SOFT X-RAYS FROM COMPACT PLASMA FOCUS

Summary

This doctoral thesis investigates soft X-ray (SXR) emission from a compact Mather-type dense plasma focus device (NIE-SSC-PFF) operated with neon, argon, and deuterium. A radiative plasma focus theoretical model was developed incorporating shock dynamics and radiative phases, which was confirmed through experiments employing pinhole imaging, transmission grating, flat crystal spectroscopy, filtered PIN diode arrays, and calorimetry, aimed at optimizing SXR sources for semiconductor proximity lithography.

Title Page

A THESIS SUBMITTED BY LIU MAHE

FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

SCHOOL OF SCIENCE NANYANG TECHNOLOGICAL UNIVERSITY DECEMBER 1996

NATIONAL INSTITUTE OF EDUCATION LIBRARY, SINGAPORE

Acknowledgments

I wish to express my deepest gratitude and indebtedness to my supervisor Prof. Lee Sing, Head of Division of Physics, School of Science, National Institute of Education, Nanyang Technological University, for his constant help, inspiring guidance, stimulating and invaluable advice throughout the entire course of this project and the writing of this thesis, without which it would not have been possible for me to complete this work.

I express my gratitude to Dr. Stuart Springham for his help, useful suggestions and discussions during the first period of this work.

I would like to take this opportunity to express my sincere gratitude to Dr. Feng Xianping for his invaluable suggestions and advice during the experimental work of this project. He joined and helped me with the experiments on some occasions.

I am thankful to National Institute of Education, Nanyang Technological University, for hosting my research and providing me with the necessary facilities. I would like to acknowledge Prof. Leo Tan Wee Hin, Director of National Institute of Education, and Dean of School of Science for his support, encouragement and confidence in me.

I am also thankful to the following members of the plasma research group for their help and friendship, in particular: Mr. Suresh Kumar, Dr. Paul Lee, Mr. Zhang Guixin, Dr. Adrian Serban and Miss Cecelia M .N. Selvam.

The cooperation from the General Workshop, in particular from Mr. Michael Ng Yiow Piow and Mr. Lee is acknowledged.

Finally, I wish to dedicate this thesis to all members of my family: my father, my mother, all my sisters and brothers for their moral support from afar in China, and especially, my wife, Du Dongmei, and our child Liu Chang, for their continuous loving support, encouragement and forbearance during my long hours of work and study.

Abstract

This thesis reports investigations of soft x-ray emission from a compact plasma focus. Experiments were carried out under various operational conditions with (a) three different working gases, neon, argon or deuterium, and (b) with the central electrode operating at initial positive and negative charging voltages.

A current transformer, a Rogowski current derivative coil, a resistive voltage divider, a PIN optical speed detector and magnetic probe arrays were used to study the evolution, gross dynamics, and discharge characteristics of this plasma focus device.

Soft x-rays (SXR) in the spectral regime 3 - 30 Å from the neon plasma focus have been investigated in detail. An x-ray pinhole camera, a pinhole transmission grating spectrograph, a flat crystal spectrograph, a filtered 5-channel PIN soft x-ray detector, a photoelectric effect x-ray detector and an x-ray calorimeter were the diagnostics viewing the x-ray output of the pinched plasma region. The pinhole camera, the pinhole transmission grating spectrograph and the spatially resolved flat crystal spectrograph observed a non-uniform column-like x-ray source with ~ 300 µm diameter and ~ 7 mm length centred at the axis under optimum operational conditions. The x-ray spectrum with high resolution from this neon plasma source is obtained by the flat crystal spectrograph. The x-ray emission is mainly within the wavelength range from 8 Å to 14 Å. The hydrogenlike alpha line (Ly-α) at 12.132 Å and the helium alpha line (He-α) at 13.447 Å are observed to be the most intense features of the neon spectrum, contributing 53 ~ 67% of the total spectrum emission. The x-ray spectrum deduced from the 5-channel PIN detector shows that 44% of the total soft x-ray energy is at 13.447 Å, 20% at 12.132 Å and 36% in the wavelength range of 8 ~ 11.568 Å, which is consistent with the results obtained by the flat crystal spectrograph. The calorimeter is used to measure the total SXR yield. At optimum condition (14 kV, 4 mbar) a total SXR yield of 6 J/shot at source into 4π steradians is observed from this plasma source.

A radiative plasma focus model was developed. Reflected shock phase and radiative phase are added to the earlier model to simulate the x-ray emission from the plasma focus. Electron temperature of 360 eV and electron density of 10²⁶ m⁻³ were computed for the uniform radiative compression. Radiation from this compression was also computed. Line radiation comprises 70% of the total x-ray emission. These results show good agreement with the experimentally measured values. The radiative plasma focus model also shows that for a good SXR yield from neon plasma a temperature range of 300 ~ 500 eV is optimum. Computations also indicate the need to reduce circuit inductance. Reduction of stray inductance from 110 nH to 10 nH will result in a 10-fold increase in proportion of stored energy converted into focused plasma energy. SXR yield will rise correspondingly. The results of this thesis form a data base for the development of a high performance, high repetition rate SXR source for lithography applications which is now in progress in our laboratory.

Table of Contents

Acknowledgments … i Abstract … iii List of Figures … xi List of Tables … xvi

Chapter 1 Introduction … 1 1.1 Introduction … 1 1.2 X-ray Sources … 2 1.2.1 X-ray Emission Process … 2 1.2.2 X-rays from Plasma Focus … 3 1.3 Plasma Focus: Candidate of SXR Source for X-ray Lithography … 5 1.3.1 X-ray Lithography … 5 1.3.2 Plasma Focus as a Source of Choice for X-ray Lithography … 6 1.4 Scope of Research … 7 1.5 Layout of this Thesis … 9

Chapter 2 Plasma Focus and X-ray Emission … 11 2.1 Introduction … 11 2.2 Dynamics of Plasma Focus … 14 2.2.1 The Breakdown Phase … 14 2.2.2 The Axial Rundown Phase … 17 2.2.3 The Radial Phase … 19 2.2.3.1 The Compression Phase … 20 2.2.3.2 The Quiescent Phase … 21 2.2.3.3 The Unstable Phase … 22 2.2.3.4 The Decay Phase … 23 2.3 X-ray Radiation from Plasma Focus … 24 2.3.1 X-ray Emission Processes in Plasmas … 24 2.3.1.1 General … 24 2.3.1.2 Emission Processes … 25 2.3.1.3 Plasma Sources for X-rays … 28 2.3.2 DPF as an X-ray Emitter … 28

Chapter 3 Radiative Plasma Focus Model … 33 3.1 Introduction … 33 3.2 Modelling of Plasma Focus … 34 3.3 Radiative Plasma Focus Model … 36 3.3.1 General Consideration of X-ray Emission from Plasmas … 37 3.3.1.1 Radiation Power Density … 38 3.3.1.2 Calculation of Nz, Nz,n, Zeff … 41 3.3.1.3 Specific heat ratio (γ) of hot plasma … 46 3.3.1.4 Calculation of Temperature Te … 48 3.3.2 Axial Phase … 51 3.3.2.1 Snowplow Equation of Motion … 51 3.3.2.2 Circuit Equation … 52 3.3.2.3 Related Physical Quantities … 54 3.3.3 Radial Inward Shock Phase … 54 3.3.3.1 Radial Shock Motion … 55 3.3.3.2 Radial Piston Motion … 55 3.3.3.3 Slug Model Considering Finite Time Signal Communication between SF and MP … 57 3.3.3.4 Axial Elongation of the Focus Pinch … 59 3.3.3.5 Circuit Equation … 60 3.3.3.6 Related Physical Quantities … 60 3.3.4 Reflected Shock Phase … 61 3.3.4.1 Equations of Motion … 61 3.3.4.2 Related Physical Quantities … 62 3.3.5 Slow Compression Phase … 62 3.3.5.1 Equation of Motion … 62 3.3.5.2 Related Physical Quantities … 63 3.4 Numerical Computation … 63 3.4.1 Normalization for Axial and Radial Shock Inward Phase … 63 3.4.1.1 Axial Phase … 64 3.4.1.2 Radial Inward Shock Phase … 65 3.4.1.3 Normalization of Tube Voltage … 65 3.4.2 Description of Numerical Computation … 66 3.4.2.1 Numerical Method for Integrating … 66 3.4.2.2 Computational Procedure … 66 3.5 Computational Results … 67 3.5.1 Typical Results … 68 3.5.2 Discussion … 71

Chapter 4 Apparatus and Diagnostic Techniques … 74 4.1 The Plasma Focus Device: NIE-SSC-PFF … 74 4.2 Description of NIE-SSC-PFF … 75 4.2.1 System Arrangement … 75 4.2.2 Equivalent Circuit and Parameters of NIE-SSC-PFF … 80 4.3 Basic Electrical Diagnostic Methods … 81 4.3.1 Rogowski Coil … 81 4.3.1.1 Introduction … 81 4.3.1.2 Calibration … 82 4.3.2 Voltage Probe … 84 4.4 Optical Measurement of Plasma Sheath Velocity … 86 4.4.1 Design of Light-pipe Detector … 86 4.4.2 Optical Probe Array for Study of Axial Dynamics … 89 4.4.3 Axial Speed Detector … 89 4.5 Magnetic Probe Measurements … 89 4.5.1 Basic Design … 89 4.5.2 Magnetic Array for Determination of Current Shedding Factor … 93 4.6 X-ray Diagnostics … 94 4.6.1 X-ray Pinhole Camera … 94 4.6.2 Pinhole Transmission Grating Spectrograph … 96 4.6.2.1 Basic Structure and Parameters … 96 4.6.2.2 Resolution and Dispersion … 98 4.6.2.3 Set-up … 101 4.6.2.4 Recording Films … 103 4.6.3 Crystal Spectrograph … 104 4.6.3.1 Flat Crystal Spectrograph … 104 4.6.3.2 General Considerations and Precautions … 105 4.6.3.3 Data Analyzing --- Identification of the Spectrum … 112 4.6.3.4 Resolution and Dispersion … 114 4.6.3.5 Set-up … 115 4.6.3.6 Calibration … 117 4.6.4 The 5-Channel PIN Detector … 119 4.6.4.1 BPX65 as Soft X-ray Detector … 119 4.6.4.2 Set-up of the 5-Channel Detector … 120 4.6.5 X-ray Detector Based on Photoelectric Effect … 123 4.6.5.1 Operating Principle of the Detector … 123 4.6.5.2 Design … 125 4.6.6 Calorimeter … 127 4.6.6.1 Principle of the Calorimeter … 127 4.6.6.2 Calibration … 127 4.7 Data Acquisition and Analysis System … 130

Chapter 5 Experimental Results … 131 5.1 Introduction … 131 5.2 Basic Measurements … 132 5.2.1 Current and Voltage Waveforms … 132 5.2.1.1 Gross Dynamics of Plasma Focus … 133 5.2.1.2 Focusing Quality … 137 5.2.1.3 Focusing Time … 138 5.2.1.4 Correlation with other time-resolved diagnostics … 140 5.2.2 Magnetic Field Probing … 140 5.2.2.1 Radially Located 3-MP Array … 140 5.2.2.2 Current Factors … 144 5.2.2.3 Mass Loading Factor … 145 5.2.2.4 Profile Characteristics … 145 5.2.3 Optical Probing … 148 5.2.3.1 Axial Speed Detector … 148 5.2.3.2 Measurements with 8-light pipes … 150 5.3 X-ray Observations … 152 5.3.1 X-ray Time Integrated Pinhole Photography … 152 5.3.2 Pinhole Transmission Grating Spectrography … 157 5.3.2.1 Experimental Conditions … 157 5.3.2.2 Experimental data and results … 157 5.3.2.3 Summary … 163 5.3.3 Flat Crystal Spectrography … 164 5.3.3.1 General … 164 5.3.3.2 Evaluation of Plasma parameters - General Consideration … 165 5.3.3.3 Observations with Spectrograph FCS-B … 168 5.3.3.4 Observations with Spectrograph FCS-C … 172 5.3.3.5 Observations with Spectrograph FCS-E … 176 5.3.3.6 Summary … 180 5.3.4 Filtered PIN Diodes Detection … 181 5.3.4.1 Characteristics of the 5-channel Detector … 181 5.3.4.2 Time correlation observations … 185 5.3.4.3 Comparison with Signals Detected by the Photoelectric Effect X-ray Detector … 189 5.3.5 Total X-ray Yield Determinations … 190 5.3.5.1 Methods for Determining X-ray Flux … 190 5.3.5.2 Experimental Set-up … 190 5.3.5.3 Estimation of Total X-ray Yield by PIN detector … 191 5.3.5.4 Estimation of Absolute X-ray Yield by Calorimeter … 193 5.3.5.5 Operating with Different Charging Voltages and Polarities … 196 5.3.5.6 Reproducibility of X-ray Emission … 199 5.3.5.7 Discussion and Summary … 200 5.4 Discussion … 200 5.4.1 Summary on X-ray Measurements … 200 5.4.2 Comparison with Numerical Computation … 203 5.4.3 Neon Plasma Focus for SXR Source … 205

Chapter 6 Conclusions and Suggested Future Work … 207 6.1 Conclusions … 207 6.2 Some Suggestions for Future Studies … 212

References … 215

Chapter 1: Introduction

1.1 Introduction

Since the original experiments of Roentgen, x-rays have become a most versatile tool for fundamental research and applications spanning physical, chemical and life sciences as well as materials technology, engineering and medicine. X-rays, including x-ray sources, their measurements and applications, have been extensively investigated. The stream of technological innovations using information derived from x-ray investigation includes semiconductor materials and devices, catalysts, magnetic storage media, drugs and enzyme analysis, micromachined components, chemical and mechanical sensors.

Some modern uses and applications of x-rays cover [1]: • digital subtraction angiography • x-ray diffraction • EXAFS (Extended X-ray Absorption Fine Structure) • x-ray microscopy • x-ray astronomy • x-ray tomography • x-ray used for plasma diagnostics • x-ray lithography and • medical and dental radiography, etc.

The studies of x-ray radiation from plasmas began to play an important role from 1930 [2], when x-ray emission from plasmas was first observed by Edlén and Ericson [3], Ekefors [4] and others in high voltage vacuum sparks. Spectrometers, e.g. grazing incidence spectrometer, were used to identify line spectra of highly ionized atoms during that period of time. Much more attention has been concentrated on this subject since 1960, when several plasma devices developed for nuclear fusion research were observed to emit strong x-ray spectra. A great deal of work has been done showing that x-rays radiated from plasmas (laboratory produced or solar plasmas) cover a wide range of spectra, intensities, and temporal profiles (continuous and pulsed) and thus are capable of being widely used in various applications.

It can be seen that laboratory plasma devices, including those built for nuclear fusion research, have enriched our knowledge of x-rays, their diagnostics and various kinds of applications. Dense (Compact) Plasma Focus (DPF or CPF) is one type of these plasma facilities.

1.2 X-ray Sources 1.2.1 X-ray Emission Process An important component in connection with x-ray studies is the source. Demand for higher energy, more powerful sources for industrial applications has increased recently. X-rays are produced in two main types of process: acceleration of charged particles (usually electrons) and when an electron changes from an atomic or ionic energy level to a lower one. Examples of the first type are synchrotron radiation (from relativistic charged particles caused to travel in curved paths by magnetic fields) and Bremsstrahlung (from electrons decelerated by collisions with heavy nuclei). These normally give continuous spectra, although it is possible to obtain quasi-monochromatic lines from insertion devices (undulators) in storage rings (synchrotron sources). The second type of process, which occurs when electrons bombard a low atomic number target or when a plasma is formed from a low atomic number material, gives discrete line spectra. Highly ionized plasmas can be made to behave as x-ray lasers. Other processes [5] such as transition radiation (which occurs when a particle crosses an interface between two materials) and channeling radiation (which occurs when a particle moves along channels formed by planes in a crystal) can give rise to x-rays, but as yet no sources using them have been built.

Generally, x-ray sources can be divided into four main groups, i.e.: 1) Solid target sources, 2) Synchrotron radiation, 3) Plasmas and 4) X-ray lasers. A comparison of different sources concerning their applications on x-ray lithography is given in Ref. [6].

1.2.2 X-rays from Plasma Focus Pinch plasmas are promising as emitters of soft x-ray pulses with duration from nanoseconds to hundreds of nanoseconds. In general they enjoy growing interest for the following applications: (1) production of soft x-rays in the energy range from 1 Å to beyond 200 Å (hν < 12.3keV) for (a) x-ray microscopy [7-10] and x-ray lithography [6,11,12]; (2) basic research in spectroscopy and plasma physics [13-15]; (3) measurement of the population dynamics of transient plasma producing data for comparison of experimental with plasma modelling in order to predict soft x-ray laser action [16,17].

The emitted x-ray energy per pulse from z-pinch devices is higher than the one produced by other available sources. The Plasma Focus (PF) is a special z-pinch-like device capable of producing plasma electron density Ne > 10²⁰ cm⁻³ and temperature Te > 500eV. Because of its simple construction, cost-effectiveness and easy maintenance, the plasma focus appears to be a promising device for x-rays. Experiments show that the radiation spectrum of the plasma focus in the x-ray region covers a large range from below 1 keV up to 500 keV in a time span ranging from a few nanoseconds to a few hundred nanoseconds [18].

Since early 1960’s the plasma focus has been studied as a nuclear fusion facility. The research has been more concentrated on improving neutron yield usually using deuterium as the working gas, although argon plasma (or other noble gas seeded deuterium plasma) has been used to produce more intense bursts of x-rays.

The emission of x-rays from DPF is characterized by high intensity and wide spectral range. The pinched plasma is column-like and viewed end-on appears like a point. Because of these distinct characteristics DPFs are suitable to be used as a pulsed point source for some special applications such as microscopy, x-ray lithography, etc. One of the promising applications is x-ray lithography. The present project studies a small plasma focus for its characteristics in the context of lithography.

1.3 Plasma Focus: Candidate of Soft X-ray (SXR) Source for X-ray Lithography 1.3.1 X-ray Lithography X-ray lithography is an advanced technology for ULSI (ultra large scale integrated) manufacturing. Since R. Kilby and R. Noyce invented the first integrated circuit (IC) in 1961, the number of devices that can be fabricated on semiconductor substrates, typically silicon wafers, has steadily increased [19]. Simultaneous fabrication of millions of electronic devices on a single silicon wafer reduces the cost and improves the performance and reliability of electrical circuits. The impetus comes from both the increased memory requirements of DRAM (dynamic random access memory) and also from the speed needs of SRAM (static RAM).

The “size” of each element, the so called critical dimension (CD), has decreased from >20µm in early 60s to ~ 0.35µm in today’s state of art 64 Mbits DRAMS. Miniaturization of electronic devices gives high density, high speed and low threshold voltage - all beneficial properties. DRAMs have the largest production volume among the IC devices. In the past 20 years, they have been the technology driver. The general trends of DRAM evolution are given by Moore’s law, which predicts 4X increase of bits in A DRAM chip every 3 years. Table 1.1 shows such a evolution chart [20].

Table 1.1. IC product evolution DRAM generation | First Mfg. Year | Chip Size (mm²) | CD (µm) | LW Control (nm) | Overlay Accuracy (nm) 4 Mb | 1989 | 80-90 | 0.7 | 70 | 240 16 Mb | 1991 | 120-140 | 0.5 | 50 | 170 64 Mb | 1994 | 170-200 | 0.35 | 35 | 120 256 Mb | 1997 | 250-300 | 0.25 | 25 | 80 1 Gb | 2000 | 350-400 | 0.18 | 18 | 60 note: CD is critical dimension, LW is line width

Silicon, a semiconductor, forms the basic starting material for a large class of integrated circuits. In the six processing steps lithography is the technique to print patterns onto the silicon wafer [21,22] for subsequent etching, deposition, or implanting. It is one of the key elements of semiconductor (microelectronics) manufacturing. The development of new IC devices relies on the evolution of processing technologies, especially lithography. Lithography determines the minimal feature size on a IC chip. It is the single most expensive processing step in today’s IC fabrication, accounting for more than 30% of the manufacturing cost.

The use of soft x-rays (~ 10 Å wavelength) for lithography has several advantages. The diffraction effect that limits optical proximity lithography is greatly reduced by the short wavelength. X-ray proximity lithography can be used at larger gaps (10 - 50 µm) whilst retaining a very high resolution. Particles such as skin flakes are transparent to x-rays at this wavelength range.

1.3.2 Plasma Focus as a Source of Choice for X-ray Lithography To develop x-ray lithography for industrial applications, a bright soft x-ray source has become important. The two main approaches being pursued for such sources are: the multi-beam synchrotron orbital radiation source (SOR), and single-beam point sources of various types. Point sources are generally less complex and much cheaper than the SOR source, however issues of SXR flux and exposure field uniformity are critical for point sources if they are to match the performance of the SOR source. The point source concepts which have been investigated are plasma sources such as laser-plasma, z-pinch device, dense plasma focus device, etc. Among these sources, it is known that plasma focus is very compact, cost-effective and easy to maintain.

Recent investigations with plasma focus sources designed specifically for SXR proximity lithography appear promising [11,23-25]. X-ray output of up to several hundred watts, in the wavelength range from 8 to 14 Å has been achieved [11,25]. There are still a lot of question marks in this area. Work has to be done on this so as to meet the requirements by industry. But before approaching the stage of application, some fundamental investigations must be conducted, which leads to the necessity of this project work.

1.4 Scope of Research Studies on neon plasma focus are still very limited thus far. This project is mainly intended for studying the characteristics of x-ray emission from a compact plasma focus operated in neon both experimentally and by theoretical modelling. The studies include: (a) diagnostic methods for measuring x-ray radiation from plasma focus (spectral, spatial, temporal and total fluence characteristics of x-ray emission, mainly from neon plasmas); (b) mechanisms of plasma focus x-ray emission (origins of the emission and their contributions to the total yield); (c) dependence of the x-ray emission on operating parameters (working gas, its filling pressure, charging voltage and its polarity, etc.) and regimes; (d) characteristics of the x-ray emission from neon plasma focus; (e) using the information from x-ray radiation to reveal relevant plasma phenomena; (f) comparison of dynamic characteristics among neon, argon and deuterium plasmas by using magnetic probing, optical probing and using the help of physical model.

To study the gross dynamics of plasma focus in neon, a speed detector made of photodiodes was built to detect the optical luminous front to get the maximum axial speed. Magnetic probes were used to obtain the current shedding factor as well as the current profile in the axial run down phase.

Several diagnostics were developed and employed to perform detailed measurements on x-ray emission as well as basic parameters from the small plasma focus. A pinhole camera was used to obtain the side-on and end-on time-integrated x-ray source image. A pinhole transmission grating spectrograph was set up to survey the gross spatially resolved x-ray spectrum. A flat crystal spectrograph was developed to measure spatially resolved x-ray spectrum with high resolution. A 5-channel PIN detector was used to obtain the time-resolved x-ray signal and also to estimate the total x-ray yield. A SXR detector based on the photoelectric effect was fabricated and used to measure the time-resolved x-ray signal. A calorimeter detector for absolute flux measurement was employed.

With the help of x-ray spectrum information we obtained 1) the electron temperature by means of relative line or continuum intensity; 2) the electron density by comparing with the density-sensitive satellite lines.

A model concerning x-ray emission based on Lee’s model [26] was developed to theoretically simulate the procedure. The model has included the finite small disturbance speed between the shock front and the magnetic piston to solve some problems encountered by the previous model. More realistic results are obtained. The model has also shown its possibility for optimizing neon plasma focus for larger x-ray output.

The theoretical results were compared with experimental results. Some general conclusions about x-radiations from plasma focus were obtained providing a better understanding for both the experiments and the model itself.

The experimental results were obtained in the small NIE-SSC-PFF (National Institute of Education - School of Science - Plasma Focus Facility) plasma focus. With the help of modelling, however, it is possible to extract the common points for DPF and some of the features can be generalized enabling us to check and design other devices which are dedicated for effective x-ray production.

1.5 Layout of this Thesis The thesis is organized as follows: Chapter 2 (Plasma Focus and X-ray Emission) describes general aspects of the plasma focus device and gives an overview of its dynamics. Following that is a short review of works done by other researchers on the area of x-ray emission from plasmas, especially from DPF. In Chapter 3 (Radiative Plasma Focus Model), radiative plasma focus model is introduced in detail. A part of the results is discussed. This mainly includes some general conclusions of the x-rays from plasma focus device operated in neon. Some of the numerical results are left to be discussed in Chapter 5 for comparison with the experimental results. Chapter 4 (Apparatus and Diagnostic Techniques) describes in detail the NIE-SSC-PFF plasma focus facility, the diagnostic techniques and experimental set-up to be used for this project. The first section introduces the details of the plasma focus facility. The conventional monitors like voltage, current and current derivative probes are in the second section followed by a description of the magnetic probe, and the speed detector. In the final part the x-ray diagnostics (pinhole imaging, pinhole transmission grating, flat crystal spectrograph, 5-channel PIN detector, flux calorimeter) are described. Chapter 5 presents the experimental results. Some basic measurements, e.g. current, tube voltage, optical and magnetic probings on neon plasma focus are shown. Then results from various x-ray diagnostics such as the pinhole imaging, pinhole transmission grating spectrograph, crystal spectrograph and absolute x-ray yield determination, etc. are presented. Plasma parameters are evaluated from these measurements. A discussion of optimizing plasma focus for soft x-ray radiation is followed. Chapter 6 (Conclusions and Suggested Future Work) contains the summary of the results and interpretations, the conclusions and suggested future research work.

Chapter 6: Conclusions and Suggested Future Work

6.1 Conclusions

This thesis reports investigations on a 3 kJ compact plasma focus. Both experiments and computational simulation were carried out under various operational conditions with (a) three different working gases, neon, argon or deuterium, and (b) the central electrode operating at initial positive and negative charging voltages (i.e., positive and negative polarities).

The discharges were carried out at 14 kV or 13 kV charging voltage for both positive and negative polarities. The filling pressures for the three working gases were varied between 0.5 ~ 10 mbar for neon, 0.4 ~ 2 mbar for argon and 0.5 ~ 10 mbar for deuterium. A current transformer, a current derivative Rogowski coil, a resistive voltage divider, a PIN optical speed detector and magnetic probe arrays were used to study the evolution, gross dynamics, and discharge characteristics of this plasma focus device.

Current shedding factor is measured by three radially located magnetic probes (3-MP). For the same gas and same pressure the current factor of the positive polarity operation is higher than that of negative operation. Neon and argon plasma have bigger current factor than deuterium plasma under the same condition, suggesting that a bigger fraction of the total current drives the neon and argon plasmas relative to deuterium plasma. The mass loading factor in the axial rundown phase is obtained by using the experimentally measured current factor and by matching the arrival time of plasma sheath in the computational model with that determined by the magnetic probe. The mass factor is found to be 0.04 ~ 0.08 for neon and argon focus. Deuterium focus has a higher mass loading factor (0.08 ~ 0.16).

The profile of the plasma sheath in the axial rundown phase is studied using the 3-MP probe. At lower pressure the plasma sheath is more canted. For the same gas and same pressure the plasma sheath is more canted for the positive polarity than for the negative polarity.

A simple optical speed detector made of two light pipes with PIN photodiodes as sensors was developed and used to monitor the axial velocity of the plasma sheath. This detector was used in collaboration with the 3-MP array probe to study the characteristics of the current profile. Another detector with 8 light pipes was used to obtain speeds at several positions along the axial direction. It is found using this detector that the plasma sheet becomes steady only after it has traversed 8 cm from the backwall.

The main goal of this project work is to study the x-ray emissions from plasma focus. We have carried out detailed experiments only in neon because it is known from preliminary experiments that the neon plasma focus emits SXR in the wavelength range suitable for SXR lithography. We studied the neon focus both experimentally by various x-ray diagnostics and theoretically by a radiative plasma focus model. A variety of diagnostics was developed and used to monitor the radiation from the neon plasma focus in the soft x-ray regime (5 to 20 Å) under conditions of 14 kV and 13 kV charging voltages at both polarities. For comparison, measurements of emission from argon plasma was also conducted.

Using an x-ray pinhole camera, images were recorded with both end-on and side-on viewing to determine the dimensions and spatial extent of the neon plasma emission. For single discharges, the end-on x-ray images were nearly circular. The size of the emission was determined to be 280 to 360 microns in diameter. Images from multiple shots were also nearly circular with diameter varying to about 700 microns for images of 7 shots. The side-on image of plasma emission had the appearance of a thin column with 6 - 8 mm length. For multi-discharge exposure the diameter was less than 650 microns on average. All the images of the PF discharges indicate that the plasma emission is centred at the axis.

A pinhole transmission spectrograph was developed allowing one to study a wide range of soft x-ray emission characteristics. It provides two-dimensional spatial resolution simultaneously with spectrum over 3 - 300 Å wavelength range. K-band and L-band spectra for neon plasma focus were identified. For Au target Laser plasma N- and O-band spectra were clearly identified. This spectrograph is found to be a good detector to survey the specified spectrum.

For the wavelength range of our interest (from 5 to 20 Å), a flat crystal spectrograph was then developed and used to obtain the spectrum with higher resolution. Three configurations were designed for different purposes, i.e., focusing on the line radiation part, continuum part, or a wider spectrum range. For neon plasma focus the emission is found to be mainly in the wavelength range from 8 to 14 Å. The hydrogenlike alpha line (Ly-α) at 13.447 Å and the helium alpha line (He-α) at 12.132 Å are the most intense features of the neon spectra, contributing 53 ~ 67% of the total spectrum emission. From the spectroscopic information the electron temperature is estimated to be 300 ~ 380 eV using the method of ratio of line intensities and 160 ~ 250 eV by the slope of the logarithm of the continua. The electron density is estimated to be 10²¹ cm⁻³.

Bright spots within the plasma column were observed both from pinhole imaging and the spatially resolved flat crystal spectrograph. For lower pressure these ‘hot spots’ assumed a longish shape. In the case of higher pressure, point-like spots were observed. The temperature in the hot spots is higher than the rest of the plasma column.

A 5-channel PIN SXR detector was designed for detection of radiation in the soft x-ray region. The absolute sensitivity of the photodiode used (BPX65) was computed. It was used to obtain the time-resolved x-ray signals, to estimate the x-ray spectrum and to evaluate the total SXR yield. The neon focus is found to be a better soft x-ray emitter (>5 Å) than argon and deuterium. Hard x-rays are more rarely observed compared to argon and deuterium foci. Usually one x-ray burst with two or three peaks are observed. The x-ray pulse has a duration of 10 ~ 20 ns on average. With the help of five different filters each covering one PIN diode, the approximate spectrum information was unfolded. Using an assumption of dividing the spectrum into two-peaks and one-flat-portion we estimated the following: ~ 44% of the total x-ray energy is at 13.447 Å (He-α), 20% at 12.132 Å (Ly-α) and 36% in the wavelength range of 8 ~ 11.568 Å. This is consistent with the results from crystal spectrography.

Another time-resolved SXR detector based on the photoelectric effect was made and tested. The rise time of this detector was less than 0.5 ns and was suitable for the x-ray measurement for our purpose in this work. The results are in good agreement with those from PIN detector. This detector is easily fabricated.

Total SXR yield was successfully measured by calorimeter correlated with the 5-channel detector. The calorimeter has a flat response to radiations of different wavelength. The detector was calibrated using an absolute method. At the charging voltage of 14 kV and the corresponding optimum pressure of 4 mbar, total SXR yield of 6 J/shot into 4π steradians was observed from this plasma focus.

The total x-ray yield estimated by the 5-channel PIN detector is consistent with that from the calorimeter. The SXR yield for 13 kV charging voltage at positive and negative polarities was also measured by the 5-channel detector. Comparing the three conditions (14 kV, positive; 13 kV, positive and 13 kV, negative) we found (a) the SXR yield for 14 kV charging voltage is 5.5 J (by 5-channel detector), larger than the other two which are 3.5 J and 1.5 J respectively; (b) at the same pressure and charging voltage, the x-ray output for the case of positive polarity is about 2 ~ 3 times larger than that for negative polarity; (c) The focus operated at 14 kV and positive polarity has the widest optimum operational pressure range, whereas the focus at 13 kV and at negative polarity has a very narrow range of pressure giving good focusing. The input energy into the plasma taken by integrating the peak of the product of the current and voltage signals was also calculated for comparison. It is found that higher input energy into the focus corresponds to higher x-ray output. It is surmised that this is because the soft x-ray emission is related to the plasma thermal energy which is related to the energy input into the focus.

The optimum pressures for charging voltages of 14 kV at positive polarity, 13 kV at positive polarity and 13 kV at negative polarity are close to 4 mbar, 2.5 mbar and 1.9 mbar respectively. The energy input into the pinched plasma of 40 ~ 65 J is measured from the area of VxI spike at optimum conditions, corresponding to ~ 2% of the bank stored energy. This is low for a plasma focus and is due to the large (110 nH) stray inductance of the discharge system.

The reproducibility of this plasma focus as an x-ray source has been tested. It is found that it maintains good focusing quality and produces large amount of x-rays over 100 shots in 2 hours without re-pumping and refilling the working gas. The decrease of the outputs at the last shots results from leakage and outgassing.

In parallel with the experiments, a radiative plasma focus model was developed. Based on earlier work, in this thesis the radiative part was added in to simulate the radiation from the pinched plasma. To calculate the radiation power densities and the ionisation levels a corona model was used. In the axial phase both current shedding factor and mass factor are fixed with reference to experimental data. In the radial inward shock phase the finite signal communication delay was considered and a reflected shock phase was included, which gives a more realistic picture of plasma sheath motion and minimum compression radius.

Computation is done for a typical case of neon plasma focus operating at 13 kV and 2.5 mbar pressure. The minimum radius of 0.2 ~ 0.3 mm is obtained and the speed of imploding plasma sheath is 30 cm/µs, which are in agreement with the work done on similar machines. The gross dimensions of the pinched plasma from simulation agrees with that obtained by side-on x-ray pinhole imaging. The average electron temperature of 360 eV and electron density of ~ 10²⁶ m⁻³ are computed. The line emission is predominant in the total emission and Bremsstrahlung is small compared to line and recombination radiations. Computing for 10 ns in the radiative phase we obtain total yield of ~ 11 J, in which the line radiation takes 70%, the radiative recombination takes 27% and Bremsstrahlung only 3%.

The model is also useful to obtain the optimum electron temperature for soft x-ray (<20 Å) yield. For a neon (coronal) plasma a temperature from 300 eV to 500 eV is found to be suitable to give strong x-ray emission in soft x-ray regime.

6.2 Some Suggestions for Future Studies

The diagnostics employed in this work, the plasma focus model and even the plasma focus system itself can definitely be improved. We shall list a few suggestions in this final part of the thesis for further studies in this area in future.

To get a faster recording of the spectral information on a shot-to-shot basis an intensified CCD combined with x-ray scintillator may be used instead of using x-ray film which needs tedious processing. A curved crystal can be used to obtain a wider spectral range with high resolution. The time-resolved spectral information is most difficult to obtain, but also of most importance and may be carried out in future to study in more detail some x-ray related topics such as the formation of hot spots.

In the aspect of modelling, the collisional-radiative plasma equilibrium model instead of the coronal model in the radial phase may be used to obtain more accurate results. Of course, a magnetohydrodynamic (MHD) model for plasma focus including radiative terms may be a good choice for simulating the plasma focus.

As for the focus device, we have already found both by experiments and by the dynamic model [26] that the present focus machine has a low efficiency of energy conversion when used as a SXR source. This is expected because of the high external (stray) inductance of 110 nH of this device. This stray inductance is very large compared to the focus tube inductance which rises from a low value to some 20 nH at the end of the axial phase and then to some 40 nH during the radial phase. The computation shows that only 3% of stored energy goes into the energy of the focussed plasma. This low proportion of energy transferred to the focussed plasma is consistent with the voltage-current measurements which indicates also a low proportion (of the order of 2%) of stored energy converted into electromagnetic energy transferred to the focus pinch region.

To gain further insight computations were also carried out with the same system but with L₀ reduced to 10 nH. As expected there is a dramatic change to the distribution of energies in various parts of the system, with more than 10% of stored energy going into the plasma. Moreover reducing L₀ from 110 nH to 10 nH almost doubles the current into the focus tube whilst also almost halving the current rise time. This allows, indeed requires [82] a corresponding increase in anode radius ‘a’ and a decrease in anode length ‘L’ from considerations of optimum value of ‘I/a’ (current per cm of anode radius) and time matching. The corresponding change, by a factor of almost 4, of the aspect ratio a/L, towards a ‘fatter’ anode leads to a further rise of conversion efficiency into plasma energy to greater than 25%. Since the scaling of the modelling is such that the temperature and density of the focussed plasma remains approximately the same [82] for the various configurations considered when each configuration is optimized it is reasonable to assume that the SXR yield will depend on the plasma energy content. Thus reduction of L₀ as above will lead to an increase, many-fold, of the SXR yield. Technically to achieve such a low inductance in the capacitor bank requires a system which splits the required capacitance into many small parallel capacitors with many switches also operated in parallel. Such a low-inductance system combined with high repetition rate is necessary for the high performance needed for applications as a high intensity SXR source. Our laboratory is already in the process of developing such a high performance system for SXR lithography applications.