Application of Ion Scattering Techniques to Characterize Polymer Surfaces and Interfaces

Materials Science and Engineering R 38 (2002) 107±180

Application of ion scattering techniques to characterize polymer surfaces and interfaces

Russell J. Compostoa,*, Russel M. Waltersb, Jan Genzerc aLaboratory for Research on the Structure of Matter, Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104-6272, USA bDepartment of Chemical Engineering, University of Pennsylvania, Philadelphia, PA 19104-6272, USA cDepartment of Chemical Engineering, North Carolina State University, Raleigh, NC 27695-7905, USA

Abstract

Ion beam analysis techniques, particularly elastic recoil detection (ERD) also known as forward recoil spectrometry (Frcs) has proven to be a value tool to investigate polymer surfaces and interfaces. A review of ERD, related techniques and their impact on the field of polymer science is presented. The physics of the technique is described as well as the underlying principles of the interaction of ions with matter. Methods for optimization of ERD for polymer systems are also introduced, specifically techniques to improve the depth resolution and sensitivity. Details of the experimental setup and requirements are also laid out. After a discussion of ERD, strategies for the subsequent data analysis are described. The review ends with the breakthroughs in polymer science that ERD enabled in polymer diffusion, surfaces, interfaces, critical phenomena, and polymer modification. # 2002 Elsevier Science B.V. All rights reserved.

Keywords: Ion scattering; Polymer surface; Polymer interface; Elastic recoil detection; Forward recoil spectrometry; Depth profiling

1. Introduction

Breakthroughs in polymer science typically correlate with the discovery and application of new experimental tools. One of the first examples was the prediction by P.J. Flory that the single chain conformation in a dense system (i.e. a polymer melt) is ideal and follows (nearly) Gaussian statistics [1]. In the Flory model, chains interpenetrate and have a radius of gyration that varies as a(N/6)1/2 where N and a are the segment number and size, respectively. Although polymer scientists now take this fundamental law for granted, over 20 years passed before this model was proven. By blending a dilute concentration of deuterated molecules with identical chains (natural abundance of hydrogen), small-angle neutron scattering (SANS) experiments were able to directly determine chain conformation [2±4]. SANS is now a standard technique in the polymer scientist's toolbox for studying the bulk thermodynamic properties of polymer mixtures and solutions. Today new experimental techniques continue to push the frontiers as demonstrated by the recent imaging of individual molecules using the scanning force microscope [5]. Relevant to this review, our understanding of polymer surfaces and interface problems of fundamental and technological importance has been greatly advanced by ion beam analysis IBA, techniques. When light ions at MeV energies are incident on a target, some ions transfer energy to lighter target nuclei in an elastic collision such that the target nucleus recoils and ejects from the

* Corresponding author. Tel.: 1-215-985-1386; fax: 1-215-573-2128. E-mail address: [email protected] (R.J. Composto).

target. By detecting the energy of the recoiling nuclei the depth-profile perpendicular to the surface of the target is measured. In ``cleaning up the tower of babel of acronyms (CUTBA) in IBA'', the consensus of the ion beam community was to call this technique elastic recoil detection (ERD) analysis [6]. Although forward recoil spectrometry (FRES) is the acronym most used by polymer scientists, it is time for the polymer community to adopt the ERD convention to avoid further confusion. For several reasons ERD is a natural technique to study polymer systems. Whereas polymers are predominantly comprised of carbon and hydrogen, many polymers are available in their deuterated analogs. For example, the same polybutadiene can be deuterated or hydrogenated to produce isotopic blends having identical values of N. Because N and a are typically 1000 and 5 AÊ , respectively, the natural length scale for many surface and interface phenomena is 100 AÊ , comparable to the depth resolution of ERD. Since no one technique can provide the necessary depth resolution, lateral resolution, sensitivity and quantification, physical scientist are increasingly using a combination of complementary depth profiling techniques to better understand surface and interfacial issues. For example, consider the enrichment of one component at the surface of a two component blend. ERD, a direct profiling technique, can be used to determine the surface excess independent of any models, whereas neutron reflectivity, a model dependent technique provides details about the shape of the profile. Because patterning is an area of increasing interest, techniques with good depth and lateral resolution will be needed in the future. Ideally, such techniques will allow scientists to address interface issues regardless of geometry (e.g. fibers). The most comprehensive guide to ERD is ``FRES'' by Tirira et al. [7]. This text includes a detailed analysis of ion interactions in solids, provides a review of cross-sections important in recoil analysis, and describes variations of ERD including conventional, time-of-flight (TOF) and coincidence techniques. A general background for ERD is provided in [8,9]. Several brief review articles covering ion beam analysis of polymers are also available [10±13]. This review is intended to educate polymer scientists about ion beam techniques, particularly ERD, and make ion beam users aware of breakthroughs in polymer science brought about by ion beam analysis. Thus, Sections 2 and 3 are dedicated to reviewing the fundamental interaction between ions and solids, and the basic principles of ion beam techniques with an emphasis on ERD. To help polymer scientist optimize ERD experiments, Section 4 describes depth resolution, sensitivity and beam damage. In Section 5, strategies for analyzing and simulating data are presented. Section 6 reviews related IBA techniques as well as complementary ones. To demonstrate the impact of ion scattering on polymer science, Section 7 presents selected case studies in diffusion, surfaces, interfaces, critical phenomena and polymer modification. Although these studies mainly focus on ERD, the utilization of other ion beam techniques such as nuclear reaction analysis (NRA) are also included.

2. Overview of ion beam analysis techniques

2.1. Introduction

When a beam of high-energy, MeV, incident atoms strikes a surface, three main interactions are possible. An incident atom could strike a target atom on the surface of greater atomic number, say an incident 4He striking a target 12C. In this case, the incident atom undergoes an elastic collision and the 4He will be repelled back toward the source of the beam, or backscattered. This interaction is the basis of Rutherford backscattering spectrometry (RBS). In RBS, the energy of the backscattered R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 109

incident ions are detected and the elemental composition of the sample can be determined. Another possible outcome occurs when the incident atom posses greater mass than the target atom, 4He striking 1H. In this case, after the collision event due to the physics of an elastic collision, the incident 4He atom cannot be backscattered, but will continue in the direction forward and the 1H will be recoiled and expelled from the target sample. This interaction is the basis of ERD. The energy of the expelled recoiled 1H atom is detected in the forward direction to determine the depth-profile of 1H. The third possibility is that the incident atoms penetrate the surface and simply lose energy via low impact collisions with electrons. Eventually, at some depth below the surface, the incident ion undergoes an elastic collision and then travels back out of the sample again losing some energy. This well-defined loss of energy as the incident atom travels through the sample provides the unique depth profiling capability of RBS.

2.2. Rutherford backscattering spectrometry (RBS)

The basic principles of ion beam analysis of materials were discovered more than 90 years ago by Rutherford when he bombarded solid targets with alpha particles [14]. His experiments provided the foundation for RBS. A detailed description of RBS can be found in the literature [11,15±17]. Here, we restrict ourselves to a brief description. RBS can be used for elemental determination and to probe the depth-profile of heavier elements. In order for backscattering to occur, the target elements must posses a larger atomic mass than the incident ion. For polymer investigations, the usual incident ion is 4He, so any element larger than helium can be identified, although it does become increasingly more difficult to distinguish elements with very large atomic masses. Most elements of interest in polymer studies 12C, 14N, 16O, 19F, 31P, 32S and 35Cl, can be resolved using RBS or some variation of RBS such as glancing angle RBS. A schematic of a typical set up is shown in Fig. 1. The RBS experiment consists of a monoenergetic beam of ions typically produced by a tandem accelerator (cf. Fig. 17), accelerated to an energy, Ein,0, of a few MeV that are then focused on a sample. After colliding with a heavier atom in the sample, the projectile is backscattered with an energy Eout,0 and travels outward to a solid state

Fig. 1. Experimental configuration of RBS. An accelerator provides high-energy light ions that strike a planar surface and are backscattered to a detector. The detector registers the energy of each backscattered ion. The entire beam line and sample chamber is under vacuum. 110 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 2. Schematic representation of an elastic collision between a projectile of mass Mp and velocity vp, and energy, Ein and 0 0 a target mass, Mt, which is initially at rest. After the collision, the projectile and the target mass have velocities vp, and vt, respectively. The angle F is positive as shown. All quantities refer to a laboratory frame of reference.

detector that is placed at angle y with respect to the incident beam. Since the interaction between the projectiles and the target atoms is elastic, the simple rules of conservation of energy and momentum transfer can be applied to derive the relations between the scattering geometry and the energies of the incoming and scattered projectiles. Fig. 2 shows pictorially the motion of the atoms before and after

a scattering event. At the sample surface, the energy of a projectile with mass Mp that is backscattered from a target atom with mass Mt is related to the energy of the incoming ion via Eq. (1):

Eout;0 KEin;0 (1) where K is the kinematic scattering factor defined by

2 q32 2 2 2 Mp cos y Mt À Mp sin y K 4 5 (2) Mp Mt

Eq. (2) demonstrates that each element at the sample surface can produce a backscattered ion with a

characteristic value of energy, Eout,0. In addition, projectiles scattering from heavier atoms in the target lose a smaller portion of their energy because the kinematic factor is larger. So larger target atoms produce a backscattered ion with higher energy, and consequently an elemental signature that appears at higher energy. However, a majority of the incident 4He atoms do not strike a surface atom, but instead penetrate into the sample before scattering. As the 4He ions traverse the sample, they collide with electrons and loss a well-defined amount of energy that is proportional to the distance of the path traveled. Although this energy loss occurs by discrete interactions, statistically the overall process can be considered continuous. At some depth, x, in the sample the ion can undergo a scattering event and the backscattered ion loses more energy as it travels back out of the sample again proportional to the distance traveled through the sample (cf. Fig. 1). This is the origin of the depth profiling capability of RBS. Finally, the backscattered ion travels to the detector where the ion is converted to a count with a specific energy. Fig. 1 steps through the sources of energy loss in an RBS experiment. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 111

For a beam directed normal to the sample surface, the detected energy of an ion backscattered from depth t is

energy detectedK incident energyÀenergy lost on inward pathÀenergy lost on outward path or "# dE dE t ED xKEin;0 À t À (3) dx He;in dx He;outcos y RBS is useful in analyzing polymers such as ionomers that contain heavy elements. For an incident 2.8 MeV 4He2 beam, Fig. 3 shows an RBS spectra from a poly(styrene-co-Zn sulfonate) containing 5 mol% sulfonic acid groups. For each acid group there are 0.5 65Zn counter ions. The ionomer film is 5000 AÊ thick and on a silicon wafer substrate. So the elements in the film that will backscatter are 12C, 16O, 32S and 65Zn having kinematic factors of 0.25, 0.36, 0.61 and 0.78, respectively. Therefore, the front edges energies are 0, 7, 1.0, 1.7, and 2.2 MeV, respectively. Because the film is on an infinitely thick 28Si wafer, a silicon shelf appears in the spectrum. The front edge is suppressed by 0.35 MeV due to energy loss in the film. At lower energies are the 16O and 12C yields, which superimpose on the silicon signal. Because the yields are proportional to elemental concentration, the polymer stoichiometry can be determined.

2.3. Elastic recoil detection (ERD)

Whereas it is a useful technique for determining the concentrations of heavy elements in the target, RBS is not suitable for studying the concentration distributions of lighter elements. This

Fig. 3. Typical RBS spectrum, from a 5000 AÊ film of poly(styrene-co-Zn sulfonate) with 5 mol% sulfonic acid groups and 50% neutralized with 65Zn. Due to the kinematic factor the heavy elements appear at higher energies. Also the silicon signal from the substrate is suppressed because it is buried below the film. 112 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

drawback limits the application of RBS analysis of polymers to limited cases. In some experiments, labeling the polymers with a heavy element marker or even mixing with non-polymeric materials that bear heavier elements can overcome this obstacle. However, one has to be aware that this approach could strongly affect the thermodynamic behavior of the system. In spite of this, with just a small adjustment of the scattering geometry, one can use the same ion beam to study the concentration profiles of light target elements, i.e. hydrogen. The necessary contrast is achieved by labeling one of the components with deuterium. In most cases, the deuterium labeling does not produce drastic changes to the thermodynamic behavior of the analyzed polymers. A technique used to depth-profile 1H and/or 2D in materials is called ERD. Introduced by L'Ecuyer and co-workers in 1976 [18] and later optimized by Doyle and Peercy in 1979 [19], ERD became a valuable tool for studying the distribution of 1H and 2D in many materials including polymers [20]. Traditional ERD provides 1H and 2D concentration profiles with a surface resolution of ca. 800 AÊ and can probe ca. 7000 AÊ below the surface. By decreasing the beam energy and optimizing the geometry, surface resolutions as good as 80 AÊ have been measured with a probe depth of 700 AÊ . ERD is also sensitive enough to measure less than a monolayer of hydrogen or deuterium, if a large dose is used. These attributes make ERD an attractive technique for studying diffusion, surface/ interface segregation, polymer adsorption and phase separation. To perform ERD, the only change in the RBS experimental apparatus is a detector in the forward direction of the beam and a goniometer to rotate the sample to glancing angles. A diagram of a sample chamber for doing RBS and ERD is shown in Fig. 4. The ERD and RBS geometries are depicted with dotted and solid lines, respectively. Typically ERD uses 4He incident particles to determine the concentration profile of both 1Hand2D in a polymer sample. Since 4Hehasanatomicmassof4amu the only species that it can forward scatter are 1Hand2D; hence, the necessity of the detector in the forward position. Also since the lighter atom is recoiled in the forward direction the sample must be positioned so that a forward recoil particle can escape the sample and travel to the detector. This is achieved by tilting the sample holder so that the incident beam impinges on the sample at a low angle. Fig. 5 shows the path of the incident and exiting beam in a typical ERD set-up. Unlike RBS, after the recoil event the ion of interest is now the lighter 1Hor2D. A beam of 4He or 4He2 is accelerated to energies of 1±4 MeV. The beam is focused and then collimated so that when it strikes the sample surface the shape of the beam is well defined and of a limited width, typically 1 mm. The 4 4 He beam intersects the plane of the sample with at an angle a1. The He atoms that impinge on the surface cause some of the 1H and 2D atoms to be recoiled and expelled from the sample, but again just as in RBS most of the 4He atoms enter the sample and lose energy along the path. On the inward 4 1 path, the He ions lose an amount of energy that will depend on the path-length via the angle a1. H and 2D atoms are recoiled from the sample at all angles, but only those atoms that are expelled at an 1 2 angle a2 reach the detector. On the outward path the Hor D ion also loses some amount of energy.

Fig. 4. Design of a sample chamber for both RBS (solid lines) and ERD (doted lines) experiments. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 113

Fig. 5. Experimental configuration of ERD. The high energy 4He ions recoil 1H and 2D out of the sample. A detector then registers the energy of the recoiled 1H and 2D.

Thus, in an ERD experiment, recoiled 1H and 2D leave the sample surface with energies characteristic of their depths and kinematic factors. In addition, a high flux of 4He ions are forward scattered by heavy atoms in the substrate (i.e. silicon) with an energy that again depends on the depth of the scattering event. This high flux of 4He would overwhelm the relatively low flux of 1H and 2D. In order to reduce the number and energy of the scattered 4He particles that reach the detector, a thin filter of either aluminum foil or MylarTM, between 2 and 10 mm, is placed in front of the ERD detector. The filter stops the low-energy 4He and slows down the high-energy 4He such that their energy does not interfere with the 1Hor2D signal. However, the filter also slightly slows down both the 1H and 2D recoiled particles and introduces signal broadening due to straggling. Thus, the detector ``sees'' both 1H and 2D at energies related to the depth from which they where recoiled in the sample as well as the glancing incident 4He ions at even lower energies. The final energy of the recoiled 1Hor2D atom that emerges from a sample of thickness t is described by

energy detected K incident energy À energy lost on inward path À energy lost on outward path À energy lost passing through filter or "# dE t dE t ED KEin;0 À À À DEfilter (4) dx He;insin a1 dx H=D;outsin a2 where K is now the kinematic factor for forward scattering (cf. Eq. (10)). The energies of these events are shown pictorially in Fig. 6.

Fig. 6. Schematic representation of a recoil event. A high energy 4He ion recoiling a 1H ion out of the sample, as in an ERD experiment. 114 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 7. ERD spectra of a thin (20 nm) dPS tracer film on a thick (500 nm) PS matrix. The dPS tracer film has diffused into the matrix after annealing at 145 8C for 1 h.

Fig. 7 shows the ERD spectrum from a thin, 200 AÊ , deuterated polystyrene (dPS) film on a thick 5000 AÊ PS matrix film that was annealed for 1 h at 145 8C. The high and low-energy peaks correspond to the 1H and 2D originating from the dPS and PS, respectively. Because it is the heavier atom, 2D is detected at higher energies than the hydrogen. The energy at the front edge corresponds to the sample surface, whereas the lower energies correspond to 2D(1H) below the surface. The dPS tracer film has diffused into the PS matrix as demonstrated by the diffuse 2D signal. This profile can be fitted to Fick's second law to determine the dPS tracer diffusion coefficient.

3. Interaction of ions with matter

Rutherford backscattering and related ion analysis techniques are used to identify species type and concentration, and determine the depth distribution of a given species. For most ion beam techniques, light MeV incident probes undergo a single-collision with a positively charged nucleus located within the target material. The kinematics of this elastic collision can be treated by applying the principles of conservation of energy and momentum. Thus, by measuring the energy of a backscattered or forward scattered particle involved in an elastic collision, the mass of a target atom can be identified. As discussed in Section 3.1, mass analysis is the ability to distinguish between atomic masses of elements present in a target. Because interactions are based on classical scattering in a central-force field, the scattering cross-section or collision probability can be derived using simple Coulomb scattering and related to fundamental parameters such as the energy of the incident particle. Knowledge of the scattering cross-section underlies converting the measured number of scattering events from a given target with the actual elemental concentration in the target (Section 3.2). One of the beautiful aspects of MeV ion scattering is that most of us are already familiar with the key concepts underlying mass sensitivity and elemental concentration. The third unique feature of ion analysis techniques involves the energy loss of MeV light ions traveling through solids. This is the second mechanism of energy loss in an ion/solid interaction. The energy loss of incident or exiting particles occurs in a regular manner through the energy transfer from a heavy incident R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 115

particle to a bound or free electron in the target. Although understanding the energy loss mechanism is still a topic of current research, knowledge of the energy loss in a solid allows one to convert the measured energy of backscattering from target atoms deep in the sample to a depth-profile (Section 3.3). In summary, ion scattering is a unique quantitative analysis tool because it is based on relatively well-understood fundamental interactions of ions with matter.

3.1. Mass analysis

The kinematic factor provides ion scattering with mass sensitivity. The atomic level interaction 4 that gives rise to the kinematic factor is depicted in Fig. 2, where a projectile ion, He, of mass Mp 12 and velocity, vp, strikes a stationary target ion, C, of mass Mt and zero velocity at a scattering angle y. Because this is an elastic collision between two particles (i.e. a billiard ball collision), the incident energy after scattering can be found by applying conservation of energy and momentum parallel and perpendicular to the direction of incidence, namely,

1 2 1 0 2 1 0 2 energy : 2 Mpv 2 Mp vp 2 Mt vt (5) 0 0 X-axis : Mpvp Mpvp cos y Mtvt cos F (6) 0 0 Y-axis : 0 Mpvp sin y À Mtvt sin F (7) Using Eqs. (5)±(7), the ratio of particle velocities can be found. Using the non-relativistic energy 2 E 0:5 Mv and taking Mp < Mt as in RBS:

"#2 2 2 2 1=2 E M À M sin y Mp cos y out;0 t p K (8) Ein;0 Mt Mp or

Eout;0 KEin;0 where K is the kinematic factor for elastic scattering. Physically, K determines the amount of energy transferred to the target atom. The key observation is that the energy after scattering depends only on the masses of the incident and target atom and the scattering angle. Eq. (8) reduces to 2 K Mt À Mp= Mt Mp at 1808. Note that the kinematic energy loss is greatest for a direct backscattering event. Therefore, the optimum mass resolution is achieved when the detector is placed as close as possible to the backscattered direction. Sometimes annular detectors are used in order to achieve this condition. Mass resolution is a practical question particularly when backscattering from polymers. Since 1H is usually lighter than the incident particle (i.e. 4He), backscattering from 1H is not allowed according to the principles of conservation of energy and momentum. RBS may have trouble resolving neighboring elements on the periodic table using standard beam energies and angles. We know this by determining the smallest difference in mass DMt that can be resolved. For elements a and b, the corresponding energy difference is given by

DEout;0 Ka À KbEin;0 (9)

There are several strategies for maximizing DEout,0. First, one could maximize Ka À Kb by using y 1808. In practice, the detector has a finite size (diameter) and is usually located as physically 116 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

close to 1808 as possible. As shown in Fig. 4, detectors are usually placed near 1708 either collinear with the incident beam or below. Furthermore, the incident beam energy can be increased to maximize

Eout,0. The mass resolution for RBS is mainly limited by the energy resolution of the detector.

Semiconductor detectors are typically used to measure the energy Eout,0 of backscattered particles. The physics of charged-particle detectors will be reviewed in Section 4.2. Typical energy resolutions,

DED, range from 10 to 20 keV.

Example 1 (Mass resolution in RBS). Consider backscattering 2.0 MeV 4He ions from a mono-

layer (10 nm) of poly(tetrafluoroethylene), C2F4 at 180 8C. Determine whether the carbon and fluorine signals are resolved in a backscattering spectrum?

Element Mass Kinematic factor C 12 0.25 F 19 0.42

So, DEout;0 340 keV. Thus, the maxima of the Gaussian shaped yields would be separated by 340 keV which is @DED. In practice, such measurements are difficult because the C and F peaks are relatively small and usually superimposed on a large background signal from the substrate (e.g. silicon).

3.1.1. Elastic recoil detection RBS is most effective for studying a film of heavy elements on a substrate of light elements. Although some polymer interface problems involve heavy elements (i.e. diffusion of halogenated solvent), most problems involve systems where two or more polymers are chemically similar (e.g. mainly hydrogen and carbon). However, in many cases it is relatively straightforward to prepare or purchase a deuterated version of one component. Under these conditions, mass sensitivity involves differentiating the hydrogen and deuterium signals. Fig. 5 shows the ERD geometry for a 4 monoenergetic beam of He ions of energy Ein,0 impinging on a sample at an angle a1 with respect to the sample surface. The lighter target element recoils after undergoing an elastic collision with the heavy incident particle and gets sent in the forward direction at an angle f with respect to the

incident beam. As in backscattering, the energy Eout,0 imparted to the target element is determined by conservation of energy and momentum where

E M M out K 4 p t cos2 F (10) 2 Ein Mp Mt Note that the maximum energy is transferred to the recoiling target particle at F. Traditionally, the standard ERD geometry utilizes the same path-length into and out of the sample as shown in Fig. 5, 4 TM namely, a1 a2 158 and F 308. Using 3.0 MeV He and a 10.6 mm thick Mylar stopper filter, the accessible depth (about 800 nm) and depth resolution (about 80 nm) is suitable for a wide variety of polymer surface and interface problems. As shown in Section 4.2, the depth resolution can be greatly enhanced by varying the incident and/or exiting angles.

Example 2 (Mass resolution in ERD). For 3.0 MeV 4He incident on monolayer mixture of deuterated and natural abundance PS, determine the energy difference between forward scattered 1H and 2DatF 308. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 117

Fig. 8. The forward recoil spectra of 1H and 2H (deuterium) of a thin dPS:PS mixture using 3.0 MeV 4He ions. The detector is at F 308 and a 10 mm thick MylarTM filter is used (taken from [21]).

From Eq. (10), the kinematic factors are K 1H 1=2 and K 2D 2=3. Thus, the 2D nuclei recoiling from the surface receive a higher fraction of the incident energy than the 1H nuclei. 2 So, Eout DÀEout H 1=6Â3:0 MeV 0:5 MeV. Therefore, the D peak is well separated from 1H compared to the detector resolution. Fig. 8 shows a spectrum for 1H and 2D recoils from a thin dPS:hPS mixture in a typical ERD experiment [21]. Rather than being at 2.0 and 1.5 MeV, the peak positions of the 2D and 1H signals are located at much lower energies, 1.59 and 1.15 MeV, respectively. The energies of the detected recoils are shifted to lower values because of energy loss in the stopper filter, which is placed in front of the detector. When an ion enters this detector a current pulse whose height is proportional to the ion energy is produced. Thus, the detector does not distinguish between the forward recoiled 1Hor 2D and the forward scattered 4He which glance off the heavier nuclei in the film or substrate. The purpose of the stopper filter is to slow down the heavier 4He ions and prevent them from overwhelming the 1H and 2D recoil signals. The recoils themselves get slowed down by the stopper filter but still reach the detector with sufficient energy. Straggling of the recoiling nuclei through the filter is a major limitation to the energy and depth resolution of conventional ERD.

3.2. Elemental sensitivity

Scattering of the incident ion from a target atom is a rare event. A vast majority of incident ions penetrate many microns into the sample or substrate before stopping. The concentration, or more accurately the number Ns of target atoms (molecules) per unit area, is directly proportional to the yield, Y, or number of detected particles QD: Q Y QD s yO Ns (11) qe where Q is the total integrated charge of incident ions on the sample, qe the charge per incident ion, so Q/qe then the total number of incident ions and O is the solid angle of the detector. The fundamental parameter which determines the probability of scattering is the average differential 118 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

scattering cross section, defined here as s. Physically, s represents the ``area'' presented to the incident particle by a given target atom. Typically, the solid angle is kept small, on the order of a millisteradian, so that the cross section is taken as a constant value. If the solid angle is large, the integral scattering cross-section must be used to account for the range of the scattering angle, y.A major difference between MeV ion scattering and most other characterization techniques is that ion scattering is an absolute technique requiring no calibration. This unique advantage results from the ion±ion cross-section, which is well defined, readily available and accurately known. The cross section is based on a Coulombic force between a positively charged incident ion and target nuclei. Because of this interaction, the incident nuclei deviates from its original path and the target nuclei will recoil. The two-body scattering cross section is "# Z Z e2 2 4 f1 À M =M sin y21=2 cos yg2 s y p t p t (12) 4E 4 2 1=2 in sin y 1 À Mp=Mtsin y

were Zp is the atomic number of the incident projectile ions of mass Mp, Zt the atomic number of 2 target ions of mass Mt, and e is the electron charge. The cross-section is defined in CGS units (cm ) so that Eq. (12) can be solved simply by using e2 14:4eVAÊ . To demonstrate the interplay between atomic mass, atomic number and their respective physical parameters, namely, kinematic factor and cross-section, respectively, Fig. 9 shows a backscattering simulation for 2.0 MeV 4He incident on a 12 24À26 79;81 monolayer of C, Mg and Br (i.e. C0.33Mg0.33Br0.33)aty 1708. Each signal is well separated due to the widely different masses. Furthermore, the heavy elements clearly scatter more strongly than the larger ones due the contrast in Z. The isotopes of Br and Mg demonstrate how the mass sensitivity decreases as the atomic number increases. Based on Example 1, the reader should be able to determine why the yields from the Mg isotopes (79% of 24Mg, 10% of 25Mg and 11% of 26Mg) can be resolved and conversely why the isotopes of Br (50.5% of 79Br and 49% of 81Br) are indistinguishable. In Eq. (12), the bracketed mass dependent term accounts for the recoiling of the

Fig. 9. RUMP simulation of a stochiometric 12C, 24;25;26Mg and 79;81Br monolayer. Heavier elements have larger cross sections and consequently higher yields. Note that isotopes of Mg are distinguished whereas those from Br are not. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 119

Fig. 10. The carbon cross-section at y 170:58 for 4He energies between 1.6 and 5.0 MeV, normalized by the Rutherford c cross-section, sR. Note that the cross-section is enhanced by a factor of 6 at energies just below 3.583 MeV (taken from [22]). target atom and acts to decrease the probability for scattering. For heavy targets like silicon the correction is small, 4% at 1808, even though the energy transferred to silicon is about 50%. However, for light elements like those found in polymers, the correction can be significant. For example, the cross-section correction for 4He incident on 12C is 22%. 2 Because the cross-section scales as Zt backscattering is most sensitive to heavy target elements. In fact, backscattering using light incident ions like 4He has not been used frequently to study polymer interfaces because the low Zt and small Mt produces a low yield and small Eout,0, respectively. Consequently, the backscattering peaks from these light elements in the polymer are usually small and overlap with much stronger signals coming from either the substrate or heavier target elements. However, for selected problems, RBS is a powerful technique for characterizing thin polymer films. In this case, accurate cross-sections are critical for determining the composition of polymeric films. As a rule of thumb, for incident 4He ions at energies of 2.0 MeV, the Rutherford cross-section is usually valid. Fig. 10 shows that the carbon cross section at a y of 170.58 is Rutherford up to about 2.2 MeV [22]. Note that the cross section is reduced below the Rutherford value between 2.5 and 3.0 MeV. Although this behavior decreases elemental sensitivity, as long as one uses the proper cross-sections RBS can still be used. On the contrary, utilizing the enhanced cross section at, for example, an incident energy of 3.4 MeV can enhance carbon sensitivity. This method was used to determine the carbon-on-glass concentration in spin polymer films exposed to thermal and ultra violet-irradiation [23,24]. The profiling of light elements such as 1H and 2D in polymers involves knowing the scattering cross-section for the recoiled elements. Also, the resonant and non-resonant nuclear reaction techniques require an accurate measurement of the cross-section. Unlike Rutherford scattering, no simple analytical form of the cross-section is available to describe the probability of reaction between an incident particle like 4He and a light target nucleus. A rigorous study of the absolute cross section for hydrogen forward scattering was carried out by Baglin et al. [25] and compared 120 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

4 Fig. 11. Hydrogen forward recoil cross-sections, sH, plotted as a function of He ion energy for F 308. The solid lines through the data points are arbitrary polynomial fits to the data points. For comparison, the cross-section derived from the Rutherford formula is shown (taken from [25]).

with literature values. The hydrogen cross-section for 1.0±2.9 MeV 4He at f of 20, 25, 30 and 358

were measured using a thin PS film. PS was chosen because the monomer unit (C8H8) contains 50 at.% hydrogen. Moreover, because it mainly cross-links, PS is relatively stable during exposure to MeV 4He radiation. Fig. 11 shows the 1H cross-sections in mb/sr at 308 along with the calculated Rutherford values [25]. Although scattering is approximately Rutherford at energies near 1.0 MeV, the hydrogen cross-section decreases much more weakly with increasing energy compared with the Rutherford 1/E2 behavior. For example, at 2.9 MeV the cross-section is enhanced by a factor of 2.5 over the Rutherford value. Conventional and TOF±ERD are performed using 3.0 MeV 4He ions whereas low-energy ERD (LE-ERD) requires knowledge of the cross-section at energies ranging from 1 to 2.5 MeV. The deuterium cross section for 1.0±2.9 MeV 4He was also measured by Kellock and Baglin

[28] and compared with literature values. Once again polymeric films, in this case dPS (C8D8), were used as standards. The deuterium cross section was found to have a resonance at 2.135 MeV with a 60 keV full-width half maximum (FWHM). The resonance was strongest at 208 and systematically decreased as the angle was increased to 408. For simplicity, ERD experiments on deuterated samples should be carried out either far above or below the resonance range, i.e. 2.0 MeV < Ein < 2:3 MeV. This is one reason why Genzer et al. developed LE-ERD using 1.3 MeV 4He [26]. To increase accessible depth, Genzer et al. increased the energy to 2.0 MeV 4He which is still below the resonance range [27]. Fig. 12 shows the deuterium cross section at 308, the conventional scattering angle in ERD [28]. Note the resonance near 2.1 MeV. As in the hydrogen case, the Rutherford cross- section falls below the experimentally measured one. In contrast to hydrogen, the deuterium cross- section does not agree with the Rutherford prediction near 1.0 MeV. As mentioned by Kellock and Baglin, Rutherford scattering for 4He on 2D is not expected for 4He energies greater than 0.3 MeV. Unlike the hydrogen case, the literature values for the 2D cross-section seem to agree with each other. As an example, we consider the yield from a thin (200 AÊ ) film containing a mixture of PS and dPS. Fig. 8 shows the resulting yields of 1H and 2D using an incident beam energy, recoil angle, and integrated charge of 3.0 MeV 4He, 308, and 20 mC, respectively. From Figs. 11 and 12, the 2Dto1H

cross section ratio is 1.90. Correspondingly, the ratio of Ns,D to Ns,H is 0.53 and, thus the film R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 121

Fig. 12. Deuterium cross-section as a function of energy plotted at F 308. The uncertainty of the cross-section scale is estimated to be Æ5%. The polynomial fit is continuous, with the data points in the resonance region omitted, as explained in the text. The dotted line is the cross-section given by the Rutherford formula (taken from [28]).

2 1 contains approximately 33 at.% D and 66 at.% H (i.e. PS0.66dPS0.33). As mentioned in Section 3.1, the 2D nuclei receive a higher fraction of the incident energy than the 1H nuclei and, therefore, the 2D peak is shifted to higher energies. Although the kinematic factors are about two-thirds and one- half for 2D and 1H, respectively, the energies of the detected recoils are shifted to lower values than the calculated ones. This shift results from energy loss in a stopper filter placed in front of the detector in ERD experiments. The energy loss of 2D and 1H in the stopper filter involves the same mechanism that imparts ion scattering with depth profiling capabilities.

3.3. Depth sensitivity and energy loss

Ions traversing through a solid lose energy by screened Coulomb collisions with target nuclei and interactions with bound and free target electrons [29]. For MeV scattering the nuclear energy loss is approximately three orders of magnitude smaller than the electronic energy loss. Nuclei energy loss is mainly of interest in ion implantation and sputter±etching techniques like secondary ion mass spectrometry SIMS. Electronic interactions are the dominant mechanism for energy loss in the ion scattering analysis techniques of interest to this review and will be the focus of this section. The Stopping and range of ions in matter (SRIM1) is a flexible software program for calculating the interaction of ions with solids [30]. SRIM1 calculates the distribution of ions in complex materials with up to eight layers. One can select the incident beam species and energy in addition to a material composition. This latter feature is particularly useful for polymer scientists because the stopping power has been directly measured in only a limited number of polymers. However, before using such a program, one must understand how energetic ions interact with matter. As an energetic ion moves through matter, the ion loses energy by exciting or ejecting electrons from the target atom. This interaction is through a Coulomb force acting on the electron due to the passing of a charged-particle. Because of the light electron mass, the path of the incident ion does not change significantly. Moreover, because there are numerous electrons in the target, the incident ion slows down in a nearly continuous fashion. One can readily calculate the energy loss per unit path- length, À(dE/dx), due to the momentum transfer between incident particle and target electrons. A second contribution due to incident particles outside the electron orbit undergoing small momentum transfers resulting from electron excitation is more difficult to derive. At high incident energies, the 122 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

electronic stopping power is given by 2 4 2 ÀdE 2pZ e Mp 2mev NZt ln (13) dx Ein;0 me I

where N is the atomic density, me the electron mass, v the ion velocity, and I the excitation energy of an electron. Not only does À(dE/dx) decrease with increasing incident energy but dE/dx varies systematically as 1/E. Because of this systematic variation, the detected energy range can be readily converted into a depth-profile. The energy loss has been measured for elemental targets and some compounds [30]. For new compounds and polymers, Bragg's rule can be used to calculate the stopping power from the individual components. Alternatively, the stopping power can be determined experimentally by measuring the energy loss, dE, in a film of known thickness, dx [31,32]. To account for the atomic density, the stopping cross-section is frequently used:

1 dE e eV cm2 (14) N dx where N is the atomic density. Fig. 13 shows the energy loss, dE/dx, for 1H ions in PS. The maximum energy loss is near 0.11 MeV and corresponds, approximately, to the conditions when the incident ion velocity is equal to the Bohr velocity of an electron, v0 2:188 Â 108 cm/s. For ion velocities much greater than v0, the fast collision regime described by Eq. (13) is valid. Fig. 13 shows that in this regime the stopping power displays decreases monotonically for energies greater than 0.6 MeV. As seen from the plot, 2.0 MeV 1H ions will lose 18 eV while passing through each AÊ , or about 1800 eV while traversing a film whose thickness is comparable to the size of a typical polymer Ê chain, Rg100 A. Note that this energy loss (1.8 keV) is much less than the detector resolution. As mentioned earlier, for compounds, molecules, and mixtures, the stopping cross section can be calculated using Bragg's rule, which assumes that the target atoms contribute independently to the total energy loss regardless of bonding. For example, in an A/B mixture the stopping power of the

Fig. 13. Stopping power for 1H ions traversing a PS matrix over a wide range of energies. Note that the stopping power decreases monotonically >0.6 MeV. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 123

compound is determined from the weighted average of the stopping powers of the two pure elemental targets:

e xeA yeB (15)

Tabulated values of elemental stopping powers are widely available [33]. Although one can use Eq. (15), the stopping powers of polymers should be directly measured when possible because elemental densities used in Eq. (15) will not necessarily match the known polymer density. For example, Wallace et al. measured the stopping powers of 1±3 MeV hydrogen and helium in both PS [31] and polyimide [32] using a thin-film backscattering method by sandwiching a polymer layer between very thin gold layers. This method is particularly sensitive to the energy loss in the film. In polyimide, the measured 1Hand4He stopping powers were found to be in excellent agreement with both Bragg's rule (Eq. (15)) and the cores-and-bonds model, which accounts for chemical bonding in compounds. Similar results were found for the 1H stopping power in PS. 4 15 2 Fig. 14 shows that the Hestoppingpowervariesfrom27.4to14.1eV/(10 atoms/cm )asEin increases from 1 to 3 MeV [31]. The measured stopping power agrees well with Bragg's rule at energies above 1.5 MeV and with the CAB model below 1.5 MeV. Further studies are needed to clearly differentiate between these models. Leblanc et al. [34] showed that corrections to the stopping power due to chemical bonding are generally small except near the maximum stopping power region. Calculations of light ion stopping powers near the maximum have been worked out by Sigmund [35]. Including bonding effects could be particularly important in the case of LE- ERD where one uses low-energy 1MeV 4He ions. This observation reinforces the need to directly measure the stopping powers of polymers whenever possible rather than rely solely on software calculations based on Eq. (15). To determine a depth-profile from ion analysis one relies on knowledge of the energy loss of the incident ion along the inward path and the exiting ion along the outward path. The objective is to relate the energy of the detected particle to the depth at which the incident ion collides with the target atom. As a rule of thumb, the energy loss of MeV 4He ions in most hard materials is 30 to 60 eV/AÊ . For polymers, this value is usually smaller. For example, for 1.5 MeV 4He ions in PS the energy loss is about 20 eV/AÊ . The thin-film analysis method is one approach for approximating the energy loss. For example, for an incoming ion incident perpendicular to the sample surface, the total energy loss

Fig. 14. Stopping power (filled circles) for helium in polystyrene. The stopping powers predicted by Bragg's rule (dashed line) and the cores-and-bonds model (solid line) are also shown (taken from [31]). 124 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

is proportional to the path-length traversed: dE DEin;1 x (16) dx in Because the film is thin, the energy loss is evaluated using an average value between the initial 4 energy Ein,0 and the energy before impact. The outward energy loss of He in RBS and light ions in ERD can be determined in a similar manner. For RBS, the energy width of a backscattering signal is

dE 1 dE DE tK tS (17) dx in jcos yj dx out where t, y and [S] are the thickness, scattering angle and backscattering energy loss factor, respectively. The key result here is that the energy width is directly proportional to the film thickness. Thus, by assuming a constant energy loss, Eq. (17) demonstrates that the energy axis is linearly related to the depth scale. Eq. (17) can also be presented as t DE tKe e te (18) in jcos yj in It is important to point out that ions lose energy continuously (cf. Figs. 13 and 14) and, therefore, using one value to represent energy lose is only valid for very thin-films. Fig. 15 shows the RBS spectrum from a poly(xylenyl either) (PXE) thin-film (about 1 mm) which has been stained with bromine [36]. With increasing energy, the carbon and oxygen signals from the polymer film, and the silicon substrate signals are given. The sharp step in yield at 1.76 MeV is due to 4He ions scattered from the bromine at the surface. From the bromine energy width, the thickness of the film was found to be about 1 mm. To improve accuracy, RUMP [37] was used to simulate the spectrum using a film thickness of 915 nm. Note that the thickness calculation is based on knowing the composition, which in turn is used to determine the stopping power from Bragg's rule.

Fig. 15. RBS spectra (*) of 2.20 MeV 4He ions backscattered from pure PXE (F 0:0). The sample was stained in a bromine and methanol solution for 24 h. Simulated spectrum (Ð) where the thickness and mer unit of PXE are 915 nm and 4 12 16 28 80 C8H7.7OBr0.14. The energies at which the He ions would be backscattered by C, O, Si and Br nuclei at the surface are marked (taken from [36]). R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 125

Depth profiling in ERD is similar to RBS except that the outgoing energy loss results from a light ion, either 1Hor2D, exiting the target. The energy of the outgoing particle is given by

Eout;0 KEin;1 ÀSt (19) where

KS S S in out (20) cos 90 À a1 cos 90 À a2

For ERD and LE-ERD, the energy loss of the recoil in the stopper filter, dEs, must be included so 1 2 that ED Eout;0 À dEs. Therefore, the Hor D energy width is given by

DE Sx dEs;x0 À dEs;x (21) where the second term accounts for energy broadening in the stopper filter. At high energies, where S decreases as 1/E, the second term is negative and, therefore, the detected energy width is compressed. For energies near the stopping power maximum of MylarTM the stopping power will change in a non-linear fashion. Under these conditions, the second term is positive and the energy width is expanded. As a detailed example of applying Eq. (21), Barbour and Doyle [8] demonstrate the slab analysis technique to determine the energy of a 2.397 MeV 1H nucleus as it traverses 12 mm of MylarTM. Fig. 16 shows a conventional ERD spectrum from a PS:dPS film which is 4500 AÊ thick. The TM beam parameters are a1 158, a1 a2 308 and 3.0 MeV. The integrated charge and Mylar thickness are 20 mC and 12 mm, respectively. As always, because of its larger kinematic factor, the deuterium signal is shifted to higher energies than hydrogen. Because of the energy loss in the 2 1 stopper filter, dEs, the D and H front edges are decreased with respect to KDEin;0 2:0 MeV and 2 1 KHEin;0 1:5 MeV, respectively. Note that D has a larger energy width than H mainly because of

Fig. 16. ERD spectrum of a homogeneous blend of hydrogenated and deuterated polystyrene. Two distinct peaks, corresponding to hydrogen (1H) and deuterium (2D) are obtained. The solid line is a simulation of the experimental data (taken from [12]). 126 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

its larger stopping power in MylarTM. For example, the electronic stopping power can be calculated using SRIM1. For the same conditions, the back 2D edge will overlap with the front 1H edge for a PS:dPS thickness near 7000 AÊ , which defines the accessible depth. The depth resolution is about 700 AÊ for this conventional version of ERD. For routine analysis, a 3.0 MeV 4He ion energy and a symmetric beam path geometry provides a good trade-off between large accessible depth and decent depth resolution. As will be discussed in Section 4.2, depth resolution can be greatly improved by varying the incident energy and ERD geometry. With some minor drawbacks this technique provides the best accessible depth because only the individual 1H and 4D signals are extracted from the detector. Furthermore, since no stopper filter is needed, the depth resolution is mainly due to the detector, geometry and straggling in the sample.

4. Experimental considerations

4.1. Instrumentation

Accelerators originally developed for fundamental nuclear physics studies are readily available and capable of producing MeV light ions for materials analysis. With only a slight modification, these accelerators are easily reconfigured for material analysis. Another route is to purchase a commercial accelerator designed for materials analysis techniques. Fig. 17 shows a typical facility including the injector source, accelerator tank, magnets, target chamber, and accelerator controls. Although a detailed description of each component is beyond the scope of this review, a polymer or materials scientist with little understanding of basic instrumentation will not be able to take advantage of the versatility of ion scattering nor optimize its sensitivity and depth resolution for a particular interface problem. Let us point out a simple example. Since 1984, polymer scientists followed the ``recipe'' established in the seminal introduction of ERD to the polymer community by Mills et al. [20]. However, with the recent introduction of LE-ERD, polymer scientists have optimized beam energy and scattering geometry to decrease depth resolution by a factor of 7, opening up a new range of problems accessible by ERD. In this section, we briefly review the accelerator components including ion beam production, acceleration, and selection. Most ERD users are particularly interested in understanding the scattering chamber, which contains the sample manipulator, beam current measurement system, and detector system. The processing of the detector signal includes the preamplifier, main amplifier and multichannel analyzer. Although this aspect of data processing will not be covered, the user must be

Fig. 17. Schematic layout of the ion scattering facility at the University of Pennsylvania. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 127

aware of certain pitfalls outlined in [17], such as dead time and pulse pileup, which lower the accuracy of ion beam analysis. For the interested reader, the major components of ion beam analysis have been previously reviewed in textbooks [7,17,38]. Furthermore, brochures and catalogues provided by acceleration, detector, and electronics manufactures provide a wealth of theoretical and practical information.

4.1.1. Accelerator Ion source: For materials analysis applications, the purpose of the source is to create a high flux of ions and inject them at low-energy into the accelerator [38]. To achieve nanoampere current over a cm2 target area requires an ion source that produces tens of microamperes. A radio frequency ion source, based on electrical discharge in a gas, is ideal for producing predominantly positive ions of 1H, 4He, 14N and 16O containing a cocktail of atomic and molecular species and charge states. Duoplasmatron and sputter sources are also used in high-energy applications. Because most accelerators have positively charged terminals, positive ions must be converted to negative species, usually by passing through an alkali metal vapor (e.g. rubidium or lithium). The negative ion beam current at this stage is ca. nanoampere. An extractor and double gap lens assembly draw the negative ions from this mixture by acceleration to about 25 keV. The positive ions are repelled. A velocity selector then steers the desired negative ion (4HeÀ) into the accelerator. The main purpose of an accelerator is to produce a stable high voltage. Van de Graaff and Tandetron accelerators are the two main types used in materials analysis. The Van de Graaff was invented at the behest of Rutherford who needed a high flux of alpha particles to ``accelerate'' his studies of the nucleus [39]. Whereas the Van de Graaff produces charge via a moving belt, the Tandetron is a solid state system with no moving parts. Pelletrons provide an inexpensive alternative, generating a high voltage by means of a metal pellet charge transfer system (i.e. alternating insulating and metal pellets). The popular tandem accelerators use an external source to create negative ions which are accelerated from ground to the terminal, stripped of their negative charge and accelerated through a second tube to ground to give an energy of (n 1)V eV, where V is the terminal voltage and n the positive charge state after stripping. After exiting the accelerator, the beam contains a range of species, charge states, and energies. The desired ions must then be extracted and focused on target. Typically, the ion beam passes through a magnetic field set-up by an analyzing-switching magnet whose field is set to allow only the desired species to pass. For example, one can select either 4He or 4He2, a selection usually based on the highest beam current. Beam shaping and steering is further carried out using a series of magnetic or electrostatic quadupole or einzel lenses, electrostatic steering or scanning in the x- and y-directions. Apertures or x, y slits placed immediately after the switcher and immediately before the target chamber are used to help define the size of the beam. Beam profile monitors in front of the slits provide a remote way to view beam shape and intensity in the x±y-directions. The typical beam size for a well-tuned system ranges from 0.1 to 3 mm in diameter. For spot sizes less than 0.1 mm, a microprobe technique requiring special ion optics and source is needed. Such microprobe techniques have not been applied to polymers because the high current density results in tremendous beam damage.

4.1.2. End station For an analysis chamber dedicated to ERD, the system must provide beam current integration, a detector, and sample manipulator as shown in Fig. 4. The beam current is usually measured by determining the electrical current, which flows between the target and ground. Accurate measurement of dose, Q, is arguably the greatest limitation for absolute determination of 128 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

concentration. Although most polymer depth-profiles rely on standards, the interaction of ions with a sample should be understood. When MeV ions impinge on a sample, electrons are emitted with energies ranging from a few eV to over 1 keV [17]. Because an electron leaving the sample is indistinguishable from a positive ion hitting the target, electrons must either be prevented from leaving the sample or counted. In the former case, the target is biased at a few kV to prevent low-E electrons from escaping. For polymers, the production of inner-shell vacancies leading to photon emission is a key problem. These photons (i.e. UV and visible) leave the transparent polymer sample, interact with chamber walls, and create a flux of secondary electrons. In fact, the light emitted by polymers such as PS can be easily seen by eye and facilitates locating the beam footprint. For MeV 4He, Venkatesan [17] reports that the secondary electron current can be comparable to the ion beam current. An electrostatically shielded Faraday cup surrounding the sample provides a reliable method to detect secondary electron emission. Beam current integration can also be measured upstream using a ``transmission'' design. Here, a rotating wire intercepts the beam several times per second to provide a relative measure of beam current. In ERD, the sample is tilted so that the incident beam makes a glancing angle, typically 158 with the plane of the surface. A semiconductor detector is placed in the forward direction to capture the recoiled 1Hand2D nuclei. Silicon surface barrier (SB) and passivated implanted planar silicon (PIPS) detectors are commonly used because of their reliability, efficiency and energy resolution. Typical resolutions range from 15 to 20 keV for most ERD applications. The principle of operation of silicon detectors has been described [17,40]. Briefly, incoming ions traverse a metal window or dead layer before entering the active detector region. Energy losses in this dead layer and that due to nuclear collisions are taken into account when calibrating the detector system. Upon colliding with electrons (i.e. electronic energy loss), charge carriers are produced. For silicon the formation energy of one electron±hole pair is 3.67 eV. Charge carriers are swept from the depletion zone, which must be thick enough to stop the highest energy particle. The resultant charge pulse of a few nanoseconds duration is integrated in a charge-sensitive preamplifier to produce a voltage pulse for further processing. A good description of semiconductor detectors can be found in manufacturer catalogues (EG&G Ortec, 100 Midland Road, Oak Ridge, TN 37831; Canberra Industries Inc., Meriden, CT 06450). An excellent introduction to the processing of detector signals has been published [17]. An aperture immediately in front of the detector is particularly important in the forward scattering geometry to reduce kinematic broadening, which in turn limits depth resolution, and prevent ions from reaching the outside edge of the detector where resolution is poor. For a rectangular slit, Doyle and Peercy [19] have reported on the optimum conditions needed to minimize the depth resolution resulting from kinematic broadening. This broadening is mainly due to the finite size of the detector aperture. Since the kinematic factor varies as cos2 f, a spread in f results in a

range of recoil energies, KEin,0, associated with surface atoms. Recently, calculations by Brice and Doyle showed that curved slits, having the same area as rectangular ones, improved the energy resolution by 50% [41]. An absorber or stopper filter is also placed in front of the detector. This filter prevents the large flux of elastically scattered 4He from overwhelming the detector. MylarTM (polyethylene terephthlate) and aluminum are common filter materials because they are available over a wide range of uniform thickness. Choosing a filter thickness depends on the range of the 4He in the filter and the range of the recoiled nuclei in the filter. For example, 2.5 MeV 4He ions scattered from a high mass nucleus will be completely stopped by a 10.6 mm filter whereas recoiling 1H will only lose about 400 keV. This difference is mainly due to the much lower stopping power for 1H in MylarTM. Unfortunately, the absorber filter can spread the 1H energy by ca. 50 keV because of straggling in the R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 129

thick filter. Filter straggling is a major component of the overall depth resolution. Thus, the stopper filter should be as thin as possible to maximize resolution. The program SRIM1 provides a convenient method to calculate the filter thickness needed to stop a given incident ion or the straggling of 1Hor2D through such a filter. As discussed in Section 4.2.3, LE-ERD is based on decreasing the incident beam energy in order to minimize filter thickness. For example, using a 2.85 MeV He2 ion in conjunction with 8.0 mm of MylarTM results in a FWHM resolution of 600 AÊ at the surface. However, a combination of 1.00 MeV 4He2 with a 3 micron MylarTM filter provides a resolution of 170 AÊ . It is important to note that the accessible depth decreases from 6000 to 1000 AÊ , respectively. Presently, the best surface resolution achieved with LE-ERD is 80 AÊ with an accessible depth of 300 AÊ [42]. This section demonstrates that the optimum characterization of polymer surfaces and interfaces will only be achieved if polymer scientists understand the rudiments of accelerator instrumentation. Furthermore, an understanding of how detector systems work can open up new areas within the polymer field that have yet to be explored. LE-ERD is an example of such a breakthrough.

4.1.3. Radiation safety notes Because polymer scientists are not usually trained in nuclear physics a brief discussion of radiation safety is appropriate [17,38,43]. Although extremely safe under most conditions, commercial accelerators for materials analysis can produce unwanted radiation, X-rays, g-rays, and neutrons. The main problem is usually Bremsstrahlung radiation. Electrons are produced by the interaction of the ion beam with background gas and the beam line, thus the need for good vacuum and collimation, respectively. These electrons are accelerated through the high voltage region back towards the ion source resulting in Bremsstrahlung radiation. Users also need to anticipate nuclear reactions between the incident projectile and target nucleus. Fortunately, for a 4He or 1H beam energy below 3 MeV, nuclear reactions with the target are not serious problems unless the target contains tritium, lithium or beryllium [38]. Tesmer and Nastasi have tabulated the Coulomb barriers for the production of neutrons and g. Because this barrier scales with the incident and target particle atomic numbers, nuclear reactions are mainly important for protons on light element targets. However, some low-energy nuclear reactions exist and can be quite useful. For example, Kerle et al. have recently used the 2H(3He, 1H)4He nuclear reaction to achieve a surface resolution of 6 nm FWHM [44].

4.2. Depth resolution

As with other experimental techniques, a thorough understanding of the parameters that affect an ERD experiment is required to optimize the resolution and sensitivity for a particular surface or interface problem. In ERD, the key parameters are beam energy, stopper filter thickness, scattering angle, F, and the total charge. The effect of these parameters on depth resolution and sensitivity will be discussed in Sections 4.2.2 and 4.2.3. Methods for optimization will be discussed as well as how optimization of one factor, such as resolution, often comes at the expense of another factor. For instance, the optimization of the depth resolution using LE-ERD leads to a decrease in the depth below the surface that can be probed. The major disadvantage of conventional ERD is its relatively poor surface depth resolution which is ca. 800 AÊ using a 10.5 mm Al filter and a beam energy of 3.0 MeV. This results mainly from the energy loss due to straggling inside the thick stopper filter, either MylarTM or Al. There are three relatively simple ways in which the depth resolution of ERD can be improved while still maintaining TM its simplicity: (i) lowering E0, which allows the use of a thinner Mylar filter and also increases the 130 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 18. The volume fraction profile (dotted line) for surface segregation in a polymer blend having surface and bulk concentrations of 0.8 and 0.1, and a surface excess of 6 nm. The solid lines are obtained by convoluting the dotted line with a Gaussian instrumental resolution function having FWHM (a) 800 AÊ , (b) 300 AÊ , (c) 140 AÊ , and (d) 50 AÊ .

stopping power of the sample, (ii) varying F, the scattering angle, and (iii) using heavier projectiles. The first two effects constitute the basis of LE-ERD. Direct depth profiling techniques, such as the ion beam techniques discussed in this review, measure the polymer concentration in direct space perpendicular to the sample surface. Because of the statistical nature of the measurement each technique has a limited depth resolution. As a result, the concentration profiles that emerge from the measurements are smeared by the instrumental resolution of the technique. This effect can be simulated by convoluting the ``real'' profile with a Gaussian resolution function having a certain characteristic ``instrumental'' broadening characterized usually by the FWHM of the function. In a case of ``ideal'' resolution (FWHM ! 0), the measured profile would be indistinguishable from the ``real'' one. We illustrate the effect of a finite instrumental resolution on a simple example that involves surface segregation of a polymer from a polymer blend. Such a situation is shown in Fig. 18. The ``real'' volume fraction of the segregated species (dotted line) varies smoothly from its bulk value of 0.1 to 0.8 at the surface. The solid lines in Fig. 18 denote the volume fraction profiles convoluted with Gaussian functions having resolutions of: (a) 800 AÊ , (b) 300 AÊ , (c) 140 AÊ , and (d) 50 AÊ . These values are the depth resolutions at the sample surface corresponding to the different techniques mentioned in this review including (a) ERD, (b) non-resonant 2H(3He, 1H)4He NRA in the Payne et al. [45] geometry, (c) LE-ERD or non- resonant 2H(3He, 1H)4He NRA in the Chaturvedi et al. [46] geometry, and (d) resonant 1H(15N, 4He g)12C NRA. Fig. 18 clearly demonstrates that the techniques with the best depth resolution more closely resemble the ``real'' experimental situation. Depth resolution is, thus, a key factor to consider when choosing a technique for interfacial studies.

4.2.1. Contributions to ERD depth resolution Several factors influence the depth resolution of ERD. Through careful design of the experimental set-up, many of these factors can be mitigated to achieve the best depth resolution, R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 131

which is defined as

DE dx tot (22) dE=dxeff where DEtot is the total energy resolution and (dE/dx)eff is the ``effective'' stopping power of ions penetrating the sample. This expression shows that the best depth resolution is achieved when the energy resolution is a minimum and the effective stopping power a maximum.

To evaluate Eq. (22), the contributions to DEtot must be identified and determined. These are

1. DED, detector energy resolution [38,39]; 2. DEM, energy broadening due to multiple scattering; 3. DES, energy straggling in the sample; 4. DEF, energy straggling in the stopper filter; 5. DEG, geometrical broadening due to beam divergence and finite acceptance angle of detector. Assuming they are uncorrelated and can be characterized by a Gaussian distribution, these factors add in quadrature:

2 2 2 2 2 2 DEtot DED DEM DES DEF DEG (23)

In a real experiment, only the energy resolution of the detector, DED, is constant (although it can decay with time).1 Factors 2±4 can be calculated for a particular experimental set-up and sample [26,47±51]. A brief description of each contribution to the total energy resolution is given below. A comprehensive discussion can be found in references [17,38,48±51].

Straggling, DES, is a result of the statistical nature of the interactions between the incident particles and the sample. Moreover, as the incident ion beam traverses the sample, the diameter of the beam broadens because the ions make multiple small-angle collisions with the nuclei in the sample. The lateral and angular spread, including path-length fluctuations, of the incoming and outgoing particles have been estimated from theories of multiple scattering [51,52]. Because of the statistical nature of these interactions, the energy loss by the ions has a Gaussian distribution with a width corresponding to the energy straggling. The energy spread due to straggling can be approximated from the Bohr theory [53], which predicts that straggling is independent of energy and increases as the square root of the film thickness (i.e. either sample or filter).

As discussed elsewhere [26,48,49], multiple scattering, DEM, is particularly important for glancing angle geometry and recoil collisions below the surface. Energy straggling is similar to multiple scattering in that an energetic particle loses energy via many individual encounters with electrons in the sample and stopper filter.

The error associated with geometric broadening, DEG, occurs because the ion beam has finite width and the detector has finite area. These two contributions produce two sources of error that can be evaluated following the procedure of Turos and Mayer [48]. The first contribution comes from the strong dependence of the kinematic factor K on F as can be seen in Eq. (10). Due to the finite width of the beam and detector, different spots on the sample will have different values of F, and thus, different values of K, as depicted schematically in Fig. 19. The second mechanism reflects a distribution of path-lengths as well as distribution of energy losses in the material. For a well collimated incident beam, only geometric broadening due to the beam width and finite detector acceptance angle are important. As shown by Turos and Mayer [48], kinematical spread and

1 Depending on the manufacturer, the energy resolution of the detector usually ranges from 10 to 20 keV. 132 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 19. Geometric broadening, DEG, is due to the variation in the recoil angle, F, caused by the finite width of the beam and the spread due to the solid angle of the detector.

path-length differences compensate each other near a1 12:58 and, therefore, geometric broadening is minimized near this angle (cf. Fig. 19). However, at lower values of a1, this broadening makes a significant contribution to the overall resolution. A detailed discussion of geometric broadening is given in [41,48] and [54]. For most samples, the effect of lateral inhomogeneities, such as surface

roughness, on DEtot can be ignored. However, in cases where a glancing scattering geometry is applied, the effect of surface roughness on depth resolution may become important. Geometric broadening is reduced by having a well collimated, narrow beam incident on the sample.

Energy straggling in the stopper filter, DEF, is the largest error in a conventional ERD experiment. The straggling process in the filter is the same as the straggling in the sample. While this filter is needed to reduce the energy of the scattered 4He ion, it also decreases the energy of the recoiled 1H and 2D ions while increasing the energy spread. Several different experimental designs have focused on reducing or eliminating this error.

4.2.2. Optimizing depth resolution in ERD

The depth resolution can be improved by increasing (dE/dx)eff as shown in Eq. (22). Fig. 20 shows pathways for the incoming ion and the outgoing recoils in ERD. The energy losses of the 4He projectiles and the recoiled 1H on their inward and outward paths, respectively are denoted as (dE/

dx)in,He and (dE/dx)out,H. The scattering geometry is defined via F and a1. Because the incident beam enters the end station at a fixed geometry, and the detector position is typically fixed, the scattering 2 angle, F, is fixed (e.g. typically 308). However, the angle between the incident beam and sample, a1, can be varied by rotating the sample. As shown below, optimizing a1 can greatly improve depth resolution. The effective energy loss is then obtained from Eq. (22), where dE=dxeff S is comprised of dE=dxin;He Sin and dE=dxout;H Sout for the inward and outward paths. There are three ways to maximize (dE/dx)eff. First, because (dE/dx)He is about an order of magnitude greater than (dE/dx)H, the overall (dE/dx)eff can be greatly increased by increasing the 4 path-length of the incident He ions. This is accomplished by decreasing a1 which changes the path- length, t/sin a1, as seen in Fig. 21. On the other hand, increasing the path-lengths of the ions inside the sample may produce a substantial increase in the multiple scattering, which deteriorates the depth resolution. Thus, in order to improve the depth resolution by tilting the sample with respect to the incoming ion beam, a compromise between these opposite tendencies has to be found. The

2 In [48], Turos and Mayer showed that the optimum angle for the analysis of the forward recoiled particles is at F 308. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 133

Fig. 20. Schematic of the energy loss in an ERD experiment as the incident 4He ion traverses the sample, collides with a 1H atom and finally the 1H(D) ion leaves the sample. The parameters are defined in the text.

second way to maximize (dE/dx)eff, is by decreasing Ein,0, which causes both (dE/dx)in,He and (dE/ dx)out,H to increase [55]. However, the trade-off here is that at lower beam energies there is a decrease in the depth that is accessible. Finally, increasing the atomic number of the projectile will also increase (dE/dx)eff. This modification increases the kinematic scattering factor K (cf. Eq. (8)) and also leads to higher (dE/dx)in,He and (dE/dx)out,H. However, heavy projectiles may lead to undesirable modification of the sample as discussed in Section 7.4.

The depth resolution can also be improved by reducing the magnitude of DEtot by focusing on the largest contribution to DEtot, which is the straggling in the filter, DEF. To reduce DEF, Genzer et al. [26] decreased the beam energy, Ein,0, from 3 to 1.3 MeV which consequently allowed for a reduction in the stopper filter thickness from 11 to 3 mm. As a result, the filter straggling decreased by a factor of 1.5. A lower beam energy also increases (dE/dx)eff, by a factor of 1.6, which further enhances the resolution. By using a lower beam energy and thinner filter, the depth resolution improves by a factor of 4 in LE-ERD. Fig. 22 shows the total and individual energy resolutions calculated for 2D in PS using 1.3 MeV 4 TM He (LE-ERD) at F 308, and a1 208 with a Mylar filter thickness of 3.0 mm [26]. By increasing the thickness of the stopper filter to ca. 11 mm (ERD) the contribution due to DEF increases substantially (from 13 to 22 keV). The energy resolution is 20 keV at the surface and

Fig. 21. This schematic shows how to increase (dE/dx)eff by decreasing a1 which consequently increases the path-length of 4 4 the incoming He ions. Although the path-length out decreases, (dE/dx)eff increases overall because (dE/dx)of He is four 1 2 times greater than that of H at the same velocity (i.e. dE/dx is proportional to Z1 at the same velocity). 134 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 22. Theoretical energy resolution of 2D in deuterated polystyrene as a function of depth in the sample. The TM experimental parameters are E0 1:3 MeV, a 3.0 mm thick Mylar stopper filter, F 30, and a1 208. The calculated curves correspond to the detector resolution (thin solid line), energy straggling in the stopper filter (thick dashed line), energy straggling in the sample (thin dotted line), geometrical broadening (dash-dotted line), multiple scattering (dash-dot- dotted line), and total energy resolution (thick solid line) (taken from [26]).

slowly increases to 32 keV at a depth of 1000 AÊ . Examination of the individual contributions shows that near the surface (<500 AÊ ), the total energy resolution is dominated by straggling in the stopper filter, the detector resolution, and geometry. However, beneath the surface (>400 AÊ ), multiple scattering dominates and drives the total energy resolution to larger values. The increase in multiple scattering is even stronger at glancing angles because of the increase in the total path-length in the sample.

4.2.3. Improved depth resolution with LE-ERD Using four alternating layers of normal PS and its deuterated analogue (dPS), each 300 AÊ TM thick, Genzer et al. [26] demonstrated that lowering Ein,0 and consequently using a thinner Mylar filter produced radical improvement in depth resolution. Fig. 23a shows the ERD spectrum of a Si/ PS/dPS/PS/dPS sample analyzed with a 3.0 MeV 4He beam and a 10.35 mm thick Al filter at a1 158 and F 308. Because of the straggling in the stopper filter, the deuterium yields from the two dPS layers overlap, suggesting that the near-surface spatial resolution is greater than the thickness of the PS spacer. Likewise, the two PS layers cannot be resolved. The fit to the experimental data reveals that the depth resolution for 2D and 1H is 750 and 780 AÊ , respectively [26]. By decreasing the incident beam energy to 1.3 MeV and the MylarTM stopper filter thickness to 4.5 mM, the depth resolution improves dramatically, as demonstrated by the two distinguishable deuterium maxima shown in Fig. 23b. Qualitatively, this observation indicates that the 2D resolution is comparable to the thickness (250 AÊ ) of the PS spacer. The depth resolutions of 2H and 1H are 250 and 300 AÊ , respectively, which is a three-fold improvement relative to conventional ERD.

The depth resolution can be further improved by varying a1, the angle between the incoming 4He beam and the sample, to achieve glancing incident and/or exit geometries. From the scattering geometry, the range for a1 is 0 > a1 > 30 . In a typical set up F 308, and thus, a1 can range from >08 to <308. In the standard ERD geometry (a1 158) the path-lengths of the incoming and outgoing ions are the same. However, in the glancing exit geometry (a1 > 158) the path-length of the outgoing particle is longer than the incident particle. Correspondingly, at glancing incident R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 135

1 2 4 Fig. 23. The ERD and LE-ERD spectra of H and D for He ions incident at a1 158 and F 308, respectively. The incident beam energy is (a) E0 3:0 MeV and stopper filter is 10.35 mm thick aluminum filter and (b) E0 1:3 MeV and stopper filter is a 4.5 mm thick MylarTM filter. The solid line represents fit to experimental data (taken from [26]).

4 angles (a1 < 158), the incoming He particle travels a longer path in the sample than the outgoing particles. Fig. 24 shows LE-ERD spectra from the sample above as a function of increasing incident TM angle, a1 10, 7.5 and 58. Here, a 4.5 mm thick Mylar filter is used with a 1.3 MeV energy beam. Using Fig. 23b as a guide, the depth resolution has further improved, as demonstrated by the two 2 1 distinguishable D (and H) maxima in Fig. 24. Upon decreasing a1 from 0 to 58 the depth resolution of 2D and 1H at the surface improves from 200 and 215 to 145 and 155 AÊ , respectively. Similar improvements in the depth resolution can be achieved using the glancing exit geometry, which has the advantage of a smaller incident beam footprint on the sample [26]. One drawback of LE-ERD is that the probing depth in the sample decreases from 7000 AÊ for conventional ERD to 800 AÊ . Thus, LE-ERD is best suited to study surface or near-surface phenomena. However, as discussed in Section 7.3, LE-ERD combined with sputtering can be used to probe interfaces buried much deeper than the nominal probing depth of LE-ERD. In order to maximize depth resolution, the lowest beam energy and thinnest MylarTM filters should be chosen to meet the probing depth requirements. 136 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

4 Fig. 24. LE-ERD spectra for 1.3 MeV He ions incident on Si/PS/dPS/PS/dPS sample at a1 10 (open circles), 7.58 (crosses), and 58 (closed triangles). A 4.5 mm thick MylarTM stopper filter is used (taken from [26]).

4.3. Elemental sensitivity

After depth resolution, elemental sensitivity is the next critical parameter. In an ERD experiment, sensitivity is defined as the minimum amount of hydrogen or deuterium that can be detected. In theory, the detection limit of ERD is infinitesimal if the beam current is small, and the operator's time is unlimited. That is to say, as long as any 2D exists in the sample, an incident 4He particle will eventually recoil it from the sample into the detector. However, in practice, analysis time per sample is an issue as well as the collection of a statistically significant number of counts. For practical purposes, two main factors limit the sensitivity (1) the 1Hor2D signal must be resolved from the background signal, and (2) the time to obtain an acceptable number of counts must be reasonable. The absolute sensitivity (AS) defines the minimum of 1Hor2D counts to achieve a certain precision. Usually expressed in the number of 1Hor2D per cm2, AS can be evaluated from 100% 2 sin a AS 1 (24) p Os Q=qe where p is the percent precision and is determined by the total detected yield: p Y 100% p Â 100% p (25) Y Y Eqs. (24) and (25) show that in addition to the required precision the absolute sensitivity strongly depends on the detector solid angle, O, the scattering cross-section, s, and the total number of

incident particles, Q/qe. In principle, the AS can be improved by moving the detector closer to the sample to increase O. However, the energy spread of the recoils limits how much one can increase O before the depth resolution begins to increase. Two practical methods to improve AS involve increasing the incident beam flux or decreasing the incident beam energy to increase s. Other routes include increasing Q (and Y) by increasing beam current or exposure time. In this case, the amount of current that can be tolerated by a sample should be carefully considered. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 137

The background signal in an ERD spectrum is mainly due to pulse pile-up, which occurs at high beam current. When two ions strike the detector at the same time, the detector is unable to distinguish between particles and registers one count at the combined energy of the two ions. Pulse pile-up creates a background signal that can mask a 1Hor2D signal, particularly at low concentrations. Pulse pile-up can be reduced by using a thicker filter that prevents the large flux of forward scattered 4He ions from reaching the detector. The great majority of particles that are recorded by the detector are forward scattered 4He ions. For example, a 2.8 MeV 4He beam incident on a 4000 AÊ PS film on silicon will result in 40 forward scattered 4He ions for every recoiled 1H that reaches the detector covered by a 8 mm MylarTM filter. Because 2D ions recoil at higher energies than 1H ions, the 2D signal has a lower background and is, therefore, easier to resolve. Moreover, the 2D resonance near 2.15 MeV (cf. Fig. 12) can be utilized to dramatically increase the sensitivity to 2D. The AS can be understood by calculating the number of counts from a 10 nm molecular layer of 1 3 23 PS. The atomic density of HinPSisHPS 1:05 g=cm Â 8 atoms=monomer Â 6:023 Â 10 atoms=mole= 104 g=mole,or4:86 Â 1023 atoms/cm3. For a 3.0 MeV 4He ion incident at 308, the 1H yield is about 760 counts per 10 mC of integrated charge.

4.4. Sample modification

During ion beam analysis, the 1H and/or 2D that recoil from the sample are removed from the polymer. This modification during the analysis may complicate the data analysis. An estimate of the number of atoms that are elastically recoiled from the sample during an ERD experiment can be obtained from a simplified version of Eq. (26):

Q t Y sO N (26) qe sin a1 In Eq. (26), N is the bulk density of the sample and t is the sample thickness. The geometry is shown schematically in Fig. 25. As an example, the total number of 1H nuclei recoiled from the volume intersected by an incident beam having a 0.02 cm2 cross-section is calculated. For Q 10 mC, the total number of recoiled 1H in the forward direction is about 2:5 Â 106. This value is quite small

Fig. 25. Schematic illustrating the volume of the sample irradiated by the incoming beam. 138 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

compared to the total number of 1H atoms in this volume, which is 3:7 Â 1015 atoms. Thus, the elastic collisions that produce the ERD signal do not significantly change the 1H and/or 2D concentration in the polymer. The structure of polymers can be changed by the large amount of energy deposited in the sample through inelastic energy loss processes. Ion interactions with the polymer can lead to chain scission, cross-linking, and molecular emission. The extent to which these effects occur depends on the primary ion beam type, energy, flux, etc. and the properties of the polymer (structure, molecular weight, etc.). Some general rules for predicting sample modification have been established ([56] and the references therein). For example, ion beam bombardment of poly(methyl methacrylate) causes chain scission because the quaternary carbon atoms (bonded to four other carbon atoms) tend to degrade the main chain. As a consequence small molecule fragments can volatilize. In contrast, because PS mainly cross-links upon irradiation the material loss is small (<1±3%) and usually uniform throughout the sample. As a general rule, polymers with stabilizing phenyl rings tend to be stable under the ion beam. Although irradiation can be used to improve bulk and surface properties (cf. Section 7.4), polymer modification by the incident beam may also complicate depth profiling analysis. To acquire accurate spectra, sample modification during irradiation should be reduced as much as possible. In some cases, cooling the sample with liquid nitrogen helps to decrease the concentration of volatile species emitted from the sample. Scanning the ion beam over the sample also decreases polymer degradation by spreading the damage over a larger area. In addition, sample degradation can be reduced by using a lower dose and higher beam energy; in both cases, however, the signal will be lower and the statistics poorer.

4.5. Sample requirements and preparation

The sample requirements are rather modest. The sample must be stable under ``modest'' vacuum, typically 10À6 Torr in the sample chamber. The vacuum is required because the 4He ions have a small mean free path through a gas at atmospheric pressure. In special cases, an environmental chamber can be used to expose samples to a vapor (e.g. water) at pressures of up to 10À3 Torr. A second requirement is that the sample must allow the charge from the incident ion beam to reach the sample holder, which is connected to the current integration system. Typically samples are mounted with conducting tape to the holder. If the sample is a thick insulator, charging can be avoided by coating with a metal, rubbing with an eraser or providing a conducting pathway from the surface to the holder. A third requirement is sample geometry, which is mainly limited by the sample holder size, typically 5cm2. The cross-section of the incident beam, 1±2 mm2, sets the minimum sample size. Samples can be up to 3 cm thick. For ERD analysis, polymer films are usually mounted on flat, solid substrates. Because of their low price and availability, silicon substrates are commonly used. Polymer films are typically deposited on the substrate by spin-coating from a polymer solution. This technique, originally developed by the semiconductor industry for depositing photoresist films, produces smooth, laterally uniform films having small variations in thickness (<15 AÊ ). Because of the grazing incident and exit geometry, sample roughness will tend to spread out the back edge of a signal and/or degrade the depth resolution. Film thickness and quality depends on the (i) substrate properties such as surface energy and roughness, (ii) polymer, (iii) molecular weight, (iv) solvent, (v) solution concentration, and (vi) spinning speed and time, etc. The relationship between these parameters and the sample thickness can be established empirically [57]. The thickness of films prepared by spin-coating can range from nanometers [58,59] to a micron. For very thick samples, the thickness becomes less R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 139

uniform. For thicknesses up to several micrometers, films can be prepared by pulling a substrate at a constant rate from a concentrated polymer solution or by using a doctor blade to spread the solution. To prepare a bilayer (or a multilayer), two possible strategies can be utilized. In both cases, the bottom layer is prepared using the procedure described earlier. If the polymer to be placed on the top dissolves in a solvent that does not dissolve the bottom layer, the top layer can be prepared by spin- coating a solution directly on the bottom layer. Otherwise, the top layer is spin-coated on a microscope glass slide, scored around the edges, floated on deionized water, and picked up with the bottom layer/silicon sample. If the top polymer does not float off glass, one can use a different supporting media, such as single crystal NaCl or mica.

5. Data analysis

5.1. Data conversion

The aim of many ERD experiments is to obtain a depth-profile of a light element in a sample. In Section 3, the origin of the depth and concentration resolutions in an ERD experiment was

Fig. 26. (a) ERD spectrum of a thin film of PS on a dPS matrix after annealing for 240 s at 171 8C; (b) volume fraction of PS derived from the ERD spectrum in (a). The solid line is a theoretical fit to the data using a DÃ of 5:3 Â 10À13 cm2/s (taken from [111]). 140 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

examined. However, as was previously mentioned, the data output from the ERD detector is simply a column of numbers that corresponds to the quantity of counts that were recorded in each channel. Fig. 26a shows an ERD plot of the normalized yield at each channel number from a thin dPS layer, 200 AÊ on top of a thick PS. Normalized yield is the raw counts divided by the beam dose, detector solid angle, and the channel energy width. This raw data in counts per channel must be converted into a concentration versus depth-profile as shown in Fig. 26b. Note how the concentration versus depth plot is the mirror image of the raw data; this is because moving to lower energy, to the left, is equivalent to moving deeper into the sample, to the right. Another feature is the apparent observation of dPS at negative depths. This anomaly is a direct result of surface broadening due to the finite system resolution of 80 nm. This section will outline how to perform this conversion from counts versus channel to concentration versus depth. The first step is to convert from channel number to the energy of the detected ions. Each channel number corresponds to a specific energy range, and a calibration is used to convert from channel number to the energy of the detected particle. Using known parameters such as the stopping powers of the projectile and the recoiled ion and the kinematic factor, the energy can be converted to depth in the sample. Likewise the number of counts registered in each channel and can be converted to the concentration of the species at that depth. The resultant ERD spectrum is governed by a set of parameters defining the scattering geometry, incident beam characteristics and the parameters of the target and the stopper filter; the following is a complete catalog of the information necessary to conduct the energy to depth and the counts to concentration conversion. The scattering geometry can be completely defined by the angle

between the incident beam and the sample, a1, and the recoil angle between the incident beam and detector, F. For convenience in determining the path-length of the ions in the sample, the outgoing

beam angle a2, is also introduced (a2 is simply the difference between a1 and F). This geometry is described in Fig. 20. The relevant parameters of the incident projectile are its mass, Mp, initial energy, Ein,0, and charge, Zp. The mass, Mt, and scattering cross-section, s(E, F), of the recoiled target are known as well as the stopping powers of the incident particles, Sin, and the recoiled particles, Sout in both the samples and the stopper filter. The stopping powers are a direct measure of the energy loss rate of the projectiles and the recoils as

they penetrate through the sample. Generally, Sin,andSout are not constant, but are strong functions of the energies of the incoming or outgoing ion. The stopping power of many materials has been tabulated [60] or they can be determined from SRIM1, the stopping and range of ions in matter, a program developed by Ziegler et al. [30]. This program provides a plot of particle energy versus stopping power, (dE/dx). From this data, a polynomial equation can be fited to the relevant energy region of the dE/dx curve, as shown in Fig. 27 for both 1Hand4He. As for the stopper filter, the type of material and its thickness determines the amount of energy lost by the recoiled ions as they pass through the filter. The stopping power of the stopper filter can be determined theoretically or by SRIM1. Because the stopper filter is usually several microns thick, the precision in determining the energy loss of the recoils is limited by the uncertainty in filter thickness. A direct experimental determination of the stopping power is the best. For a known beam energy incident on a sample with a surface target atom, say 1H, the stopping power of the filter can be determined by measuring the recoiled particle energy after passing through the filter. Using the incident beam energy and kinematic factor as in Eq. (10), the energy of the recoiled 1H immediately after leaving the sample surface can be determined. The energy of same recoiled 1H after it leaves the filter corresponds to the front edge of the 1H spectrum. The energy lost due to the stopper filter is then simply the difference:

Efilter KEin;0 À ED (27) R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 141

Fig. 27. Stopping power for 1H and 4He in PS over a wide range of 4He energies. For the energy to depth conversion, a polynomial has been fit over the energy region of interest.

By repeating this experiment with various incident beam energies, a plot of recoiled particle energy versus stopping power can be constructed, and fited with a polynomial equation to describe how the stopping power in the filter varies with the energy of the recoiled particles. The results of such experiments are shown in Fig. 28 for both 1H and 2D.

5.1.1. Channel to energy To convert from channel number to energy requires a calibration plot of particle energy versus recorded channel number. To reduce unknowns, the calibration is conducted without a stopper filter in front of the ERD detector. The optimum calibration sample has at least one heavy element that is

Fig. 28. Experimental determination of the stopping power for both 1H and 2D though 7.5 mm of MylarTM. The integrated energy loss through MylarTM is measured from a standard (e.g. hPS:dPS blend) over numerous beam energies. 142 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 29. Experimental calibration of a detector. The plot was constructed using five 4He beam energies over the region of interest. The offset and channel width (slope) are 96.95 keV and 5.29 keV per channel, respectively.

known to be at the surface. The energy of a 4He forward scattered from the surface is the product of

the kinematic factor and beam energy. By a one-to-one correspondence, the energy, KE0, for that particular channel is known. Repeating this procedure for a range of incident beam energies yields a linear relationship, E a channel no:b where a is the energy width of each channel, usually in keV per channel and b is the multichannel analyzer offset. Fig. 29 shows a typical calibration curve. Calibration samples with two or more surface atoms are particularly useful because each experiment yields two or more data points for conversion. The calibration energy range should be similar to the experimental range to ensure accuracy.

5.2. Direct conversion of experimental data

5.2.1. Energy to depth conversion The procedure that relates the detected recoil energy to the depth t of the scattering event inside the sample is straightforward for very thin targets. Because the stopping powers are relatively constant in thin-films, the conversion simply follows the recipe outlined in Section 3.3. However, for thick targets the energy losses of the incoming 4He and exiting 1Hor2D are significant and, therefore, the energy dependence of the stopping power in the sample must be included by using the ``thick target approximation'' [11], which is outlined in the following sections. In the thick target approximation, the sample is divided into N layers, each having thickness Dx.3 The total sample thickness is N Dx. For sufficiently small Dx, the stopping power inside each layer can be considered constant. The energy to depth conversion is performed via a sequential calculation of the energy losses of the incident ion and recoils for each layer. Fig. 30 shows a schematic representation of the thick target approximation for an incident 4He ion, with initial 2 1 energy Ein,0, recoiling a Dor H nucleus at depth t. The energy of the incident ion entering layer j is Ein,jÀ1. The energy of this ion in layer j can be derived from the recurrent relation: Dx Ein;j Ein;jÀ1 À Sin;jÀ1Ein;jÀ1 (28) sin a1

3 To simplify the analysis, we have chosen the thicknesses of every sublayer to be the same. However, in general, each sublayer can have a different thickness. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 143

Fig. 30. Schematic of the thick target approximation for an ERD experiment. To account for the dependence of the stopping power on the ion energy, the `thick' sample is divided into N slabs of thickness Dx. If the slab thickness is thin enough, the stopping power in each slab is taken as a constant.

where Sin,jÀ1 is evaluated at Ein,jÀ1. The values of Sin and Sout are derived from the stopping powers of the constituent elements by applying Bragg's rule as outlined in Section 3.3. At each layer, Ein and Eout are related as

Ein;j KEout;j (29) where K is defined in Eq. (10). Similar to the incident ion procedure, the energy of a recoiled ion leaving layer j is Eout,jÀ1, and the energy of a recoiled ion passing through layer j À 1 can be evaluated from the recurrent relation

Dx Eout;jÀ1 Eout;j À Sout;jEout;j (30) sin a2 where Sout,j is evaluated at Eout,j. As shown in Fig. 30, the energy of the recoils, ED is given by

ED Eout;0 À Efilter Eout;0 (31) where Efilter is the total energy loss of the recoils in the stopper filter which can be calculated using a similar procedure or determined experimentally as discussed earlier. An example of the energy to depth conversion is given in Table 1 for a 2.8 MeV 4He projectile into dPS with a layer thickness of Ê TM 150 A, with angles of a1 a2 158, and a stopper filter of 8 mm Mylar . Note that the stopping power changes by 4% over the thickness 3000 AÊ of the target dPS. Even though the layers are relatively thick, the stopping power between any two adjacent layers is nearly constant, affirming the assumption of our thick target approximation.

5.2.2. Counts to concentration The yield (counts) of the recoiled ions can be converted to the concentration of atoms within a given layer. The concentration in layer j, Nj, is related to the yield, Yj,as

Q=qeNjs Ein;jÀ1; fOdEdet Yj (32) cos F dE=dxeff;j

In Eq. (32), Q/qe is the total number of incident ions, s(Ein,jÀ1, F) the scattering cross-section evaluated at Ein,jÀ1 and F, O the detector solid angle, dEdet is the energy width of a channel in the 144 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Table 1 Conversion of energy to depth for in an ERD experiment using 2.8 MeV 4He incident on PS (3000 AÊ ) and an 8 mm MylarTM filter Ê Ã Layer Depth (A) Ein;x DxSin;x K Ein;x DxSout;x Eout,0 Efilter ED (4He, MeV) (4He, MeV) (2D, MeV) (2D, MeV) (2D, MeV) (2D, MeV) (2D, MeV) 0 0 2.80 0 1.87 0 1.87 0.31 1.56 1 150 2.79 0.0087 1.86 0.0018 1.86 0.31 1.55 2 300 2.78 0.0087 1.86 0.0018 1.85 0.31 1.54 3 450 2.77 0.0087 1.85 0.0018 1.84 0.31 1.53 4 600 2.77 0.0087 1.84 0.0018 1.84 0.31 1.52 5 750 2.76 0.0087 1.84 0.0018 1.83 0.31 1.52 6 900 2.75 0.0088 1.83 0.0018 1.82 0.31 1.51 7 1050 2.74 0.0088 1.83 0.0018 1.81 0.31 1.50 8 1200 2.73 0.0088 1.82 0.0018 1.81 0.32 1.49 9 1350 2.72 0.0088 1.81 0.0018 1.80 0.32 1.48 10 1500 2.71 0.0088 1.81 0.0018 1.79 0.32 1.47 11 1650 2.70 0.0088 1.80 0.0018 1.78 0.32 1.46 12 1800 2.69 0.0089 1.80 0.0018 1.77 0.32 1.46 13 1950 2.69 0.0089 1.79 0.0018 1.77 0.32 1.45 14 2100 2.68 0.0089 1.78 0.0018 1.76 0.32 1.44 15 2250 2.67 0.0089 1.78 0.0018 1.75 0.32 1.43 16 2400 2.66 0.0089 1.77 0.0019 1.74 0.32 1.42 17 2550 2.65 0.0090 1.77 0.0019 1.74 0.32 1.41 18 2700 2.64 0.0090 1.76 0.0019 1.73 0.32 1.40 19 2850 2.63 0.0090 1.75 0.0019 1.72 0.33 1.40 20 3000 2.62 0.0090 1.75 0.0019 1.71 0.33 1.39

multichannel analyzer, and (dE/dx)eff,j is the effective stopping power of the recoiled nuclei [11,19,54] originating from the jth layer: dE Yj S S r;iÀ1 r;det S (33) dx S S j eff;j i1 r;i r;0 The first term on the right-hand side of Eq. (33) is the ratio of the stopping powers at both interfaces of each sublayer, the second term represents the ratio of the stopping powers of the recoils after passing through and before reaching the stopper filter, respectively. The third term in Eq. (33) is the

stopping power of the recoils in layer j defined using the stopping power of the projectile Sp,j and the recoil Sr,j:

kS S S p;j r;j (34) j cos y cos f À y

Eqs. (28)±(34) provide the framework for determining the concentration of light elements. For samples of a known composition, a simulated ERD spectrum can be calculated using the previous approach. This spectrum can be convoluted with the resolution function, a Gaussian, to account for instrumental resolution and then compared directly with the experimental spectrum. If this comparison is unsatisfactory, a new composition is used to simulate another ERD spectrum for comparison with the experimental one. This procedure is repeated until satisfactory agreement is found as discussed later. The analysis of NRA data is in principle similar to that of ERD [11,61]. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 145

5.3. Scaling approach to convert experimental data

The scaling approach is a fast and straightforward method for analyzing the experimental ERD spectrum. In this section, a brief description of the scaling method is given. A more comprehensive version can be found elsewhere [17,19]. One advantage of this approach, relative to computer simulation, is that the absolute values of s and dE/dx are no longer required. The key parameters that must be accurately known are the functional dependencies of s and (dE/dx)eff on E0. The scaling approach is most useful when the signals originating from 1H and 2D do not overlap.

Using the thick target approximation, s and (dE/dx)eff are calculated for a series of layers and tabulated as a function of the recoil energies. The previous method for converting the recoil yield into concentration is then followed. Each data point in the recoil spectrum is divided by s(Ein,j)/s(Ein,0) and multiplied by (dE/dx)eff,j/(dE/dx)eff,0,wheres(Ein,0)and(dE/dx)eff,0 are the scattering cross- section and effective stopping power evaluated at the sample surface, respectively, and s(Ein,j)and (dE/dx)eff,k are their corresponding quantities in layer j. Note that the energy of the recoil originating from layer j corresponds to the energy of the data point to be converted. In this way, the recoil yield has been normalized to account for the changing values of s and (dE/dx)eff in the sample. The absolute values of the concentration are obtained by multiplying a correction factor, which is determined by either conservation of material or a priori knowledge of the concentration. In some cases, the placement of a calibration layer on the sample of interest proves useful. For example, a thin- film with a known concentration, i.e. dPS, is deposited over part of the sample before ERD analysis.

After accounting for s and (dE/dx)eff, the spectrum is normalized using the internal standard. In some limited cases, the recoiled yield can be directly converted into a concentration profile very easily. First, an ERD spectrum is taken from the sample to be analyzed (sample A). Then, using the same experimental conditions (incident beam energy and type of the projectiles, beam flux, scattering geometry, etc.), an additional ERD spectrum is recorded from a ``normalization'' sample (sample N), usually a thick polymer film. The concentration profile is then obtained by dividing the spectrum from sample A by the one from N. Note that the polymer used for normalization must have a similar stopping power behavior as sample A. After the yield to concentration conversion, the energy scale is converted into the depth scale using the energy-depth dependence determined using the thick target approximation.

5.4. Computer simulation

Two methods can be used to analyze experimental ERD spectra. The first one numerically deconvolves the experimental spectrum as outlined earlier. Although the most direct method, this approach is rather cumbersome and usually complex. A second way of interpreting spectra is based on computer simulations. In this approach, a composition profile is first estimated and its simulated spectrum compared with the experimental one [15,17]. An interactive process then ensues until there is satisfactory agreement between the simulated and experimental spectra. In 1994, Vizkelethy [62] catalogued many of the computer simulation programs used for ion beam analysis. However, many of these programs, mostly DOS based, are dated, unavailable or no longer used. Table 2 provides a selective list of the current computer programs used for RBS and/or ERD including RUMP, GISA, SIMNRA and IBA [37,63±66]. These programs may include fitting routines and non-Rutherford cross-sections including resonance cross-sections. As discussed in Section 3, the energy spread of the projectiles and recoils in the target, and the recoils in the stopper filter, DEtot, is included in the experimental spectrum but not the spectrum calculated using the approach in Section 5.1. An exact calculation of the total energy spread can be made [26]. An 146 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Table 2 Selected list of several readily available simulation programs for RBS and ERD analysis Program name Operating system (computer) Technique Reference RUMP ANSIC RBS, ERD [37,63] SIMNRA Win 95/98/NT RBS, ERD [65] GISA DOS RBS, ERD [64] IBA Win 95/OS-2 RBS, ERD [66]

alternative approach is to convolute the ``ideal'' spectrum with an energy distribution function that

includes the particular contributions to DEtot. In summary, the accuracy of computer simulations depends on how well the following parameters are known: (i) scattering cross-sections, (ii) stopping powers of the incident particles and recoils in the target, and (iii) stopping powers of the recoils in the stopper filter.

6. Ion beam and complementary techniques

Conventional ERD has been modified to improve upon the nominal depth resolution or sensitivity. For example, emission angle ERD (EA-ERD) benefits from a superb depth resolution [67], coincidence detection ERD (CD-ERD) has a superior sensitivity (below ppm) [68,69] or electromagnetic filter detection ERD (E and B ERD) which benefits from a depth resolution of ca. 100 AÊ and sensitivity better than 0.2 at.% [70,71]. The improvements offered by these techniques have not been widely applied to polymer systems. In Section 6.1, ion beam techniques are presented including TOF±ERD, resonant and non-resonant NRA, and heavy ion ERD (HI-ERD) (Table 3). In Section 6.2, a brief review of techniques for characterizing polymer surfaces (Table 4) and polymer interfaces (Table 5) is presented.

6.1. Related ion beam techniques

6.1.1. Time-of-flight±ERD (TOF±ERD) The principles of TOF±ERD are identical to ERD. The main difference lies in the detection system. As discussed previously, the main factor limiting the depth resolution of ERD is straggling in

Table 3 Summary of key features and specifications for RBS, ERD and NRA depth profiling techniques Technique Incident Detected Contrast Information Depth Probing Profiling beam particles due to content resolution (AÊ ) depth (mm) sensitivity (1020 cmÀ3) RBS 4He 4He Heavy atoms Marker depth profile 80±300a 1 0.01±1a ERD 4He 1H, 2H 1H, 2H 1H, 2H depth profiles 800 0.7 1 LE-ERD 4He 1H, 2H 1H, 2H 1H, 2H depth profiles 80±400a 0.1 <1 TOF±ERD 4He 1H, 2H, 4He 1H, 2H 1H, 2H depth profiles 250 1 1 NRAb 3He 4He 2H 2H depth profile 140 1>1 NRAc 3He 1H 2H 2H depth profile 300 8>1 NRAd 15N g-Rays 1H 1H depth profile 50 3 1 a Depends on (i) beam type, (ii) incident beam energy, (iii) sample type, and (iv) scattering geometry. b Based on the 2H(3He, 4He)1H non-resonant nuclear reactionÐfollowing Chaturvedi et al. [46]. c Based on the 2H(3He, 4He)1H non-resonant nuclear reactionÐfollowing Payne et al. [45]. d Based on the 1H(15N, 4He g) resonant nuclear reaction. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 147

Table 4 Polymer surface analysis techniques and their characteristics Technique Acronym Chemical Lateral Information Comment Reference sensitivity resolution type Contact angle CA ± mm Surface hydrophobicity [98,99] Optical microscopy OM ± 10 mm Surface image [104] Scanning near-field SNOM ± 1000 AÊ Surface topography [105] optical microscopy Scanning tunneling STM Possible 1AÊ Molecular imaging, a,b [106] microscopy surface topography Scanning electron SEM Quantitative 50 AÊ Surface topography, a,c [102,108] microscopy surface image Transmission electron TEM ± 30 AÊ Two-dimensional profile a,c,d [108] microscopy Atomic force microscopy AFM Possible 5AÊ Molecular imaging, [109] surface topography Static secondary ion SSIMS Elemental 1 mm Surface composition a,c [100±102] mass spectrometry X-ray reflectivity XR ± ± Surface roughness a [84,110] X-ray photoelectron XPS Chemical 10 mm Surface composition a,c [100] spectroscopy (ESCA) Infra-red attenuated IR-ATR Semi- Several mm Surface vibrational [98,99] total reflection quantitative spectrum High-resolution electron HREELS ± 1 mm Surface vibrational a,c [103] energy loss spectroscopy spectrum Auger electron spectroscopy AES Elemental 1 mm Surface composition, a,c,e [97] composition topography a Sample damage likely. b Requires conducting substrate. c Requires vacuum. d Requires special sample preparation (microtoming, staining, etc.). e Depth profile obtained in combination with sputtering. the stopper filter. Whereas straggling is greatly reduced by using low beam energies and thinner stopper filters, the probing depth is greatly reduced by this method, called LE-ERD. Rather than using a stopper filter, TOF±ERD separates the 1H and 2D recoils from the forward scattered 4He by using an electronic discriminating system. Introduced by both the Groleau and Thomas groups [72,73], TOF±ERD was first applied to polymers by Sokolov et al. to study the surface structure of polymer blends [74]. The geometry and detector system for TOF±ERD are illustrated Fig. 31. The forward scattered 4He and recoiled 1H and 2D pass through a thin carbon filter placed between the sample and detector. As the ions penetrate the carbon filter, secondary electrons are emitted from the filter. To minimize straggling, the carbon filter is very thin (500±1000 AÊ ). The secondary electrons are then amplified and generate a start signal for an electronic clock. A corresponding stop signal is then generated when an ion arrives at the detector. Because the distance between the detector and carbon filter, Dx, is known (usually 15±

90 cm) the TOF of the particle, tF, is also known. The TOF of each particle is a function of its mass with heavier particles having longer flight times than lighter ones. In this way, the 4He projectiles and 1H and 2D recoils can be discriminated without using a stopper filter. For ions recoiling from the sample surface, the TOF can be estimated from r M t Dx t (35) 2KE0 148 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Table 5 Polymer interface analysis techniques and their characteristicsa Technique Acronym Contrast Depth Information Comment Reference resolution Pendant drop technique PDT ± ± Interfacial tension [85,88] Transmission electron TEM Staining 10 AÊ Cross-sectional view b,c,d [108] microscopy Atomic force microscopy AFM Friction/modulus 5AÊ Cross-sectional view [109] Dynamic secondary DSIMS Elemental 90±130 AÊ Elemental depth profile b,c,e [86] ion mass spectrometry X-ray reflectivity XR Elemental 5AÊ Marker depth profile b [84,110] (heavy atoms) Neutron reflectivity NR Elemental 10 AÊ 1H and 2H [84] (1H, 2H) depth profiles Ellipsometry ELLIRefractive index 10 AÊ Film thickness, [89] refractive index profile X-ray photoelectron XPS Chemical 10 AÊ Elemental depth profile b,c,e [100] spectroscopy (ESCA) Infrared densitometry IR-D Elemental 10 mm Elemental depth profile [90] (1H, 2H) Small angle neutron SANS Elemental 10 AÊ Elemental depth profile f [92] scattering (1H, 2H) a See Table 3 for ion beam techniques. b Possible beam damage to specimen. c Requires vacuum. d Requires special sample preparation (microtoming, staining, etc.). e Relative concentration. f Provides optical transform of profile.

where Mt is the ion mass and K and E0 are the kinematic factor and the incident energy, respectively. Because 1H and 2D have slightly different masses and, thus, different kinematic factors, they also can be discriminated by TOF±ERD. The results are recorded as a three-dimensional spectrum, where the recoiled yield is a function of both the detected energy and the TOF. The main advantage of TOF±ERD over the conventional ERD is improved depth resolution. The reported surface depth resolution for PS is 250±300 AÊ , similar to RBS. In principle, the depth resolution of TOF±ERD is determined by the resolution of the SB detector. TOF±ERD also has the ability to distinguish 1H from 2D and to depth-profile these elements to several micrometers

Fig. 31. TOF±ERD geometry showing incident ion, sample, and detection system. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 149

below the surface. As with conventional ERD or LE-ERD, depth resolution deteriorates with probing depth. In spite of these advantages, TOF±ERD is not as widely used as ERD for several reasons. First, extremely sensitive and rather complicated electronics is required to produce and amplify the start and stop signals. Any small changes in the stability of the electronics will degrade the quality of the detected signal. Moreover, the carbon foil is extremely sensitive to sudden changes in the pressure and must be kept in a very dry environment. Also, the sensitivity of TOF±ERD for detecting 1H and 2D(40%) is worse than that of ERD because the efficiency in generating the secondary electrons decreases with decreasing atomic number [74]. Several methods to improve efficiency have been proposed. For example, Gujrathi and Bultena [75] found that covering the carbon foil with a thin layer of MgO improved the detection efficiency of detecting 1Hto90%.

6.1.2. Heavy ion ERD The depth resolution of conventional ERD can be improved by using heavier projectiles. While this method has been used extensively to study the hydrogen distribution in solid materials [76], HI- ERD has not been extensively applied to polymers because of concern for beam damage. In the first application, Green and Doyle [77] used HI-ERD to study diffusion in polymer blends. Using a 28Si beam the depth resolution was found to be 300 AÊ and the probing depth 9200 AÊ . These improvements over ERD were, however, nullified by heavy radiation damage to the polymer which was 30 times greater than using a 4He projectile. Radiation damage in polymers and routes to reduce beam damage are discussed in Section 4.4. Using 2.4 MeV 12C incident ions, Geoghegan and Abel [78] applied ERD to study surface segregation from a PS polymer network with a depth resolution of 80 AÊ at the sample surface. In addition, the depth resolution was found to remain relatively constant up to the maximum accessible depth of 1000 AÊ beneath the sample surface. In order to mitigate beam damage to the sample the dose on any one spot of the sample was limited. Based on knowledge of the damage caused by a 12C beam [79], the dose on each spot was kept below 0.1 eVAÊ À3. The sample was translated across the beam and the yield from each spot was summed to obtain sufficient statistics. While HI-ERD has been shown to work on PS systems [78,80], in comparison with other polymers, PS is particularly stable to beam damage. Other polymers would require an even lower dose per sample spot possibly making HI-ERD impracticable.

6.1.3. Non-resonant nuclear reaction analysis In contrast to ERD, which is based on a billiard ball-like collision, the incident ion in a NRA experiment penetrates into the target nucleus to excite a nuclear cascade. Figure 32 shows the most 2 3 2 common nuclear reaction for detecting D. When an incident He particle having energy E0 hits a D

Fig. 32. Non-resonant nuclear reaction between incident 3He particle and target 2D nuclei. This reaction, denoted as 2H(3He, 1H)4He, is exothermic (Q 18:352 MeV). 150 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 33. Non-resonant nuclear reaction geometry showing incident ion, sample, and detection system consisting of a magnet for deflection and solid state detector.

4 1 atom in the target material, a nuclear reaction occurs to produce He and H with energies E1 and E2, respectively. This reaction, denoted as 2H(3He, 1H)4He, is quite exothermic (Q 18:352 MeV). 4 1 Therefore, the outgoing He and H ions have energies that are much higher than E0. The scattering cross-section for this nuclear reaction, s, is much smaller than that for elastic scattering of 4He from 2D (i.e. ERD). Therefore, the incident beam energy is chosen to produce the maximum s (i.e. 4 1 E0 600 keV) [81]. In a typical set up with E0 700 keV the outgoing He and H have energies of 4 1 E1 5:84 MeV and E2 13:24 MeV. Depending on whether He or H are detected, two variations of NRA have been developed. Klein and co-workers [46] at the Weizmann Institute perform depth profiling by detecting 4He. As shown in Fig. 33, the outgoing particles travel towards the detector placed at F 308. Before reaching the detector the particles are separated by a magnetic field so that only the 4He particles reach the detector. Both the neutral 3He particles, which are not deflected, and the 1H ions, which are strongly deflected, are stopped by slits placed in front of the detector as shown in Fig. 33. The main purpose of the magnetic filter is to prevent the electronic detection system from being saturated by the signal from the elastically scattered 3He.4 The depth distribution of 2D is obtained from the energy distribution of the outgoing 4He particles. Similar to ERD, the nuclear reactions originating at larger depths beneath the sample surface correspond to 4He with lower energies. In NRA, the depth resolution is improved because no stopper foil is needed and the energy loss in the sample is larger [61]. The depth resolution at the surface of PS was found to be 140 AÊ . IntheNRAtechniquedevelopedbyPayneetal.[45],the1H products of the nuclear reaction are detected by a detector positioned at F 208. Similar to the Weizmann group approach, a depth-profile is determined by monitoring the energy of 1H emitted from the sample. In contrast to the previous approach, the nuclear reaction originating deeper in the sample produces 1Hwithhigherenergy.As before, no stopper filter is required. Because the number of elastically scattered 3He is negligible, magnetic separation of the particles is no longer necessary. The depth resolution can be further 3 improved by increasing the path-length of the incoming He. For E0 700 keV, the depth resolution at the surface improves from 1000 to 300 AÊ as the angle between the sample normal and the incident beam increases from 0 to 758. While the depth resolution is worse than in the Weizmann group approach, the set up adopted by Payne et al. benefits from much larger probing depths (up to 8 mm) [45]. Moreover, the depth resolution in the latter set up deteriorates more slowly with increasing depth.

6.1.4. Resonant nuclear reaction analysis Whereas non-resonant NRA is useful for profiling 2D, resonant NRA provides a direct method for profiling 1H. In contrast non-resonant nuclear reactions, where the cross-sections for the reaction

4 The number of the elastically scattered 3He particles is much larger than that of 4He produced by the nuclear reaction. By ``filtering-off'' the signal arising from 3He one can, thus, significantly decrease the ``dead time'' of the detector. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 151

vary smoothly with the energy of the projectile, the resonant nuclear reactions take place only within a narrow energy window. One of the most useful reactions is 1H(15N, 4He g)12C, which has a strong resonance at an incident energy of 6.40 MeV [82]. This reaction produces 4.44 MeV g-rays, which are counted by a g-ray detector. The number of g-rays is proportional to the 1H concentration at the depth of the reaction. To depth-profile 1H, the energy of the incident 15N projectiles is systematically increased from 6.40 MeV to higher energies. Measuring the 1H distribution in thin polymer films, Endisch et al. [83] measured a depth resolution of 50 AÊ at the sample surface. This value is very close to the best resolution obtained with the most sensitive depth profiling techniques such as neutron or X-ray scattering. Unfortunately, NRA based on the 1H(15N, 4He g)12C reactions suffers from several drawbacks that limit its ability to study polymers. First, the sample must be very large (several cm2) because of the large incident beam cross-section (40 mm2). Second, the sample must be placed inside a bore-hole of a bismuth germanate g-ray detector to increase the reaction yield by increasing the solid angle to almost p [83]. Third, the nuclear reaction produces an undesirable background of g-rays that must be distinguished from the g-ray signal. Although no substantial damage was reported [84], radiation damage to polymers in general is likely due to the g-rays as well as the heavy projectiles. In spite of these drawbacks, resonant NRA can be an extremely useful technique to study phenomena on the size scale of a polymer coil.

6.2. Complementary techniques

Because of the great interest in polymer surface and interface problems, polymer scientists have had a renewed interest in advancing existing techniques as well as developing new methods with improved depth resolution and sensitivity. The ion beam techniques described in this review are listed in Table 3. One approach for selecting a technique is to identify whether the problem of interest is located at the surface or interface. Tables 4 and 5 list the experimental techniques frequently used in surface and interfacial polymer science. For surface studies (Table 4), chemical information, lateral resolution, and information type are important parameters. For interface studies (Table 5), contrast, depth resolution, and information type are important [85±94]. A detailed discussion of each technique is found in the reference list (last column). Technique theory, specifications and applications to polymer science have been previously reviewed [84,93± 97]. Some polymer surface characteristics of interest include surface topography, surface chemical composition, molecular orientation, and molecular imaging. Traditional surface science techniques include contact angle measurements [98,99], X-ray photoelectron spectroscopy [100], static secondary ion mass spectrometry [100±102] infrared attenuated total reflection, and high-resolution electron energy loss spectroscopy [103]. Microscopy (cf. Table 4) also provides a versatile array of tools for studying surface properties [102,104±109]. These techniques usually provide information about the sample surface and the near-surface region, a few nanometers below the surface. The lateral resolution of the surface sensitive techniques ranges from several AÊ to several millimeters. Two or more techniques with complementary strengths and weaknesses provide the best method for a complete surface characterization. Depth-profiling techniques provide a measure of the concentration profile perpendicular to the sample surface. These techniques can be subdivided into two main groups depending on whether the concentration profiles are obtained in reciprocal or real space. In the first category are scattering techniques based on light (ellipsometry, modified optical schlieren technique (MOST)), X-rays (X- ray reflectivity) [84,110] or neutrons (neutron reflectivity, small-angle neutron diffraction) as the source of incoming radiation (particles). On the other hand, real space depth-profiling techniques 152 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

mainly use beams of accelerated ions to probe the composition. These techniques include dynamic secondary ion mass spectrometry and the ion beam techniques in this review. Sensitivity and depth resolution are key parameters for choosing a depth-profiling technique. While the depth resolution of scattering techniques is usually excellent (several AÊ ), elemental sensitivity is highest for abrupt changes in the concentration. In addition, the depth-profile is obtained from an optical transform of scattering intensity. Only in special cases can this information be directly converted into a real space profile. In practice, the data are analyzed by model fitting, which can lead to some uncertainty in interpreting experimental results if more than one model concentration profile is suitable. In most cases, independent information about the concentration in the sample is required using real space depth-profiling techniques. In spite of their poorer depth resolution, real space techniques based on the interaction of ions with the sample provide useful information about polymers near surfaces and interfaces. Because their depth resolution can be as small as a single (large) polymer molecule, ion beam techniques can be used as standalone experimental tools. In addition to their excellent sensitivity (usually <1 at.%), real space depth- profiling techniques are not limited to sharp concentration gradients. Since the mid-1980s ion beam techniques have provided polymer scientists with a powerful tool for depth-profiling polymers in thin-films. In Section 7, of this review, selected case studies are presented to demonstrate the range of polymer surface and interface problems addressed by ERD.

7. Polymer surface and interface case studies

Since it was first applied in the mid-1980s, ERD has become a standard technique in the characterization toolbox of polymer scientists. In this section, selected case studies are presented to provide the reader with insight about the range of surface and interface problems that ERD has already addressed either by itself or in conjunction with complimentary techniques. In particular, tracer and mutual diffusion of macromolecules as well as small molecule diffusion are presented in Section 7.1. Section 7.2 discusses polymers at surfaces, which involves understanding the enrichment of one polymer in a multi-component system at the polymer/air, polymer/polymer, and polymer/solid interfaces. In Section 7.3, polymer/polymer interfaces problems are addressed including the application of ERD to determine phase diagrams, understand phase separation, and investigate wetting behavior. Finally, in Section 7.4, polymer modification by ion beam irradiation is presented.

7.1. Polymer diffusion

Polymer dynamics was one of the first significant problems to be addressed by ERD. Using ERD, Green and co-workers [20,111] firmly established the range of tracer and matrix molecular weights over which the reptation mechanism [112] dominates diffusion in polystyrene (PS). Although first proposed in 1971, the first definitive studies of reptation were performed many years later using an innovative version of infrared spectroscopy [113,114]. In a sense, these infrared spectroscopy studies nucleated the application of a wide range of new techniques to study polymer diffusion, including fluorescence recovery after pattern photobleaching, forced Rayleigh scattering (FRS), neutron and X-ray small-angle neutron scattering, nuclear magnet resonance, RBS, NRA and ERD [11,115]. Due to their outstanding spatial resolution, secondary ion mass spectrometry and neutron reflectivity have been the most recent additions to the experimentalists toolbox of surface and interface techniques. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 153

7.1.1. Self and tracer diffusion In this section, we focus on how ERD is used to determine tracer and self-diffusion coefficients. Rather than provide a comprehensive review of polymer diffusion we refer the interested reader to a review article [116]. We start by discussing the ground-breaking experiments by Green et al. [20,111] which set the stage for a decade of diffusion, surface, and interface studies. A thin polystyrene (PS) layer 15 nm thick was deposited on a thicker (650 nm) layer of deuterated PS (dPS). It is important to point out that a true tracer diffusion measurement requires a low volume fraction (i.e. trace amount) of the diffusing species in the matrix, and therefore, the top film should be made as thin as possible. The volume fraction versus depth profile of polystyrene chains of molecular weight 1:1 Â 105 is shown in Fig. 26b [111]. The characteristic diffusion distance, x Dt0:5, of 300 nm is optimum for these experimental conditions because it is much greater than the depth resolution of 80 nm, but much less than the matrix film thickness. Furthermore, the measured value of the maximum volume fraction f is only 0.03 suggesting a trace amount of PS in the dPS matrix. The true maximum is greater than this because the profile in Fig. 26b is not deconvolved with the instrumental resolution, about 80 nm FWHM. This instrumental broadening is also responsible for the apparent observation of PS at negative depths. Whereas Fig. 26b utilizes a thin PS tracer film, a tracer film of dPS has the advantage of an unlimited PS matrix thickness, cost reduction, and accuracy. Mills et al. [20] used ERD to depth profile dPS in a thick PS matrix. Using a thin dPS film on a thick PS matrix allows one to make the matrix film many microns thick. Here, the accessible depth is now limited by overlap between the 2D yield from beneath the surface and the 1H yield from the surface layer. The ERD spectrum before and after annealing is shown in Fig. 34 [20]. For 3 MeV 4He2, F 308, and a 10.6 micrometer MylarTM filter, the accessible depth was about 800 nm. To determine the diffusion coefficient, DÃ, the dPS volume fraction profile is fited with the solution to

7 Fig. 34. ERD spectra from a bilayer film consisting of 12 nm of dPS (Mw 225,000) on PS (Mw 2 Â 10 ) before diffusion (triangles) and after diffusion for 3600 s at 170 8C (crosses) (taken from [20]). 154 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 35. The tracer diffusion coefficient, DÃ, of polystyrene of molecular weight M diffusing in polystyrene at 171 8Cis plotted as a function of M. DÃ measured by ERD is in excellent agreement with other ion beam techniques (RBS and NRA) and FRS (taken from [11]).

the thin film diffusion equation "# h À x h x f x0:5 erf erf (36) 4DÃt0:5 4DÃt0:5

where h is the film thickness and t the annealing time. Fig. 35 shows the tracer diffusion coefficient of PS at 171 8C measured by ERD and other techniques [11]. For the diffusion of high molecular Ã À2 weight polymers (M @ Me) into a high molecular weight matrix, D was observed to vary as M ,in agreement with the reptation prediction. These ERD studies supported earlier diffusion studies using FRS [117]. This brings up the question of technique choice. For example, relative to say FRS, the ERD equipment is more complex and costly. However, ERD has a higher spatial resolution and provides a direct spatial profile. To choose a technique to study diffusion, the slow diffusion rate of polymers is a limiting factor. For entangled polymers, DÃ typically ranges from 10À11 to 10À15 cm2/s at temperatures ca. 70 8C above the glass transition. Thus, in 1 h, the diffusion distance ranges from 2 mm to 200 AÊ , respectively and therefore, techniques that provide a high spatial resolution, 100 AÊ , are most attractive. Contrast between the diffusing species and medium is also an important consideration. Some techniques such as FRS require fluorescent labels on the diffusant. ERD simply requires that one of the polymers is deuterated, usually the diffusant. Although many deuterated polymers and monomers are available, isotopic contrast can be a deterrent when studying unusual systems. Another consideration is the sensitivity of polymers to radiation. Polymers exposed to light ions undergo cross-linking, chain scission or a combination of both. This topic is discussed in Section 7.4. Following the entangled PS diffusion studies, ERD was soon applied to study tracer and self- diffusion in other systems, and as a function of diffusing species architecture and matrix species molecular weight and architecture. In particular, ERD was used to clarify whether short matrix R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 155

Fig. 36. ERD spectra converted to volume fraction versus depth profiles corresponding to (a) a tracer dPS film and (b) a 5 tracer dPXE film diffused into a PS0.55:PXE0.45 matrix for 1:56 Â 10 s at 206 8C. The solid lines are theoretical fits using Ã À14 Ã À15 2 (a) DdPS 1:2 Â 10 and (b) DdPXE 2:2 Â 10 cm /s for dPS and dPXE, respectively (taken from [119]). chains provide ``moving'' constraints for the diffusant, and increase diffusivity [118]. ERD also played an important role in the study of star, cyclic and block copolymer diffusion [116]. Tracer diffusion in chemically dissimilar, yet miscible, polymer pairs was first studied by ERD [119,120]. The tracer diffusion of dPS and deuterated poly(xylenyl ether) (dPXE) into PS:PXE blends was measured. Fig. 36 shows the depth profiles, converted from ERD spectra, for tracer films of (a) dPS and (b) dPXE diffused into a PS:PXE matrix [119]. Note the similarity with Fig. 34 for the dPS/PS isotopic blend. The main difference between these two studies is that the conversion from Fig. 36a and b utilizes the stopping powers of 4He, 1H, and 2D in the PS:PXE blend. Because of their different composition and structure, the stopping power difference between polymers (such as PS and PS:PXE blends) can be significant. For example, the stopping powers for 2 MeV 4He in polyimide and PS are 25 eV/(1015 atoms/cm2) and 18 eV/(1015 atoms/cm2), respectively [31,32]. Thus, each matrix species (composition) requires its own set of stopping powers for conversion. If the tracer component is very dilute after annealing, the stopping power (and therefore, depth scale) in the matrix is not significantly changed by the diffusing species. As in the dPS/PS case, the tracer diffusion coefficients of dPS and dPXE, respectively in PS:PXE matrices scale as M2À, in agreement with reptation [120]. 156 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

ERD has also been used to study tracer diffusion of dPS in PS:poly(vinyl methyl ether) blends [121], and both dPS and deuterated tetramethylbisphenol-A polycarbonate (dTMPC) in PS:TMPC blends [122]. In both studies, the diffusion coefficient scaled as MÀ2. The tracer diffusion coefficient of dPMMA in PMMA: poly(styrene-ran-acrylonitrile) blends was found to vary as MÀ2.2, in fair agreement with reptation [123]. Note that in two of the above studies, the analysis of reptation in polymers blends was limited by the availability of both components in deuterated form.

7.1.2. Mutual diffusion The first quantitative studies of mutual diffusion between chemically dissimilar polymers were carried out by Jones et al. [124] using microprobe analysis and Composto et al. [125] using ERD. In the latter study, the interdiffusion coefficient was determined from the polymer volume fraction

profile between two blends of dPS:PXE having slightly different dPS composition, fdPS. Fig. 37 shows the volume fraction of dPS across the interface of a diffusion couple before and after annealing for 1800 s at 206 8C [125]. The initial fdPS of the bottom film is 0.60 while that of the top film is 0.51. In Fig. 37a, the interfacial broadening between the two films reflects the instrumental resolution of about 80 nm. The solid line corresponds to a step function convoluted with the instrumental resolution function, a Gaussian with a FWHM of 80 nm. After diffusion, the interface broadens as shown in Fig. 37b. Because the glass transition of PS and PXE are quite different, 100 versus 206 8C, respectively, the D between pure couples is a strong function of concentration. However, by using a composition difference between blends of 10%, a single mutual diffusion

Fig. 37. Volume fraction of deuterated polystyrene in a dPS:PXE thin-film diffusion couple: (a) as deposited, and (b) after diffusion for 1800 s at 206 8C. The bulk volume fractions of the top and bottom films differ by ca. 10% to minimize the composition dependence of the mutual diffusion coefficient (taken from [125]). R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 157

coefficient D should control the diffusion across the interface and, hence, we expect a concentration profile given by h À x h À x f z0:5 f À f erf erf f (37) 2 1 w w 1 where h is the top film thickness and w 2(Dt)0.5. The solid line in Fig. 37b represents the best fit of this equation to the data using D 1:1 Â 10À13 cm2/s. By varying the PS degree of polymerization, À1 NPS, D was found to scale as NPS [126]. Since PS is the faster-moving species in these blends this variation of D is strong evidence for the fast theory of mutual diffusion. The mutual diffusion coefficient is enhanced, relative to the tracer diffusion coefficient, by the negative w, which drives intermixing between the attractive PS and PXE, segments. Accelerated diffusion was also observed in the poly(vinyl chloride)/polycaprolactone system studied by Jones et al. [124]. In a related study, Green and Doyle measured the mutual diffusion coefficient of dPS/PS, an isotopic alloy having a small positive w [127]. By using high molecular weight polymers, the unfavorable segmental interaction parameter was found to inhibit diffusion. Using NRA, subsequent studies by Losch et al. [128] were carried out below the critical temperature, TC, but in the one-phase region using NRA. Bilayers having 10% difference in composition were annealed at T < TC. Critical slowing down was observed as the average blend composition approached the coexisting composition.

7.1.3. Small molecule diffusion through polymers Because of their low vapor pressure, small molecule diffusion studies in a vacuum environment pose a greater challenge than polymer diffusion studies. A majority of the small molecule studies have focused on using RBS to depth profile solvents in glassy polymers [129±132]. In such cases, the solvents contained an internal label (e.g. iodine or chlorine) for analysis. It is instructive to recall the sample preparation route because the same route can be used to prepare samples for ERD. Polymer coatings were exposed to vapor in a temperature bath containing solvent. After the diffusion time, samples were quickly removed, quenched in liquid nitrogen to ``freeze in'' the small molecule profile, and transferred to a pre-cooled sample holder in a glove bag backfilled with nitrogen. The sample holder is then quickly attached to a sample manipulator which itself is cooled, usually by liquid nitrogen. ERD has been infrequently applied to study small molecule diffusion in part because volatility will cause profile redistribution unless special sample handling is carried out as described. Furthermore, small molecule diffusion through glassy polymers is much faster than polymer diffusion in a melt. For example, the diffusion coefficient of water in polyimide is 5:6 Â 10À9 cm2/s [133]. Next, we review one innovative adaptation of ERD to study small molecule adsorption in polymers. Polyimide (PI) is a commonly used in microelectronics packaging applications. However, PI films immersed in water debond from the silicon substrate after a few days because of water adsorption. Wallace and co-workers [25,134] carried out in situ studies of deuterated water absorption by PIduring 1.3 MeV 4He irradiation. When the pressure in the target chamber was À2 raised to 1:3 Â 10 Pa by the addition of D2O vapor through a leak valve, deuterium was readily incorporated into the PI. Fig. 38 shows two 1.3 MeV ERD spectra taken after modifying 60 nm PI films with 5:25 Â 1014 and 3:15 Â 1015 ions/cm2 [134]. The peaks centered at channels 375 and 250 correspond to deuterium and hydrogen, respectively. This study found that water adsorption could be greatly enhanced >3 wt.% by simultaneously exposing PIto water vapor and ion beam irradiation. 158 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 38. ERD spectra showing the deuterium oxide uptake in polyimide at doses of 0:525 Â 1015 ions/cm2 (filled circles) and 3:15 Â 1015 ions/cm2 (open triangles) (taken from [134]).

Furthermore, within the limits of the depth resolution (25 nm), no excess of D2O at the substrate could be observed. Certain ERD techniques with better depth resolution should be able to resolve whether water preferentially segregates to oxide surfaces or is uniformly distributed within the film. External ion beam analysis in which samples are analyzed under atmospheric conditions offer one route to increase the applicability of ERD [135]. In this method, the ion beam exits the target chamber, crosses a short air gap, before encountering a film covering a water reservoir.

7.2. Polymers at surfaces

7.2.1. Surface segregation In liquid and solid mixtures, the surface composition usually differs from the bulk because the lower surface energy component tends to bloom to the surface [136]. In 1989, Jones et al. [137] made the first observation of surface enrichment in polymer blends using an ion scattering technique, ERD. The surface of a dPS:PS mixture was enriched with dPS as shown in Fig. 39. The dPS surface excess, zÃ, the hatched area in Fig. 39b, increased strongly as the dPS bulk concentration increased, which is in general agreement with mean field theory. It was surprising that the small difference between PS and dPS (i.e. the dPS surface energy is only 0.078 dyn/cm less than PS) can produce a large surface excess, 100 AÊ . This study was the first of many on the dPS:PS system. Later studies invoked higher resolution techniques, including TOF±ERD, to determine the detailed depth distribution [74,138±140]. The effect of molecular weight on the surface enrichment was also studied [141,142]. Surface segregation studies were also performed on isotopic blends of deuterated poly(ethylene propylene) and poly(ethylene propylene) [143]. In addition to isotopic blends, surface segregation in statistical copolymers has received attention. For example Steiner and co-workers [144] used nuclear reaction analysis (NRA) to Ã measure z of poly(ethylene-ran-ethylethylene) E-EEx copolymers, where x is the fraction of EE groups. The component with the higher ethyl branching fraction x was found to enrich the surface. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 159

Fig. 39. Volume fraction profile of dPS at the surface of a dPS:PS blend (a) before and (b) after annealing at 184 8C for 5 days. The solid lines are simulations assuming (a) a uniform 0.15 blend and (b) a surface excess of 110 AÊ denoted by the cross-hatched area (taken from [137]).

This enthalpically driven segregation was justified by the lower surface energy of the more branched chains. Surface enrichment in chemically dissimilar blends has also received much attention. Bruder and Brenn [145] and Gluckenbiehl et al. [146] studied mixtures of dPS and poly(styrene-co-4- bromostyrene), PBrxS, where x is the mole fraction of bromostyrene, and observed surface enrichment of dPS, the lower surface energy component. Using both neutron reflectivity and LE- Ã ERD, Genzer et al. [27] measured both the surface concentration and z in dPS:PBrxS blends and were able to perform a comprehensive test of existing models. As shown in Fig. 40, the dPS surface excess measured by NR (solid circles) was in excellent agreement with that determined by LE-ERD (open circles). In this study, the self consistent mean field (SCF) model is in better agreement with experimental results than the Schmidt and Binder (SB) model. These measurements of zÃ also provide strong evidence for the scattering length density profile extracted from NR, which relies on a trial and error fitting procedure. A main advantage of LE-ERD is that it can accurately measure zÃ independent of any model. As a compliment to ERD, NR provides excellent depth resolution (5AÊ ) and is quite sensitive to small variations of steep concentration gradients. In the same spirit, NR, DSIMS, TOF±SIMS and LE-ERD were used to investigate surface segregation in binary mixtures of poly(styrene-co-acrylonitrile)'s, SANx and dSAN. The SAN with the lower AN content segregates to the surface. In one study [147], the dSANx profile was found to deviate from the predicted exponential profile shape. At high bulk dSANx volume fractions (e.g. 0.6), the experimental profile displays a flattening relative to SCMF model predictions as shown in Fig. 41. 160 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 40. Surface excess of dPS as a function of dPS volume fraction. The solid and open circles are from NR and LE-ERD, respectively. The dotted, dashed and dash-dotted lines correspond to the Schmidt±Binder prediction, the SCF model with short range interactions, and SCF with long range interactions, respectively (taken from [27]).

7.2.2. Segregation of polymers to the polymer/polymer interface In this section, we examine polymer adsorption to the interface between two homopolymers, which are incompatible with each other. The driving force for segregation is the decrease in interfacial tension that also produces a small dispersion size and a broader interface. Buried interfaces are notoriously difficult to characterize because many surface analysis techniques, such as AES and XPS, only probe the very near surface region (<100 AÊ ). Ion scattering, in particularly ERD, allows direct profiling of interfaces even if they are ``buried'' 0.5 mm below the sample surface. The first quantitative study of diblock copolymer segregation to interfaces between immiscible homopolymers was carried out with ERD. Shull and co-workers [148] measured the interfacial

Fig. 41. Volume fraction profile of dSAN23 in SAN27 obtained from NR (solid line), calculated using the monodisperse SCF (dashed line) and polydisperse SCF (dotted line) models (taken from [147]). R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 161

Fig. 42. Volume fraction profile of dPS-b-PVP copolymer at the PS/PVP immiscible interface after 8 h at 178 8C. The copolymer concentration in the top film is 2.1% and interface copolymer excess is 100 AÊ (taken from [148]). excess of a diblock copolymer of deuterated polystyrene and poly(2-vinylpyridine) (dPS-b-PVP) at interfaces between PS and PVP homopolymers. Fig. 42 shows the copolymer distribution after 8 h at 178 8C [148]. From this profile, the equilibrium volume fraction of copolymer in the PS phase and the interface copolymer excess are 2.1% and 100 AÊ , respectively. Upon increasing the equilibrium

Fig. 43. Volume fraction profile of dPS-b-PVP copolymer at the PS/PVP immiscible interface after 8 h at 178 8C at a high bulk copolymer concentration, 5.8%. The interface excess has increased to 155 AÊ . A large surface excess is also evident (taken from [148]). 162 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

volume fraction to 5.8% a new feature is observed, namely a surface excess of copolymer as shown in Fig. 43 [148]. The authors attribute this surface excess to the formation of micelles, which segregate to the surface. We conclude by noting that the a priori identification of this surface activity by NR would be extremely difficult in this case. Green and Russell [149] used ERD to study the segregation of symmetric diblock copolymers at the interface between immiscible polystyrene and poly(methylmethacrylate) layers. ERD and SIMS were used to characterize dPS-b-PVP adsorption at the interface between PS and a random copolymer of PS and poly(4-hydroxy styrene) P(S-ran-PPHS) [150]. Above a critical copolymer concentration, the copolymer interfacial excess increases dramatically but without any corresponding surface excess of dPS-b-PVP. Although SIMS is used to locate the dPS and PVP blocks, depth profiling techniques that laterally average over millimeters or centimeters are incapable of identifying whether the dPS-PVP copolymer chains are free or assemble into micelles or microemulsion morphologies. As materials with nanostructures becoming increasingly important, the combination of depth profiling techniques, like ERD, with laterally profiling techniques, like AFM, will become more widely used. The interfacial properties of an immiscible polymer blend A/C can be controlled by adding a third component B, which is miscible with C but not with A. In 1992, Helfand [151] predicted that B will enrich the interface if A/B interactions are favored over A/C ones (i.e. wAB < wAC). In 1995, Faldi et al. [152] produced the first experimental evidence for interfacial segregation in A/BC systems. The system included polystyrene (PS or A) and two miscible random copolymers of

poly(styrene-co-4 bromostyrene) (dPBrxSorB,andPBry SorC)havingx 0:09 and y 0:13 mole fraction of bromostyrene, respectively. Fig. 44 shows the depth profile of B before (open circles) and after annealing at 170 8C for 41 days (closed circles). The interfacial excess of B, about 120 AÊ , is represented by the shaded region. The solubility of B in the A layer contributes to broadening of the interfacial profile. Fig. 45 shows the experimental profile and the model profile before (dotted line) and after (solid line) including the system resolution. The solid line underestimates the measured broadening because it does not include the solubility of B in the A layer. The profile was corrected for instrumental resolution by convolving the model profile with Gaussian functions having a FWHM that increased linearly from 400 to 650 AÊ from the sample

Fig. 44. LE-ERD volume fraction profile of dPBr0.09S (component B) at the A/BC interface as cast (open circles) and after 41 days at 170 8C (closed circles). The B interfacial excess is given by the shaded area (taken from [152]). R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 163

Fig. 45. Volume fraction profile of dPBr0.09S (B) determined by LE-ERD (closed circles). The SCF profiles with (solid line) and without (dotted line) instrumental resolution are also shown (taken from [152]).

surface to a depth of 2000 AÊ , respectively. These FWHM values were determined from standards and are specific to the ion beam conditions, namely, 2.0 MeV 4He at 158 glancing incident and exit angles using a 7.5 mmMylarTM filter. In complimentary studies, the interfacial width was measured by NR [153]. In a subsequent study, ERD was used to study the effect of molecular weight on the interfacial excess of B [154].

7.2.3. Polymer adsorption to the polymer/substrate interface Polymer adsorption from a melt plays an important role in many materials technologies such as coatings, adhesives, and microelectronics. One strategy to improve adhesion is to add a polymeric adhesion agent, i.e. a molecule that migrates to the interface, anchors to the substrate, and entangles with matrix polymers. The 1990s have witnessed numerous studies aimed at providing a fundamental understanding of the key factors that influence polymer adsorption from the melt. A recent review has been published by Composto and Oslanec [155]. This review includes contributions made by ERD to study the adsorption of end-functionalized homopolymers [156] and block copolymer adsorption [157±161].

7.3. Polymer/polymer interfaces and critical phenomena

Because of their technological and fundamental importance, multi-component, multi-phase polymer blend thin films have been the subject of many theoretical and experimental studies both in the past and in recent years. In this section, we will review experiments in which ion beam techniques were used to probe the behavior of A/B polymer blends. The first class of studies includes the investigation of the interfacial region between the A-rich and B-rich phases. In the second part, we will discuss how the presence of additional interfaces (polymer/surface and polymer/substrate) influences the overall behavior of systems undergoing phase separation. Focusing mainly on experiments using NRA, a recent review [162] examines phase coexistence and segregation in thin polymer films. 164 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

7.3.1. Microscopic phenomena at coexistence

7.3.1.1. Interfacial width. The interfacial width between two coexisting phases in phase separated polymer blends provides direct information about the thermodynamics of mixing. The polymer volume fraction profiles vary smoothly across the interfacial region separating the two coexisting phases. For a blend with an upper critical solution temperature in the infinite molecular weight limit, Helfand and Tagami [163,164] showed that the width of the interface, w, scales as: a w p ; (38) wAB

where a is the polymer segment size and wAB the Flory±Huggins interaction parameter. This approach assumes T ! TC, the critical temperature. Close to TC, Binder [165] found that w scales as: a w p (39) wAB=wCÀ1

where wC is the value of wAB at the critical point. Eq. (39) predicts that far from TC where wAB is the high (0.001±0.1), w is on the order on nanometers. On the other hand, Eq. (39) demonstrates that upon approaching TC wAB ! wC, w increases rapidly. Because of their large size, polymers are model systems for studying coexistence phenomena. Polymer behavior is also simplified because the entropy of mixing in polymer mixtures is strongly reduced by a factor of 1/N, where N is degree of polymerization, as compared to small molecule mixtures. As a result, the thermodynamic behavior of the polymer blends is typically dominated by the repulsive enthalpic interactions between segments. An additional benefit of the large N is the slowing down of polymer motion, which in turn allows for detailed dynamic studies [166]. The large size of polymer coils is also an advantage because spatial dimensions that scale with the size of the

coil (e.g. w) are greatly magnified, particularly near TC. Because of their depth resolution, ion beam techniques are well suited for studying the interfacial properties of immiscible interfaces. Rafailovich et al. [167] provided the first study of interface formation in partially immiscible polymer blends using RBS. This study also reported the first experimental measurements of the critical slowing down of the mutual diffusion as a function of temperature. Their results indicated that the interfacial width grew more slowly than the expected Fickian prediction w t1/2. The equilibrium and kinetic properties were later extensively studied at the Weizmann Institute and Freiburg. Using NRA, Steiner and co-workers [168,169] found that w increased according to

Eq. (39) for T near TC. Steiner and co-workers [170,171] also followed the kinetics of formation of the interfacial region between two partially immiscible polymers and found that w increased as w ta, where a ranges from 0.27 to 0.38 in agreement with previous experiments. Bruder and co- workers [172±174] used conventional ERD to measure w between dPS and poly(styrene-co-4-

bromostyrene) (PBrxS) where x was the mole fraction of bromostyrene. For x 0:062 and 0.119 segment/segment interactions were ca. 1- and 1.5-orders of magnitude more repulsive than those in the isotopic dPS/PS system. Nevertheless, the interfacial width behavior was in good qualitative agreement with previous experiments [168±171].

7.3.1.2. Phase diagram. Bruder and co-workers [172±174] were the first to show that interdiffusion experiments can be used to determine the coexisting compositions of partially immiscible polymers. Using NRA, Budkowski et al. [175] extended these studies to map out the temperature-composition phase diagram for high-molecular weight dPS/PS mixtures. Fig. 46 shows the dPS volume fraction in R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 165

Fig. 46. Volume fraction profile of dPS at the dPS/PS interface determined using 2H(3He, 4He)1H NRA. The various symbols indicate the volume fraction of dPS in as-cast sample (diamonds) and samples annealed at 170 8C for 6 days (open circles) and 29.7 days (closed circles). The arrows in the figure indicate the coexisting compositions of dPS in the PS-rich (f1) and dPS-rich (f2) phases (taken from [175]). the dPS rich phase (0.8) and dPS poor phase (0.2). In subsequent studies, Budkowski et al. [176] investigated the effects of film confinement on the interfacial properties of dPS/PS system. They found that for film thickness near w the composition profiles of the coexisting layers were modified. This method of determining phase coexistence between two immiscible polymers was later extended to other systems, such as polyolefin [144,177] and random copolymer [178]. As discussed in Section 4, the depth resolution of ion beam techniques deteriorates with probing depth. Therefore, in most cases, the depth resolution at a buried interface is insufficient to measure w between highly immiscible polymers (i.e. narrow interfaces). A simple sample modification step prior to ERD analysis significantly improves the depth resolution below the surface. Genzer and Composto [179] determined the interfacial width between dPS and poly(1,4-butadiene) (PB) using LE-ERD. Prior to depth profiling, the sample was ``thinned'' by partially sputtering the top dPS layer using a low-energy Ar beam. In this way, only 200 AÊ of dPS was left over the buried interface. Using LE-ERD and a grazing exit angle geometry the interfacial width was 60 Æ 35 AÊ , in a good agreement with the predicted value. This study shows that ion beam techniques, combined with sample modification, can be used to measure features on the order of a polymer coil.

7.3.2. Macroscopic phenomena at coexistence Binary polymer mixtures phase separate upon quenching into the unstable region of the phase diagram. In the bulk, the concentration fluctuations that govern the phase separation process are random. However, in thin polymer films the presence of interfaces, such as the polymer/surface or the polymer/substrate, imposes directionality on the compositional waves in the blend. In particular, close to the surface (and substrate), the resultant phases are oriented parallel to the surface. Thus, phase demixing is governed by the interplay between phase separation and wetting. While the first phenomenon is governed by the polymer/polymer interactions, the latter is controlled by the interactions between the polymer and the interface. Because of their low interfacial energy, polymer blends are model systems for studying wetting phenomena. Moreover, because the resultant morphology has a strong preference to form a layered structure parallel to the surface (and substrate), ion beam depth profiling techniques are ideal tools for studying wetting. The surface induced ordering in phase separated polymer blends has been a subject of both theoretical [180,181] and experimental [182] interest. In this section, we will briefly outline the 166 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 47. Volume fraction vs. depth profiles of dPEP in a 50/50 mixture after 172,800 s at 35 8C. The oscillatory profile is representative of SDSD (taken from [183]).

experiments carried out with ion beam techniques. Interested readers should consult a review by Krausch [182].

7.3.2.1. Surface directed spinodal decomposition. Jones et al. [183] reported the first experimental observation of ``surface directed spinodal decomposition'' (SDSD). The system was a mixture of poly(ethylene propylene) (PEP) and its deuterated analogue (dPEP). Critical mixtures of PEP/dPEP5 were quenched into the two-phase region of the phase diagram and conventional ERD was used to monitor the volume fraction profiles of both polymers. The resultant spectra revealed the oscillatory composition profile shown in Fig. 47. Namely, the dPEP-rich phase present at the surface was followed by a PEP-rich phase, which in turn was followed by another dPEP-rich phase. The authors attributed SDSD to the preferential surface adsorption of dPEP, the lower surface energy species. Limited depth resolution of conventional ERD did not allow for a detailed study of the growth rate. Krausch et al. [184] preformed the first rigorous kinetic study of spinodal decomposition at the polymer mixture/air interface. Using TOF±ERD, the researchers studied the growth of the wetting layer formed at the surface of critical mixtures of dPEP/PEP. Their results unambiguously showed that the thickness of the surface wetting layer grew as t1/3 and the composition profiles exhibited universal scaling behavior in the near surface region. Fig. 48 shows the normalized dPEP volume fraction profiles as a function of depth divided by the wetting layer thickness. The dPEP volume fraction profiles at various times fall onto a single master curve. In subsequent studies, Krausch et al. used NRA to investigate the interplay between surface fields and domain ordering during SDSD [185] and TOF±ERD to study off-critical compositions [186]. Using NRA to investigate SDSD in critical mixtures of dPS and poly(a-methyl styrene) (PaMS), Geoghegan et al. [187] reported the formation of a four-layer structure dPS-rich/PaMS-rich/dPS-rich/PaMS-rich. Geoghegan reported that the surface dPS-rich layer grew as t0.14 (or logarithmically), in contrast to prior studies. This group [188] also investigated the kinetics of SDSD in off-critical mixtures using NRA. Thin film confinement can perturb the thermodynamic and kinetic behavior of SDSD. Krausch et al. [189] carried out experiments on dPEP/PEP films with a range of thickness. Using NRA, Fig. 49 displays the dPEP volume fraction profiles for (a) thick and (b) thin samples after 5.5 h in the two-phase region. For a thickness much greater than the spinodal wavelength, the SDSD wave gradually decays into the bulk. Upon decreasing the thickness, the spinodal waves originating from both interfaces appear as shown in Fig. 49b. The profile was described by the superposition of two

5 By critical mixtures, we understand systems in which their composition coincides with the composition of the critical point. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 167

Fig. 48. Deviation of the dPEP volume fraction from its average value vs. depth normalized by the wetting layer thickness l(t) at 296 K for annealing times of: 308 min (solid circles), 594 min (stars), 1168 min (triangles), 1898 min (open squares) and 2752 min (open circles) (taken from [184]). damped cosine waves originating from both interfaces. The calculated profiles (cf. solid lines) were corrected for the instrumental resolution by convoluting with a Gaussian function. In addition, these results were in excellent agreement with cell-dynamical simulations [180,181,189] that provided complementary information by ``visualizing'' the in-plane morphology. Jandt et al. [190] extended the phase separation studies to thin dPEP/PEP films with a sample thickness that is smaller than the wavelength of the spinodal wave. TOF±ERD and AFM were simultaneously used to probe the polymer volume fraction profiles and lateral morphology in the samples, respectively. Their results showed that the surface of films 2000 AÊ thick was initially smooth but after a certain annealing time developed a regular roughness pattern because of phase separation. TOF±ERD measurements revealed that the time at which the new surface morphology appeared corresponded to the transition from four to two layers. At much longer times the two-layer films became smooth again. Using LE-ERD and AFM, Wang and Composto [191,192] identified three distinct regimes of evolution for deuterated poly(methyl methacryate) dPMMA and poly(styrene-ran-acrylonitrile) SAN blends undergoing simultaneous phase separation and wetting. Fig. 50 shows the dPMMA volume

Fig. 49. Volume fraction profile of dPEP in a 50/50 mixture determined by NRA at a film thickness d of: (a) d > 1000 nm, and (b) d 282 nm. The solid lines represent a model profile convoluted with a Gaussian of increasing FWHM. The thickness in (b) is denoted by a vertical line (taken from [189]). 168 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 50. ERD volume fraction profiles of dPMMA in a 495 nm dPMMA:SAN film having an initial dPMMA volume fraction of 0.47 after (a) no anneal, (b) 2 h, (c) 8 h, (d) 48 h, (e) 72 h, and (f) 136 h (taken from [191]).

fraction profiles during the early (a±b), intermediate (c±d) and late (e±f) stages of evolution. The trilayer structure formed during the early stage eventually decays into a pseudo-uniform profile and then finally a thick wetting layer appears. By selectively etching the dPMMA, AFM was used to show that the constant composition during the intermediate stage actually corresponds to an average profile from a two-phase mixture (i.e. dPMMA-rich columns in a SAN-rich matrix). This example shows the ability of ERD to provide useful depth profiling information even in phase separated systems. Whereas previous SDSD studies focused on UCST systems, Kim et al. [193] observed quantitatively similar behavior in mixtures of dPS and tetramethylbisphenol-A polycarbonate, a LCST system. Samples of various thicknesses were depth-profiled using both conventional ERD and TOF±ERD. The polymer volume fraction profiles were similar to those observed in dPEP/PEP mixtures. These results, thus, demonstrated that SDSD is a general phenomenon regardless of system thermodynamics. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 169

7.3.2.2. Wetting and interface induced self-assembly. A binary polymer mixture in contact with the surface exhibits a preferential attraction of the lower surface energy component at the surface. For mixtures in the one-phase region of the phase diagram this phenomenon is called surface segregation (enrichment). In a two-phase mixture, the phase with a higher content of the surface preferred component enriches the surface of the system forming either a microscopically thin or macroscopically thick layer. The former situation is the so-called partial wetting cases whereas the latter describes the complete wetting state. Upon changing external parameters of the system (e.g. temperature, chemical potential, surface/polymer interactions), a transition from partial to complete wetting (or vice versa) can occur. While the wetting transitions have been investigated quite extensively in small molecular systems [194], studies using polymer systems have been limited. Steiner et al. [195] reported the first experimental study of wetting from binary polymer blends. Using two random copolymers of polyethylene (PE) and poly(ethyl ethylene) (PEE), bilayer samples were prepared where the lower surface energy component (deuterated) was deposited on the substrate and covered with a film of the high surface energy component. NRA was used to characterize the thickness of the wetting layer growth as shown in Fig. 51. Note the growth of the surface layer as well as the constant concentration in the depletion zone. In contrast to SDSD studies, the thickness of the surface layer increased logarithmically with time. Using NRA and optical microscopy, Steiner et al. [196] later demonstrated that the copolymer layers eventually invert if the original bilayer is not too thick. This group [197] also investigated the formation of the wetting layer from dPS/PS mixtures and observed the growth of a dPS-rich wetting layer. Geoghegan and Krausch have prepared the most recent review about wetting at polymer surfaces and interfaces [198]. As mentioned previously, the wetting behavior of binary polymer mixtures depends on several parameters, including temperature and polymer/substrate interactions. Although temperature is the easiest parameter to vary, the polymer/substrate interactions can be tuned by a judicious choice of the substrate onto which the polymers are cast. Bruder and Brenn [199] published the first experimental report of polymer/substrate interactions on wetting from phase-separated mixtures. TOF±ERD and optical microscopy were simultaneously used to determine the polymer volume fraction profiles and morphology of critical mixtures of dPS and PBr0.119S spin-coated on two different substrates, silicon wafers with either its native oxide (SiOx) or a chromium (Cr) layer. In both cases, the dPS-rich phase was found to preferentially enrich the surface. In the case of SiOx both the dPS-rich and PBr0.119S- rich phases were found to be in contact with the substrate. Although TOF±FRES only detects the average composition of a multiphase film, AFM was able to provide the necessary lateral information about the phase structure. On the other hand, Cr substrates were covered entirely by the

PBr0.119S-rich phase and the system formed a bilayer structure. The kinetics of phase-separation from dPS/PBr0.097S mixtures on SiOx surfaces was later studied by TOF±ERD and scanning near- field optical microscopy or SNOM [200]. By systematically varying the polymer/substrate interaction, both the wetting and ``drying''6 of the substrate by one of the phases can be explored. Genzer and co-workers [201,202] used ERD to monitor the polymer volume fraction profiles in critical mixtures of dPEP and PEP spin-coated onto Si wafers covered with Au onto which a self-assembled monolayer (SAM) mixture of

HS(CH2)17CH3 and HS(CH2)15COOH was adsorbed. By varying the mole fraction of the COOH terminated component in the SAM layer from 0 to 1, the substrate surface energy was varied from 20 to 81 mJ/m2, respectively. Whereas the surface was always enriched by dPEP-rich phase, the substrate could be wet by the dPEP-rich phase or the PEP as x is varied from 0 to 1, resulting in the

6 While wetting describes a substrate covered by a macroscopically thick layer of A-rich phase, ``drying'' denotes an A- rich phase excluded from the substrate, which is wet by the B-rich phase. 170 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 51. Composition-depth profile of dPE0.12-co-PEE0.88 copolymer in the bilayer of dPE0.12-co-PEE0.88/PE0.22-co- PEE0.78 after annealing 110 8C for (A) 0, (B) 30 min, (C) 8.0 h, and (D) 3 days. Depths of 0 and 650 nm correspond to the air and silicon surfaces, respectively. The surface wetting layer grows at the expense of material adjacent to the silicon (taken from [195]).

formation of three or two layer structures, respectively. The precursor to this transition was also investigated with ERD [203]. Controlling the wetting properties of polymer mixtures by adjusting the polymer/substrate interactions is a novel route to tailor film morphology. For example, one can extend studies of phase separation and wetting on laterally homogeneous substrates to substrates that are chemically patterned. Krausch et al. [204] investigated spinodal decomposition in polymer mixtures on a

patterned substrate. The system was a mixture of dPS and PBr0.5S spun-cast on substrates consisting of stripes of Cr deposited onto Si substrate that was (i) covered with native oxide, and (ii) hydrogen terminated. TOF±ERD demonstrated that the dPS-rich phase was always present at the surface. In R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 171

addition, TOF±ERD spectra showed that both the dPS-rich and PBr0.5S-rich phases had the same affinity towards SiOx and Cr substrates, but only the PBr0.5S-rich phase wetted the hydrogen- terminated substrate. Optical microscopy revealed that the strong differences in the polymer behavior at the substrates led to lateral ordering in the phase separated mixtures. In the case of Cr strips on the SiOx substrate, a typical in-plane isotropic pattern of spinodal decomposition was observed. In contrast, the substrate consisting of Cr on a hydrogen terminated substrate drove the phase separation to occur in stripe-like domain structures. This study nicely demonstrated that complete information about the system behavior can be achieved by simultaneously applying a high- resolution ion beam depth profiling technique, such as TOF±ERD, and a technique that provides information about the sample morphology, such as optical microscopy. Finally, we conclude this section by briefly discussing the self-assembly in thin films of diblock copolymers. Due to different interactions of the two blocks with the surface and substrate, thin copolymer films exhibit ordering that propagates from both the surface and substrate into the bulk. Depending of the thickness of the sample and the amplitude of the oscillations, the two waves may be either damped or interfere. Russell and co-workers carried out a series of experiments investigating the self-assembly in thin block copolymer films. These and other studies were summarized in a review by Krausch [182]. Because of their small spatial features, block copolymer ordering requires techniques with the best possible depth resolution. Because of their excellent depth resolution (10 AÊ ) NR and XR are suitable tools for investigating the self-assembly in block copolymers. Recently, Stamm et al. [205] showed that resonant NRA based on the 1H(15N ag)12C nuclear reaction can be used to depth-profile block copolymer films. As discussed in Section 6.1, this type of NRA benefits from excellent depth resolution (50 AÊ ) and, in contrast to NR or XR, provides a direct volume fraction profile. The system investigated was a diblock copolymer of poly(d8-styrene-b-4-methylstyrene) (dPS-b-PMS). Because the styrene block was labeled with deuterium the signal coming from PMS was detected with the NRA. In thick films, the PMS block is always present at the surface and alternating lamellae of dPS and PMS decay slowly into the bulk [205]. In a subsequent study, Giebler and co-workers [206] extended the study to very thin dPS-b- PMS films and found interesting ordering phenomena when the film thickness becomes smaller than the periodicity of the lamellae.

7.4. Ion beam modification of polymer films

The interaction of ions with polymers underlies applications ranging from semiconductor fabrication to space technology where polymer foils protect spacecraft components from solar wind. Whereas polymer properties are usually dictated by their molecular characteristics such as chain stiffness and length, ion irradiation provides an alternative route to modify their optical, electrical, and mechanical properties [207±209]. Calcagno et al. [208] have studied the effect of ion irradiation on the microstructure of polystyrene and several other polymers. At low fluence (1014 ions/cm2), 300 keV protons mainly produce inter-chain crosslinks in PS, suggesting that transport [210] and mechanical properties are modified. After implanting ions into polymers, Lee et al. [207] observed substantial improvements in the hardness and wear resistance demonstrating that the interaction of ions with polymers can be beneficial. An incident ion beam traversing a polymer undergoes two mechanisms of energy loss. In nuclear stopping, the ion will colloid with a target atom through a screened Coulomb collision. Nuclear stopping is dominant at low (keV) energies and, therefore, only of minor importance in materials characterization of the outer micron using MeV light ions. The electronic stopping power is determined by the incident ion interacting with the electrons in the polymer. At high energy 172 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

transfer, electrons can be stripped from the molecule resulting in a free radical. Ion beam modification then leads to oxidation in the case of simple hydrocarbons (e.g. polyvinylchloride), chain scission (e.g. PMMA, PTFE), and cross-linking (e.g. PS, polyimide). Typically, chain scission and cross-linking both occur to some degree in polymers although one mechanism typically dominates. Irradiation produces two readily visible changes in polymers. Typically, the surface of hydrophobic polymers becomes hydrophilic. This can be easily demonstrated by gently blowing moisture across the sample and observing the wetting of droplets in the modified region. This modified region is usually easily identified because most polymers turn brown or black after irradiation. The mechanism responsible for this coloration was studied by optical adsorption at different depths from the surface [211]. The formation of graphite was proposed as a possible reason for the darkening. Similarly, MeV 4He ions were found to induce carbonization in a partially cured phenolic resin [209]. As previously mentioned, ion beams can actually improve polymer properties. As one example 4He and 16O incident particles were used to modify the transport and mechanical properties of PS coatings [212]. Over a 6 mm Â 6 mm area, PS thin films (1.4 mm) were irradiated by either 400 keV 16O or 400 keV 4He ions at a beam current of 2 or 8 nA, respectively. The fluence was varied from 1:7 Â 1013 to 34:0 Â 1013 ions/cm2. Using SRIM [30], the stopping powers for 4He and 16OinPS were found to be 27 and 589 keV/mm, respectively. Although the 4He stopping power was mainly electronic, the nuclear contribution to the 16O stopping power was significant, about 5%. The depth range of the 4He and 16O ions in PS was 2.18 and 0.904 mm, respectively. After modification, a thin dPS film (23 nm) was deposited onto the PS matrix. The diffusion couples were annealed in a vacuum oven at 170 8C and analyzed by ERD. Fig. 52 shows LE-ERD spectra for dPS/PS diffusion couples annealed for 7800 s [212]. The 1H yield in the 16O modified (34:0 Â 1013 ions/cm2) PS is much lower than in the standard PS. Moreover, for the oxygen modified matrix the 2D yield has a Gaussian shape with a 30 keV FWHM (i.e. instrumental resolution) suggesting that an insignificant amount of dPS has diffused into the modified PS. Fig. 52 also shows that dPS diffuses readily into the unmodified PS matrix. Using Fick's second law [213], a dPS diffusion coefficient of 2:6 Â 10À15 cm2/s was determined. After modification and before placing the dPS on top, the PS surface topography was characterized using AFM. Post-indentation surface scans were taken to determine if morphological

Fig. 52. LE-ERD spectra of dPS/PS diffusion couples with unmodified PS (solid line) and 16O modified PS (broken line). The 16O fluence into the modified PS is 3:4 Â 1014 ions/cm2. Diffusion into the modified PS is arrested (taken from [212]). R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 173

Fig. 53. Atomic force microscopy image of unmodified PS after a force displacement indentation. The PS mound was created upon withdrawing the AFM tip from the film (taken from [214]).

changes occurred during the force displacement measurements. Indentation of the unmodified film produced a PS mound having a height of 316 nm and a half-height diameter of 1 mm (Fig. 53) [214]. These mounds are produced at room temperature, far below the glass transition temperature. Post- indentation surface scans of 16O modified PS showed no evidence of tip indentation suggesting that the modified PS is hardened either by crosslinking or the formation of a carbon rich material. Lee and co-workers studied the depth dependent hardness of PS after irradiation with 2 MeV 4He ions [215] and found that the hardness variation followed the stopping power for ionization. Namely, hardness increased as a function of depth and displayed a maximum at 6.5 mm below the surface. Crosslinking due to ionization was used to justify this result.

8. Future trends

In 1976, the first elastic recoil experiment was performed using a heavy, high energy incident ion, namely, 35.0 MeV Cl, to depth profile lithium in multilayer targets [18]. In 1979, Doyle and 4 Peercy demonstrated that 2.4 MeV He ions incident at a1 of 158 was an excellent choice for depth profiling hydrogen in silicon nitride layers [19]. It was this version of ERD that was first applied to polymer surfaces and interfaces in 1984 by Mills et al. [20]. As reviewed in Section 7, since this time, ERD has played a central role in the study of polymer and small molecule diffusion, surface segregation, interfacial segregation, surface directed spinodal decomposition, wetting and phase separation in thin films. Future developments in ERD applied to polymer surfaces and interfaces will be driven by the desire for better depth resolution, simultaneous depth resolution and accessible depth, and most importantly quantitative depth profiling with excellent lateral resolution. To improve depth resolution, the challenge has been to selectively detect the light recoiling target nuclei from the intense forward scattered probe particles without loss of resolution. Conventional ERD uses a filter foil to exclude these forward scattered particles. However, energy straggling in the foil greatly limits 174 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Fig. 54. TOF±ERD spectrum of Si/SiO2/Si multilayer with nitrogen segregation to the SiO2 interfaces (taken from [217]).

the depth resolution. Low-energy ERD uses a much thinner stopper foil to optimize depth resolution. Wang [42] has achieved a surface depth resolution of 8 nm FWHM using a 500 keV 4He and a 1.45 mm PS filter foil. Whereas LE-ERD provides outstanding surface resolution, this technique is not appropriate to probe profiles deep below the surface (i.e. 0.5 mm). Good depth resolution and excellent accessible depth can be achieved by replacing the filter foil with other means of particle discrimination. Although it has great potential, TOF±ERD has received relatively limited attention by the polymer community [74]. Relative to ERD and LE-ERD, the TOF±ERD technique is more costly (up to US$ 20k) and complex to interpret. For example, in the TOF technique each recoiled species has a different probability of detection whereas conventional silicon detectors are nearly 100% efficient for each species. TOF±ERD has been reported to have a depth resolution of 30 nm at the polymer surface [216]. One exciting variation of TOF±ERD, which has not been applied to polymers, is called mass and energy dispersive recoil spectrometry [217]. Using a high energy, HI

beam, Whitlow [217] analyzed a Si/SiO2/Si multilayer which had nitrogen segregation at both 14 16 28 SiO2 interfaces. Fig. 54 shows a spectrum in which the N, Oand Si yields are clearly separated according to mass and energy (i.e. depth). Thus, this technique shows excellent promise for polymer interface studies. However, because the present version relies on heavy incident ions (e.g. Br), polymer scientists will need to modify experimental conditions to minimize sample damage. Green and Doyle used silicon ERD to measure the 1H and 2D profiles in polymers [218]. Unfortunately, the incident silicon in these studies resulted in extensive damage and H(D) loss. Geoghegan and Abel [78] demonstrated carbon ERD results in minimum damage by accumulating spectra at a low dose over fresh regions of the sample. A comprehensive analysis of HI-ERD has been previously published [8]. R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180 175

Many polymer surface and interface problems now require both spatial and lateral resolution. Microbeam ERD analysis has been performed by Tirira et al. using 3.0 MeV 4He and a transmission geometry in which the recoiled nuclei pass through the back of the sample [219]. In this study, the hydrogen concentration in a film was mapped with a lateral resolution of 10 mm and a depth resolution of 30±40 nm. Another outstanding feature was the tremendous accessible depth of 6 mm. In the past, polymer scientists have stayed away from microbeams because of the obvious damage due to squeezing a nanoampere beam into an area of 100 mm2. However, the same argument was also made when conventional ERD was first applied to polymers. This section ends with a brief discussion of ion beams for materials modification. As mentioned earlier, the interaction of ions with matter leads to both desired (Section 7.4) and undesired (Section 4.4) changes in the properties of thin polymer films. In the future, new efforts should be made to take advantage of the controlled manor of energy loss of ions in matter. In particular, as opposed to gamma and electron beams, ion beams can be tuned via energy and incident mass to modify only the very near surface region while leaving the underlying film unmodified. Although some empirical studies have been made, designed barrier films with outstanding wear, hardness and corrosion resistance should evolve. Another possible area for ion beams to contribute is in the area of electroactive polymers for thin film transistors. Here, ion beams should play a role in the characterization of metal/polymer, polymer/dielectric; and polymer/substrate interfaces, and possibly the doping of plastic transistors. In general, ion beam analysis of polymers for information and communication technologies should increase in the next few years.

9. Conclusion

In this review, we have presented the fundamental parameters underlying ERD, namely the kinematic factor, cross-section, and stopping-power. The basic principles of ERD and related ion beam techniques are also reviewed. In choosing an experimental technique for a particular problem, depth resolution and the means of contrast are of great importance. A brief discussion of instrumentation is given along with a review of data analysis strategies. Since no single technique is suitable for every surface and interface problem, a discussion of complimentary depth profiling techniques is provided as well as their strengths and weaknesses. The aforementioned topics are aimed to bring a polymer scientists up to speed in the area of ion beam analysis, particularly ERD. The aim of the case study section is to educate both the polymer and ion beam communities about the contributions made by ERD to address outstanding problems in the areas of polymer diffusion, polymer surfaces and interfaces, and polymer modification. Because an exhaustive review is impossible, only selected studies involving ERD are included. NRA has also made important contributions and apologies are made to proponents of this technique. Looking towards the future demands addressing new problems in polymer surfaces and interfaces. In the future, depth profiling over a small lateral area will be of increasing importance for example to study electroactive polymer devices, arrays on a chip, etc. Because of radiation damage, new developments in microbeam analysis are needed before this technique can be applied to polymers with the same regularity as hard materials. Improvements in depth resolution are also always in demand. It is not clear whether HI- ERD will make significant inroads because of sample damage. However, other ERD techniques, such as those based on coincidence methods and E and B filters, have been making important contributions to characterizing hard materials, but have yet been applied to address polymer surface and interface problems. These techniques are readily available to the polymer community and should be evaluated in the near future. 176 R.J. Composto et al. / Materials Science and Engineering R 38 (2002) 107±180

Acknowledgements

We dedicate this review to the early pioneers who introduced ERD to the polymer community, namely, J.W. Mayer, C.J. Palmstrùm, P.J. Mills, P.F. Green, and E.J. Kramer. In particular, we acknowledge the leadership of E.J. Kramer who nucleated the use of ERD among the polymer community and encouraged future innovations including low-energy ERD. There are many people who provided sage advice or innovative ideas to the ion scattering facility at the University of Pennsylvania. J.B. Rothman provided invaluable suggestions that lead to the development of low- energy ERD and other unique capabilities that we now take for granted. Many others provided their expertise including D. Jacobson, J.E.E. Baglin, A. Faldi, W.E. Wallace, R. Oslanec, H. Wang, M. Geoghegan and D. Yates. The NSF MRSEC program (DMR00-79909) at the University of Pennsylvania has provided longstanding support for the facility under the former and current directors, E.W. Plummer and M.L. Klein. Russell J. Composto acknowledges financial support for ion beam experiments from NSF DMR-9974366 and ACS-PRF-34081. Russel M. Walters acknowledges support from the NSF MRSEC and Aston Fellowship Program. Jan Genzer is a Camille Dreyfus Teacher-Scholar.

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