Introduction 1
Overview of application of ion implantation
Ion implantation is a widely utilized technique in various scientific and technological fields, offering precise control over dopant concentration while eliminating contamination and preventing secondary phases (Bonanni, 2007) This method involves embedding energetic ions into a substrate to modify its properties or create new materials It enhances the chemical and physical attributes of materials, improving characteristics like anti-corrosion, wear resistance, and electrical conductivity In these applications, the cost of the ion beam is often prioritized over its quality (Cho et al., 2009).
1.1.1 Ion implantation in fabrication of semiconductor
The semiconductor production process typically involves around 140 operations, with 70 of these focused on ion implantation into the crystal lattice Advanced techniques allow for precise ion implantation at specific sites and the intentional creation of defects The energy of the ions used, ranging from 2 keV to 600 keV, is determined by the desired depth of the implant Similarly, superconducting materials are produced using ion implantation to effectively 'pin' atomic planes.
The bombardment of materials with energetic ions has become a powerful technique for materials modification Despite of unquestionably the most
The implantation of dopants in semiconductor production is just one of several important applications; for instance, high current oxygen beams are utilized to form buried SiO2 layers in silicon, while nitrogen beams with energies exceeding 70 keV are employed to develop highly wear-resistant surfaces.
Ions play a crucial role in the surface treatment of metals within the engineering industry By implanting ions like tungsten, chromium, tantalum, nitrogen, and boron into steel components, such as ball bearings and cutting tools, the process effectively enhances corrosion resistance.
Ion beam technology offers a distinct advantage over traditional surface hardening methods, as it operates without heating the surface and often eliminates the need for further annealing This innovative approach is commonly utilized in the production of artificial hip and knee joints, as well as in the manufacturing of fuel rods for nuclear reactors, highlighting its significance beyond semiconductor applications The energy levels for ion beam processes typically range from 50 keV to 200 keV, with ion fluxes between 10^15 to 10^17 ions/cm², making it a versatile choice for various industrial applications.
1.1.3 Precision machining and membranes manufacture
Ion beam technology serves as a highly precise method for machining plastic surfaces, allowing for depth processing that surpasses the surface's transverse dimensions A notable application of this technique is ion track etching, which enables the creation of exceptionally fine filters from polymers.
4 foil It is possible to make membrane with track diameter from 10um down to 10 nm and densities from 1 to 10 9 pores per cm 2
Overview of accelerator use in ion implantation
Ion implantation utilizes various types of accelerators, including electrostatic accelerators, tandem accelerators, Radio Frequency Quadrupole (RFQ) accelerators, and Radio Frequency (RF) linear accelerators Each accelerator type offers unique advantages and disadvantages, which are summarized below The electrostatic accelerators-based implanter is one of the key technologies in this field.
The single-ended electrostatic accelerator has long been a valuable research tool, with a typical 4 MV machine providing a diverse array of ion species (Rathmell and Sundquist, 1985) These machines operate similarly to standard low-energy implanters, utilizing a positive ion source at high potential to extract and accelerate ions to ground However, they present challenges such as requiring significant space and necessitating careful management of high voltage maintenance, insulation, and safety concerns.
1.2.2 The tandem accelerators-based implanter
The tandem accelerator generates a beam using a negative ion source at ground level, which is then accelerated to a high positive potential At the terminal, a gas or foil stripper removes electrons from the high-energy ions, resulting in positively charged ions These ions are subsequently accelerated back to ground level, enabling efficient ion acceleration and manipulation.
MV terminal potential can produce 2 MeV beams Since more than two electrons
Tandem accelerators can generate higher energy beams and typically produce milliamperes of current; however, current limitations arise from the challenges in creating high current sources of negative ions across various atomic species The available high current negative ion sources are often complex, and when sufficient currents are achieved, beam transmission is hindered by the machine's optics Additionally, the terminal stripping mechanism scatters the beam, further reducing the final current Notably, the source region of the tandem accelerator is at ground level, making it more accessible compared to single-ended machines.
1.2.3 The Radio Frequency Quadrupole (RFQ)-based implanter
The RFQ (Radio Frequency Quadrupole) operates on the principle of periodic acceleration to generate high current ion beams, utilizing a quadrupole arrangement of four electrodes that create a spatially varying field along the central channel By employing a high-frequency signal, the RFQ effectively bunches, focuses, and accelerates ion beams, demonstrating potential for extremely high beam currents at megavolt energies As a resonating structure tailored to a specific operating frequency, the RFQ maintains a fixed velocity profile along its length, making it a fixed energy device for each ion species This technology shows significant promise for dedicated implantation applications, while also serving as a versatile general-purpose machine.
6 appears at present to be limited by the difficulty of producing a variable- frequency structure without excessive mechanical complexity
1.2.4 The Radio Frequency (RF) –based implanter (the RF implanter)
In an RF linac, a low-energy ion beam is progressively accelerated through multiple stages, with each stage contributing additional energy without the need for high voltage gradients Each stage consists of a tubular electrode that the beam traverses, an LC resonator that produces RF high voltage, and a power supply that energizes the resonator This acceleration process shares a notable similarity with tandem accelerators, as ions are accelerated both when entering and exiting an electrode; however, in the RF linac, it is the polarity of the electrode that changes rather than the ion's charge.
Recent advancements in RF implanters include the compact Interdigital H – Alternative Phase Focusing linac, developed by Matsui et al in 2000, and the Spiral Loaded Cavity linac, introduced by Dehen et al in 1994 These linacs operate at frequencies of 70MHz and 80MHz, respectively, and are designed for heavy ion implantation.
The compact Interdigital H – Alternative Phase Focusing linac
Motivation and Objective of the Thesis
The accelerated part of an RF implanter is a significant cost driver, making it crucial to optimize the power delivered to the cavity to reduce overall beam costs Glavish introduced a resonator featuring a single coil and a high voltage electrode operating at frequencies of 13.56MHz, 10.4MHz, and 5.2MHz This resonator was further developed and commercialized by the Eaton group, leading to the widespread adoption of Eaton’s ion implanters by semiconductor manufacturers, thanks to their outstanding performance The cavity's power dissipation is 3kW, with an effective shunt impedance of 7.5 MOhm.
High energy ion implanter using helical coil resonator
This thesis introduces an innovative cavity design operating at 13 MHz, building on previous work by incorporating an additional coil to enhance performance This modification lowers the resonant frequency and boosts the quality factor The choice of 13.56 MHz is strategic, as it aligns with a cost-effective generator that is widely accessible, approximately half the cost of a linac The core focus of this research encompasses the design, analysis, fabrication, assembly, tuning, and testing of the cavity's RF properties and overall performance.
Chapter 2 presents a new design concept for each component of the cavity, focusing on the analysis of lumped circuits and the results of simulations This section will review, discuss, and compare these findings with the previous cavity model, alongside insights into the fabrication process of the cavity.
This article explores the design and analysis of a high power input coupler, detailing RF properties such as frequency spectrum, coupling coefficient, quality factor, and field distribution within the cavity It also presents experimental setups and outcomes from high power RF tests and beam acceleration experiments Subsequent sections characterize beam energy spread experiments and their results The thesis concludes with a summary of achievements, emphasizing the pursuit of a high quality factor, effective shunt impedance, and cavity stability This innovative approach significantly reduces both beam costs and machine size.
Design and fabrication of the cavity 10
Design of the cavity
The circuit in Fig 2.2a can be analyzed by the alternating circuit theory We have
For steady state solution, p operator is replaced by , we have the following simultaneous differential equations:
The rms values of the input voltage and current source are denoted as and , respectively, with the assumption that the current source is sinusoidal Consequently, the determinant is calculated based on these rms values.
The voltage at node 1 and 2 is given by
15 where D is determinant of the set of equation, Y1,2 and Z are the complex admittance and complex impedance, respectively
The cavity model can be effectively simulated using a computer program, as illustrated in Fig 2.3 (top) This resonator features an inductor L1 in the series arm and capacitors C2 and C3 in the shunt arm An RF signal is introduced to the cavity through the coupling capacitor C1, with the RF amplitude and phase detailed in the figure.
Lumped model of the cavity
With values given the circuit, voltage at node 1 and node 2 were simulated and given in Fig 2.3 (bottom) The peak accelerated voltage is therefore to be 133kV
The working principle of the cavity involves the acceleration of positively charged ions through a series of gaps during alternating cycles of RF sinusoidal electrode voltage Initially, ions are accelerated by the electric field in the first gap during the first half cycle As the electrode reaches a neutral state, ions drift through at a constant velocity In the subsequent full cycle, the electric field reverses direction, further accelerating the ions in the second and third gaps Finally, during the next half cycle, the field direction changes again, allowing ions to gain additional energy while passing through the fourth gap The RF phase of the accelerating electrodes is carefully adjusted to ensure that ions arrive at the appropriate gap at the optimal time in the RF cycle for maximum acceleration.
Working principle of the cavity
2.1.2 Design of the RF coil
To construct the inductive coil, a copper tube is selected for its excellent electrical properties, with a diameter of 10mm to accommodate a cooling line if required The coil features a mean diameter of D = 2a, a winding pitch of p, a winding tube diameter of d, and a total length determined by the number of turns, which is set at nine This design is illustrated in Fig 2.5.
Design of RF coil
From the above lumped circuit analysis, a coil with inductance of 43uH is needed To determine the inductance of the coil, Nagaoka formula (Nagaoka,
In 1909, a calculation method was developed based on the established formula for the inductance of an infinite-length cylindrical current sheet, incorporating a correction to account for the effects of the ends.
Nagaoka’s inductance formula is usually written in the form
(2.14) in which K is the factor that takes account of the effect of the ends, given by (Nagaoka, 1911)
(2.15) in which For as large as 0.25, three terms will suffice for an accuracy better than 1 %
Normally, we are concerned with the coil efficiency which may best be defined by its quality factor at a particular frequency
20 in which RAC is the AC resistance of the coil given by
(2.18) and n is the winding density
The quality factor of a coil is then defined by
For copper, taking , we find that
√ (2.20) where is a function of and which is experimentally determined (Medhurst,
1947) and R is the coil radius in cm
To optimize the performance of the coil at a fixed working frequency and specific inductance, it is essential to maximize the coil's radius Consequently, both the length and diameter of the coil were adjusted while maintaining consistent spacing.
To achieve the highest quality factor of the coil, a 21:1 ratio of copper tube diameter to pitch is essential At the target frequency of 13MHz, the optimal coil dimensions were determined to be 240mm in length, 235mm in diameter, with a spacing ratio of 0.4.
In the configuration illustrated in Fig 2.4, particles traverse the first and third electrodes during half of the period, while they complete a full period in the second electrode For radio frequency (RF) acceleration, the relationship between cell length (L) and the energy gained is defined by the principles outlined by Wangler.
In a full period (2.21b), the free space wavelength of the RF is considered, with particle velocity expressed in terms of the speed of light For a synchronous particle, the energy per nucleon acquired at the gap is significant.
(2.22) where is the charge to mass ratio of the particle, is the peak voltage between the gap, T is the transit time factor and is the synchronous phase
The 4 He ion beam was chosen for a case study There are some reasons for choosing this ion Implantation of low energy helium ions (~ a hundred keV) have been adopted to study the radiation damage accumulation and the bubble formation in material which are very important in evaluating the service time of material in the nuclear reactors (Sharafat et al, 2009; Zhang et al, 2007; Li et al,
Helium ions are utilized to enhance the structure, optical properties, hardness, and catalytic abilities of materials, as noted in several studies (Hamby et al., 2006; Lee et al., 2007; Rangel et al., 2002; Johnson et al., 2001) A recent trend in research has emerged, focusing on helium implantation in the fields of medical and health science (Hanawa et al., 2003) By applying specific parameters, the design of a cavity for accelerating helium ions was established, with a beam aperture set at 20mm for optimal transmission The synchronous phase was effectively determined at -30 degrees to maximize energy gain for particles traversing the RF field, with the optimal cavity values detailed in Table 2.1.
Design parameters of the cavity
Input beam energy [keV/amu] 6.75 (for He-4)
Output beam energy [keV/amu] 30 (for He-4)
The TRACE-3D simulation for the trajectory of a 4 He +1 ion in a cavity, as presented by Crandall and Rusthoi (1997), is illustrated in Fig 2.6, with an input beam energy of 27 keV The electrode lengths for the He +1 ions measured 59 mm, 144.5 mm, and 79.5 mm, respectively The normalized rms transverse emittance was recorded at 0.2 π mm·mrad To ensure beam envelope stability, the zero current phase advance per focusing period must remain below 180 degrees, as noted by Wangler (1998) In this study, the phase advance was carefully monitored.
158 0 fulfilling the requirement for beam stability
TRACE 3D analysis 2.1.4 Field distribution simulation
A uniform coil is characterized by its radius, wire spacing between turns, and pitch angle, which indicates the angle of the helix's tangent relative to a plane perpendicular to its axis In helical coordinates, the wave equation cannot be separated, and a rigorous solution to Maxwell's equations is lacking Nonetheless, at radio frequencies, a wire-wound coil can be effectively modeled as an idealized anisotropically conducting cylinder.
A surface exhibits conductivity exclusively in the helical direction, with zero conductivity perpendicular to this path In the context of time-harmonic fields, the governing equations are represented by the homogeneous vector Helmholtz equations.
To solve Equation (2.21), it is essential to apply suitable boundary conditions The helical structure facilitates wave propagation along the longitudinal (z) axis, characterized by traveling wave variations The electromagnetic field can be divided into transverse and longitudinal components, with both transverse electric and transverse magnetic modes existing The Laplacian operator can be separated into distinct transverse and longitudinal operators, allowing for a reformulation of the equation.
26 and on the longitudinal field
In these expressions, the important radial wave number, is given by
Dependence of resonance frequency on temperature
Temperature variations in the cavity and electrodes can significantly impact the resonant frequency of the cavity due to geometry distortion caused by thermal expansion or contraction This thesis examines the frequency changes resulting from the thermal expansion of both the electrodes and the cavity The influence of temperature on the coil is minimal, as its inductance primarily relies on the square of the number of turns, which is substantial To assess frequency sensitivity to temperature changes, MicroWave Studio code was utilized, incorporating the thermal expansion coefficient of stainless steel.
The results presented in Tables 2.4 and 2.5 indicate that the resonant frequency is linearly proportional to the temperature of both the cavity and electrodes Notably, the frequency change is more significant when temperature variations occur simultaneously in both the cavity and electrodes, compared to changes in temperature occurring solely in the electrodes, as explained by Kim (2006).
The thermal expansion of the cell caused by rising temperatures results in an increase in tank radius and length, while the gap length decreases This leads to a lower resonant frequency due to the increased tank radius and decreased gap length, although the longer tank length counteracts this effect When both the cavity and electrode temperatures rise, the frequency decrease from the shortened gap is offset by the increased tank length, leaving only the frequency reduction from the tank radius increase Conversely, if the tank temperature remains constant while the drift tube temperature rises, only the frequency decrease from the shortened gap is observed Overall, for every 1°C increase in temperature, the frequency decreases approximately 1.5 kHz due to the tank radius increase and about 1.1 kHz due to the gap length decrease.
Frequency shifts due to the temperature change for low energy side
Frequency shifts due to the temperature change for high energy side
Fabrication and assembly of the cavity
To minimize RF loss, the cavity was plated with a 100 µm thick layer of copper, which is essential given the skin depth of 18 µm at 13 MHz To ensure stability during operation in high electric fields, the coil windings are supported by alumina posts A CAD drawing (Fig 2.11) illustrates the support structure for both the high-energy and low-energy sides Additionally, the windings are secured to the insulators using stainless steel strips and bolts.
CAD drawing of the coil winding supporter
When dielectric part is inserted in the cavity, quality factor will decrease due to the dielectric loss In this aspect, quality factor is given by (Kusunoki et al,
The quality factor of a supporter material is inversely related to its loss tangent, as indicated by equation (2.41) This relationship highlights the significance of material properties in determining performance According to Table 2.6, which lists the loss tangents of various insulators, alumina and Teflon exhibit nearly identical loss tangent values, while G- shows a different characteristic Understanding these values is crucial for optimizing material selection in applications.
10 and wood is much higher Therefore, we manufactured the supporters with two materials (alumina and Teflon) (Fig 2.12)
Dielectric constant and loss tangent of winding supporter material
Substance Dielectric constant (relative to air) Loss tangent Alumina-96%
0.0002@1GHz 0.0002@100MHz 0.0003@10GHz G-10 low resin
Alumina winding supporters with dielectric bolt
The structure will be installed within a vacuum tank that maintains the high vacuum necessary for the beam, RF power, and linac structure This tank will be evacuated using a 280 l/s turbomolecular vacuum pump, typically achieving a vacuum level of 1x10 -7 Torr Grills have been incorporated to prevent unwanted interference.
RF loss through the pumping port, but they also reduce the conductance of the port A picture of the cavity under construction is shown in Fig 2.13
O-rings and metal strings serve as effective vacuum and RF seals, with viton exhibiting a compression set of approximately 20% at temperatures below 200°C and requiring a compression force of around 1.6 kg/cm The sealing material utilized is silver-coated indium, manufactured by Bal Seal Engineering.
Pictures of assembled cavity
RF power coupling to the cavity
2.4.1 Overview of cavity response to the rectangular RF pulse
The reflected power waveform of RF power input with a square pulse shape exhibits varying transient behaviors based on the coupling coefficient (Kurokawa et al., 2002) Analyzing the reflected power waveform allows for the experimental determination of the external Q and coupling coefficient In an initially empty cavity devoid of stored energy, both the cavity field and stored energy rise from zero to their equilibrium states in response to the rectangular RF power input.
] (2.43) where is the time constant with respect to the cavity energy and given by
In addition, the reflected power from the cavity can be expressed as
44 where is a coupling coefficient If the RF power is abruptly switched off, then the field and the stored energy decay exponentially, and the reflected power can be expressed as
The reflected power waveforms are intricately linked to the time constant, which is influenced by the loaded Q of the cavity, as indicated by Eq 2.44 and Eq 2.45 Assuming a resonant frequency of 13 MHz and an unloaded Q of 2500, the reflected waveforms for under-coupled, critical-coupled, and over-coupled cases can be illustrated, as shown in Figs 2.14(a), 2.14(b), and 2.14(c) Each scenario features a rectangular RF input lasting 100 μs In the case of critical coupling, the resonator's effective resistance is matched to the characteristic impedance of the coaxial cable, maximizing power transfer to the cavity and resulting in zero reflected power.
Reflected waveform for the under coupling case (beta = 0.8)
Reflected waveform for the critical coupled case (beta =1)
Reflected waveform for the over coupling case (beta = 1.5) 2.4.2 Design and fabrication of the loop coupler
The RF feed-through for the cavity model employs a loop coupling, illustrated in Fig 2.15, featuring a loop attached to the end of a type N connector's conductor An RF signal from the generator is conveyed to the cavity through a coaxial cable The interaction between the resonant cavity and the cable is represented by a lumped equivalent circuit, as depicted in Fig 2.16.
Model of the RF feed-through
Equivalent circuit of the inductive coupling to the cavity
The circuit equations for Fig 2.16, determined by summing all the voltages around each closed path to zero are:
(2.47) where is the mutual inductance between two loops The mutual inductance is given by (Theodoridis and Mollov, 2010)
The equation (2.48) defines the parameters involved in the coupling loop, including the radius of the coupling loop, the radius of the coil, the distance between the loop and coil planes, and the distance between their axes Additionally, 𝐽 and 𝐽 represent the first kind Bessel functions of orders 0 and 1, respectively, while x serves as the integration variable.
If v1 is assumed to have sinusoidal wave form and all circuit parameters are constants, the above equation may be written in term of effective values as follows:
)] where are the individual primary winding impedance, mutual impedance and load impedance, respectively, the equivalent impedance of the
50 arranged circuit is defined as the ratio of the applied voltage to the primary current
If coupling coefficient k, angular resonant frequency and quality factor are defined by
For critical coupling to occur, the real component of the impedance must match the characteristic impedance of the coaxial cable, while the imaginary component must be zero Consequently, at the frequency designated for critical coupling, these conditions must be satisfied.
The coupling coefficient can be modified by adjusting the inductance of the loop, primarily achieved by altering its diameter Figure 2.17 illustrates the relationship between the coupling coefficient and loop diameter, revealing that critical coupling is attained with a loop diameter of 6.36 cm.
Coupling coefficient as a function of coupling loop diameter The reflection coefficient, given by:
(2.55) where is zero at critical coupling condition This means that the power is effectively forwarded to the cavity without any reflection
Figure 2.18 illustrates the relationship between the reflection coefficient and frequency at critical coupling for a loop coupler with a diameter of 6.36 cm When the coupling coefficient of the cavity is set to 1, the reflected waveform is anticipated to resemble the one depicted in Fig 2.14 (b).
Reflection coefficient with 6.4cm diameter loop coupler
Copper pipe was selected for the loop due to its excellent electrical properties and mechanical stability The loop was installed at the end of the conductor of a type N connector (Amphenol® RF, 2011), with specifications detailed in Table 2.7 Figure 2.19 displays images of both the type N connector and the fabricated loop coupler.
Frequency range DC-11 GHz (flexible cable)
VSWR 1.3 max @DC-11GHz (straight)
1.3 max @DC-11GHz (right-angle)
RF leakage 90 dB minimum @3GHz
Contact resistance Center contact: