PRINCIPLES OF PRODUCTION OF NEW DEVICES FOR MICRO- AND NANOELECTRONICS ON THE BASE OF MATERIALS WITH ION TRACKS
Dissertation zur Erlangung des akademischen Grades DOKTOR-INGENIEUR
des Fachbereichs Elektrotechnik und Informationstechnik der FernUniversität in Hagen
von ALEXANDER PETROV Minsk/Weißrussland
Hagen 2004
ii
Eingereicht: 18.05.2004 Mündliche Prüfung: 13.10.2004 1. Berichterstatter: Univ. Prof. Dr. W.R.Fahrner 2. Berichterstatter: Univ. Prof. Dr. G.Gerlach i
CONTENTS
ABSTRACT ...... iii
INTRODUCTION ...... 1
Part 1. GENERAL PROPERTIES OF MATERIALS WITH ION TRACKS
AND METHODS OF THEIR STUDY
1.1. WORKING MATERIALS
1.1.1. Polymers ...... 1.1.2. Semiconductors ...... 4 1.1.3. Carbon-based materials ...... 6 14 1.2. TECHNICAL MEANS AND METHODS FOR CHARACTERIZATION OF THE OBTAINED STRUCTURES
1.2.1. Optical microscopy ...... 1.2.2. Scanning electron microscopy ...... 17 1.2.3. X-ray diffraction spectroscopy ...... 23 1.2.4. Ion transmission spectrometry ...... 29 1.2.5. Electrical measurements ...... 31 47 1.3. ION IRRADIATION
1.3.1. General principles ...... 1.3.1.1. Electrostatic accelerators ...... 52 1.3.1.2. High frequency accelerators – cyclotron s ...... 53 1.3.2. Technologies used in the present research ...... 56 57 1.4. LATENT ION TRACKS: FORMATION AND PROPERTIES
1.4.1. Physics of ion-solid interaction and track formati on ...... 1.4.2. Track properties ...... 61 1.4.3. Some applications of latent ion tracks ...... 69 72 1.5. ETCHED ION TRACKS: FORMATION AND PROPERTIES
1.5.1. Wetting and swelling processes ...... 1.5.2. Etching of ion tracks ...... 76 1.5.3. Properties of the etched tracks ...... 81 88 ii
DEPOSITION TECHNIQUES, APPLIED FOR THIS STUDY
1.5.4. Tubules formation by evaporation ...... 95 1.5.5. Galvanic deposition of matter along etched tracks ...... 98 1.5.6. Deposition from a saturated solution ...... 99 1.5.7. Electrodeless or chemical deposition ...... 100
PART 2. ION-TRACK-BASED DEVICES FOR MICRO- AND NANOELECTRONICS
2.1. DEVICES ON THE BASE OF POLYMERS
2.1.1. SPECIFIC FEATURES OF THE ION TRACK MANIPULATIONS
2.1.1.1. Metal tubules formation in tracks ...... 107 2.1.1.2. Thermal behavior of manipulated tracks ...... 127
2.1.2. ION - TRACK – BASED MICRODEVICES
2.1.2.1. Magnets and transformers ...... 135 2.1.2.1.1. Micromagnets ...... 142 2.1.2.1.2. Microtransformers ...... 147 2.1.2.2. Capacitors...... 151
2.1.3. ION - TRACK – BASED NANODEVICES
2.1.3.1. Temperature sensors on the base of PET foils ...... 161 2.1.3.2. Pressure sensors on the base of PI foils ...... 166
2.2. DEVICES ON THE BASE OF SEMICONDUCTORS (TEMPOS)
2.2.1. Basic principles of the TEMPOS ...... 171 2.2.2. TEMPOS with continuous deposited layers in the trac ks ...... 176 2.2.3. TEMPOS with nanoparticles in the tracks ...... 181
SUMMARY AND CONCLUSIONS ...... 189
REFERENCES ...... 192
PUBLICATION LIST ...... 212
ACKNOWLEDGEMENTS ...... 218
CURRICULUM VITAE ...... 220 iii
ABSTRACT
The goal of this work was the investigation of the possibilities of creation of micro- and nanoelectronic devices on the base of th e swift heavy ion tracks, for the sake of the future technology. During the implement ation of the work, the ways of realization of that goal were studied, and some fir st prototypes of ion-track-based micro- and nanoelectronic devices on the base of po lymers and semiconductors were created. Thus, the most important results of t his work are as follows: 1. First prototypes of micromagnets and microtransform ers on the base of PI foils with etched ion tracks have been created. They have been shown to exhibit good quality factors up to ~7 at working frequencie s of about ½ GHz, and reasonable coupling factor of ~90%, respectively; 2. A first prototype of the microcapacitor on the base of PI foil with etched ion tracks has been created. It has shown practically f requency-independent capacity of 0.5 pF - 0.6 pF up to 1 GHz. This resul t was confirmed by a theoretical estimation; 3. According to the studies of temperature and pressur e dependences of resistance of PI and PET polymer foils with fullerite tubules in the ion tracks, it was shown, that temperature and pressure sensors can be created in this way; 4. A family of new electronic devices, denoted by the acronym "TEMPOS" (Tunable Electronic Material with Pores in Oxide on Silicon) has been
fabricated for SiO 2/Si and SiON/Si structures with etched ion tracks i n the
SiO 2 and SiON dielectric layers. The functioning of the TEMPOS structures is determined not only by the material and the thickne ss of the dielectric layer, but also by the type of silicon substrate, the diam eter, the length, the shape and areal distribution of the etched tracks, and by the type and the distribution of the (semi)conducting matter deposited within these tracks and on the dielectric surface. Two main classes of the TEMPOS devices hav e been studied: (1) the structures with contunuous deposited layers in the tracks, and (2) the structures with nanoparticles in the tracks. It was found that , depending on the TEMPOS iv
preparation recipe and electrical working point, th e devices may resemble gatable resistors, capacitors, diodes, transistors, photocells or sensors, and therefore they will be are rather universally appli cable in electronics. TEMPOS structures are often sensitive to temperature, ligh t, humidity and organic gases. Light-emitting TEMPOS structures have been produced as well. About 35 TEMPOS-based circuits such as thermosensors, photos ensors, humidity and alcohol sensors, amplifiers, frequency multipliers, amplitude modulators, oscillators, flip-flops, and many others have been already designed and successfully tested. Relative simplicity and low co st of production together with compact size can be attributed to the advantag es of the TEMPOS structures. In general, it can be concluded from the present re search, that etched ion tracks in polymer foils and silicon-based dielectric layer s can be useful for production of micro- and nanoelectronic devices. A large range of possible applications for these structures can be determined. The present scientifi c and technological state-of-the art makes it possible to realize the creation of th e new ion-track-based devices.
v
KURZFASSUNG
Das Ziel dieser Arbeit war die Untersuchung der Mög lichkeiten der Schöpfung mikro- und nanoeletronischer Strukturen auf der Gru ndlage von Spuren hochenergetischer schneller Ionen für die Technolog ie der Zukunft. Während der Fertigstellung dieser Arbeit wurden die Wege studie rt, wie dieses Ziel realisiert werden kann, und einige allererste Prototypen von i onenspur-basierenden mikro- und naoelektronischen Strukturen wurden auf der Gru ndlage von Polymeren und Halbleitern geschaffen. Die wichtigsten Resultate d ieser Arbeit sind: 1. Es wurden erste Prototypen von Mikromagneten und Mi krotransformatoren in PI-Folien mit geätzten Ionenspuren hergestellt. Es konnte gezeigt werden, daß sie gute Qualitätsfaktoren biz zu ~7 bei Arbeitsfrequenzen in der Größenordnung von etwa ½ GHz haben, bzw. daß sie se lbst bei GHz- Frequenzen noch zufriedenstellende Kopplungsfaktore n von etwa 90% aufweisen. 2. Die Studien über Temperatur-und Druckabhängigkeit der Widerstände von Fullerit-Röhrchen in PI-und PET-Folien zeigten, daß auf diese Weise Temperatur-und Drucksensoren hergestellt werden kön nen. 3. Eine Familie neuartiger Bauelemente, durch das Akro nym: „TEMPOS“ (Tunable Electronic Material with Pores in Oxide on Silicon = einstellbares elektronisches Material mit Poren in Oxyd auf Siliz ium) bezeichnet, wurde für
SiO 2/Si- und SiON/Si-Strukturen mit geätzten Ionenspuren in den betr. dielektrischen Schichten geschaffen. Die Funktionsweise der TEMPOS-Strukturen wird nicht nur durch das Material und die Dicke der dielektrischen Schicht sowie den Typ des Silizium-Substrates bestimmt, sondern auch durch den Durchmesser, die Länge, die Form und die Verteilung der geätzten Spuren, und durch den Typ und die Verteilung der halbleitenden Schicht innerhalb dieser Spuren und a uf der Oberfläche des Dielektrikums. vi
Es wurden zwei Hauptklassen von TEMPOS-Struktur en untersucht: (1) Strukturen, bei denen kontinuierliche Schichten auf den Spurenwänden und an der Oberfläche abgelagert wurden, und (2) Strukturen mit Nanopartikeln in Spuren und an der Oberfläche. Es wurde gefunden, daß abhängig von der Herstellungsart und dem elektrischen Arbeitspunkt d er TEMPOS-Strukturen, jene steuerbaren Widerständen, Kondensatoren, Dioden, Transistoren, Photozellen oder diversen Sensoren entsprechen könn en und daß sie deshalb relativ universell in der Elektronik einsetzbar sei n sollten. TEMPOS-Strukturen reagieren oft empfindlich auf Temperatur, Licht, Fe uchte oder organische Gase. Auch lichtemittierende TEMPOS-Strukturen wurden her gestellt. Insgesamt wurden mit TEMPOS-Strukturen bereits etwa 35 Schalt kreise entwickelt, hergestellt und getestet, wie z.B. Thermosensoren, Phtotozellen, Feuchte- und Alkoholsensoren, Verstärker, Frequenzvervielfacher, Amplitudenmodulatoren, Oszillatoren, Flip-Flops, sowie viele andere. Struk turelle Einfachheit, relativ niedrige Produktionskosten und Kompaktheit zählen zu den Vorteilen der TEMPOS-Strukturen. Zusammenfassend kann aus der gegenwärtigen Forschung der Schluß gezogen werden, daß geätzte Ionenspuren in Polymerfolien und dielektrischen Schichten auf Silizium-Grundlage nützlich für die Produktion mikro-und nanoelektronischer Bauelemente eingesetzt werden können. Diese Struktu ren zeichnen sich durch eine große Reichweite möglicher Anwendungen aus. Der geg enwärtige wissenschaftliche und technologische Stand der Fors chung macht es möglich, diese neuartigen Ionenspur-gestützten Strukturen pr oblemlos herzustellen.
INTRODUCTION
The miniaturization of electronic devices belongs t o one of the greatest success stories of the past century. It has been enabled by the consequent development of suitable semiconductor materials, digitalization, l arge-scale integration of switching elements, and their continuous reduction to smaller dimensions, which have now reached typically the order of 100 nm. Pos sibilities of further miniaturization of electronic devices require the u se of new efficient technologies. In this concern the present research, which is conn ected with ion irradiation of various materials, appears to be quite prospective. The impact of energetic ions into matter results in the formation of narrow trails of damage (with diameters ~ 5-10 nm), being at the same time quite long (ranges ~ 30 to 300 m); these are often called as the "ion tracks" [i1] . In insulating targets these tracks are frequently easily etchable, giving rise to well-defined nanopores [i2, i3]. This has been commercially applied since several decades for creation, for instance, the polymeric filter foils [i4]. During t he past 15 years attempts have been made to fill such tracks with suitable conducting, semiconducting, or insulating materials to form new nanometric structures for app lications in (electro)chemistry, electronics and optics. Several techniques can be a pplied here, such as drying of an embedded solution, pressure injection, galvanic dep osition, chemical deposition, evaporation, decomposition reactions in the gaseous or liquid phase, etc. [i2, i5]. The embedded matter can be put into the shapes of c ompact nanowires or nanotubules. One can also deposit sponge-like matte r or dispersed individual nanoparticles on the inner pore walls. Then, the em bedded matter in its peculiar nanoscaled geometrical arrangement gives rise to th e desired electronic properties of the ion-track-based devices. After having studied the basic possibilities of “Si ngle (Swift heavy) Ion Track Electronics“ („SITE“) in the past years [i6, i7], w e have concentrated on the one hand on the production of polymer-based electronic microstructures, such as transformers, capacitors and sensors [i2, i8], and on the other hand we created 2 electronic devices by making use of etched tracks i n silicon oxide and silicon oxynitride on silicon [i9]. These new devices appea r to be capable to cover the bridge between the "classical" silicon-based, and t he new polymer-based electronics. In the first part of the work, a general characteri stic of the materials and samples used in the research, namely polymers, semiconducto rs and fullerenes, is given. The salient features of materials preparation are a lso considered. The main methods of sample characterization, used in the pre sent research, are described, namely optical microscopy, scanning electron micros copy, X-ray diffraction microscopy, ion transmission spectroscopy and elect rical measurements. In the next chapters the technologies of ion irradiation o f studied materials and ion track formation are considered. In this concern it was im portant to give a review about the formation of latent ion tracks in the materials and their possible applications in electronics. Further, the etching procedures are co nsidered, which make it possible to create etched ion tracks of various shapes and d imensions in the investigated samples. Etching recepies used in the preparation o f the samples studied in the present work, prior to some properties of the etche d tracks, are also provided. Thereafter, the various possibilities of deposition of matter into the etched ion tracks, namely evaporation, galvanic deposition and electrodeless deposition, are considered. Main emphasis here is given to the elec trodeless deposition, as it was the main method of material deposition used in this work. In the second part of the work, its main results co ncerning the possibilities of creation of micro- and nanoelectronic devices in p olymers and semiconductors are considered. First, the characteristic features of m etallic tubules formation in the etched tracks in polymer foils are discussed, toget her with the analysis of electrical properties and temperature dependences of the obtai ned structures. In the next chapters the creation and properties of the first prototypes of the micro- and nanodevices on the base of polymer foils with ion tracks, and devices made on the base of SiO 2 and SiON layers containing etched tracks are descr ibed. Two principle strategies can be used for making of these devices. On one hand, it 3 is possible to build up structures, consisting of s everal tracks, being connected with each other by miniaturized electrical wires in a pr e-planned way. On the other hand, one can create the whole structure within one individual etched track each in a polymer foil. The obtained devices can be classif ied as follows: (a) Applications in electrotechnics. The first prototypes of ion-track-based micromagnets, microtransformers and microcapacitors were created by a combined use of electrodeless deposition of metals through s pecial masks with subsequent evaporation of contacts. (b) Applications in sensorics. The second strategy was used for the creation of ion-track-based nanodevices, namely sensors for tem perature and pressure on the base of polymer foils with fullerite tubules in the tracks. The geometry of these structures enables a rapid access of a gas or liqui d to be probed to the sensor material, so that the resulting device has short re sponse times. (c) Applications in electronics. During investigations of structures, consisting of : (1) a n- or p-doped silicon wafer, (2) a SiO 2 or SiON dielectric layer on top of the silicon wafer, (3) an electrically highly resis tive layer on top of the dielectric layer, (4) very narrow conducting connections (etch ed ion tracks) traversing the whole dielectric layer thus connecting top and bott om, and (5) three electrical contacts, two of them being on the top of the sampl e and one being on its back side, we developed a novel family of electronic dev ices which has been denoted by the acronym "TEMPOS" ( Tunable Electronic Material with Pores in Oxide on Silicon). The last chapter of part 2 is devoted to the comple x characterization of these new structures. Depending on the preparation recipe and electrical working point of the TEMPOS devices, they may resemble gatable re sistors, capacitors, diodes, transistors, photocells or sensors, and therefore t hey will be rather universally applicable in electronics [i9]. Relative simplicity and low cost of production together with compact size can be attributed to the advantages of the TEMPOS structures.
4
PART 1. GENERAL PROPERTIES OF MATERIALS WITH ION TRACKS AND METHODS OF THEIR STUDY
1.1. WORKING MATERIALS
1.1.1. POLYMERS
Polymers are macromolecules, which are built up by a large number of repeated molecular units, being linked together by covalent bonds. Different molecules, and separate segments of the same molecule are attracte d to each other by intermolecular van der Waals forces. The involved c ovalent bonds are characterized by high energies (146 kJ - mole -l to 628 kJ - mole -l), short inter- atomic distances (0.11 nm to 0.16 nm) and relativel y constant angles between successive bonds. Covalent bonds govern the thermal and the photochemical stability of the polymers. Polymers have a high str ength to weight ratio, they are easy of moulding and lightness, and their productio n is very cheap. In this research, we have used two polymer material s: polyimide (PI, Kapton, produced in Russia) and polyethylene terephthalate (PET, Mylar, produced in Russia). Polyimides (PI’s) form a class of thermally stable polymers that can withstand higher operational temperatures than most of the po lymeric materials in use today [1.1]. The chemical formula of PI is given in Fig. 1.1. Aromatic PI’s belong to the environmentally most resistant heterochain polymers . The presence of imide and aromatic rings in the structure of the polymer is t he chemical reason for the improved heat resistance and stability to ionizing radiation. The backbone of these aromatized polyethers is quite rigid. The chain can rotate around the phenyl ether linkage. The high density reflects a compact struct ure. The average molecular chain separation distance is about 0.5 nm and the i ntramolecular periodicity is 1.55 nm. PI’s forms ordered aggregates of 2 to 2.5 nm thickness that cannot, however, be considered crystalline as they do not yield well-defined intermolecular
5
Fig. 1.1. Chemical formula of PI [1.5]
reflections. The local alignment of chains is order ed in a smectic fashion along the chain axis for several monomeric units. In addition to the segmental ordering a molecular orientation parallel to the surface of sp in coated films has been observed, being most pronounced for films in the mi crometer range [1.2]. Morphologies ranging from semicrystalline to struct ureless glass have been reported that apparently depend critically on the i nitial imidization temperature. The molecular order of oriented films improves slig htly above 350 °C, and unoriented films show increasing crystallinity abov e 400 °C. PI can withstand temperatures from –269 °C to at least 430 ° C without any marked degradation. Therefore it finds, application s e.g. in surface coating of supersonic aircrafts. PI does not have a melting po int, and the glass transition temperature is expected to be between 360 ° C and 410 ° C [1.3]. Polyimides are widely used not only for electrical insulation but also for passivation and multilayer interconnection in microelectronics, bec ause of their good electrical insulation and dielectric properties, excellent the rmostability and mechanical strength. Photo-sensitive PI is used in high-energy implantation for IC fabrication as a marking material [1.4]. In the present study, we have used PI foils, which were prepared in JNRI, Dubna, Russia, and had a thicknes s d = 25 m . The PET is formed by repetitive addition of 1,2 eth an diol (´glycol´) and terephthalic acid, and therefore contains two hydro xyl groups (–OH) and two carboxyl groups (-COOH). As this reaction is denote d as “estering”, PET belongs to the category of polyesters [1.1]. Its chemical f ormula is given in Fig. 1.2. PET films are biaxially stretched during their produc tion, so that its crystallites orient
6
Fig. 1.2. Chemical formula of PET [1.5]
parallel to the foil surface. The crystalline fract ion can be quite high - in the order of 50% - and therefore its permeability, for inst ance, is quite low for gases. The crystalline lamella surrounded by the amorphous reg ion makes the whole structure mechanically intact. It possesses a very good mecha nical strength from –196°C to +175°C [1.6]. PET foils, used in the present study, were prepared in JNRI, Dubna, Russia, and had the thickness d = 10 m .
1.1.2. SEMICONDUCTORS
As it is well known from the basic physics, materia ls can be categorised into conductors, semiconductors and insulators by their ability to conduct electricity.
The band theory of materials explains qualitatively the difference between these types of materials [1.7]. Electrons occupy energy l evels from the lowest energies upwards. However, some energy levels are forbidden because of the wavelike properties of atoms in the material. The allowed en ergy levels tend to form bands. The highest filled level at T = 0 K is known as the valence band. Electrons in the valence band do not participate in the conduction p rocess. The first unfilled level above the valence band at T = 0 K is known as the conduction band.
Electrons are fermions, and thus follow the Fermi – Dirac distribution function: 1 )E(f = (1.1) Exp []E( - m k/) b )T +1 where kb is the Boltzmann's constant, T is a temperature, E is an energy, and mm mm is the Fermi energy, often denoted as EF , or chemical potential. In semiconductor 7 physics the Fermi energy is the energy, at which th ere would be a fifty percent chance of finding an electron, if all energy levels were allowed. Energy level, corresponding to the Fermi energy is named the Fermi level. In order to apply the statistics, we need the density of states in the c onduction and valence bands. These are derived from the basic principle that the densi ty of states is constant in k-space. In the conduction band, the density of states is gi ven by:
V 2/3 2/1 )E(g = 2( me ) E( - Eg ) (1.2) 2p 2h3 where V is a potential energy, h is the Plank's constant, m e is the electron mass, and E g is the energy gap value.
Fig. 1.3. shows the differences in metals, semicond uctors and insulators in terms of how the energy bands are separated.
Insulators do not conduct electricity, because their valence electrons are not free to migrate throughout the material. In princip le the electrons are free to move around, but, in an insulator there are as many elec trons as there are energy levels for them to occupy. If an electron swaps place with another electron no change is made since electrons are indistinguishable. There a re higher energy levels, but to promote the electrons to these energy levels requir es more energy than is usually practical in insulators, because an energy gap that is far greater than the thermal energy of the electron.
In metals there is no energy gap. The conduction band and th e valence band overlap, allowing free electrons to participate in the conduction process. Therefore, in metals there are more energy levels available th an there are electrons to fill them so very little energy is required to find new energ ies for electrons to occupy, and metals conduct electricity easily.
Semiconductors have the energy gap, the width of which is typically ar ound 1eV. Their conductivity is worse than that of m etals, the resistivity being in the 8
Fig. 1.3. Determination of metals, semiconductors and insulators from the point of view of the band theory [1.7]
9 range between 10 -4 Ohm-m and 10 8 Ohm-m. Specific features of conductive processes in semiconductors will be considered belo w.
It should be mentioned, that polymers are in genera l insulators, but some polymers, especially the ones having undergone a sp ecial treatment or development (irradiation, chemical treatment, etc.) can reveal semiconductor properties and even conductor properties (though, o f course, not as good as those of a metal).
Elementary semiconductors are the ones, where each atom is of the same type, such as Ge, Si. These atoms are bound together by c ovalent bonds, so that each atom shares an electron with its nearest neighbour, forming strong bonds.
Compound semiconductors are made of two or more elements. Common examples are GaAs or InP. These compound semiconduc tors belong to the III-V semiconductors so called because first and second e lements can be found in group III and group V of the periodic table, respectively . In compound semiconductors, the difference in electro-negativity leads to a com bination of covalent and ionic bonding. Ternary semiconductors are formed by the addition of a small quantity of a third element to the mixture, e.g. Al xGa 1-xAs. The subscript x refers to the alloy content of the material, which fraction of th e material is added and which fraction is replaced by the alloy material. Alloying semiconductors in this way allows the energy gap and lattice spacing of the cr ystal to be chosen to suit the application.
Intrinsic semiconductors are pure semiconductors. Both elementary and compound semiconductors can be intrinsic semiconduc tors. At room temperature, the thermal energy of the atoms may allow a small n umber of the electrons to participate in the conduction process. Unlike metal s, where the resistance of semiconductor material decreases with temperature, for semiconductors, as the temperature increases, the thermal energy of the va lence electrons increases, allowing more of them to breach the energy gap into the conduction band. When 10 an electron gains enough energy to escape from the electrostatic attraction of its parent atom, it leaves behind a vacancy which may b e filled be another electron. The vacancy produced can be thought of as a carrier of positive charge. It is known as a hole . As electrons flow through the semiconductor, hole s flow in the opposite direction. If there are n free electrons in an intr insic semiconductor, then there must also be n holes in the equilibrium state. Holes and electrons created in this way are known as intrinsic charge carriers. The carrier con centration or charge density defines the number of charge carriers per unit volu me. This relationship can be expressed as n = p = n i where n i is the intrinsic density; p and n are the numbers of holes and electrons per unit volume, respectively. The variation in the energy gap between different semiconductor materials means tha t the intrinsic carrier concentration at a given temperature varies, too.
An extrinsic semiconductor can be formed from an intrinsic semiconductor by added impurity atoms to the crystal in a process kn own as doping. To take the most simple example, one can consider silicon. Since silicon belongs to group IV of the periodic table, it has four valence electron s. In the crystal form, each atom shares an electron with a neighbouring atom. In thi s state it is an intrinsic semiconductor. B, Al, In and Ga have three electron s in the valence band. When a small fraction of these atoms (less than 1 ´ 10 6) is incorporated into the crystal the dopant atom has an insufficient number of bonds to share bonds with the surrounding silicon atoms. One of the silicon atoms has a vacancy for an electron. It creates a hole, that contributes to the conducti on process at all temperatures. Dopants, that create holes in this manner, are know n as acceptors. This type of extrinsic semiconductor is known as the p-type, as it creates positive charge carriers. Elements that belong to group V of the pe riodic table, such as As, P and Sb, have an extra electron in the valence band. Whe n added as a dopant to intrinsic silicon, the dopant atom contributes an additional electron to the crystal.
Dopants that add electrons to the crystal are known as donors and the semiconductor material is said to be the n-type (see Fig. 1.4). 11
intrinsic p-type n-type
Fig. 1.4. A schematic diagram, showing only the valence electron shell to illustrate intrinsic, p-type and n-type semiconductors [1.7] Doping of compound semiconductors is slightly more complicated. The effect of the dopant atom depends the site occupied by the at om on the lattice. In III-V semiconductors, atoms from group II act as a accept ors when occupying the site of a group III atom, while atoms in group VI act as do nors when they replace atoms from group V. Dopant atoms from group IV have the p roperty that they can act as acceptors or donor depending on whether they occupy the site of group III or group V atoms respectively. Such impurities are known as amphoteric impurities.
Quite often one is interested in transitions, that occur near the bottom of the conduction band minimum to valence band maximum . In this case, it is useful to
draw the band structure energy as a function of pos ition, setting the wave vector k=0. In this representation of the energy bands, the donors and acceptors form levels in the energy gap region. At T = 0 K, any fr ee carriers from donors and acceptors are bound to their atoms, so there is no conduction. For non-zero temperatures, the sites can be thermally ionized, r eleasing carriers in the bands so that conduction can occur (see Fig. 1.5).
These shallow level impurities are known as hydroge nic impurities. For donor atoms, an electron orbits around a lattice site, wh ile for acceptors a hole orbits
around a lattice site with residual negative charge . The energy E n required to ionize this carrier is much less than the binding e nergy of the hydrogen atom since 12
EF
Fig. 1.5. Position of the donor and acceptor levels in the band diagram [1.7] the effective mass is smaller and the radius of the carrier orbit larger than that of the hydrogen atom:
m e4 E = - e (1.3) n 2h2 2 2 2e n 4( pe 0 ) where e is the charge of the electron, h is the Plank's constant, m e is the electron mass, e 0 is the permittivity in vacuum, e is the dielectric constant of a semiconductor material, and n is the number of elec tron energy level.
1 A rough estimate for the temperature of ionization is: k bT ~ E d , k bT = eV at 40 room temperature (E d is the donor level energy, and V is electron poten tial). When the temperature is low, excitation from donors and acceptors can be the only source of carriers: in this range the conductivity is intrinsic. In this regime, the doping of the semiconductor determines whether the semiconductor is n-type or p- type. At higher temperatures, direct thermal excita tion from the valence band to the conduction band swaps the extrinsic density. Then, there is an equal number of electrons and holes; the conductivity is extrinsic with distinction between n and p. 13
In our research we have used n- and p-type silicon wafers (in that case, Si was doped with As, P and B, correspondingly) from 256 m m to 380 m m thickness and resistivities from 0.005 to 35 Ohm-cm, being cut in [111] or [100] direction, as a carrier material. The wafers were cleaned as usual (5 min acetone in an ultrasonic bath, rinsing in distilled (DI) water of 17 M W , 5 min methanol in ultrasonic bath, rinsing in DI water, exposure to a 5H 2O/1H 2O2/1HCL mixture for 15 min at 80 °C , rinsing in DI water, 1 min HF of 1 wt.% at ambi ent temperature, rinsing in
DI water, drying with N 2 gun) and then oxidized. The oxidation took place i n dry atmosphere at 1100 °C for 95 min, with 2 liters of O 2 passing the furnace per minute. In this way, oxide layers between 86 to 135 nm were obtained. Alternatively, silicon oxynitride (SiON) layers of ~ 500 nm to 1 m m thickness were deposited onto the Si wafers by means of plasma che mical vapor deposition (PCVD). For this process the following mixture of g ases was used: 4 sccm (standard cm 3, being the unit which is usually used for the meas uremet of gas flow) of SiH 4 , 4 sccm of NH 3 , 100 sccm of H 2 and 120 sccm of N 2O2. Frequency of plasma was 13.56 MHz, power was 10 Wt, pressure was 200 mTorr, temperature was 390°C, and the deposition process took 10 min. Then the top layers of the wafers were protected by depositing a spin-coated (3000 rpm, 40 s) and baked (110°C, 90 s) photoresist (XAR-P5300/1 from Allresist Ltd.) film, and the oxide of the rear sid e was etched away with the commercial ammoniacal fluoride etchant solution AF8 7.5-12.5 from Merck Ltd. After that, a 2 m m thick Al layer was electron-gun evaporated onto t he rear side at 2 nm/s evaporation speed. All these semiconductor materials were prepared in the Chair of Electronic Devices of the University of Hagen, Germany.
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1.1.3. CARBON-BASED MATERIALS
In general, carbon-based electronic materials compr ise: fullerenes, which are zero-dimensional quantum dots, carbon nanotubes, be ing one-dimensional quantum wires, graphite which is two-dimensional la yered anisotropic material, and diamond, being a three-dimensional wide gap sem iconductor [1.8 – 1.10]. Within this row of carbon materials, fullerenes and carbon nanotubes occupy a particular place, as the most modern carbon allotro pic modifications.
Each molecule of the fullerene family (C m) appears as a sphere or a spheroid containing carbon atoms [1.8]. The thickness of suc h carbon sphere is about 1Å, which corresponds to size of carbon atom. There are two types of the bonds between carbon atoms on C 60 structure: (a) C–C bond, being a common side of t he pentagon and the hexagon; (b) C =C bond, being the common side of the hexagon couple. Each carbon atom belongs to one pentagon an d two hexagons, and its valence requirements are satisfied completely. The structure of C 60 molecule posesses a truncated icosahedron form, Fig.1.6. Fullerenes and their films are attractive for the c reation of electronic devices, because the spherical shape and the large size o f the fullerene molecule provide a substantial volume of empty intermolecular space in a face-centred cubic lattice of solid fullerite. As a consequence, this material is easily intercalated by different impurities changing its properties. Usually, a pure fullerene possesses dielectric properties, but it can reveal a semiconductor behav ior as a result of intercalation [1.8]. Besides, fullerene in solid fullerite under definite action, for example high pressure, UV irradiation and chemical interaction w ith intercalating substances, can form structures with linear, flat or volumetric polymerization processes.
A solid composed of C 60 molecules forms the van der Waals - bonded crystal , named fullerite, which can be an insulator or a sem iconductor, due to fully occupied valence bonds of each carbon atom. Fulleri te is a molecular crystal, where interaction between carbon atoms in the C 60 molecule is much stronger than the interaction between carbon atoms of neighboring molecules [1.10, 1.11].
15
Fig. 1.6. An example of the closed-shell fullerene C 60 configuration [1.8]
The crystalline structure of the fullerite exists i n two forms, namely the face- cubic centered (fcc) one and the hexagonal one. The form of crystallization depends on interaction of carbon atoms and technolo gy of fullerite preparation.
Some physical constants for the crystalline C 60 are given in the Table 1.1. It is important to note, that during the present re search, we mostly worked with thin layers of polycrystalline fullerite, which res istivity was correspondingly anisotropic. Partial oxidation of fullerene in solid fullerite i s accompanied by the polymerization of fullerene molecules, which is confirmed by the appearance of broad bands in IR spectra in the range of stretc hing vibrations at 800 cm -1 and 1000 cm -1 , being characteristic of fullerite polymerized at high pressures [1.8, 1.11]. Partial polymerization proceeds with the dec rease of the distance between the polymerized fullerene molecules and thus with t he increase of the distance between fullerene molecules bound by van der Waals interaction, which causes the strain in crystallites, as well as between sepa rate fullerite crystallites comprising the film (their size being about 200 nm – 300 n m). As a result of this process,
16
Table 1.1. The main physical constants for С60 [1.8]
Quantity Value fcc lattice constant 1.417 nm C60 - C 60 distance 1.002 nm C60 - C 60 cohesive energy 1.6 eV Mass density 1.72 g/cm 3 Molecular density 1.44 × 10 21 cm -3 Temperature of phase transition 261 K Vol. coeff. of thermal expansion 6.1 × 10 -5 K -1 Band gap 1.7 eV Work function 4.7 ±0.1 eV Thermal conductivity (300 K) 0.4 W/mK Electrical conductivity (300 K) 1.7 ×10 -7 S ×cm -1 Static dielectric constant 4.0 ¸ 4.5 Melting temperature 1180 °C Sublimation temperature 434 °C Heat of sublimation 40.1 kcal/mol Latent heat 1.65 eV/C 60
the film becomes stressed and possesses a large num ber of defects in intermolecular bonds and in the interactions betwee n the crystallites comprising the film. The number of conducting electrical chain s and their conductivity in these films depend on the isotropic pressure. It is typic al, that the dependence of resistance on pressure is observed also at pressure s above the atmospheric pressure.
17
1.2. TECHNICAL MEANS AND METHODS FOR CHARACTERIZATION OF THE OBTAINED STRUCTURES
1.2.1. OPTICAL MICROSCOPY
Optical microscopy can be considered as one of the most versatile and useful methods of the characterization of materials struct ures, since quite a lot of the structure features are sufficiently large to be see n by means of the compound optical microscope. However, the optical microscopy loses ist usefulness as the feature sizes shrink to the submicron regime. In th is case, one would need a help of an electron microscope. The basic optical microscop e can be enhanced by adding phase and differential interference contrast, as we ll as polarizing filters. In general, the optical microscopy is most useful for structure s, larger than one micrometer, and the analysis depends on matching the unknown st ructure with the data on the known one. The essential elements of a compound optical micros cope are illustrated in Fig. 1.30 [1.12]. Its optical elements, the objective and the ocular or eyepiece , are shown as simple lenses; in modern microscopes they consist of six or more highly corrected compound lenses. The object O is placed j ust beyond the first focal point fobj of the objective lens that forms a real and enlarg ed image I. This image lies just within the first focal point foc of the ocular, forming a virtual image of I at I ' . The position of I ' may lie anywhere between near and f ar points of the eye. The objective merely forms an enlarged real image which is examined by the eye, looking through the ocular. The overall magnificati on M is a product of the lateral magnification of the objective and the angular magn ification of the ocular. The simplest microscope is the monocular microscope, wh ich has only one eyepiece. The binocular instrument has two eyepieces essentia lly to make viewing of the sample more convenient. When one objective is used with a binocular microscope, the observed image is generally not stereoscopic.
18
Fig. 1.7. Simplified representation of a compound microscope's optical path [1.12].
Light waves interfere with each other, placing cert ain limits on the performance of microscopes. Airy first computed the diffracted image and showed in 1834 that for diffraction at a circular aperture of diameter d, the angular position of the first minimum (measured from the center) is given by (see Fig. 1.8, a ) [1.13] :
sin ( α) = 1.22 λ / d (1.4) where λ is the wavelength of light in a free space. The ce ntral spot, that contains most of the light, is called the Airy or dif fraction disc. One can do one's own experiment by looking at a bright point source at a distance of several meters, for example, at a lamp, through a small pinhole in a cardboard sheet. The same kind of pattern is formed when a point object is imaged by a microscope. There is no lower limit to the size of an object that can be detected in isolation
19
Fig. 1.8. (a) Diffraction at the aperture of a lens showing the Airy disc and (b) the Raleigh criterion for resolution. I represents the intensity [1.13].
under adequate illumination conditions. Generally, one is not interested in detecting a poi nt object, but a two- or three- dimensional object. Two point objects, a distance s apart, produce overlapping images, as shown in Fig. 1.8, b. If they are too cl ose together, it is impossible to resolve them. As they are separated, it becomes pos sible to tell that there are two objects. The definition of this spacing is somewhat arbitrary. Raleigh suggested that two objects can be distinguished when the cent ral maximum of one coincides with the first minimum of the other. Then, the inte nsity between the two peaks decreases to 80% of the peak height. This is shown in Fig. 1.9 for a microscope. The equ ation
s = 0.61 λ / n sin (Θ) = 0.61 λ / NA (1.5) gives the resolution (the minimum distance between points or parts of an object) and satisfies Raileigh's criterion [1.13]. In the equation, n is the refractive index of the medium separating the object from the objective, and Θ is the half angle 20
Fig. 1.9. The resolution limit of an optical microscope [1.12]. subtended by the lens at the object. The numerical aperture (NA), usually engraved on the objective mount, is a number that expresses the resolving power of the lens and the brightness of the image it forms. The highe r the NA of a lens, the higher is the quality of the lens. For high resolution, that is, small s, NA should be made as large as possible. However, high NA does not only correspond to high resolution, but also to shallow depth of field and shallow wor king distance – the distance from the working point of the object plane to the f ront surface of the objective. The depth of focus Dfocus – the thickness of the image space that is simulta neously in focus – is given by
l Dfocus = (1.6) (4 NA )2
Dfocus is insufficient for both the top and bottom surfac es of an integrated circuit to be in focus simultaneously at 200 ´ magnification. The depth of field Dfield – the thickness of the object space, that is sim ultaneously in focus – is given by
21
n 2 - (NA )2 Dfield = l (1.7) (NA )2
Both Dfocus and Dfield decrease with increasing NA, but the resolution i ncreases. It is possible to purchase long working distance ob jectives that allow greater clearance between the objective lens and the sample . Whereas normal objectives may have working distances of 3 mm ( 20 ´ magnification, 0.46 NA) or 0.5 mm (50 ´ , 0.8 NA), long working objectives have 11 mm (20 ´ , 0.4 NA) or 8 mm (50 ´ , 0.55 NA). However, they generally have lower NA and require higher illumination. The magnification M is related to the resolving power of the microscope objective and the eye. However, the image must be m agnified sufficiently for details to become visible to the eye. The resolving power is the ability to reveal details in an object by means of the eye, microscop e, camera or photograph. An approximate relationship for the magnification is [ 1.14]:
M = (maximum NA (microscope)) / (minimum NA (eye)) = =1.4 / 0.002 = 700 ´ (1.8)
The magnification is sometimes expressed as the rat io of the resolution limits
M = (limit of resolution (eye)) / (limit of resolutio n (microscope)) = = 0.15 mm / 0.0002 mm = 750 ´ (1.9) where the eye resolution is set by the distance bet ween the rod and cone receptors on the retina of the eye. The maximum magnification of a microscope when the image is viewed by the eye is around 750 ´ . Magnification above this is empty magnification; it does not give any additional info rmation. M ≈ 400 ´ - 500 ´ with air as the immersion medium. 22
The eye fatigues easily if used at its limits of re solving power, and it is desirable to supply more magnification than the minimum requi red for convenience. A reasonable rule is to make the magnification about 700 NA, but one should always use the lowest magnification that permits comfortab le viewing. Excessive magnification produces images of lower brilliance a nd poorer definition, with the result that the amount of object details that can b e seen is frequently reduced. Recent objectives have been made with magnification s up to 150 ´ with a "dry" NA of 0.95. The contrast – the ability to distinguish between parts of an o bject – depends on many factors [1.14]. Dirty eyepieces or objectives degrade the image quality. Glare will reduce contrast, especially if the sample is h ighly reflecting. It is most serious when viewing samples with little contrast, and it c an be controlled to some extent by controlling the field diaphragm, the opening tha t controls the area of the lighted region. The diaphragm should never be open more tha n just enough to illuminate the complete field of the microscope. For critical cases it may be reduced to illuminate only a small portion of the normal field . The contrast of the surface-height variation can be improved considerably by the dark-field microscopy. Instead of the light impingi ng vertically onto the sample, it is deflected by appropriate condenser lens and impi nges on the sample at an angle. Only the scattered light reaches the objective, all owing small height variations to be seen. Flat portions of the sample do not reflect the light and appear black. The effect is not unlike the observation of dust partic les in air that appear dramatically when illuminated by sunlight streaming through a wi ndow. The eye sees the light scattered from the dust particles.
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1.2.2. SCANNING ELECTRON MICROSCOPY
An electron microscope utilizes an electron beam (e -beam) to produce a magnified image of the sample [1.12]. There are thr ee types of electron microscopes: scanning, transmission and emission ones. In the scanning and transmission electron microscopes an electron beam incident on the sample produces an image, whereas in the field-emission mi croscope the specimen itself is the source of electrons. Scanning electron microsco py (SEM) is similar to the light microscopy, with the exception that electrons are u sed instead of photons. This has two main advantages: much larger magnifications are possible, since electron wavelengths are much smaller than photon wavelength s, and the depth of field is much larger. De Broglie proposed in 1923, that particles can als o behave as waves [1.15]. The electron wavelength l e depends on the electron velocity v or the accelera ting voltage V as
h h 12 2. l e = = = (Å) (1.10) mv 2qmV V
The wavelength is 0.12 Å for V = 10.000 V – a wavelength significantly below the 4000 Å to 7000Å - wavelength range of visible l ight. Hence the resolution of an SEM can be much higher than that of an optical m icroscope. The image in an SEM is produced by scanning the sam ple with a focused electron beam and detecting the secondary and / or backscattered electrons. Electrons and phonons are emitted at each beam loca tion and subsequently detected. Secondary electrons form the conventional SEM image, and backscattered electrons can also form an image. Fur ther, X-rays are used in the electron microprobe for the information about the m aterial composition. All these signals can be detected and amplified to control th e brightness of a cathode ray display tube (CRT) synchronously with the sample be am scan in the SEM. A one- to-one correspondence is thus established between e ach point on the display and 24 each point on the sample. The magnification M of the mapping process results from the ratio of the dimension scanned on the CRT to the dimension of the scanned sample.
M = (length of CRT display) / (length of sample scan) (1.11)
For a 10-cm-wide CRT displaying a sample scanned ov er a 100 m length, the magnification is 1000 ´ . Modifications of 100,000 ´ or slightly higher are possible in SEMs. It is obvious, that high magnifications ar e easily achieved with SEMs, but low magnifications are more difficult to obtain . For a magnification of 10 ´ the scanned length on the sample is one centimeter, onl y 10 ´ smaller than the CRT scan. Typically, SEM has a large viewing CRT and a high-resolution CRT with typically 2500 lines resolution for photography. The contrast in SEM depends on a number of factors. For a flat, uniform sample the image does not show any contrast. If, however, the sample consists of materials with different atomic numbers, a contrast is observ ed if the signal is obtained from backscattered electrons, because the backscattering coefficient increases with the atomic number Z . The secondary electron emission c oefficient, however, is not a strong function of Z, and atomic number variations do not give appreciable contrast. Contrast is also influenced by surface co nditions and by local electric fields. But the main contrast-enhancing feature is the sample topography. Secondary electrons are emitted from the top 100 Å or so of the sample surface. When the sample surface is tilted from normal beam incidence, the electron beam path depth, lying within 100 Å is decreased by the factor 1 / cos Q , where Q is the angle from normal incidence ( Q = 0 for normal incidence). The interaction of the incident beam with the sample increases with path l ength and the secondary electron emission coefficient increases. The contra st C depends on the angle as [1.16]:
C = tan Q d Q (1.12) 25
For Q = 45 ° a change in angle of d Q = 1 ° produces a contrast of 1.75% , and at 60 ° the contrast increases to 3% for d Q = 1 ° . The sample stage is an important component in SEMs. It must allow precise movement i n tilt and rotation to be able to view the sample at the appropriate angle. The angular effect is responsible for the three-dim ensional nature of SEM images. But this effect also results from the signa l collection. Secondary electrons are attracted and collected by the detector, even i f they leave the sample in a direction away from the detector. This does not hap pen in optical microscopes, where light reflected away from the detector (the e ye) is not observed. SEM forms its picture in an entirely different manner than a n optical microscope, where light reflected from a sample passes through a lens and i s formed into an image. In an SEM no true image exists. The secondary electrons t hat make up the conventional SEM image are collected, and their density is ampli fied and displayed on a CRT. Image formation is produced by the mapping which tr ansforms information from space to CRT space. A schematic representation of SEM is shown in Fig. 1.10. Electrons emitted from an electron gun pass through a series of lense s to be focused and scanned across the sample. The electron beam should be brig ht with small energy spread. The most common electron gun is a tungsten “hairpin ” filament, emitting electrons thermionically with an energy spread of around 2 eV . Tungsten sources have been replaced to some extent by lanthanum hexaboride (La B 6) sources with higher brightness, lower energy spread ( ≈ 1 eV) and longer life, and field emission guns with an energy spread of about 0.2 eV to 0.3 eV. F ield emission guns are about
100 ´ brighter than LaB 6 sources and 1000 ´ brighter than tungsten sources. The incident or primary electron beam causes second ary electrons to be emitted from the sample and these are ultimately accelerate d to 10 kV to 12 kV. They are most commonly detected with an Everhart-Thornl ey (ET) detector [1.18]. The basic component of this detector is a scintillation material that emits light when struck by energetic secondary electrons accelerated from the sample to detector.
26
Fig. 1.10. Schematic view of a scanning electron microscope [1.17].
The light from the scintillator is channeled throug h a light pipe to a photomultiplier, where the light incident on a phot ocathode produces electrons that are multiplied creating the very high gains, necess ary to drive the CRT. High potentials of 10 kV to 12 kV are necessary for effi cient light emission by the scintillator. For the electron beam not to be influ enced by the high ET detector potential, the scintillator is surrounded by a Fara day cage at a few hundred volt potential. The beam diameter in SEMs is in the range of 50 Å t o 100 Å. Yet the resolution of e-beam measurements is slightly inferior due to the finite shape of the electron- hole cloud, generated in the semiconductor. When el ectrons impinge on a solid, they lose energy by elastic scattering (change of d irection with negligible energy loss) and inelastic scattering (energy loss with ne gligible change in direction). Elastic scattering is caused mainly by interactions of electrons with nuclei and is 27 more probable in high atomic number materials and a t low beam energies. Inelastic scattering is caused mainly by scattering from valence and core electrons. The result of these scattering events is a broadeni ng of the original nearly collimated, well-focused electron beam within the s ample. The generation volume is a function of the e-beam energy and the atomic n umber Z of the sample. Secondary electrons, backscattered electrons, chara cteristic and continuum X-rays, Auger electrons, phonons of various energies, and e lectron-hole pairs are produced. For low-Z samples most electrons penetrat e deeply into the sample and are absorbed. For high-Z samples there is considera ble scattering near the surface and a large fraction of the incident electrons is b ackscattered. The shape of the electron distribution within the sample depends on the atomic number. For low-Z material ( Z £ 15) the distribution is “teardrop” – shaped, as sh own in Fig. 1.12. As Z increases ( 15 < Z < 40), the shape becomes more spherical, and for Z ³ 40, it becomes hemispherical. Teardrop shapes have actuall y been observed by Everhart et al. by exposing polymethylmethacrylate to an ele ctron beam and etching the exposed portion of the material [1.16]. Electron trajectories, calculated with Monte Carlo techniques, also agree with these shape s [1.19].
The depth of electron penetration is the electron r ange Re , defined as the average total distance from the sample surface that an electron travels in the sample along a trajectory. A number of empirical ex pressions have been derived for Re . One such expression is [1.20]:
-6 1.75 Re = ( 4.28 ´´ ´´ 10 E ) / r (cm) (1.13) where r is the sample density (g/cm 3) and E is the electron energy (keV). Thus, the
3 -6 1.75 electron range for Si ( r = 2.33 g/cm ), is: Re (Si) = 1.84 ´ 10 E . Equation (1.13) is sufficiently accurate for 20 keV < E < 200 keV, but underestimates the range slightly, as compared to a more accurate expression , provided by Everhart and Hoff [1.21].
28
Fig. 1.11. Summary of the range and spatial resolut ion of backscattered electrons, secondary electrons, X-rays, and Auger electrons fo r electrons incident on a solid [1.16]
29
1.2.3. X-RAY DIFFRACTION SPECTROSCOPY
Scattering of X-rays with wavelength λ from a crystal with lattice constant d by an angle Θ is described by the Bragg´s rule [1.1] :
n λ = 2 d sin Θ (1.14)
where n is the order of the X-ray reflex (see also Fig.1.12).
Fig. 1.12. Bragg's explanation of specular reflection of definite angles [1.12].
Thus, aiming the beam of X-rays on a sample and reg istering the reflex rays, one can get information about the structure of the mate rial, using the reflection peaks on the X-ray diffraction (XRD) spectrum. An example of such a spectrum is presented in Fig. 1.13.
Fig. 1.13. The example of an X-ray diffraction spectrum [1.12]. 30
The width of the X-ray reflection peaks yields an i nformation about the size of the crystals under examination. According to Debeye and Scherrer [1.22], the full width half maximum of the peak (FWHM D) is correlated with the average crystal or crystallite size
It is important to note, that FWHM D signifies the half width corrected by the
2 2 instrumental width FWHM instr : FWHM D = FWHM meas + FWHM instr . Such examinations are of use, for example, during the s tudying of the changes in polymeric crystallinity under irradiation. In our i nvestigations, we have used the XRD method for evaluation of the size of the metal crystallites in ion tracks in polymer foils. These results will be described in t he Part 2 of this work. In the XRD diffractometer (Fig. 1.14), a Geiger cou nter or other electronic detector is used to detect both the presence and in tensity of each of the reflections. In our study, a computer-controlled diffractometer was used, which required only that the sample should be aligned correctly in the X-ray beam and then the instrument in turn records all the reflections up t o a chosen maximum angle Θ, and punches out the values of intensity and estimated error for each reflection [1.12].
Fig. 1.14. The schematic view of the X-ray diffractometer [1.12]. 31
1.2.4. ION TRANSMISSION SPECTROMETRY
A principle idea of the Ion Transmission Spectromet ry (ITS) is illustrated in Fig.
1.15 [1.1]. One can assume, that a monoenergetic io n beam with energy E 0 (a dashed spectrum after inclusion of the detector resolution function in the Fig. 1.15, a) penetrates perpendicularly through an unirradiated thin polymer foil having thickness d and density ρprist . Then the ions will undergo an energy loss dE = S ×d (where S is a stopping power), so that they arrive in a detector placed behind the foil with the energy:
Eprist = E 0 – Sd (1.16)
(smooth spectrum in Fig. 1.15, a, with an account o f the detector resolution). For simplicity, we will restrict ourselves to a penetra tion of light ions through thin target polymer foils (a few m thickness), which is the main field of applicatio n of the special ITS case, being introduced here. In the frame of these restrictions, one can neglect the energy dependence of the stopping p ower and the influence of both energy loss straggling and angular scattering.
a b c Fig. 1.15. Principle sketch of ion transmission spectrometry [1.1]: a) through a pristine polymer foil; b) through a pristine foil with a pore (e.g. an etched track); c) through a foil with a latent track.
32
Let us suppose, that we have n circular pores (e.g . etched ion tracks) with average radii r 0 in our polymer foil of unit area, their axes coinc iding with the surface normal. Then the majority of all ions, impi nging perpendicularly onto the foil, will still suffer the energy loss E prist = E 0 - Sd as before, however particles which happen to pass right through the pores will a rrive at the detector with their full energy E 0 (see the double-peaked spectrum in Figure 1.15, b) . The fraction of these particles is given by the expression: 2 f = n πr0 (1. 17)
This means, that by measuring the ratio of particle s detected with the energies E 0 and E det , one can calculate the pore radius r 0:
1/2 r 0 = (N 0/(n πNtot )) (1.18) were N tot is a total number of particles transmitted per un it area and N 0 is a number of particles, transmitted through all pinholes in t he unit area at full energy E 0. The assumptions that have been made in this direct evaluation procedure, or which are required later for the ITS application, a re: 1. The ion tracks are embedded at random positions wit hin a homogeneous polymeric medium. This always holds for the statistical ion impact. 2. The trajectories of the probing ions have exact par allelity to each other and to the pores to be examined. This is given within the limits of the precision of the analyzing ion beam and of the available goniometer.
3. The lateral deviations δz = L ×δα scat of the trajectories of the probing ions during
their flight paths along the tracks with length L, due to angular scattering δα scat ,
are much less than the average width r 0 of the radial density distribution to be
determined: δz << r 0. Here, δα scat can be approximated by:
1/2 δα scat » 2.36 ×(< >×L) (1.19)
with 33
<