Surface Analysis and Material Characterization Consulting
Thomas F. Fister, Ph.D.
Rutherford Backscattering Spectroscopy (RBS)
In a Nutshell
Take Home Point:
Film composition and thickness without sputtering
What It Provides:
Provides atomic composition, very accurate concentration and thicknesses (or density if thickness is known) of thin films without sputtering (i.e. o sputter artifacts). Also provides H concentration of same films (via HFS). Channeling experiments can examine degree of crystal damage or the amount of substitutional or interstitial species within a lattice.
Brief Description:
Ion In/Ion Out
In RBS, samples are hit with a beam of high energy ions, typically He2+ (alpha particles). While the majority of the ions are embedded into the sample, some elastically scatter off of the atomic nuclei within the sample. By measuring the energy and knowing the angle from which the ions scatter, one can determine the elements present and their location (i.e. depth) within the sample. From this information, depth profiles are non-destructively constructed, avoiding sputter-induced artifacts present in typical sputter-based profiling techniques. While He2+ won't scatter off of the lighter H atoms, these heavier ions will cause H atoms to be scattered from the sample allowing their measurement making it one of the few techniques capable of reporting H concentrations. The measurement of backscattered ions from crystalline materials can be used to provide details on crystalline damage that may be present. This is possible because damaged crystals have atoms outside of the normal crystalline lattice and such atoms result in stronger signals relative to undamaged crystals whereby atoms at greater depths are 'shielded' from the top crystalline layer.
What is Detected:
B-U (RBS)
H (HFS)
Detection Limits:
~0.001-10 Atomic % (RBS, Z Dependent)
0.1 Atomic % (HFS)
Information Depth:
~2um
Spot Size:
~1-2mm
Applications:
-
Determine thin film composition and thickness
-
Determine thin film density
-
Determine extent of crystal damage nondestructively
-
Determine H concentrations in polymeric and other films
Manufacturers:
Greater Detail
History
Ernest Rutherford is considered the father of nuclear physics. He supervised Hans Geiger and Ernest Marsden in a set of experiments from 1909 to 1914 in which alpha particles were shot at a Au foil. They expected the particles to pass straight through the foil based on the Thomson or ‘plum pudding’ model of atoms popular at the time which said atoms consisted of uniform spheres of positively charged matter in which electrons were embedded. However, the team found that some of the alpha particles were instead scattered. Rutherford determined that a mass was the cause of the scattering and proposed that atoms consisted of a compact core of positive ions, later called the nucleus. This led to the Rutherford model of the atom and later the Bohr model.
Overview and Theory
In the analytical techniqe RBS, a beam of high energy ions is directed at a sample. Some of these ions scatter off of the sample. By measuring the energy and knowing the angle from which the ions scatter, one can determine the elements present and their location (i.e. depth) within the sample. This information allows depth profiles to be obtained non-destructively, avoiding sputter-induced artifacts present in typical sputter-based profiling techniques.
The ion beam typically consists of He2+ ions (i.e. alpha particle) or less commonly H+ ions (i.e. a proton) with energies typically in the range of 0.5-4MeV. These ions can collide with nuclei (the core of the atoms containing the protons and neutrons) and scatter off of them. The vast majority of the ions impinging on the sample are embedded within because the space in between nuclei (~0.1nm) is so much larger than actual nuclei diameters (~0.00001nm). Thus, it is simply more likely that the ions will encounter void space than strike a nucleus. However, a small percentage of ions will collide with nuclei of the sample. This collision can be modeled as an elastic collision (total kinetic energy of the two species involved before and after collision are identical) in classical physics. Some of the momentum of the ion will be transferred to the target nucleus reducing the energy of the impinging ion that is then scattered. The amount of momentum transferred is dependent on the masses of the ion and the target atom. Thus, measuring the energy of the backscattered ion allows the identification of the target atom. Measurement of the energy after collision can be determined by:
E1=kE0
where k is the ‘kinematic factor’ that is equal to:
where
-
E1: Energy of recoiling alpha particle
-
E0: Beam Energy
-
m1: Mass of incident particle
-
m2: Mass of impacted atom
-
θ: Scatter Angle
As the mass of the target atom increases, less momentum is transferred from the ion and the energy of the ion becomes closer to the initial ion energy. Thus, it is more difficult to distinguish between heavier elements than lighter elements (i.e. the technique has better mass resolution for lighter elements).
Lighter atoms have smaller nuclei than larger atoms. Thus, the probability of an ion striking their nuclei will be less than that of striking heavier atoms. The likelihood of an ion striking a particular type of atom can be calculated through differential (aka Rutherford) cross-sections which take into account the atomic numbers and masses of the ion and target atom, the energy of the ion and the backscatter angle.
where
-
E0: Beam Energy
-
Z1: Atomic number of incident particle
-
Z2: Atomic number of impacted atom
-
e: Electron Charge
-
θ: Scatter Angle
The cross-section is roughly proportional to the square of the atomic number of the target atom which makes RBS more than 100 times more sensitive for heavier (e.g. Pb, Bi) than light elements (e.g. C, B). These cross-sections are well known allowing RBS to be quantitative without the use of standards.
The elastic collision of the ion striking the nuclei isn’t the only way that the incident ions can lose energy. Glancing collisions with nuclei and interaction with sample electrons also result in energy loss. These are inelastic collisions (i.e. kinetic energy is NOT conserved). Ions that don’t strike a nucleus at the surface but instead travel a certain distance within the sample before striking a nucleus will have gradually lost energy along the way (ELoss Entry). Thus, backscattering off of interior nuclei occurs with a lower incident energy than at the surface. The ion loses additional energy on the way out of the sample (ELoss Exit). The overall energy measured (EMeasured) will be less than if the backscattering event had occurred at the surface.
EMeasured = E0 - ELoss Entry - EBackscatter - ELoss Exit
where
-
EMeasured: Actual Energy Measured
-
E0: Beam Energy
-
ELoss Entry: Energy loss due to inelastic collisions prior to Backscatter event
-
EBackscatter: Energy Loss due to elastic Backscatter event
-
ELoss Exit: Energy loss due to inelastic collisions after Backscatter event
From the equation above, EBackscatter determines the identity of the atom involved in the scattering event while ELoss Entry and ELoss Exit are used to determine the depth of the atom. As such, elements appearing within a film of a sample results in a broad signal with the width corresponding to the film thickness.
Generally, the information depth is ~2um for incident He2+ ions and ~20um for incident H+, but is ultimately dependent on the nature of the sample matrix. The ability of material to cause ions to lose energy as they travel within is called the Stopping Power and is typically proportional to the square of the atomic number divided by the energy. Thus, denser material will have a larger stopping power resulting in greater energy loss per distant traveled relative to less dense material. So to calculate actual thicknesses of films, the density must be known. For films that are pure metals (e.g. Cr, Si) elemental densities are assumed and accurate thicknesses can be calculated. But for multi-element films (e.g. TiN) in which the density isn't known, then the film density is estimated by summing the density of each element normalized to its concentration. This type of estimate is usually good to within 25% of the actual value but in some cases it can be considerably worse. Conversely, if the thickness of the film is accurately known (e.g. via an SEM cross-section) then an accurate density can be calculated. These calculations are possible because the RBS fundamental unit of concentration is in atoms/cm2 and the relationship between thickness, density and concentration is as follows:
TRBS x DRBS = atoms/cm2 = TActual x DActual
where
-
atoms/cm2: RBS Reported Concentrations
-
TRBS: RBS Reported Thickness which is calculated based on an estimated density
-
DRBS: RBS Input Density which is estimated as per above
-
TActual: Actual Thickness measured by microscopy (or calculated if accurate density known)
-
DActual: Actual Density calculated via equation (or input if already known)
RBS can also be used to study the structure of single crystal samples by a process called channeling. Here, the ion beam is aligned with the major symmetry of axis of the crystal. Only the atoms at the surface will result in backscattering of the ions. The atoms within the interior of the crystal lattice will be ‘shielded’ by the surface atoms. However, if a crystal has atoms that are displaced from their crystalline lattice (i.e. damage) then these can cause backscattering and will result in a signal. The extent of crystalline damage can be calculated by comparing the signal from a sample with damage to that with none (i.e. the one with more damage will have greater signal). Additionally, the energy at which the increased backscattering signal occurs determines the depth of this damage.
Other Analysis Modes
In addition to the RBS process described above, a number of additional events can occur when samples are exposed to high energy ion beams. Most RBS instruments have additional detectors to take advantage of these events. These additional analysis modes provide complementary information and can often overcome many of the shortcomings of RBS (e.g. inability to detect H, poor sensitivity of low Z elements and poor mass resolution for high Z elements).
Hydrogen Forward Scattering (HFS) or Elastic Recoil Detection (ERD)
H and He (when the ion beam is He2+) can’t be analyzed by RBS because heavy ions can’t backscatter off of lighter ones. However, heavier ions can cause lighter nuclei to recoil from the sample (i.e. the H nuclei are knocked from the sample) allowing H to be measured (with a different detector) when using He2+ as the ion source. Both the amount and depth distribution of H can be determined.
PIXE
As previously mentioned, while RBS has good sensitivity for heavy elements, its mass resolution decreases with increasing Z making it difficult to distinguish between heavier elements with similar atomic numbers. Most RBS instruments can also perform PIXE (Particle Induced X-Ray Emission) to account for this deficiency. When an ion interacts with the sample some of the atoms can become ionized. The emission of characteristic X-rays occur when electrons from outer shells drop down to fill inner shell vacancies produced during the ionization process. PIXE involves measuring these X-rays allowing the identify of the heavier elements to be conclusively determined.
NRA
The poor sensitivity of low Z elements (e.g. B, Li, C) is compensated in some systems by using NRA (Nuclear Reaction Analysis). This technique is based on the fact that some interactions between a high energy ion and the target nuclei result in a nuclear reaction that releases products (e.g. gamma rays). Measuring the energy of these products provides information on the specific type of nucleus from which the reaction occurred as well as the depth of the reaction event. NRA sensitivity for these light elements is much better than that obtained by RBS.
Data
RBS spectra plot signal intensity versus backscatter energy (sometimes listed as 'channel' in the spectra). The elements present within a sample are determined from the peak positions in the energy spectrum with signals from higher mass nuclei appearing further to the right (i.e. higher energy) of the spectra. Depths at which an element appears are determined from the shift in the signal from where it would appear if present at the surface. The thickness of the layer in which an element appears (e.g. a thin film) is determined from the width of the signal. And finally, the relative concentrations are determined from the peak heights. Putting this information together allows film composition to be calculated and a depth profile constructed.
Once RBS data is acquired it must be modeled (i.e. fitted) via a data simulation program (e.g. SIMNRA, RUMP). Because of the convoluted mass and depth scales, the analysis of unknowns is not a strength of RBS. Instead, approximate layer thickness and composition are fed into the models as fitting parameters. Users input and manipulate the data entered to match the curves as closely as possible. However, since backscatter cross-sections are well known, the simulations produce quantitative results without the use of standards. Because of this RBS is often used to measure samples used to calibrate other techniques.
Instrumentation
An RBS instrument consists of an ion source, an accelerator and an analytical chamber that houses the Sample Holder and a variety of Detectors. There are two general types of RBS instruments, Single Stage and Two Stage (i.e. Tandem) accelerators. In the former, the ion source is located within the acceleration tube and is held at a high positive potential (it is the terminal) while the opposite end of the tube (the exit) is held at ground. This system utilizes positive ions from the ion source. While simple and capable of producing relatively high beam currents (e.g. 1mA), these instruments are more difficult to maintain (since the ion source is located within the large accelerator) and can be difficult to achieve beam energies larger than 1MeV.
In the Tandem accelerator the ion source is located outside of the accelerator and utilizes negative ions from the ion source. In this design negative ions enter the accelerator and are accelerated towards the terminal at the center which contains a high positive charge. At the terminal they are converted from He- to He2+ and are repelled from the central terminal towards the end of the accelerator. This design typically results in lower beam currents (e.g. 100nA) than the Single Stage design but can achieve higher accelerations (i.e. higher ion voltages) with lower applied voltages.
The most common ion sources for RBS are the Duoplasmatron and the RF Plasma Source. In the Duoplasmatron, He (or H2) gas is fed into the device. A combination of electrons emitted from a heated cathode and an arc between a cathode and anode form a plasma (an ionized gas consisting of positive ions and free electrons in proportions resulting in roughly no overall electric charge). The resulting He+, He2+ (or H+) ions are extracted out of the device. In the RF Plasma source He (or H2) gas enters a region of a tube exposed to 100MHz Radio Frequency (RF) electromagnetic energy producing He+, He2+ (or H+). A potential difference is applied across the tube to accelerate the ions out of the tube.
For Single Stage accelerators, the positive ions produced by the ion source are formed and used as is within the accelerator. However, for Tandem accelerators the positive ions are first sent through a charge exchanger device where they are exposed to alkali vapor (e.g. Rb) resulting in the charge exchange producing He- (or H-). The negative ions (only at a 20-30keV at this point) are then directed into the accelerator.
Accelerators consist of a large tank (or pressure vessel) that is filled with up to 80 PSIG of SF6, an insulating gas with a dielectric strength ~2.5-3 times that of air to prevent electrical breakdown, for higher voltage systems. Inside the tank consists of a high voltage terminal located near the entrance on a Single Stage accelerator and in the center of a Tandem Accelerator. This terminal is the heart of the accelerator allowing the ions to achieve the high energies necessary for the backscattering experiments.
There are a number of high voltage charging systems that can be used within the accelerator. The oldest is the Van de Graaff charging system which is based on the principle that when a charged conductor is brought internally into contact with an external hollow metallic conductor, then all charges can be transferred to the outside surface of the metallic conductor and the potential can be continually increased. The Van de Graaff charging system is a mechanical device in which charge is deposited on a rotating non-conductive belt (e.g. rubber) using a comb of corona points. A second set of points continuously removes and transfers the charge to the sphere of the terminal allowing it to build up to high values.
The Peletron is an improvement of the Van de Graaff where the belt is replaced by a chain consisting of metal pellets connected by insulating Nylon links. Inductor electrodes are used to deposit and remove the charges such that there is no rubbing contacts or corona discharges (like what happens with the Van de Graaff).
Finally, the Tandetron is a solid state device (i.e. no moving parts) which instead utilizes a Cockcroft Walton voltage multiplier which uses a network of capacitors and diodes to produce the high DC voltage at the terminal.
In the Single Stage accelerator the positive ions are generated in the ion source at the high voltage terminal and are thus repelled from it and travel down a long acceleration tube before exiting the end of the accelerator. In the Tandem accelerator the negative ions are attracted through an acceleration tube towards the positive high voltage terminal. At the terminal the negative ions flow through a gas (Ar or N2) or foil (Carbon) stripper where they are converted to He2+ (or H+) by removing electrons from the incoming ions via collisions. The resulting positive ions are then repelled from the positive high voltage terminal and travel down the acceleration tube and exit the tank. The acceleration tube commonly consists of a series of metal electrodes (e.g. Ti) separated by an insulator (e.g. glass or plastic).
After exiting the accelerator the ions enter the Focusing Beam Line that typically consists of bending magnets and/or analyzers to select a single ion type and energy to enter the analytical chamber. The magnet is used to remove unwanted species (e.g. He, He+) from the desired species (e.g. He2+) of the beam. A quadrupole or electrostatic lens may be present to shape and focus the beam before it is directed into the analytical chamber.
The analytical chamber typically contains a goniometer with a sample stage mounted that allows for the analysis of multiple samples as well as rotation and tilt. RBS energy sensitive detectors are mounted within the chamber and are typically Si Surface Barrier Detectors consisting of a thin (~100nm) of P-type Si on an N-type substrate to form a p-n junction. Each ion striking the detector produces some number of electron-hole pairs with the electrons being detected as a voltage pulse whose intensity is dependent on the energy of the ion. Multiple RBS detectors may be present in the chamber so that data that is more (standard condition) and less (150-170 degree backscattering angles) surface sensitive can be acquired simultaneously. Other detectors (e.g. PIXE, HFS etc…) are also commonly present to provide additional information about the sample. The chamber is equipped with a vacuum system although typical vacuums (~10E-6 Torr) are not as high as that utilized in surface analysis techniques such as XPS and TOF-SIMS.
Comparison
RBS is an excellent technique to provide film composition of matrix level species and thickness information. Other techniques that are commonly used to provide this type of information are AES and XPS depth profiles. However, the sputtering process of these two techniques results in beam damage that can alter the film stoichiometry. Additionally, film depths have to be carefully calibrated as the sputter rate can vary signficiantly through different materials. RBS does not have these problems since it is not a sputter technique. However, RBS has worse depth resolution than XPS and AES. Additionally, the spot size is much larger, than with AES in particular. As such, AES is able to analyze small areas of interest (e.g. on a patterned wafer) that are inaccessible to RBS.
SIMS is another technique that is commonly used for depth profiles. While SIMS is often less useful for quantifying matrix level species, it has vastly superior detection limits and depth resolution allowing it to measure ultra-trace level species in very thin films that are well out of the realm of RBS analyses.
Microscopy (e.g. SEM, Dual Beam FIB and TEM) of cross-sections is another method of obtaining film thickness and composition. RBS is much more quantitative than the elemental analysis techniques (e.g. EDS, EELS) used in microscopy. Additionally, RBS provides a good average thickness over a relatively large area whereas microscopy analysis of cross-sections presents a snap shot of the thickness from localized areas. However, microscopy analysis of cross-sections can look at much thinner films and additional structural details of the films can also be revealed.