeV). Neutrons Neutrons are highly penetrating particles since they do not interact through Coulomb force. Neutrons can propagate until they suffer a scattering or capture process mediated by the strong nuclear force. Even in the case of elastic scattering, neutrons may transfer some of their kinetic energy to recoil nuclei. Scattering processes involve the change of momentum of the incident neutron and the target particle but do not involve a nuclear process that changes the internal structure of the nucleus. In the case of inelastic scattering, the target may reach an excited level during a brief period before emitting a gamma particle to go back to its ground state. Lastly, absorption processes involve the capture of the neutron by a target nucleus. In the case of radiative capture, after the capture the nucleus will be in an excited state and a de-excitation gamma particle will be emitted. In a non-radiative process, the compound nucleus will emit a charged particle or a neutron. Finally, in the fission process the neutron absorption will de-stabilize the nucleus and it will divide in two daughter nuclei with approximately the same mass and the release of one or more fast neutrons that can induce fission in other nuclei. 2.1.3 Nuclear reactions Although main stopping power contribution for beam particles comes from Coulomb interactions, in hadrontherapy nuclear interactions are very relevant, either leading to an additional effective attenuation of primary beam particles or producing secondary particles through nuclear processes. Between these secondary particles we can find fast neutrons emitted mainly in the forward direction (with 20 Chapter 2. Background and state of the art an average around 0.5 neutron per primary particle for 12C beams and 0.025 for proton beams [35]) and beam particle fragments that share almost the same speed and direction of the parent particle. [36, 37]. ICRU63 [38] distinguishes three different kinds of nuclear reactions: 1. Elastic nuclear reaction: “A reaction in which the incident projectile scatters off the target nucleus, with the total kinetic energy being conserved (the internal state of the target nucleus and of the projectile are unchanged by the reaction).” 2. Nonelastic nuclear reaction: “General term referring to nuclear interactions that are not elastic (i.e. kinetic energy is not conserved). For instance, the target nucleus may undergo breakup, it may be excited into a higher quantum state, or a particle transfer reaction may occur.” 3. Inelastic nuclear reaction: “Specific type of non elastic reaction in which the kinetic energy is not conserved, but the final nucleus is the same as the bombarded nucleus.” Particles created in a nuclear reaction between a primary (incident) particle and the media are called secondary particles. If a secondary particle creates a new one by means of a nuclear reaction, that new particle is classified as tertiary particle, and so on. The possible secondary particles that can be created in nonelastic nuclear reactions between a nucleus with atomic number Zand the media are all the fragments with atomic number less or equal than Z, neutrons and gamma rays. Nuclear fragments heavier than alpha particles are quite rare but nonetheless could modify the biological dose because of their significant RBE because of the high ionisation density along its tracks, typically increasing the energy deposition beyond the range of the primary particles, as can be seen in figure 2.4.The secondary particles will typically make large angles with the beam direction axis. 2.2. Introduction to dosimetry 21 Figure 2.4: Relative ionisation of a 12C ion beam along with nuclear fragments coming from primary and secondary particles. The fragments will contribute to increase the dose along the Bragg curve, specially towards and beyond the end of the range of the primary particles. Taken from [35] 2.2 Introduction to dosimetry 2.2.1 Dosimetric quantities The amount employed to describe the quantity of energy transferred to a medium by radiation is called absorbed dose and is defined in terms of absorbed energy per unit mass of the target (J/Kg, in S.I. units) [21] as shown in the following equation. 22 Chapter 2. Background and state of the art D=d¯ε dm (2.16) where d¯εis the mean energy imparted to a site of mass dm. The size of the site must be big enough in the macroscopic approximation to avoid statistical fluctuation of the mean imparted energy, but still as small as possible to be useful in the dose calculations. Dose is expressed in gray (Gy), and one gray is equal to one joule (J) per kilogram (kg) as stated before. Dose can also be described in terms of charged particle fluence, Φ, and mass electronic stopping power, Sel/ρ, as in the following equation. D= ΦSel ρ(2.17) The term imparted energy, ε, refers to all the energy deposited in a volume of study of mass dm. That is, imparted energy is the difference between the incoming energy minus the outgoing energy. The energy can be carried out by either the primary particles (particles entering the volume) or by new particles, by-product of the different reactions that occurred inside the volume. In this balance, any energy to mass conversion or vice-versa is taken into account. The equation for imparted energy is ε≡X i εi≡(Rin)u−(Rout)u+ (Rin)c−(Rout)c+XQ(2.18) Where the sub-indexes in and out refer to energy entering and exiting the volume, respectively; cand urefer to either charged or uncharged particles, Ris the radiant energy and finally the sum over Qrepresents the net energy derived from rest mass in the volume, and can be either positive or negative depending on if there is more mass transforming to energy or vice-versa [39]. Energy is transferred to the volume discretely, in the so-called transfer points inside the volume under study. Dose alone is not useful to determine the biological effect of a given radiation. The modifications radiation does over biological media depend on the physical 2.2. Introduction to dosimetry 23 conditions of the irradiation and other chemical and biological parameters. Even though the energy imparted per unit mass (absorbed dose) is important, the quality of the radiation and the temporal distribution of the energy deposition are quantities to consider when studying the effects of the radiation in the region of interest. Quality is defined here as those features of the spatial distribution of energy transfers (along and within the tracks of the particles) that influence the effectiveness of an irradiation in producing a given effect, when other physical factors such as total energy dissipated, absorbed dose, absorbed dose rate and absorbed dose fractionation are kept constant [40]. Beam quality is described by means of the Linear Energy Transfer or LET. This quantity describes the density of energy deposition in media by incident particles. The LET of a charged particle when traversing a material, of a given type and energy is defined [21] by L∆≡dE∆ dl (2.19) Where dE∆is the mean energy lost by charged particles due to electronic interactions in traversing the distance dl minus the mean sum of the kinetic energies in excess of ∆ of all electrons released by charged particles. If no energy cut-off is imposed, thus for ∆ = ∞, unrestricted LET, is equal to the electronic stopping power, Sel and denoted by L. There are some limitations in the LET-based dosimetric analysis of the radiation beams. Rossi realised that LET is not enough to dosimetric characterise a radiation beam and specify its radiobiological effectiveness (see also section 2.4). LET is only an average value of the energy loss of a particle along the macroscopic track considered [41, 42]. The limitations of the LET analysis were the starting point of the developments in the field of microdosimetry led by Rossi and Kellerer in the 1970s. This does not mean that the LET notion must be discarded completely. In some cases an approximate evaluation of radiation quality for comparing different types of radiation is needed, and the analysis of LET distributions can fill that gap [43]. 30 Chapter 2. Background and state of the art Figure 2.5: Energy deposition spectrum (a), along with the chord length distribution (b), lg(l) in the sphere, and the obtained lineal energy distribution (c) obtained with the method described above. The convolution of (a) and (b) gives (c). Taken from [43] tional counter exposed to a mixed radiation field of 3.7 MeV neutrons with a γ-ray component. For general chord length distributions, the resolution of equation ?? may be obtained by iterative or Fourier transform methods. For convex and regularly shaped structures, under µ-randomness, the mean chord length can be described in terms of its surface Sand volume Vusing the Cauchy formula 2.3. Microdosimetry 31 ¯ l=4V S(2.37) In the case of a beam of particles with almost parallel trajectories and coming from a fixed point in the space outside the volume of interest the situation is far from µ-randomness. Additionally, in the case of the planar detectors used in this dissertation, the incidence is perpendicular to the active surface and the thickness of the detector is much less than the range of the primary particles. Thus, the thickness, h, can be used as the mean chord length value due to the high directionality of the radiation field produced [45]. A correction factor, ky(∆), can be calculated to consider the divergence between the dimensions of the detector and the mean chord length. ¯ l=Zlmax 0 lg(l)dl ≈h;y=ε ¯ l≈ε hky(∆) (2.38) ky(∆) = h Rlmax 0l g(l)dl (2.39) The correction factor described in equation 2.39 can be calculated using Monte Carlo methods and generally ky(∆) close to unity for all points up to the Bragg peak. For example, let us take a cylinder with height equal to its diameter, L= 20 µm, and irradiated with protons with an initial kinetic energy of 50 MeV. Through the use of a Monte Carlo code (in this case the Monte Carlo code SRIM was employed [29]), different chord length distributions can be calculated. Those values can be compared with the mean chord length in the case of µ-randomness for this scenario, 13.3 µm. Figure 2.6 shows the mean chord length in the case of perpendicular incidence to the bases of the cylinder for different depths in water. The correction factors for planar fluence for this example were calculated and shown in figure 2.7. By turning the cylinder around an axis parallel to its bases the chord length angular dependence can be calculated. This is shown in figure 2.8 for a depth in water of 19 mm. At this depth, the rms value for the angle of the proton tracks 32 Chapter 2. Background and state of the art Depth in water (mm) 0 5 10 15 20 25 Mean chord length (µm) 18.2 18.4 18.6 18.8 19 19.2 19.4 19.6 19.8 20 Figure 2.6: Mean chord length in the case of protons with initial kinetic energy of 50 MeV and perpendicular planar fluence with respect to the base of a cylinder with height and diameter L=20 µm for different depths in water. 2.3. Microdosimetry 33 0 5 10 15 20 25 1 1.02 1.04 1.06 1.08 1.1 1.12 Depth in water (mm) Planar fluence mean chord length correction Figure 2.7: Mean chord length correction factor in the case of protons with initial kinetic energy of 50 MeV and perpendicular planar fluence with respect to the base of a cylinder with height and diameter L=20 µm for different depths in water. 34 Chapter 2. Background and state of the art Angle between cilynder axis and beam axis (rad) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Mean chord length (µm) 12 13 14 15 16 17 18 19 Figure 2.8: Mean chord as a function of the angle between the bases of the cylinder and the initial axis of propagation of protons with an initial kinetic energy of 50 MeV after traversing 19 mm of water. with respect to the original perpendicular incidence axis is around 40 mrad. 2.4 Radiobiology Radiobiology studies effects of ionising radiation on biological tissue through the analysis of mechanisms involved in the interaction of incident radiation on cells and the subsequent biochemical responses. One of the ways to summarize the damage done by an agent (radiation, chemicals, etc.) to cells, is the determination of their survival probability as a function of delivered dose. Usually, the survival curve follows a sigmoid, with a shoulder followed by an asymptotic approach to zero with increasing dose. The cell sensit- 2.4. Radiobiology 35 Figure 2.9: Number of surviving cells as a function of dose for low and high LET radiation. The different contributions from the two parameters from the lineal-quadratic model are shown. Graph taken from [34] ivity to radiation is indicated by the dose needed to reach a certain survival level (e.g. the dose needed to obtain a surviving fraction of 0.5). Figure 2.9 shows the survival fraction of a typical cell culture when irradiated with high and low LET radiation. These curves can be fitted to a two-parameter model termed lineal-quadratic (LQ) model [48], also shown in figure 2.9. The formula for the model that gives us the probability, p(S), of a given survival fraction,S, is: 36 Chapter 2. Background and state of the art −ln(S) = αD +βD2(2.40) p(S) = e−(αD+βD2)(2.41) For a given type of radiation and tissue the ratio α/β denotes the dose value at which the linear and quadratic components have an equal contribution, and the shape of the curve also depends on this ratio. For highly ionising radiation the α/β ratio is usually high, i.e. the decay is purely exponential with small quadratic contribution. Relative Biological Efficiency, or RBE, allows to compare the effectiveness of a certain type of radiation with respect to a standard radiation, usually 60Co gamma rays or 250 keV X-rays [48]. This is done by comparing the doses needed to provoke the same effect (i.e. a determined cell survival ratio) following this relation: RBE ≡Dstd Dtest     isoeffect (2.42) In the equation 2.42, the subindex ‘std’ refers to the standard radiation quality, and ‘test’ to the radiation quality of interest for which the RBE is calculated. RBE is not only dependent on the physical properties of the particle (dose rate, total dose, fractionation, particle type and velocity, LET), but also in biological properties (end point, oxygen concentration and cell-cycle phase) [12]. 2.4.1 Relation between LET and RBE As LET increases towards 100 keV/µm, RBE also increases but once over that point, the RBE starts to decrease again. This is defined as cell overkill, that is, the dose deposited in a single cell is more than enough to kill it, wasting radiation in the process. 2.4. Radiobiology 37 Figure 2.10: Comparison of RBE values from V79 cells for different radiation qualities as a function of LET for the biological endpoint 10% survival in colony formation. Figure taken from [49] Figure 2.10 shows the RBE values for V79 cells for 10% survival colony formation as a function of LET for different particles. Protons can have similar RBE to photons (RBE around 1) even though their LET is higher, but their radiobiological properties are almost the same. Heavier particles like Carbon ions, on the other hand, offer values of RBE up to 5. In treatment planning, the RBE is used to transform the physical dose into a biological or RBE-weighted dose that considers not only the amount of radiation delivered to the target, but many biological factors as discussed earlier. RBE must be defined by using complex models instead of the use of a single factor. There are different RBE models based on in vitro data that are used in different particle therapy installations around the world [50–54]. 38 Chapter 2. Background and state of the art Dosimeters                                    -Passive          - Film (optical density) - TLD (light) - Alanine (Free radical content) - Fricke (Absorbance) -Active                -Ionometric (electrical current)      -Ioni. ch. (- Gas - Liquid - Solid state - Scintillator (light) - Calorimetre (temperature) Figure 2.11: Dosimeters classified in terms of on (active) or off-line (passive) readout. For each type of dosmieter, the main physical property employed for the radiation measurement is shown between parentheses. Ioni. ch. is an abreviature for ionisation chamber. 2.5 Dosimeters There is a wide array of detectors to be used in dosimetry and microdosimetry, each one employing different physical effects of radiation interaction with matter. A classification of dosimeters can be made by putting them into two broad groups: Active dosimeters have to be read in real time, whereas passive dosimeters do not show that capability. Figure 2.11 show an array of different dosimeters. In this work, we will cover exclusively silicon detectors, a sub-set of the solid state detectors shown in the figure. An ideal dosimeter should follow these characteristics:  Offer an accurate and precise measurement.  Linear dose response  No dose rate dependence  No energy dependence  No directional dependence 2.5. Dosimeters 39  Small size  Small spatial resolution  Ease of use and readout An ideal dosimeter showing all these characteristics is not available. A compromise must be done to ensure the correct tool is used for its intended work amongst the panoply of different detectors available. To obtain the experimental data for RBE and radiobiological calculations mentioned before, adequate instrumentation for the measurement of the microdosimetric quantities is needed. Traditionally the most common instrumentation in the field of particle therapy were tissue equivalent gas filled proportional chambers or TEPC. These devices work by measuring the ionization in a macroscopic volume that can be translated to a microscopic one by varying the gas density inside the chamber. Gaseous detectors work by collecting the ion-electron pairs formed by ionizing radiation between two electrodes with an electrical potential difference between them. The measured charge is a function of the applied voltage between the electrodes, and its sensitivity will depend on the pressure of the gas and the electronic readout system. Depending on the applied potential between the electrodes different modes of operation can be used, shown in figure 2.12. The first region employed in gaseous chambers is the ion chamber region (region I in figure 2.12). Here, the incident radiation will create electron-ion pairs that will modify the electric charge from the electrodes, with the accumulated charge (and the readout) being proportional to the ionisation in the chamber. By augmenting the potential between the electrodes, the detector will work in the proportional chamber region (region II in figure 2.12), where due to the relatively high electric field present there will be multiplication effects of the created charge inside the gas, with the collected charge being proportional to the energy deposited inside the measuring volume. The third region used and the one with the highest electrical potential between 46 Chapter 2. Background and state of the art Figure 2.14: Band structure for electron energies in a semiconductor. The bands of interest are the valence band, where the positive charge carriers can move freely through the lattice, and the conduction band, where the electrons can move freely through the lattice. Taken from [67] The size of the gap defines the electrical behaviour of the material and is used to classify the material as an insulator (high gap energies) or a semiconductor (low gap energy). The number of electrons in a lattice fills all available sites in the valence band. Therefore, at 0 K there would not be any electron occupying the conduction band and the semiconductor would behave as an insulator. It is due to thermal excitations that the electrons can jump from the valence band into the conduction band taking advantage of the low energy of the gap between the two. In the case of conductors, the band of highest energy is not fully occupied, and the electrons 2.5. Dosimeters 47 Figure 2.15: Representation of the bonds in a silicon lattice. (a) - Intrinsic silicon. (b) - N-type silicon, doped with impurities with 5 electrons in the valence band, as As. The fifth electron is not tightly bound and can the energy needed to move it to the conduction band is small. cP-type silicon, doped with impurities containing 3 electrons in the valence band, as Ga. One of the covalent bonds in the lattice is not matched. Taken from [67] can jump through the atoms as they need very little energy to do so. The jump of an electron into the conduction band will create a vacancy in the valence band (a hole). This pair (electron-hole) is the equivalent of the ion pair in gases, as the electron in the conduction band can be moved by applying an electrical field to the material, but the hole, behaving as a net positive charge would also move but in the opposite direction. These movements contribute to the conductivity of the material. Table 2.1 shows some properties of diamond, intrinsic silicon and germanium. Data is taken from [68] In an intrinsic semiconductor (like pure silicon) all the conductors would be generated by thermal excitation and every electron in the conduction band would leave a hole in the valence band. To improve the conduction in one of the bands some impurities can be added. This process is called “doping” the material. By adding impurities from groups IIIA or VA, one can have an excess of holes (p-type silicon) or electrons (n-type silicon), respectively. Figure 2.15 shows a schematic representation of the bonds in intrinsic, n and p-type silicon. The traversal of a charged particle through the semiconductor volume will create a high number of hole-electron pairs along its track picoseconds after the interaction between the radiation and the detector. This process can be done by 48 Chapter 2. Background and state of the art direct or indirect ionisation, meaning that the energy will be imparted through a mediator particle (electrons ionising the media) or directly by the parent particle. The average amount of energy needed to create an electron-hole pair is called ionisation energy, W, and it is largely independent of the type of particle and/or energy and approximately proportional to the band gap energy, Eg[69] as shown in equation 2.43. One of the greatest advantages of semiconductor detectors is the low value of W, with values 2.96 eV (77 K) and 3.63 eV (300 K) for germanium and silicon, respectively, as seen in table 2.1. W≈2.8Eg+ 0.6eV (2.43) This means a tenfold value increase when compared to the traditional gas filled detectors used in dosimetry. A higher number of charge carriers means that the relative statistical fluctuations on the number of carriers per pulse becomes smaller. Also, the signal-to-noise ratio (SNR) is increased, allowing higher sensitivity when measuring low-energy radiation. Since the gap value for silicon is 1.2 eV not all the energy imparted into the silicon detector is used in the electron-hole creation. Some of the energy will be used in other processes as lattice excitation or phonon production. In the case of silicon, around 30% of the energy imparted will create a readable signal, with the other 70% being wasted in other processes that do not generate a useful signal [70]. The variance in the number of charge carriers is very important due to its relation to the energy resolution of the detector. Both the average and variance of the number of charge carriers can be used to calculate the minimum signal threshold and the energy resolution. For any imparted energy by radiation this number Nwill fluctuate around a mean value < N >. < N >=E W(2.44) Being Ethe energy absorbed by the detector and Wthe mean energy required 2.5. Dosimeters 49 to create an electron-hole pair. This number, < N >, would also be exactly the value of the variance of Nif the system behaved following Poisson statistics, that is, if all events along the track were independent. The Fano factor is introduced as a relation between the observed experimental variance and the Poisson variance. F=σ2(N) < N > (2.45) Low values of the Fano factor will indicate a good energy resolution. True values of the Fano factor for semiconductors as silicon and germanium are experimentally determined around 0.1 but experimental and theoretical values of the Fano factor still exhibit some disagreement [71,72]. Modes of operation Generally, a solid-state semiconductor detector will work by joining two different doped semiconductor materials (p and n-type). Charge carriers will diffuse across the boundary if the two regions are in good thermodynamic contact, working together as if they were part of the same crystal lattice. Electrons from the n-side will diffuse through the contact to the p-side, and vice versa. This diffusion process will generate an electric field that counteracts the movement of the charges, creating a region with no free charges in the boundary called depletion zone. This depletion zone will act as the active area of a semiconductor sensor. A particle traversing the detector will generate electron-hole pairs along its track, with these particles moving out of the depletion region because of the electric field present. These charges will be collected by means of ohmic contacts in the semiconductor and will generate an electrical signal in the detection system in the form of a small current pulse in the order of picoamperes. Most pairs generated outside the depletion region will recombine quickly, not generating a measurable charge. Figure 2.16 shows a schematic of a typical PN-junction semiconductor detector. If no external voltage is applied (i.e. the detector is unbiased), the electric field generated in the depletion zone is inadequate to generate an electric field 50 Chapter 2. Background and state of the art Figure 2.16: Schematic of a PN-junction semiconductor traversed by a particle generating electron-hole pairs. The diode can be reverse-biased to generate a larger depletion zone, with a thickness x0depending on the voltage.Taken from [67]. large enough to make the created electron-hole pairs move quickly to the collection zones and charges could be lost to trap and recombination processes in the semiconductor. The depletion zone in an unbiased detector is also very small and its capacitance will be high, so the capabilities of an unbiased detector will be very poor. However, if an external voltage is applied by placing the n-side of the detector with a positive potential with respect to the p-side (this configuration is called reversed biasing) the depletion area of the detector will increase and the current flow through the semiconductor will be decreased. This is the usual configuration in semiconductor detectors. If the bias voltage is large enough the depletion area of the semiconductor will fill the whole volume, resulting in a fully depleted detector. Higher voltages will 2.6. Monte Carlo radiation transport 51 create an electrical breakdown, with a dramatic increase of the current flowing through the detector and the loss of accurate detection capabilities. Solid-state based radiation detectors offer another way to obtain experimental data and offer several advantages over TEPCs, but lack some of the advantages a tissue equivalent detector can offer. Use of both kind of detectors yields the best results, as they complement between them. This dissertation will discuss the use of solid-state detectors, specially silicon micro-detectors. 2.6 Monte Carlo radiation transport Monte Carlo methods are a branch of experimental mathematics that deal with experiments using random numbers [73]. These methods are computational algorithms that rely on random numbers to obtain numerical results and they have been found a use in a variety of fields. In medical physics, Monte Carlo methods help with the problem of making calculations of dose deposition in media. Dose calculation is not a simple task since the analytical models used commonly for dose deposition in simple problems do not work when translated into complex geometries. There is also a myriad of different outcomes for an incoming particle in the volume of study. If the particle is a photon, it could be annihilated, or could undergo soft or hard scattering, for example. Other kinds of particles (electrons, neutrons, protons, etc.) would yield different processes that could make the problem under study very difficult to solve2, since the analytical solution of the propagation of a small number of particles would involve many very-large square matrices. Mathematically, this resembles a Markov chain [74]. If the probability for each specific type of event is known (i.e. we know all the cross sections for the energies at play for all the possible particles) the problem could be simulated by following many particles through the area of interest and their interactions sampled by following the cross sections for said particle. The 2In our case, this would mean that the Boltzmann Transport Equation should be solved analytically. 52 Chapter 2. Background and state of the art result of the simulation would be computed as the average quantity scored by repeating the process for many particles. There are two big problems with this method: First, a good random number generator must be used to ensure the randomness of the sampling process. It is extremely difficult to generate true random numbers, as only a true random physical process (as radioactive decay, or cosmic ray spatial fluence) can generate true random numbers. This is not a problem for most applications, including radiation transport. A pseudo-random number generator could be used, sampling seemingly random numbers from a known probability distribution [75]. The second problem is that variance of the result is inversely proportional to the number of histories simulated and for very complex problems the computation time to reach an acceptable variance would be astronomically high. Furthermore, convergence to result is proportional to the square root of the number of histories. A compromise between desired uncertainty and computation time must be agreed upon. Calculation efficiency, ε, can be described by the following relation between computational time T, and variance s. ε=1 s2T(2.46) Maximisation of calculation efficiency is helped by using variance reduction techniques. Variance reduction must be used with caution since it can bias simulation results. In medical physics there are a few codes to solve the particle transport problem. Some of them are multipurpose and can simulate the propagation of all kinds of particles, whereas there are some of them that can only handle a reduced number of them. Some Monte Carlo codes normally employed in the field of medical physics are the following:  GEANT4: Monte Carlo code developed at CERN (EU) based in C++. GEANT4 is a toolkit with a complete range of functionality for tracking 2.6. Monte Carlo radiation transport 53 the particles in user defined geometries with modular physics models [76]. The main inconvenient of this code is its complexity due to the number of options available, but this is also its strong point.  MCNPX: General Monte Carlo N-Particle eXtended Transport Code. Developed by Los Alamos National Laboratory (USA) based in FORTRAN90 [77]. Capable of simulating particle interactions for up to 34 different particles and more than 2000 heavy ions at almost all energies. It is used mainly in the simulation of nuclear processes and in the nuclear industry.  EGS: Electron Gamma Shower. Code designed originally for studying the electromagnetic showers produced in the detectors and accelerator of SLAC (USA), based in FORTRAN and no longer supported. An evolution of these code is EGSnrc developed at NRC/CNRC (Canada) and designed with medical physics applications in mind [78].  PENELOPE: Code developed at University of Barcelona, also based in FORTRAN [79]. It is capable of simulating photon and electron/positron transport up to very low energies.  SRIM: A package for simulation of ion transport in amorphous materials. The Monte Carlo portion of the program is called TRIM. Developed by James Ziegler [29]. TRIM can calculate the interactions of energetic ions with amorphous targets.  FLUKA: Multi-purpose condensed history Monte Carlo code developed by CERN and INFN (Italy) based on FORTRAN77 [80]. Used for calculations of particle transport and interactions with matter and used in a very broad range of applications, including medical physics [81]. Capable of adding user routines to the code to further improve the output results. 2.6.1 FLUKA Monte Carlo code The main Monte Carlo code chosen for this work was FLUKA. This was done because the FLUKA physics settings are fixed, although the thresholds for particle 54 Chapter 2. Background and state of the art transport and other options as step-sizes can be chosen by the user. FLUKA also has a very healthy community of users and their user support is generally positive. Even though FLUKA is based in FORTRAN77, a graphical user interface (GUI) called FLAIR can be used, making its use easier for a novice user. As GEANT4, FLUKA uses combinatorial geometry to build the simulation and includes a built-in scoring system. FLUKA can simulate the transport of 60 different particles and heavy ions, can handle nucleus-nucleus interactions from the Coulomb barrier up to 104 TeV/u, electron and muon interactions from 1 keV to 104TeV, photon interactions from 100 eV to 104TeV, hadron-hadron interactions up to 104TeV and neutron and neutrino interactions. It can also handle the tracking on magnetic fields and can handle analogue or biased calculations. Furthermore, FLUKA has a pre-defined configuration set for hadrontherapy applications (‘HADROTHErapy’). This pre-defined configuration changes the particle transport thresholds, activates multiple scattering and delta-ray options, makes corrections to form factor for inelastic Compton scattering and limits the maximum kinetic energy lost per step to achieve better accuracy in the results. The following settings are changed:  Electromagnetic transport activated.  Inelastic form factor corrections to Compton scattering and Compton profiles activated.  Low-energy neutron transport down to thermal energies included.  Fully analogue absorption for low-energy neutrons.  Particle transport threshold set to 100 keV.  Multiple scattering threshold set to minimum for both primary and secondary particles.  Delta ray production activated with threshold of 100 keV. 2.6. Monte Carlo radiation transport 55  Ionisation fluctuations (straggling) activated for hadrons, muons and EM particles.  Maximum energy loss per step 2% of the original energy. A stricter additional limit to the maximum kinetic energy per simulation step was selected, changing it to the minimum energy allowed by FLUKA. This option was selected to reproduce the experimental results more accurately without adding too much additional computation time, as detailed in [82]. It should be noted that Monte Carlo simulations do not have any problems derived from measurement conditions or adequacy of the detectors. Also, the simulations follow the predictions of the model to the letter. With the proper code settings, the simulation can show the “true and real” behaviour of the radiation beam. Alas, Monte Carlo simulations cannot replace reality. The simulations are complementary to the experiment, as they rely in models to simulate reality, and quoting George E. P. Box, “All models are wrong, some of them are useful”. Monte Carlo simulations have been broadly employed in this thesis, but they have been always compared to experimental verification. 62 Chapter 3. Description of the silicon detectors and experimental device 2. A photolithography process is done to define the position of the n-columnar electrodes. The photoresist is placed on the surface of the wafer and the first mask is placed. Then, UV-light is used to expose the resist is removed with a developer solution and the SiO2is eliminated with a buffed HF solution. Figure 3.3: Photolithography process to define the poisition of columnar electrodes and SiO2etching. 3. Using a deep reactive ion etching (DRIE) process the electrode column is etched. DRIE is an anisotropic process that combines plasma etching using SF6with cycles of passivation using octafluorocyclobutane (C4F8). This allows to get vertical trenches with high aspect-ratio. After the DRIE process, the photoresist is removed. Figure 3.4: DRIE process to create the columns and photoresist removal. 4. The etched N-columns are partially filled with a 500 nm polysilicon deposition process. The polysilicon layer is then doped with phosphorous coming from a POCl3gas source to form ohmic contacts on the sensor. A phospho- 3.2. Description of the silicon detectors 63 silicate glass (PSG) layer is formed when the P atoms from the gas get in contact with the polysilicon that acts as a donor source. After the process the wafer is cleaned again. Figure 3.5: Filling of the N columns with doped polysilicon and creation of ohmnic contacts. 5. A second photolithography process is done to define the n-electrodes on the surface of the wafer, removing the exposed photoresist and polysilicon layer. Next, the photoresist is cleaned and a layer of 100 nm of SiO2is grown to protect the n+ electrodes. Figure 3.6: Photolithography process for the n+ contacts and oxide growth. 6. Steps 2-5 are repeated to create the p-type columnar electrodes. P-type impurities are added from a solid BN source. A borosilicate glass layer is grown on the wafer instead that acts as a source of acceptor impurities. 64 Chapter 3. Description of the silicon detectors and experimental device Figure 3.7: Fabrication process of the p-columnar electrodes, similar to the process of figure 3.14. 3.2. Description of the silicon detectors 65 Figure 3.8: Photolithography process to etch the SiO2on top of the columnar electrodes and metal deposition. Figure 3.9: Photolithography process and passivation layer deposition. 7. A fifth photolithography process is done to etch the SiO2layer on top of the electrodes to provide a direct contact between the doped polysilicon and the 0.5 µm Al/Cu electrodes deposited next. 8. The metal lines connecting the p+ and n+ electrodes are placed through a new process of photolithography. Then, a passivation layer consisting of SiO2and Si3N4is deposited by plasma enhanced chemical vapour deposition (PECVD) to protect the detectors from external agents. Contacts for the signal output were opened through the passivation layer with a final photolithography process. 66 Chapter 3. Description of the silicon detectors and experimental device 3.2.2 3D Cylindrical Microdosimeters The 3D cylindrical microdosimeter system consists of an array of independent reading cylindrical unit-cells with a volume like mammalian cellular structures [90]. The unit cell of the detector is a cylindrical structure with an implanted p+ junction electrode that collects the charge surrounded by a concentric threedimensional n+ electrode trench. The axis of the unit cell is perpendicular to the silicon wafer plane. There are 11 x 11 unit-cells in the detector forming a square array. The diameter and separation between p-electrodes (pitch) can take different values depending on the model. There are available diameters of 9, 10, 15, 20 and 25 µm and pitches of 25, 50, 100 and 200 µm. A detailed device schematic and cross section can be seen in figure 3.10. Figure 3.10: Electron microscope photograph and schematic cross section layout of the silicon sensor cell (not to scale). The diameter of the central electrode is 4 µm and the width of the n+ trench is 3 µm. Each p+ unit-cell is connected individually to a contact pad through metal lines, allowing independent operation and providing spatial resolution. The n-electrodes of all the unit-cells are connected to the same pad on the opposite side of the detector. The thickness of the microdosimeter is of (5.50±0.5) µm and the substrate beneath was eliminated to avoid possible particle backscattering. 3.2. Description of the silicon detectors 67 Fabrication process The 3D cylindrical microsensors were fabricated with SOI wafers from Icemos Technology Ltd, as the U3DTHIN silicon detectors. The active thickness of the wafers were 6, 10 and 20 µm. The silicon was <100>n-type doped with phosphorous with nominal resistivity >3 kΩ cm. The buried oxide had a thickness of 1µm and the support silicon thickness was 300 µm in all the wafers. The main steps of the fabrication process will be briefly described here (there are several cleaning processes between these steps, not detailed in this enumeration), and as in the previous section, all diagrams are taken from [89]: 1. Wafer cleaning and growth of 0.4 µm SiO2on both sides of the wafer. The SiO2is then etched by means of a photolithographic process in the sites where the electrodes will be placed. Figure 3.11: (a) SOI wafer ready for fabrication. (b) Wet oxidation process in which the wafer is covered by a layer of SiO2. (c) Photolitography process. (d) SiO2etching. 2. Boron implantation using an ion beam is performed to create the 4 µm diameter p+ electrodes. To prevent channeling of boron ions in the silicon 68 Chapter 3. Description of the silicon detectors and experimental device bulk a 365 ˚ A SiO2layer was grown beforehand. After the implantation, a 0.4µm SiO2layer was grown to protect the p+ from possible damage in the following steps. A photolithography process to define the n+ trench was done afterwards. Figure 3.12: Boron implantation in the p+ electrode area and photolitography to define the trenches of the cylindrical annulus surrounding the active area. 3. Etching of exposed SiO2and DRIE in the silicon to create the n+ trenches is done. Depending on the final detector thickness, the DRIE process will etch a variable depth of silicon. Figure 3.13: SiO2etching and DRIE process to create the trenches of the cylindrical annulus. 4. The etched cylindrical trench is partially filled with polysilicon and then doped with phosphorous atoms from a POCl3gas source, creating a PSG 3.2. Description of the silicon detectors 69 layer acting as a source of donor impurities for the polysilicon. Then, the PSG is etched away from both sides of the wafer. Figure 3.14: Polysilicon deposition in the trenches and doping with POCl3. 5. A photolithography process is done to keep the n-doped polysilicon over the cylindrical trench and washed away from the rest of the wafer. Figure 3.15: Photolithography process to clean the wafer of unwanted n+regions outside the trenches. 6. A Tetraethyl orthosilicate (TEOS) oxide layer is deposited filling the trenches and insulating the n-doped polysilicon. As the metal strip that will connect with the p-doped material will cross over the trench is very important to avoid any kind of shorting between the electrodes. A photolithography process is then done to open a contact between the doped regions (both p and n) and the metal that will be deposited in later steps. 70 Chapter 3. Description of the silicon detectors and experimental device Figure 3.16: SiO2growing process followed by a photolithography process to prepare the electrical contacts that will be placed next. 7. A 0.7 µm Al/Cu metal layer is deposited to create the electrical contact for each one of the unit cells over the whole wafer and then a photolithography process was done to remove the material from the undesired regions. A passivation layer was then deposited to protect the active volumes from external exposure. Figure 3.17: Metal deposition (dark blue) followed by a deposition of the passivation layer. 8. Passivation over contact pads is removed trough a photolithography process for signal output. The backside of the microcylinder can be etched in this step to remove the support silicon and avoid contribution by backscattered particles. 3.3. Detector readout 71 Figure 3.18: Final photolithography process to remove the passivation over the contact pads for signal output and etching of the support wafer in the backside of the detector. The fabricated microcylinders will have a reduced active volume compared with its design values due to the low charge collection efficiency of the n+ doped volume that cannot be considered as a completely active volume. Also, a percentage of the active silicon is consumed due to the etching and oxidation processes with a loss of at least the 40% of the active silicon volume. 3.3 Detector readout The process by which an ionising particle creates a signal in a semiconductor was described in section 2.5.2, but generally this signal is too small to be read as it leaves the detector. An amplification process is needed to correctly quantify the energy deposition in the detector. This is done by adding several different stages to the detector system that adapt and shape the inbound signal in order to be read by a multi-channel analyser and provide a spectrum. Figure 3.20 shows the different stages of a detector system. These stages can be classified as pre-amplification, shaping or amplification stages. 78 Chapter 3. Description of the silicon detectors and experimental device ADC Channel 0 500 1000 1500 2000 2500 3000 3500 4000 Pulse equivalent energy (keV) 0 200 400 600 800 1000 1200 Calibration points Linear fit Figure 3.24: Calibration curve obtained with the injection of a test square pulse into the readout system consisting of a CAEN A1422H Hybrid charge sensitive preamplifier followed by a CAEN N968 spectroscopy shaping amplifier. The output was read with an Amptek MCA8000D MCA. the laboratory experiment was executed, and the value for the most probable imparted energy was matched with the most probable ADC channel. Assuming the origin ordinate was null, a calibration using those two points (y = a x) to assign values of imparted energy to the MCA channels was done. This allowed to check whether the dynamic range of the detector was suitable to the experiment at hand or not. Figure 3.25 shows the calibration spectra recorded for an 241Am source with a 3D Cylindrical microdosimeter and the same readout electronics employed for the first calibration method shown in figure 3.24 (blue crosses) along with a FLUKA Monte Carlo simulation of the energy deposition spectra (red line). These two direct calibration methods gave different and incompatible results between them. For example, in the case of the 3D Cylindrical microdosimeters, 3.3. Detector readout 79 Imparted energy (keV) 0 500 1000 1500 2000 2500 Number of events 0 20 40 60 80 100 Experimental data FLUKA Monte Carlo Figure 3.25: Experimental (blue crosses) 241Am spectra taken with a 3D Cylindrical microdosimeter for calibration purposes along with the FLUKA Monte Carlo simulation results (red line). the energy deposited by a 5.486 MeV α-particle (the most probable energy for the 241Am α-decay) in 5.5 µm of silicon deposits around 880 keV according to FLUKA Monte Carlo with a detailed simulation of the setup. Supposing the MCA uses a full scale width of 4096 channels, according to the first method the channel for the most probable energy should be around channel number 3200, whereas the second method places this deposited energy around channel number 1500. This discrepancy can be partially explained by the 25% tolerance of the test capacitor value and also the charge collection efficiency across the detector that provokes a reduced collected charge with respect to the Monte Carlo simulations that from our data (see next section) cannot account for more than 10%. Although this difference can be produced by partial depletion of the active volume, the results of IBIC tests indicate that this effect would only change the pulse 80 Chapter 3. Description of the silicon detectors and experimental device height at most a 8% between 0 V and 3 V bias voltage (see figure 8 in [93]). The rest of the discrepancy remains unaccounted for as of the writing of this dissertation. There are several hypothesis being worked on that will be discussed in the following paragraph. In some production batches there was little control over some of the most external layers of the detector, and a difference on the thickness of some of those layers could greatly affect the Monte Carlo results due to the high ionisation density of the α-particles employed. Another possible source of uncertainty stemming from this last property of the α-particles is that if any particle enters into the detecting volume with an angle different from normal incidence the energy deposition will be larger, shifting the peak position to the right and smearing the energy deposition spectra. Due to the incompatibility of these results a different, an indirect calibration method was employed for this detection system and will be described in the following chapter. A new batch of the detectors was received by the end of 2018. These detectors had an increased thickness (nominal values of 10 µm and 20 µm) while keeping the same structure as the 3D Cylindrical Microdosimeters described in this work. The repetition of the electronics calibration and measurements with 238Pu yielded a better agreement between experimental data and simulations. In this case, the expected signal was calculated using SRIM Monte Carlo and was compared with a pulse height spectrum calibrated from the test input of the read-out system. Due to the performance of the system, the data (shown in figure 3.26), exhibits low statistics corresponding to more than 20 hours of data acquisition. 3.4 Charge collection efficiency During the study of the microdosimetric properties of the 3D Cylindrical microdosimeters some limitations to their operational capabilities were detected. A loss of collected charge produced from the track ionization due to recombination processes that affect the reconstruction of the imparted energy distributions was 3.4. Charge collection efficiency 81 0 0.5 1 1.5 2 2.5 3 3.5 4 0 2 4 6 8 10 Energy in silicon (MeV) 0 0.5 1 1.5 2 2.5 3 3.5 4 0 500 1000 1500 RUN 10859 single channel instrumented nominal thickness 10 um; Pu238; 11.2 mm air; 3 mm diam collimator; board 001 TRIM simuation for 11.0 um silicon thickness Figure 3.26: Up: Single channel spectrum from run 18059 with nominal thickness of 10 µm and diameter of 15 µm from 238Pu corresponding to α-particles of 5.499 MeV (70.91%) and 5.456 MeV (28.98%) using electronics calibration (most probable deposited energy 1.8 MeV). Down: SRIM simulated energy deposition for 11 µm that gives a most probable deposited energy of 1.89 MeV. found, provoking a modification of the microdosimetric spectra. This effect is summarized usually through the charge collection efficiency dependence on the track impact position. The intrinsic field gradients present in the device together with the charge drift and diffusion provoke that in the microdosimeter cell periphery the charge collection efficiency exhibits a relatively fast decay to null values. Partially depleted silicon volumes present in the device lead to recombination of the ionization charge and partial charge collection. Due to the intrinsic technological limits in the microelectronics manufacturing processes, this charge collection transition is not negligible in general terms and can affect the reconstructed microdosimetric spectrum from the silicon micro-cell. This issue has been addressed in the present study to evaluate its significance and the limitation consequences for the actual microdosimeter geometries. 82 Chapter 3. Description of the silicon detectors and experimental device Furthermore, in the current state of the art, solid state microdosimeters lack of intrinsic amplification and this limits seriously the signal to noise for devices in the micrometer and sub-micrometer dimensions. The active volume and charge collection properties of IMB-CNM 3D Cylindrical microdosimeters were studied. In the case of the microdetectors studied the output signal was taken as proportional to the imparted energy in the sensitive volume. From the spectra given by the detector signal, other microdosimetric quantities can be calculated. To evaluate the charge collection properties of the device, a model for the charge collection efficiency as a function of the distance to the centre of the active area was developed and then compared its results with experimental data from test runs done at the Fondazione CNAO (Pavia, Italy) synchrotron using a 12C ion beam and also in a proton microbeam in CNA (Seville). 3.4.1 Materials and methods Experimental set-up The characterization of these devices with ion therapy beams were performed using an 115.23 MeV A−1 12C ion beam at Fondazione CNAO (Pavia, Italy) [94]. Several measurements were carried out placing the microdosimeter in front of a variable depth of polymethyl methacrylate (PMMA, density 1.186 g cm−3). The depth was controlled using a motorized remote wedge system. The wedge system is formed by two 10◦PMMA wedges allowing a variable depth of 3 mm to 40 mm with an uncertainty of the depth of around 30 µm. PMMA is a tissue-equivalent material, allowing to perform measurements in the fields of microdosimetry and radiobiology, the main scope of these detectors. The set of microdosimetric spectra obtained cover from the beam entrance plateau up to the Bragg peak. A more detailed study of these measurements is presented in section 4.2.1. The microdosimeter was connected to a CAEN A1422H Hybrid charge sensitive preamplifier and to a CAEN N968 spectroscopy shaping amplifier. Then, the resulting pulse height was digitized through an Amptek MCA8000D multichannel analyser placed in the experimental room, connected via Ethernet to a computer 3.4. Charge collection efficiency 83 in the control room where the spectra were stored. For the detailed evaluation of the Charge Collection Efficiency (CCE) we used the IBIC proton microbeam facility at CNA (Seville). During the irradiation the beam was scanned through the detector with a beam FWHM varying from 3.46 µm (X) up to 4.85 µm (Y) and the readout was performed through a synchronized amplifier and digitizer chain. The kinetic energy of the proton beam employed was 600 keV in different test runs conducted in vacuum. Figure 3.27 shows the pulse height spectra for 0 V and 3 V bias voltage in the IBIC proton beam. Figure 3.27: Pulse height spectrum for 600 keV proton beam in vacuum taken at the IBIC beam at CNA (Seville, Spain). 84 Chapter 3. Description of the silicon detectors and experimental device Electrical simulations Electrical simulations were conducted with a Technological Computed Assist Design (TCAD) software, Sentaurus Synopsys. This software solves the Poisson equation for the studied geometry. Those simulations show in good detail the electrical field of the microdosimeter as also the transient of a heavy ion through any angle of the device, giving the charge collection. The simulated device is a 10 µm radius n-type (with a doping concentration of 8.61 ×1011 cm−3) microdosimeter with a 5.3 µm thickness. The silicon dioxide charge surface density used is 1x1011 cm−2.The electrical simulations were carried out with 0 V, 5 V and 10 V bias voltage. From capacitance measurement and simulation the microdosimeter is expected to be fully depleted at 5 V voltage bias. The transient simulations use the HevyIon software function, with particles that have a LETfin silicon (Linear Energy Transfer function) of 1.282x10−5pC/µm impinging perpendicularly to the surface of the microdosimeter. Monte Carlo simulations The experimental work was benchmarked against a Monte Carlo simulation of the beam energy deposition in an individual cell of the detector. Monte Carlo simulations were performed using the FLUKA Monte Carlo code [80,81], developed by CERN and INFN. The code is described in detail in section 2.6.1. For each geometry a simulation with 105histories in total was computed. The estimated relative statistical uncertainty for the simulation in the plateau region of the Bragg curve was of less than 2%. The code was commissioned against a water depth dose distribution of the same CNAO experimental beam measured with a Peakfinder variable water column and a PTW 34080 Bragg-peak chamber. This procedure is detailed in section 4.1.2. 3.4. Charge collection efficiency 85 Figure 3.28: Original measured experimental spectrum (blue dotted line) and FLUKA Monte Carlo simulation (red solid line) for 115.25 MeV A−1 12C ions traversing 25.20 mm of PMMA. 3.4.2 Results Charge Collection Efficiency Clinical 12C beam experimental spectra obtained with the new cylindrical microdosimeters exhibit a reasonable agreement with the expected results of the Monte Carlo simulations [94]. Nevertheless, experimental pulse height distributions always show a relevant tail with high number of counts in the low-energy part of the spectra and a small shift in the peak position when compared with the imparted energy distributions from simulation, as can be seen in figure 3.28. Electronic noise contribution, amplifier baseline shifts or pile-up events have not been found to be able to generate this distortion of the measured data from the 86 Chapter 3. Description of the silicon detectors and experimental device microdosimeters. The effect of spectrometry distortion in silicon microsensors has been reported previously in different devices with high granularity readout [95, 96]. The main hypothesis is that this behaviour is produced by intrinsic field gradients and charge diffusion that modify the recorded spectra by the microsensor, provoking partially depleted volumes leading to recombination and partial charge collection in the periphery of the microcylinder. As a consequence of this, the measured microdosimetric spectra is modified, taking the form seen in the aforementioned figure when it is compared with a Monte Carlo simulation with the detailed geometry of the detector. To study these effects a detailed electrical simulation of one cell of the microsensor was performed using Sentaurus TCAD. The figure 3.29 shows the electric Figure 3.29: Electric field simulation using Sentaurus TCAD inside a microcylinder for biasing potential of 0 V (top), 5 V (center) and 10 V (bottom). The white line denotes the depletion volume inside the semiconductor 3.4. Charge collection efficiency 87 field simulations inside a unit cell of the detector for different biasing potentials. The sensor lenticular shape depletion volume is shown in this figure delimited by the white solid lines. The simulations additionally reproduce the transient electric signal associated to the particle ionization event. For that scope, taking into account the 3D depletion volume that depends on the electric field inside the device, the drift and diffusion of charge carriers were simulated leading to the charge signal induction according to the 3 µs shaping time of the electronic readout. Charge collection efficiency (CCE) was studied varying the particle track impact position within the geometry of the microdosimeter. Figure 3.30: Maps of charge collection studies recorded at the IBIC test performed in CNA (Seville, Spain) with the IMB microcylindrical sensors. 94 Chapter 3. Description of the silicon detectors and experimental device Distance from the center, r (µm) 0 2 4 6 8 10 12 Charge collection efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1CCE Model TCAD Simulations Figure 3.35: Comparison between the charge collection efficiency predicted from our model and from TCAD simulations results. silicon microcylinder. In fact, the experimental results shown in figure 3.30 show additional effects as the lack of symmetry of CCE respect to the cylindrical sensor axis that was also varying between different individual cells. The detectability problem One of the main scopes in microdosimetry is the measurement of microdosimetric distributions at micrometric and submicrometric scale. In the case of submicron equivalent mass thickness devices, they would be sensitive to the track structure and charge cluster distributions in the material. As we have seen previously the fidelity of reconstruction of microdosimetric spectra can be seriously compromised specially in the low lineal energy region by effects related to CCE in the small volume of the solid state microdosimeter. On 3.4. Charge collection efficiency 95 the other hand, as current devices have no intrinsic gain, there is additionally a physical limitation on the threshold of detection for low lineal energy. Although many possible designs are feasible, in terms of simplicity we have considered here a cylindrical geometry where the cylinder radius and its height are equal to certain dimension L. Considering a simple approach we have taken that the device capacitance and its leakage current depend linearly on the microdosimeter size parameter L. If we take a standard approximation for the ENC (rms of the noise charge) of the charge sensitive amplifier, this would have a behaviour ENC =rα(Cin +β)2 τ+γτ(Id+δ) + κ whereas τis the amplifier shaping time, Cin is the detector capacitance and Id Distance from the center, r (µm) 0 1 2 3 4 5 6 7 Charge collection efficiency 0 0.2 0.4 0.6 0.8 1CCE model (convoluted) Experimental data Figure 3.36: Comparison between charge collection efficiency results from the experimental test at CNA and from a convolution between a Gaussian distribution with σ= 2µm to take into account the finite width of the proton beam that contributes to smear the experimental CCE distribution. 96 Chapter 3. Description of the silicon detectors and experimental device the detector leakage current and α,β,γ,δand κare noise parameters associated to the electronic readout chain due to shunt and series resistance, sensor bias current and amplifier contributions [98, 99]. For this work we have considered sizes Lof cylindrical microdetectors from 0.1 µm up to 40 µm with Cin ranging from 0.01 pF up to 5.3 pF and Idfrom 0.3 pA up to 133 pA. These values were taken according to our experience with similar devices. We used the parameters from the state of the art electronics [100] to calculate that ENC would yield values between 250 up to 280 electrons for a shaping time of 1 µs respectively (α = 43 pF−2µse2;β= 15 pF; γ= 8 µs−1pA−1e2;δ= 800 pA; κ= 5×104e2). We have restricted the track incidence to be parallel to the cylinder axis considered above, thus having < l >=L. For the noise separation we have assumed that the FWHM equivalent noise energy would be 2.35 times the ENC multiplied by the average energy wper ion-electron pair, thus providing a threshold on the energy imparted detection taken as two times this FWHM [98] εth ≥2×ENC ×2.35 ×W This provides also a corresponding limit on the lineal energy detection in the form of yth =εth < l > ≥4.7×ENC ×W < l > Thus we can evaluate the corresponding limits for the detection of the lineal energy considering these cylindrical microdetectors of different size L. Figure 3.37 shows the limits on the detection of lineal energy as a function of the detector size with ENC values ranging from 250 to 280 electrons. In this Figure we have included both silicon and diamond sensors just to guide the reader in terms of the physical limits expected from the different characteristics of the sensitive media. The capability to extend the detection range to 1 keV/µm would be achieved in silicon when the size of the microsensor is equal or bigger than 4.4 µm while in the case of diamond this would imply a sensor of 16 µm thickness. Additionally, it is clear that sub-micron microdosimeters would be only useful for highly ionizing 3.4. Charge collection efficiency 97 0 5 10 15 20 25 30 35 40 0 1 2 3 4 5 6 7 8 9 10 Size of microdosimeter (µm) Threshold of detection of lineal energy (keV / µm) Figure 3.37: Limit of detectability for lineal energy in cylindrical micro– dosimeters with equal diameter and height Las a function of L. Continuous line is calculated for silicon and dashed line corresponds to diamond. 98 Chapter 3. Description of the silicon detectors and experimental device particles, since for silicon (diamond) devices of 1 µm we would only be able to detect radiation with lineal energy over 4.5 keV/µm (15.7 keV/µm). This conclusion tends to exclude the feasibility of solid state microdosimeters as adequate devices for track structure measurement in the region around 0.1 µm or below, at least for non intrinsic gain sensors. In fact the use of devices of tenths of microns would yield values closer to the Linear Energy Transfer (as a macroscopic magnitude) than the stochastic lineal energy considered in microdosimetric distributions. Of course, the results of this section could be recalculated considering the particular electronic noise considering the particular sensor characteristics and the readout under study. Chapter 4 Experimental validation of the microstructured 3D thin silicon sensors 99 100 Chapter 4. Experimental validation of the microstructured 3D thin silicon sensors Summary of the chapter: In this chapter the experimental results obtained with the thin microstructured silicon detectors described in the previous chapter are presented, showing how can they characterise monoenergetic 12C ion beams. Results are compared with FLUKA Monte Carlo simulations, showing great agreement between them. 4.1. Methods 101 Several tests were performed to evaluate the performance of the microdosimeters described in the previous chapter in carbon ion beams.First, the U3DTHIN microdosimeters were tested with 12C ions at GANIL (Caen, France) to check its behaviour under irradiation. Next, the following generation of microsensors (3D cylindrical microdosimeters) was tested with both proton and 12C ion beams at the installations of Fondazione CNAO (Pavia, Italy), a public Italian particle therapy facility. For all tests, results were compared with Monte Carlo simulations using FLUKA. 4.1 Methods 4.1.1 Experimental set-up The experimental set-up for each of the different experiments performed followed the same pattern. After the beam monitoring system, a motorized PMMA wedge and the microdosimeter detection system were placed in a plane perpendicular to the beam direction. The wedge system was composed by two equal 10◦angle wedges made of 1.186 g/cm3PMMA that provided a continuous variable thickness from 3 mm up to 30 mm (40 mm in the CNAO set-up) with an uncertainty of around 40 µm for the GANIL experiment and 80 µm for the CNAO one. The relation between wedge position and thickness was calculated using a second-order polynomial fit. Figure 4.1 shows the relation between wedge position and thickness for both the GANIL and CNAO measurements. Residuals for both quadratic fits are shown in figure 4.2. The root mean square of the residuals was employed to calculate the uncertainty of the wedge position. Figure 4.3 shows a sketch of the experimental set-up. In GANIL, the 12C 94.983 MeV A−1beam was delivered at the G4 experimental area of the facility. Beam profile was tuned to have an approximate FWHM of 7 mm at the beam pipe exit window to provide a uniform irradiation of the detector active area with an intensity around 104particles per second with 102 Chapter 4. Experimental validation of the microstructured 3D thin silicon sensors -180 -160 -140 -120 -100 -80 -60 -40 -20 0 20 0 20 40 Quadratic fit Measured points Wedge position(mm) -180 -160 -140 -120 -100 -80 -60 -40 -20 0 20 0 20 40 Wedge thickness (mm) GANIL CNAO Figure 4.1: Second order polynomial fit between wedge position and thickness for the wedge systems employed in the GANIL and CNAO tests. an average fluence rate at the detector of 2.4×104s−1cm−2. The expected longitudinal range of the carbon ions in PMMA was 20.5 mm, being sampled with steps of several mm in the stopping power plateau region and with sub-millimetric precision close to the Bragg peak. The low-level discrimination threshold for the signal was set approximately to 200 keV in silicon. For each depth, several spectra of the diode signal were acquired with a total integration time of 200 s each. For the CNAO tests, 12C particles with a kinetic energy of 115.23 MeV A−1 were used. The beam had an approximate diameter of 20 mm, with a Gaussian profile with a FWHM of 5.1 mm along the horizontal axis and 8.5 mm along the vertical axis at the nozzle providing full irradiation of the detector active area. The average fluence rate was 5 ×107s−1cm−2and for each measurement a total number of approximately 109carbon ions were delivered. 4.1. Methods 103 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 20 -0.1 -0.05 0 0.05 0.1 Wedge position(mm) -180 -160 -140 -120 -100 -80 -60 -40 -20 0 20 -0.2 -0.1 0 0.1 0.2 Residuals CNAO GANIL Figure 4.2: Residuals of both second order polynomial fits between wedge position and thickness for the wedge systems employed in the GANIL and CNAO tests. The expected longitudinal range according to SRIM [29] for carbon ions in PMMA with the energy employed was 28.47 mm. The Bragg curve was sampled taking spectra in steps of several millimetres in the plateau region and submillimetre steps in the proximity of the Bragg peak. 4.1.2 FLUKA Monte Carlo Analysis of the experimental work required a detailed simulation of the beam interactions and radiation transport. Although there are different choices for carbon ion beam Monte Carlo codes with very good agreement with the experimental data, there are still some uncertainties in the benchmarking of nuclear models [82]. Due to previous experience with that Monte Carlo code, FLUKA was employed to compare with experimental data, and a discussion on the cap- 110 Chapter 4. Experimental validation of the microstructured 3D thin silicon sensors Lineal Energy, y (keV µm-1) 0 100 200 300 400 500 600 700 800 900 1000 y d(y) 0 1 2 3 4 5 6 7 8 20 mm 7 mm 15 mm 19 mm Figure 4.8: Microdosimetric distributions y d(y) in silicon from experimental data and FLUKA Monte Carlo at different depths in PMMA (see text) for the U3DTHIN detectors in GANIL. Solid lines represent Monte Carlo simulations, whereas the different symbols represent the experimental distributions. parameters. In general, the agreement between the experimental points and the Monte Carlo curve is good, but some points showed pile-up effects that modified the experimental value. This was minimizing by applying cut-offs in the experimental distributions at high energies. These cut-off values were decided by evaluating the Monte Carlo distributions and comparing them with the experimental ones to assure no real data was being modified, approximately at twice the peak value. A comparison between the experimental and Monte Carlo f(y) distributions is presented in Fig. 4.11. In the figure are shown the spectra for depths of 12.2, 25.2, 27.2 and 28.125 mm respectively. Although the agreement between experimental and Monte Carlo most probable lineal energy is remarkable, the normalization of the experimental spectra presents some problems that affect the scoring of the fluence averaged lineal energy. Charge collection efficiency modifies 4.2. Experimental Results 111 Depth in PMMA (mm) 0 5 10 15 20 25 <yD> (keV µm-1) 0 100 200 300 400 500 600 700 800 Experimental points FLUKA Monte Carlo Figure 4.9: Dose averaged lineal energy experimental (crosses) and FLUKA Monte Carlo (solid line) computed values in the U3DTHIN silicon detector at GANIL. the shape of the spectra and the position of the peak as discussed in section 3.4. In the case of spectra close to the Bragg peak (27.2 mm and 28.125 mm) the linear energy distribution peak position does not adjust very well as depths in the proximal Bragg peak area are difficult to compare since dependence on the effective mean ionization potential can modify the shape of the distributions at these depths [21,101]. Microdosimetric spectra for the same PMMA depths as in figure 4.11 were also calculated. The results are shown in figure 4.12. Although the general agreement between measured and simulated most probable values is remarkable, there are differences in the shapes of the distributions due to partial charge collection in the active volume and pile-up events at high energies modifying the spectra due to the way yd(y) is calculated, cross-talk from the other active areas and baseline shift at different energies, as well as noise added by the amplification 112 Chapter 4. Experimental validation of the microstructured 3D thin silicon sensors Depth in PMMA (mm) 0 5 10 15 20 25 30 ymp (keV µm-1) 0 100 200 300 400 500 600 Experimental points FLUKA Monte Carlo Figure 4.10: Most probable lineal energy comparison between experimental data (dots) and FLUKA Monte Carlo simulations (solid line) for the CNAO test with 3D cylindrical microdosimeters. stage and differences between the simulation geometry and the real geometry of the experiment. To add to that, the same problems as figure 4.11 are also present here. Dose averaged lineal energy distributions are presented in Fig. 4.13. 4.2.2 RBE Calculations with 3D cylindrical microdosimeters In treatment planning, RBE is used to transform the physical dose delivered into a biological dose (or RBE-weighted dose) that considers the effects other than the radiation-matter interaction. Due to strong RBE dependence on both physical and biological parameters, RBE must be described by more or less complex models instead of using a simple factor. There are different models described in the literature [50–54] based on in vitro data. An RBE calculation based on the microdosimetric kinetic model (MKM) was 4.2. Experimental Results 113 Lineal Energy, y (keV/µm) 0 100 200 300 400 500 f(y) 0 0.01 0.02 0.03 0.04 0.05 0.06 28.125 mm 27.200 mm 25.200 mm 12.200 mm Figure 4.11: Probability distributions f(y) in silicon from experimental data and FLUKA and at different depths in PMMA (see text) for the 3D Cylindrical microdosimeters in CNAO. Solid lines represent Monte Carlo simulations, whereas the different symbols represent the experimental distributions. performed using the data acquired in CNAO. In this formulation the number of lethal events is modelled as proportional to the square of the specific energy, z, and the cell nucleus is supposed to be divided into small domains of finite size of cylindrical shape (with Rnbeing the radio of the cell nucleus and rdthe radius of the domain). The parameters of the linear-quadratic model obtained from the MKM corrected model [103,104] depend on a saturation corrected, dose weighted specific energy produced by a single event (z∗ 1D). The saturation correction considers the “overkill” effect observed when a cellular line is irradiated with high LET radiation. Under this assumption, a given 114 Chapter 4. Experimental validation of the microstructured 3D thin silicon sensors Lineal Energy, y (keV/µm) 0 100 200 300 400 500 y d(y) 0 1 2 3 4 5 6 12.200 mm 25.200 mm 27.200 mm 28.125 mm Figure 4.12: Microdosimetric distributions y d(y) in silicon from experimental data and FLUKA and at different depths in PMMA (see text) for the 3D Cylindrical microdosimeters in CNAO. Solid lines represent Monte Carlo simulations, whereas the different symbols represent the experimental distributions. dose of radiation is needed to kill the cell with total probability. If the cell is exposed to a higher dose of radiation, the remaining radiation is somehow wasted in a cell that is already dead and cannot affect other sites. z∗ 1D=Z∞ 0 zsatzf(z)dz (4.2) where zsat is given by zsat =z2 0 z1−exp−z2 z2 0 (4.3) 4.2. Experimental Results 115 Depth in PMMA (mm) 0 5 10 15 20 25 30 <yD> (keV µm-1) 0 100 200 300 400 500 600 700 800 900 Experimental points FLUKA Monte Carlo Figure 4.13: Dose averaged lineal energy experimental (crosses) and FLUKA Monte Carlo (solid line) computed values in the silicon detector for the 3D Cylindrical microdosimeters in CNAO. And the characteristic saturation parameter, z0 z0=(Rn/rd)2 pβ[1 + (Rn/rd)2](4.4) The values for Rnand rdhave to be specified to get z∗ 1D. In this work, the values for aerobic human salivary gland (HSG) cells were used, with rd= 0.32 µm [104]. Considering that the quantity α0+βz∗ 1Dcan be rewritten as αMKM due to its resemblance to the αof the LQ model we can obtain the radiobiological efficiency using: RBE =Dref (S)"−αMKM +qα2 MKM −4ln(S)β 2β#−1 (4.5) 116 Chapter 4. Experimental validation of the microstructured 3D thin silicon sensors Depth in PMMA (mm) 0 5 10 15 20 25 30 z* 1D (Gy) 0 5 10 15 20 25 30 35 RBE 2 3 4 5 6 RBE FLUKA Monte Carlo Experimental points Figure 4.14: Experimental z∗ 1Dvalues from the CNAO 12C ion beam (crosses) compared to FLUKA Monte Carlo (solid line). Additionally, RBE values for experimental points (squares and dashed line) are shown. From the microdosimetric behaviour of the radiation in the energy transfer to cells, radiation weighting factors can be obtained. Lineal energy distributions can be benchmarked to a Monte Carlo model to aid experimental methods and perform beam characterization [18, 19]. To obtain the experimental data, adequate instrumentation for the measurement of the microdosimetric quantities is needed. To evaluate RBE and z∗ 1Dfrom experimental data, the imparted energy values in the microdosimeter (silicon) were converted to imparted energy in water using a look-up table of stopping power values taken from [29]. The values used to calculate the radiation endpoint in order to get the RBE were the same as [104], coming from HSG cells. Figure 4.14 shows the comparison between experimental and Monte Carlo z∗ 1D, and the RBE calculation for the experimental spectra. 4.2. Experimental Results 117 Although experimental values agree in general with Monte Carlo, this agreement is limited. Events detected at high energies alter the average values, but these events can be explained due to pile-up in the detector volume. Additionally, cross-talk noise coming from other sensitive volumes, as all the sensitive volumes are connected to the same ground, and electronic noise coming from the amplification stage add further uncertainties. There is also a limitation in the dynamic range of the instrumental setup, partial charge collection and the need for the conversion from silicon measured specific energy to water. Thus, the evaluation of z∗ 1Dincludes uncertainty components from experimental cut-off values and the limitation of the algorithm employed for this transformation. z* 1D (plateau) 5 10 15 20 25 30 ∆RBE/∆ z* 1D 0.076 0.077 0.078 0.079 0.08 0.081 0.082 z* 1D (peak) 10 20 30 40 50 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Figure 4.15: Sensitivity of the RBE function to changes in the saturated specific energy, z∗ 1D. The figure shows the RBE sensibility in terms of the relative variation of the input parameter z∗ 1D, for two different positions along the Bragg curve, the plateau (left), and the proximal Bragg peak area (right). 118 Chapter 4. Experimental validation of the microstructured 3D thin silicon sensors Depth in PMMA (mm) 4 6 8 10 12 14 16 18 20 22 γ index 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Figure 4.16: Gamma function for the most probable lineal energy obtained from experiment and FLUKA for the most probable values of lineal energy in the GANIL test. Tolerances are 2% of the most probable energy for each point and 0.5 mm. 4.2.3 Study of the uncertainty of RBE The aim of measuring lineal energy in particle therapy is the evaluation of biological dose. Thus, the issue of knowing how the uncertainty of microdosimetric distributions translates to RBE uncertainty is important. Also, to evaluate the agreement between the experimental data and Monte Carlo distributions presented in this chapter a Gamma test [105] was employed. The tolerances were chosen attending to the clinical precision needed in particle therapy; in particular, tolerance for the PMMA thickness was chosen as 0.5 mm. To select the lineal energy tolerance, RBE sensitivity to microdosimetric spectra variation was studied by assessing the effect on RBE of the variations on imparted and specific energy. By varying the input lineal energy used for the RBE calculation by a certain value (from 50 % to 150% of the experimental value) the variation in the RBE was evaluated. Due to the saturation effect applied in the RBE calculations, the 4.2. Experimental Results 119 Depth in PMMA (mm) 4 6 8 10 12 14 16 18 20 22 γ index 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Figure 4.17: Gamma function for the dose-averaged lineal energy obtained from experiment and FLUKA for the dose averaged lineal energy in the GANIL test. Tolerances are 2% of the most probable energy for each point and 0.5 mm. variation of the RBE values was more prominent in the plateau area of the Bragg curve than in the proximal peak area. Figure 4.15 shows the sensitivity of the variation as a function of the input lineal energy for the plateau and proximal Bragg peak areas. The thicknesses of the PMMA were 7.2 mm and 27.4 mm for the plateau and the proximal Bragg peak area, respectively, corresponding to the first (plateau) and maximum (Bragg peak) points in the plot of figure 4.14. Given an uncertainty of ∼10% in z∗ 1D, a relative uncertainty of ∼6% is expected in RBE. As the RBE varies greatly along the Bragg curve, and the effect of the variations in the lineal energy is so different depending on the point of the curve under evaluation, it was decided that each experimental point of the Bragg curve would have a different tolerance value, equal to 2% of the Monte Carlo lineal energy value at each point. This avoids the problem of choosing a value too small or too large for any one of the points along the Bragg curve. 126 Chapter 5. Future work and conclusions Summary of the chapter: This chapter presents the conclusions of this work along with some future improvements and possible experiments to be performed to improve the current technology of microstructured solid-state detectors for microdosimetry. 5.1. Conclusions 127 5.1 Conclusions This thesis presents two different designs of microstructured silicon detectors for microdosimetric measurements. Performance and experimental validation of both kinds of silicon microsensors are covered in this work. The tasks performed were:  Study of the feasibility of the silicon based microstructured devices for microdosimetric applications. In the case of the U3DTHIN silicon detectors, the tests in GANIL have shown the feasibility of the use of 3D diode silicon structures for the measurement of the microdosimetric distributions of ion beams. The possibility to perform actual measurements of these quantities allows a realistic analysis and commissioning of hadrontherapy beams. The silicon detectors tested were based in a novel production process that can yield thin diode three dimensional structures suitable for high fluence rate beams. The experimental setup included a PMMA motorized wedge that allowed the control of the effective thickness traversed by the beam with a precision of 40 µm in the case of the GANIL tests and 80 µm for the CNAO tests. The experimental results of the microdosimetric lineal energy spectra y d(y) were compared to those obtained with FLUKA, obtaining excellent agreement for the most probable lineal energy value as a function of depth. For the evaluation of this agreement a gamma test [105] was performed with a variable tolerance for ∆yequal to 10% of the most probable lineal energy for each point in the Bragg curve and a tolerance for ∆z= 0.5 mm between FLUKA simulations and the experimental data. The experimental results have γ < 0.65. Considering the dose averaged lineal energy, the agreement between the silicon device data and the values computed from FLUKA is better than 1.2 in the gamma test. This results indicate that 3D ultra-thin silicon structures can be used to characterize the microdosimetric properties of ion beams. Nevertheless, U3DTHIN silicon detectors have some issues regarding the sensor response dynamical range and pile-up. 128 Chapter 5. Future work and conclusions The other type of devices presented in the chapter were the silicon cylindrical microdosimeters. The test at the facilities of CNAO showed the good performance of the new silicon cylindrical microdosimeters for the measurement of microdosimetric distributions for hadrontherapy. The microdosimeters have a diameter of 15 µm and a thickness of 5.5 µm and an energy resolution of 12 % at an imparted energy of 650 keV. The detector is able to analyse LET or linear energy distributions of clinical beams, allowing the calculation of RBE and commissioning of said beams in clinical conditions, with a fluence rate of 5 ×107s−1cm−2without saturation effects becoming apparent on the detector readout. Experimental spectra were compared with Monte Carlo simulation showing a great agreement between the most probable lineal energy, with gamma values between experimental points and Monte Carlo less than 0.25. This comparison was performed with the same gamma tolerances than the U3DTHIN detectors. Dose averaged lineal energy shows in general a good agreement, although pile-up and cross-talk events within the detector and CCE effects as described in this dissertation contribute to make this calculation less accurate than the most probable value discussed before. Gamma tests in this case takes values lower than 1.2 in general, with values lower than 0.3 in the proximity of the Bragg peak.  RBE calculation and uncertainty asessment. RBE values through the use of the microdosimetric kinetic model (MKM) were also calculated from the transformation of imparted energy in silicon to saturation corrected dose-weighted specific energy, allowing the calculation of biological dose. These results indicate that the silicon cylindrical microdosimeters employed in this work can be used to characterize the microdosimetric and radiobiological properties of high LET beams as the ones used in hadrontherapy. The RBE values were also used to provide the tolerances to the gamma test done to the experimental measurements of both types of silicon detectors. By varying the input lineal energy used for the RBE calculation by a certain value the variation in the RBE was evaluated. It was estimated 5.1. Conclusions 129 that a relative uncertainty of the specific energy input parameters of ∼10% provokes a RBE relative uncertainty of ∼6%.  From µ-randomness to clinical fluence Historically different chord length distributions were used in the first formulation of microdosimetry such as µ-randomness derived from first principles in the so-called “geometrical probability”. Actual chord length distributions in the practical proton and ion therapy clinical cases are significantly different from those general distributions. The probability distributions of the chord length inside the detector for a case of a beam of particles with almost parallel trajectories coming from a focal point outside the detector and with normal incidence were studied. It was found that the thickness of the detector can be used as the mean chord length of the particles due to the high directionality of the radiation field for the cases where the range of the particles was more than the thickness of the detector. A correction factor was calculated by Monte Carlo simulations to consider the divergence between the previous assumption and the real behaviour of the chord length distribution probabilities, although for the special case of protons those correction factors can be up to 10% in the Bragg peak, as shown in section 2.3.2.  Comissioning of Monte Carlo simulations. The FLUKA Monte Carlo code developed for the simulation of the microdosimetric distributions measured with the silicon microstructured devices was benchmarked against experimental results performed with a PTW Peakfinder variable water column and a PTW 34080 Bragg-Peak chamber in a monoenergetic 115.2 MeV A−1 12C ion beam with a detailed simulation of the ionisation chamber in order to check its consistency. The local relative difference between experimental and simulation is less than 4% for all points along the Bragg curve, although the difference is higher in the distal tail. The results of this testing demonstrate that the 130 Chapter 5. Future work and conclusions benchmark of the code was successful and can be safely used for hadrontherapy applications for protons and heavy ions.  Development and testing of discrete read out electronics for its use with silicon microdosimeters. Throughout the course of this project the read out electronics were improved with the aim of getting portability, simple use, high signal to noise ratio, sensitivity and low noise levels. The last version of the readout electronics uses a tandem system of detector/pre-amplifying stage at approximately 5 cm the rest of the discrete electronic system that is housed outside the possible beam trajectory to avoid signal contamination by the event upset of the electronic components, followed by a fixed gain buffer amplifier, shaping stage, and baseline restorer. The electronics were optimized for the small input detector capacitance while providing AC readout of the detector to deal with its leakage current.  Assessment of the limitations of the detection system. Although the microdetectors are capable of the measurement of microdosimetric distributions under clinical fluence rates, charge collection efficiency (CCE) and electronic noise pose limitations on their performance. For the cylindrical device studied in this work with 15 µm diameter and 5.5 µm thickness, the intrinsic field gradients and charge diffusion in the sensitive volume of the detector modify the recorded spectra by inducing a charge collection efficiency strongly dependent on the position of the energy deposition event. These perturbations modify the raw experimental microdosimetric spectra in a systematic way, producing an artificial enhancement of the low lineal energy region. In the present work this evidence was found in 12C beam measurements at CNAO. In order to reproduce this systematic effect we constructed a first analytical model for the CCE by using exponential function and six parameters related to the physical dimensions of the microstructured detector. Electrical simulations using TCAD and proton beam IBIC tests performed to study the active volume inside the microdosimeters at different biasing voltages 5.2. Future work 131 were additionally used to validate the CCE model. Monte Carlo simulations were modified by using this model to compute the partial charge collection in the simulated energy deposition events. Reconstructed spectra including CCE effect showed considerable agreement with the experimental results. The most probable lineal energy in these experimental spectra is shifted with respect to the expectation value from Monte Carlo. This shift along the Bragg curve holds a linear relationship with the lineal energy with a maximum of 16 keV/µm, about 6% of the most probable lineal energy at that point. Additionally to the distortion of the low lineal energy spectra, the electronic noise contribution sets a theoretical limit on the smallest detectable lineal energy for microstructured solid state devices. Considering a cylindrical device with equal diameter and height L, the lineal energy threshold would be inversely proportional to this parameter. For example, for detecting events of 1 keV/µm, the dimension Lshould be greater than 4.4µm whereas in diamond this size should be at least 16 µm. 5.2 Future work There are several possible improvements to do in the solid-state microdosimetric detectors described in this work regarding their response and charge collection efficiency. First, the structure of the microdosimeters could be improved to avoid as much as possible the modification of the microdosimetric spectra due to low charge collection efficiency in the periphery of the active volume of the detector. This can be done by surrounding the current structure with new layers of detector material in a manner of a bullseye, adding further n and p doped regions in the periphery to enlarge the charge collection efficiency in the area. Currently this design is under development and this new version of the microdosimeter will be tested in the future. The read-out electronics have been improved through the development of this 132 Chapter 5. Future work and conclusions thesis. With the first designs of the read-out electronics a pre-assembled Amptek detector was employed, but a new design was made from scratch, employing CAEN first and then CREMAT modules in a customized printed circuit board that have better amplification than previous versions and an improved signal-tonoise ratio. These new versions can be further customised to take into account the energy deposition density of the measured radiation and provide a good full scale output. The readout of multiple cells can also be improved. Currently, only one cell is read, and in order to provide spatial detection (one of the initial objectives thought for this device) the rest of the cells should also be evaluated. The cylindrical 3D microdosimeter array can be connected to a customised readout electronics system. One option under consideration is based on the use of a VATAGP7.1 chip [106]. This application-specific integrated circuit (ASIC) can provide a logic trigger signal and an analog output for 128 microsensors. Each of those channels features low noise, low-power buffered preamplifiers, a shaper with sample/hold, multiplexed analogue readout and calibration facilities. Moreover, each channel has a fast shaper that gives a trigger signal. The analogue value and the address of the triggering channels can be read out with a flexible serial or sparse readout mode. The VATAGP7.1 also offers input leakage current compensation automatically adjusted in each preamplifier channel. This ASIC can be chained to others VATAGP7.1 ASICs, sharing all output lines. This feature will allow to increase the number of channels and therefore the total area of the device. Hence, the 3D microdetector array could be used as unit-cell for mimicking a cellular tissue-like piece (multiple arrays of that unit-cell) and to characterize the RBE in the hadrontherapy clinical centres. Further engineer and microfabrication developments could yield in a potential quality assurance (QA) system before patient treatment. Finally, the 3D silicon cylindrical microdosimeters are going to be used in several research projects centred in novel hadrontherapy treatments capable of enhancing the quality of the current cancer treatments. With these new treatments new tools will be needed, either to spatially characterise a very small beam 5.2. Future work 133 (in the case of mini-beam radiation therapy) or to make a very fast read-out under very large dose rates (in the case of FLASH therapy). These new treatments pose new challenges in the fields of metrology. The first of these projects is related with proton mini-beam radiation therapy (PMBRT). This technique combines small field sizes with a spatial fractionation of the dose, which increases the normal tissue resistance (and thus, more healthy tissue is spared from cell death due to ionising radiation) [107,108]. By employing sub-millimetre field sizes , with pencil beams with diameters of approximately 500-700 µm, the experiments on animals showed high resistance of the healthy tissue to very high doses of radiation, while achieving tumour control compared with a high dose irradiation through conventional means [109–113]. The spatial fractionation is made by means of a dose profile pattern consisting of peaks and valleys. The ratio between the maximum dose (at the peak) and the minimum (at the valley) is called peak-to-valley-dose-ratio (PVDR) and plays a very important role in the biological response [114]. The dose in the valleys should be kept to a minimum to preserve the normal tissue architecture and the survival of healthy cells for tissue repair. The second research project where the microstructured silicon detectors are of interest is in FLASH radiotherapy. FLASH radiotherapy uses conventional X-ray, electron, and even proton beams to apply a very high dose in a very short time spam (dose rates ≥40 Gy/s). With this ultra-high dose rate the normal tissue complications are reduced while maintaining the tumour control level [115–118]. The tools and methods established for conventional radiotherapy cannot be used in FLASH therapy, as the ion collection efficiency of the air ionisation chambers employed in standard clinical practice is reduced up to 90% for the fluence rates used in FLASH therapy. By using the technology described in this thesis, the aim of the USC (and CNM-CSIC) will be to develop a prototype active dosimeter based on microstructured silicon technology and the characterisation of detectors in proton and electron FLASH beams. Appendix A Proton test at CNAO ion beam In this appendix an additional test of the 3D cylindrical microdosimeters with 66.34 MeV proton beam will be presented. The tests were done at the cyclotron of Fondazione CNAO (Pavia, Italy). As in the 12C ion test, the results were compared with Monte Carlo simulations using the FLUKA Monte Carlo code. The materials and methods employed are the same as in chapter 4. A.1 Results and discussion As in chapter 4, the data obtained was analysed and compared with Monte Carlo simulations made with FLUKA. The proton beam was propagated in a variable thickness of PMMA and then in a detailed geometry of the detector system, reconstructing a Bragg curve. The dimensions of the detector are the same as the 12C ion test at CNAO, and were not compared with other measurements of the same beam with different detection systems (e.g. TEPCs). As in the 12C ion tests, the imparted energy εis considered proportional to the silicon detector signal while the mean chord length ¯ lis approximately equal to the detector thickness for frontal irradiation. This was further confirmed by evaluating the particle track length on the Monte Carlo simulations up to the Bragg Peak, resulting in values equal to the active area thickness with an error 135