Wikipedia – XPS

X-ray photoelectron spectroscopy (XPS) is a surface-sensitive quantitative spectroscopic technique that measures the elemental composition at the parts per thousand range, empirical formulachemical state and electronic state of the elements that exist within a material. Put more simply, XPS is a useful measurement technique because it not only shows what elements are within a film but also what other elements they are bonded to. This means if you have a metal oxide and you want to know if the metal is in a +1 or +2 state, using XPS will allow you to find that ratio. However at most the instrument will only probe 20nm into a sample.

XPS spectra are obtained by irradiating a material with a beam of X-rays while simultaneously measuring the kinetic energy and number of electrons that escape from the top 0 to 10 nm of the material being analyzed. XPS requires high vacuum (P ~ 10−8 millibar) or ultra-high vacuum (UHV; P < 10−9 millibar) conditions, although a current area of development is ambient-pressure XPS, in which samples are analyzed at pressures of a few tens of millibar.

XPS can be used to analyze the surface chemistry of a material in its as-received state, or after some treatment, for example: fracturing, cutting or scraping in air or UHV to expose the bulk chemistry, ion beam etching to clean off some or all of the surface contamination (with mild ion etching) or to intentionally expose deeper layers of the sample (with more extensive ion etching) in depth-profiling XPS, exposure to heat to study the changes due to heating, exposure to reactive gases or solutions, exposure to ion beam implant, exposure to ultraviolet light.

  • In principle XPS detects all elements. In practice, using typical laboratory-scale X-ray sources, XPS detects all elements with an atomic number (Z) of 3 (lithium) and above. It cannot easily detect hydrogen (Z = 1) or helium (Z = 2).
  • Detection limits for most of the elements (on a modern instrument) are in the parts per thousand range. Detection limits of parts per million (ppm) are possible, but require special conditions: concentration at top surface or very long collection time (overnight).
  • XPS is routinely used to analyze inorganic compoundsmetal alloyssemiconductorspolymerselementscatalystsglassesceramicspaintspapersinkswoods, plant parts, make-upteethbonesmedical implants, bio-materials, viscous oilsglues, ion-modified materials and many others. XPS is less routinely used to analyze the hydrated forms of some of the above materials by freezing the samples in their hydrated state in an ultra pure environment, and allowing or causing multilayers of ice to sublime away prior to analysis. Such hydrated XPS analysis allows hydrated sample structures, which may be different from vacuum-dehydrated sample structures, to be studied in their more relevant as-used hydrated structure. Many biomaterials such as hydrogels are examples of such samples.

Wide-scan or survey spectrum of a somewhat dirty silicon wafer, showing all elements present. A survey spectrum is usually the starting point of most XPS analyses because it shows all elements present on the sample surface and allows one to set up subsequent high-resolution XPS spectra acquisition. The inset shows a quantification table indicating all elements observed, their binding energies, and their atomic percentages.

Rough schematic of XPS physics – “Photoelectric Effect.

XPS is used to measure:

  • elemental composition of the surface (top 0 –10 nm usually)
  • empirical formula of pure materials
  • elements that contaminate a surface
  • chemical or electronic state of each element in the surface
  • uniformity of elemental composition across the top surface (or line profiling or mapping)
  • uniformity of elemental composition as a function of ion beam etching (or depth profiling)

XPS can be performed using a commercially built XPS system, a privately built XPS system, or a synchrotron-based light source combined with a custom-designed electron energy analyzer. Commercial XPS instruments in the year 2005 used either a focused 20- to 500-micrometer-diameter beam of monochromaticAl Kα X-rays, or a broad 10- to 30-mm-diameter beam of non-monochromatic (polychromatic) Al Kα X-rays or Mg Kα X-rays. A few specially designed XPS instruments can analyze volatile liquids or gases, or materials at pressures of roughly 1 torr (1.00 torr = 1.33 millibar), but there are relatively few of these types of XPS systems. The ability to heat or cool the sample during or prior to analysis is relatively common.

Because the energy of an X-ray with particular wavelength is known (for Al Kα X-rays, Ephoton = 1486.7 eV), and because the emitted electrons’ kinetic energies are measured, the electron binding energy of each of the emitted electrons can be determined by using an equation that is based on the work of Ernest Rutherford (1914):

{\displaystyle E_{\text{binding}}=E_{\text{photon}}-\left(E_{\text{kinetic}}+\phi \right)}

where Ebinding is the binding energy (BE) of the electron, Ephoton is the energy of the X-ray photons being used, Ekinetic is the kinetic energy of the electron as measured by the instrument and {\displaystyle \phi } is the work function dependent on both the spectrometer and the material. This equation is essentially a conservation of energy equation. The work function term {\displaystyle \phi } is an adjustable instrumental correction factor that accounts for the few eV of kinetic energy given up by the photoelectron as it becomes absorbed by the instrument’s detector. It is a constant that rarely needs to be adjusted in practice.

After WWIIKai Siegbahn and his research group in Uppsala (Sweden) developed several significant improvements in the equipment, and in 1954 recorded the first high-energy-resolution XPS spectrum of cleaved sodium chloride (NaCl), revealing the potential of XPS.[1] A few years later in 1967, Siegbahn published a comprehensive study of XPS, bringing instant recognition of the utility of XPS, which he referred to as Electron Spectroscopy for Chemical Analysis (ESCA). In cooperation with Siegbahn, a small group of engineers (Mike Kelly, Charles Bryson, Lavier Faye, Robert Chaney) at Hewlett-Packard in the USA, produced the first commercial monochromatic XPS instrument in 1969. Siegbahn received the Nobel Prize for Physics in 1981, to acknowledge his extensive efforts to develop XPS into a useful analytical tool.[2]

In parallel with Siegbahn’s work, David Turner at Imperial College London (and later at Oxford University) developed ultraviolet photoelectron spectroscopy (UPS) for molecular species using helium lamps.[3]

Basic physics

A typical XPS spectrum is a plot of the number of electrons detected (sometimes per unit time) (Y-axis, ordinate) versus the binding energy of the electrons detected (X-axis, abscissa). Each element produces a characteristic set of XPS peaks at characteristic binding energy values that directly identify each element that exists in or on the surface of the material being analyzed. These characteristic spectral peaks correspond to the electron configuration of the electrons within the atoms, e.g., 1s, 2s, 2p, 3s, etc. The number of detected electrons in each of the characteristic peaks is directly related to the amount of element within the XPS sampling volume. To generate atomic percentage values, each raw XPS signal must be corrected by dividing its signal intensity (number of electrons detected) by a “relative sensitivity factor” (RSF), and normalized over all of the elements detected. Since hydrogen is not detected, these atomic percentages exclude hydrogen.

To count the number of electrons during the acquisition of a spectrum with a minimum of error, XPS detectors must be operated under ultra-high vacuum (UHV) conditions because electron counting detectors in XPS instruments are typically one meter away from the material irradiated with X-rays. This long path length for detection requires such low pressures.

Surface sensitivity

XPS detects only those electrons that have actually escaped from the sample into the vacuum of the instrument, and reach the detector. In order to escape from the sample into vacuum, a photoelectron must travel through the sample. Photo-emitted electrons can undergo inelastic collisions, recombination, excitation of the sample, recapture or trapping in various excited states within the material, all of which can reduce the number of escaping photoelectrons. These effects appear as an exponential attenuation function as the depth increases, making the signals detected from analytes at the surface much stronger than the signals detected from analytes deeper below the sample surface. Thus, the signal measured by XPS is an exponentially surface-weighted signal, and this fact can be used to estimate analyte depths in layered materials.

Components of a commercial system

The main components of a commercially made XPS system include a source of X-rays, an ultra-high vacuum (UHV) stainless steel chamber with UHV pumps, an electron collection lens, an electron energy analyzer, Mu-metalmagnetic field shielding, an electron detector system, a moderate vacuum sample introduction chamber, sample mounts, a sample stage, and a set of stage manipulators.

Uses and capabilities

XPS is routinely used to determine:

  • What elements and the quantity of those elements that are present within the top 1-10 nm of the sample surface
  • What contamination, if any, exists on the surface or in the bulk of the sample
  • Empirical formula of a material that is free of excessive surface contamination
  • The chemical state identification of one or more of the elements in the sample and also give information on local bonding of atoms
  • The binding energy of one or more electronic states
  • The thickness of one or more thin layers (1–8 nm) of different materials within the top 10 nm of the surface
  • The density of electronic states

Capabilities of advanced systems

  • Measure uniformity of elemental composition across the top of the surface (or line profiling or mapping)
  • Measure uniformity of elemental composition as a function of depth by ion beam etching (or depth profiling)
  • Measure uniformity of elemental composition as a function of depth by tilting the sample (or angle-resolved XPS)

Chemical states and chemical shift

The ability to produce chemical state information (as distinguished from merely elemental information) from the topmost few nm of any surface makes XPS a unique and valuable tool for understanding the chemistry of a surface. In this context, “chemical state” refers to the local bonding environment of a species in question. The local bonding environment of a species in question is affected by its formal oxidation state, the identity of its nearest-neighbor atom, its bonding hybridization to that nearest-neighbor atom, and in some cases even the bonding hybridization between the atom in question and the next-nearest-neighbor atom. Thus, while the nominal binding energy of the C1s electron is 284.6 eV (some also use 285.0 eV as the nominal value for the binding energy of carbon), subtle but reproducible shifts in the actual binding energy, the so-called chemical shift (analogous to NMR spectroscopy), provide the chemical state information referred to here.

Chemical-state analysis is widely used for the element carbon. Chemical-state analysis of the surface of carbon-containing polymers readily reveals the presence or absence of the chemical states of carbon shown in bold, in approximate order of increasing binding energy, as: carbide (-C2−), silane (-Si-CH3), methylene/methyl/hydrocarbon (-CH2CH2-, CH3-CH2-, and –CH=CH-), amine (-CH2-NH2), alcohol (-C-OH), ketone (-C=O), organic ester (-COOR), carbonate (-CO32−), monofluoro-hydrocarbon (-CFH-CH2-), difluoro-hydrocarbon (-CF2-CH2-), and trifluorocarbon (-CH2CF3), to name but a few examples.

Chemical state analysis of the surface of a silicon wafer readily reveals chemical shifts due to the presence or absence of the chemical states of silicon in its different formal oxidation states, such as: n-doped silicon and p-doped silicon (metallic silicon in figure above), silicon suboxide (Si2O), silicon monoxide (SiO), Si2O3, and silicon dioxide (SiO2). An example of this is seen in the figure above: High-resolution spectrum of an oxidized silicon wafer in the energy range of the Si 2p signal.

Industrial use

Routine limits

Quantitative accuracy and precision

  • Quantification can be divided into two categories: absolute quantification and relative quantification. The former generally requires the use of certified (or independently verified) standard samples, is generally more challenging, and is generally less common.
  • Relative quantification is more common and involves comparisons between several samples in a set for which one or more analytes are varied while all other components (the sample matrix) are held constant.
  • Under optimum conditions, the quantitative accuracy of the atomic percent (at%) values calculated from the Major XPS Peaks is 90-95% for each major peak. If a high level quality control protocol is used, the accuracy can be further improved.
  • Under routine work conditions, where the surface is a mixture of contamination and expected material, the accuracy ranges from 80-90% of the value reported in atomic percent values.
  • Quantitative precision (the ability to repeat a measurement and obtain the same result) is an essential consideration for proper reporting of quantitative results. Standard statistical tests, such as the Student’s t test for comparison of means, should be used to determine confidence levels in the average value from a set of replicate measurements, and when comparing the average values of two or more different sets of results. In general, a p value (an output of the Student’s t test) of 0.05 or less indicates a level of confidence (95%) that is accepted in the field as significant.

Analysis time

Detection limits

Detection limits may vary greatly with the cross section of the photoelectron line of interest and the background signal level which is a function of the matrix material. In general photoelectron cross sections increase with atomic number, while the background is a function of the composition of the matrix material and the binding energy. Background signals generally increase with atomic number of the matrix material and decrease with increasing kinetic energy. For example in the case of gold on silicon where the high cross section Au4f peak is at a higher kinetic energy than the major silicon peaks, it sits on a very low background and detection limits of 1ppm or better may be achieved with reasonable acquisition times. Conversely for silicon on gold, where the modest cross section Si2p line sits on the large background below the Au4f lines, detection limits would be much worse for the same acquisition time. Detection limits are often quoted as 0.1–1.0 % atomic percent (0.1 % = 1 part per thousand = 1000 ppm) for practical analyses, but lower limits may be achieved in many circumstances.

Measured area

Sample size limits

Instruments accept small (mm range) and large samples (cm range), e.g. wafers. Limiting factor is the design of the sample holder, the sample transfer, and the size of the vacuum chamber. Large samples are laterally moved in x and y direction to analyse a larger area.

Degradation during analysis

  • Non-monochromatic X-ray sources produce a significant amount of high energy Bremsstrahlung X-rays (1–15 keV of energy) which directly degrade the surface chemistry of various materials. Non-monochromatic X-ray sources also produce a significant amount of heat (100 to 200 °C) on the surface of the sample because the anode that produces the X-rays is typically only 1 to 5 cm (2 in) away from the sample. This level of heat, when combined with the Bremsstrahlung X-rays, acts synergistically to increase the amount and rate of degradation for certain materials. Monochromatic X-ray sources, because they are far away (50–100 cm) from the sample, do not produce any heat effects.

General summary of use

  • XPS is, in effect, a non-destructive technique that measures the surface chemistry of most any material, however non-dry, outgassing, radioactive or highly magnetic materials can pose serious challenges.

Materials routinely analyzed

Inorganic compounds, metal alloys, semiconductors, polymers, pure elements, catalysts, glasses, ceramics, paints, papers, inks, woods, plant parts, make-up, teeth, bones, human implants, biomaterials,[4] viscous oils, glues, ion modified materials

Analysis details

Charge compensation techniques

  • Low-voltage electron beam (1-20 eV) (or electron flood gun)
  • UV lights
  • Low-voltage argon ion beam with low-voltage electron beam (1-10 eV)
  • Aperture masks
  • Mesh screen with low-voltage electron beams

Sample preparation

  • Sample handling
  • Sample cleaning
  • Sample mounting
  • sample grinding

Data processing

Peak identification

The number of peaks produced by a single element varies from 1 to more than 20. Tables of binding energies (BEs) that identify the shell and spin-orbit of each peak produced by a given element are included with modern XPS instruments, and can be found in various handbooks [citations] and websites.[5] Because these experimentally determined BEs are characteristic of specific elements, they can be directly used to identify experimentally measured peaks of a material with unknown elemental composition.

Before beginning the process of peak identification, the analyst must determine if the BEs of the unprocessed survey spectrum (0-1400 eV) have or have not been shifted due to a positive or negative surface charge. This is most often done by looking for two peaks that due to the presence of carbon and oxygen.

Charge referencing insulators

Charge referencing is needed when a sample suffers either a positive (+) or negative (-) charge induced shift of experimental BEs. Charge referencing is needed to obtain meaningful BEs from both wide-scan, high sensitivity (low energy resolution) survey spectra (0-1100 eV), and also narrow-scan, chemical state (high energy resolution) spectra.

Charge induced shifting causes experimentally measured BEs of XPS peaks to appear at BEs that are greater or smaller than true BEs. Charge referencing is performed by adding or subtracting a “Charge Correction Factor” to each of the experimentally measured BEs. In general, the BE of the hydrocarbon peak of the C (1s) XPS signal is used to charge reference (charge correct) all BEs obtained from non-conductive (insulating) samples or conductors that have been deliberately insulated from the sample mount.

Charge induced shifting is normally due to: a modest excess of low voltage (-1 to -20 eV) electrons attached to the surface, or a modest shortage of electrons (+1 to +15 eV) within the top 1-12 nm of the sample caused by the loss of photo-emitted electrons. The degree of charging depends on various factors. If, by chance, the charging of the surface is excessively positive, then the spectrum might appear as a series of rolling hills, not sharp peaks as shown in the example spectrum.

The C (1s) BE of the hydrocarbon species (moieties) of the “Adventitious” carbon that appears on all, air-exposed, conductive and semi-conductive materials is normally found between 284.5 eV and 285.5 eV. For convenience, the C (1s) of hydrocarbon moieties is defined to appear between 284.6 eV and 285.0 eV. A value of 284.8 eV has become popular in recent years. However, some recent reports indicate that 284.9 eV or 285.0 eV represents hydrocarbons attached on metals, not the natural native oxide. The 284.8 eV BE is routinely used as the “Reference BE” for charge referencing insulators. When the C (1s) BE is used for charge referencing, then the charge correction factor is the difference between 284.8 eV and the experimentally measured C (1s) BE of the hydrocarbon moieties.

When using a monochromatic XPS system together with a low voltage electron flood gun for charge compensation the experimental BEs of the C (1s) hydrocarbon peak is often 4-5 eV smaller than the reference BE value (284.8 eV). In this case, all experimental BEs appear at lower BEs than expected and need to be increased by adding a value ranging from 4 to 5 eV. Non-monochromatic XPS systems are not usually equipped with a low voltage electron flood gun so the BEs will normally appear at higher BEs than expected. It is normal to subtract a charge correction factor from all BEs produced by a non-monochromatic XPS system.

The process of peak-fitting high energy resolution XPS spectra is still a mixture of art, science, knowledge and experience. The peak-fit process is affected by instrument design, instrument components, experimental settings (aka analysis conditions) and sample variables. Most instrument parameters are constant while others depend on the choice of experimental settings.

Variables that affect or define peak-fit results include:

  • FWHMs
  • Chemical Shifts
  • Peakshapes
  • Instrument design factors
  • Experimental settings
  • Sample factors

Full width at half maximum (FWHM)

The full width at half maximum (FWHM) values are useful indicators of chemical state changes and physical influences. That is, broadening of a peak may indicate: a change in the number of chemical bonds contributing to a peak shape, a change in the sample condition (x-ray damage) and/or differential charging of the surface (localised differences in the charge state of the surface). However, it should be noted that the FWHM also depends on the detector, and can also increase due to the sample getting charged.

Chemical shifts

Peak shapes

Depends on instrument parameters, experimental parameters and sample characteristics

Instrument design factors

Design of electron analyzer (CMA, HSA, retarding field)

Experiment settings

Sample factors

Physical form of the sample (single crystal, polished, powder, corroded)
Number of physical defects within the analysis volume (from Argon ion etching, from laser cleaning)

Advanced instrumentation aspects

Hemispherical electron energy analyzer

hemispherical electron energy analyzer is generally used for applications where a higher resolution is needed. An ideal hemispherical analyzer consists of two concentric hemispherical electrodes (inner and outer hemispheres) held at proper voltages. It is possible to demonstrate that in such a system, (i) the electrons are linearly dispersed along the direction connecting the entrance and the exit slit, depending on their kinetic energy, while (ii) electrons with the same energy are first-order focused.[6]When two potentials, {\displaystyle V_{1}} and {\displaystyle V_{2}}, are applied to the inner and outer hemispheres, respectively, the electric potential and field in the region between the two electrodes can be calculated by solving the Laplace equation:

{\displaystyle V(r)=-\left[{\frac {(V_{2}-V_{1})}{(R_{2}-R_{1})}}\right]\cdot {\frac {(R_{1}R_{2})}{r}}+const.}

{\displaystyle |E(r)|=-\left[{\frac {(V_{2}-V_{1})}{(R_{2}-R_{1})}}\right]\cdot {\frac {(R_{1}R_{2})}{r^{2}}}}

where {\displaystyle R_{1}} and {\displaystyle R_{2}} are the radii of the two hemispheres. In order for the electrons with kinetic energy E0 to follow a circular trajectory of radius {\displaystyle R_{0}={\frac {(R1+R2)}{2}}}, the force exerted by the electric field ({\displaystyle F_{E}=-e|E(r)|}) must equal the centripetal force ({\displaystyle F_{C}}) along the whole path. After some algebra, the following expression can be derived for the potential:

{\displaystyle V(r)=\left({\frac {V_{0}R_{0}}{r}}\right)+const.},

where {\displaystyle V_{0}={\frac {E_{0}}{e}}} is the energy of the electrons expressed in eV. From this equation, we can calculate the potential difference between the two hemispheres, which is given by:

{\displaystyle V_{2}-V_{1}=V_{0}\left({\frac {R_{2}}{R_{1}}}-{\frac {R_{1}}{R_{2}}}\right)}.

The latter equation can be used to determine the potentials to be applied to the hemispheres in order to select electrons with energy {\displaystyle E_{0}=|e|V_{0}}, the so-called pass energy.

In fact, only the electrons with energy {\displaystyle E_{0}} impinging normal to the entrance slit of the analyzer describe a trajectory of radius {\displaystyle R_{0}=(R_{1}+R_{2})/2} and reach the exit slit, where they are revealed by the detector.

The instrumental energy resolution of the device depends both on the geometrical parameters of the analyzer and on the angular divergence of the incoming photoelectrons:

{\displaystyle \Delta E=E_{0}\left({\frac {w}{2R_{0}}}+{\frac {\alpha ^{2}}{4}}\right)},

where {\displaystyle w} is the average width of the two slits, and {\displaystyle \alpha } is the incidence angle of the incoming photoelectrons. Though the resolution improves with increasing {\displaystyle R_{0}}, technical problems related to the size of the analyzer put a limit on the actual value of {\displaystyle R_{0}}. Although a low pass energy {\displaystyle E_{0}} improves the resolution, the electron transmission probability is reduced at low pass energy, and the signal-to-noise ratio deteriorates, accordingly. The electrostatic lenses in front of the analyzer have two main purposes: they collect and focus the incoming photoelectrons into the entrance slit of the analyzer, and they decelerate the electrons to the kinetic energy {\displaystyle E_{0}}, in order to increase the resolution.

When acquiring spectra in sweep (or scanning) mode, the voltages of the two hemispheres {\displaystyle V_{1}} and {\displaystyle V_{2}} – and hence the pass energy- are held fixed; at the same time, the voltage applied to the electrostatic lenses is swept in such a way that each channel counts electrons with the selected kinetic energy for the selected amount of time. In order to reduce the acquisition time per spectrum, the so-called snapshot (or fixed) mode has been introduced. This mode exploits the relation between the kinetic energy of a photoelectron and its position inside the detector. If the detector energy range is wide enough, and if the photoemission signal collected from all the channels is sufficiently strong, the photoemission spectrum can be obtained in one single shot from the image of the detector.

Cylindrical mirror analyzer

Since the relevant information, in photoemission spectroscopy, is contained in the kinetic energy distribution of the photoelectrons, a specific device is needed to energy-filter the electrons emitted (or scattered) by the sample. Electrostatic monochromators are the most common choice. The older design, a CMA, represents a trade-off between the need for high count rates and high angular/energy resolution. The so-called cylindrical mirror analyzer (CMA) is mostly used for checking the elemental composition of the surface. It consists of two co-axial cylinders placed in front of the sample, the inner one being held at a positive potential, while the outer cylinder is held at a negative potential. Only the electrons with the right energy can pass through this set-up and are detected at the end. The count rates are high but the resolution (both in energy and angle) is poor.

Synchrotron based XPS

A breakthrough has been actually brought about in the last decades by the development of large scale synchrotron radiation facilities. Here, bunches of relativistic electrons kept on a circular orbit inside a storage ring are accelerated through bending magnets or insertion devices like wigglers and undulators to produce a high brilliance and high flux photon beam. The main advantages of using synchrotron light are

  • the high brilliance of this kind of radiation, which is orders of magnitude more intense and better collimated than the one produced by anode-based sources;
  • the tunability of synchrotron radiation over a wide frequency range;
  • its high polarization;
  • the high photon flux;
  • the possibility of producing extremely short pulses at a frequency as high as a MHz.

The highest spectral brightness and narrowest beam energy dispersion is attained by undulators, which consist of periodic array of dipole magnets in which the electrons are forced to wiggle and thus to emit coherent light. Besides the high intensity, energy tunability is one of the most important advantages of synchrotron light compared to the light produced by conventional X-ray sources. In fact, a wide energy range (from the IR to the Hard X-ray region, depending on the energy of the electron bunch) is accessible by changing the undulator gaps between the arrays. Continuous energy spectra available from a synchrotron radiation source allows selection of photon energies yielding optimum photoionization cross-sections appropriate for probing a particular core level. The high photon flux, in addition, makes it possible to perform XPS experiments also from low density atomic species, such as molecular and atomic adsorbates.

Electron detectors

Older style electron detector

Electrons can be detected using an electron multiplier, usually a channeltron. This device essentially consists of a glass tub with a resistive coating on the inside. A high voltage is applied between the front and the end. An electron which enters the channeltron is accelerated to the wall, where it removes more electrons, in such a way that an electron avalanche is created, until a measurable current pulse is obtained.

Theoretical aspects

Quantum mechanical treatment

{\displaystyle h\nu =|E_{b}^{v}|+E_{kin}}

where {\displaystyle h\nu } is the photon energy, {\displaystyle |E_{b}^{v}|} is the electron BE (with respect to the vacuum level) prior to ionization, and {\displaystyle E_{kin}} is the kinetic energy of the photoelectron. If reference is taken with respect to the Fermi level (as it is typically done in photoelectron spectroscopy{\displaystyle |E_{b}^{v}|} must be replaced by the sum of the binding energy (BE) relative to the Fermi level, {\displaystyle |E_{b}^{F}|}, and the sample work function, {\displaystyle \Phi _{0}} .

{\displaystyle i\hbar {\frac {\partial \psi }{\partial t}}=\left[{\frac {1}{2m}}\left(\mathbf {\hat {p}} -{\frac {e}{c}}\mathbf {\hat {A}} \right)^{2}+{\hat {V}}\right]\psi ={\hat {H}}\psi },

where {\displaystyle \psi } is the electron wave function, {\displaystyle \mathbf {A} } is the vector potential of the electromagnetic field and {\displaystyle V} is the unperturbed potential of the solid. In the Coulomb gauge ({\displaystyle \nabla \cdot \mathbf {A} =0}), the vector potential commutes with the momentum operator ({\displaystyle [\mathbf {\hat {p}} ,\mathbf {\hat {A}} ]=0}), so that the expression in brackets in the Hamiltonian simplifies to:

{\displaystyle \left(\mathbf {\hat {p}} -{\frac {e}{c}}\mathbf {\hat {A}} \right)^{2}={\hat {p}}^{2}-2{\frac {e}{c}}\mathbf {\hat {A}} \cdot \mathbf {\hat {p}} +\left({\frac {e}{c}}\right)^{2}{\hat {A}}^{2}}

Actually, neglecting the {\displaystyle \nabla \cdot \mathbf {A} } term in the Hamiltonian, we are disregarding possible photocurrent contributions.[7] Such effects are generally negligible in the bulk, but may become important at the surface. The quadratic term in {\displaystyle \mathbf {A} } can be instead safely neglected, since its contribution in a typical photoemission experiment is about one order of magnitude smaller than that of the first term .

In first-order perturbation approach, the one-electron Hamiltonian can be split into two terms, an unperturbed Hamiltonian {\displaystyle {\hat {H}}_{0}}, plus an interaction Hamiltonian {\displaystyle {\hat {H}}’}, which describes the effects of the electromagnetic field:

{\displaystyle {\hat {H}}’=-{\frac {e}{mc}}\mathbf {\hat {A}} \cdot \mathbf {\hat {p}} }

In time-dependent perturbation theory,for an harmonic or constant perturbation, the transition rate between the initial state {\displaystyle \psi _{i}} and the final state {\displaystyle \psi _{f}} is expressed by Fermi’s Golden Rule:

{\displaystyle {\frac {d\omega }{dt}}\propto {\frac {2\pi }{\hbar }}|\langle \psi _{f}|{\hat {H}}’|\psi _{i}\rangle |^{2}\delta (E_{f}-E_{i}-h\nu )},

where {\displaystyle E_{i}} and {\displaystyle E_{f}} are the eigenvalues of the unperturbed Hamiltonian in the initial and final state, respectively, and {\displaystyle h\nu } is the photon energy. Fermi’s Golden Rule uses the approximation that the perturbation acts on the system for an infinite time. This approximation is valid when the time that the perturbation acts on the system is much larger than the time needed for the transition. It should be understood that this equation needs to be integrated with the density of states {\displaystyle \rho (E)} which gives:[8]

{\displaystyle {\frac {d\omega }{dt}}\propto {\frac {2\pi }{\hbar }}|\langle \psi _{f}|{\hat {H}}’|\psi _{i}\rangle |^{2}\rho (E_{f})=|M_{fi}|^{2}\rho (E_{f})}

In a real photoemission experiment the ground state core electron BE cannot be directly probed, because the measured BE incorporates both initial state and final state effects, and the spectral linewidth is broadened owing to the finite core-hole lifetime ({\displaystyle \tau }).

Assuming an exponential decay probability for the core hole in the time domain ({\displaystyle \propto \exp {-t/\tau }}), the spectral function will have a Lorentzian shape, with a FWHM (Full Width at Half Maximum) {\displaystyle \Gamma } given by:

{\displaystyle I_{L}(E)={\frac {I_{0}}{\pi }}{\frac {\Gamma /2}{(E-E_{b})^{2}+(\Gamma /2)^{2}}}}

From the theory of Fourier transforms, {\displaystyle \Gamma } and {\displaystyle \tau } are linked by the indeterminacy relation:

{\displaystyle \Gamma \tau \geq \hbar }

The photoemission event leaves the atom in a highly excited core ionized state, from which it can decay radiatively (fluorescence) or non-radiatively (typically by Augerdecay). Besides Lorentzian broadening, photoemission spectra are also affected by a Gaussian broadening, whose contribution can be expressed by

{\displaystyle I_{G}(E)={\frac {I_{0}}{\sigma {\sqrt {2}}}}\exp {\left(-{\frac {(E-E_{b})^{2}}{2\sigma ^{2}}}\right)}}

Theory of core level photoemission of electrons

In a solid, also inelastic scattering events contribute to the photoemission process, generating electron-hole pairs which show up as an inelastic tail on the high BE side of the main photoemission peak. In some cases, we observe also energy loss features due to plasmon excitations. This can either a final state effect caused by core hole decay, which generates quantized electron wave excitations in the solid (intrinsic plasmons), or it can be due to excitations induced by photoelectrons travelling from the emitter to the surface (extrinsic plasmons). Due to the reduced coordination number of first-layer atoms, the plasma frequency of bulk and surface atoms are related by the following equation: {\displaystyle \omega _{surf}={\frac {\omega _{bulk}}{\sqrt {2}}}}, so that surface and bulk plasmons can be easily distinguished from each other. Plasmon states in a solid are typically localized at the surface, and can strongly affect the electron Inelastic Mean Free Path (IMFP).

Vibrational effects

Temperature-dependent atomic lattice vibrations, or phonons, can broaden the core level components and attenuate the interference patterns in an XPD (X-Ray Photoelectron Diffraction) experiment. The simplest way to account for vibrational effects is by multiplying the scattered single-photoelectron wave function {\displaystyle \phi _{j}} by the Debye-Waller factor:

{\displaystyle W_{j}=\exp {(-\Delta k_{j}^{2}{\bar {U_{j}^{2}}})}},

where {\displaystyle \Delta k_{j}^{2}} is the squared magnitude of the wave vector variation caused by scattering, and {\displaystyle {\bar {U_{j}^{2}}}} is the temperature-dependent one-dimensional vibrational mean squared displacement of the {\displaystyle j^{th}} emitter. In the Debye model, the mean squared displacement is calculated in terms of the Debye temperature, {\displaystyle \Theta _{D}}, as:

{\displaystyle {\bar {U_{j}^{2}}}(T)=9\hbar ^{2}T^{2}/mk_{B}\Theta _{D}}

  1. ^ Siegbahn, K.; Edvarson, K. I. Al (1956). “β-Ray spectroscopy in the precision range of 1 : 105“. Nuclear Physics1 (8): 137–159. Bibcode:1956NucPh…1..137Sdoi:10.1016/S0029-5582(56)80022-9.
  3. ^ Turner, D. W.; Jobory, M. I. Al (1962). “Determination of Ionization Potentials by Photoelectron Energy Measurement”. The Journal of Chemical Physics37 (12): 3007. Bibcode:1962JChPh..37.3007Tdoi:10.1063/1.1733134.
  5. ^ “Handbook of The Elements and Native Oxides” (PDF). XPS International, Inc. Retrieved 8 December 2012.
  6. ^ Hadjarab, F.; J.L. Erskine (1985). “Image properties of the hemispherical analyzer applied to multichannel energy detection”. Journal of Electron Spectroscopy and Related Phenomena36 (3): 227. doi:10.1016/0368-2048(85)80021-9.

Further reading

  • XPS Spectra, Databases, Spectra and Application Notes[1]
  • Handbooks of Monochromatic XPS Spectra – Fully Annotated, PDF of Volumes 1 and 2, B.V.Crist, published by XPS International LLC, 2005, Mountain View, CA, USA
  • Surface Chemical Analysis — Vocabulary, ISO 18115 : 2001, International Organisation for Standardisation (ISO), TC/201, Switzerland, [2]


Wounded Veterans Deserve Better

Wounded Veterans Deserve Better

As published in the Hill Times: Nov.15, 2021

Every November, Canadians honor those who have served in the military; especially the dead and wounded. Unfortunately, war remains a permanent feature of human existence and has become vital to neoliberalism and the interests of global capital. Canada’s long military experience in Afghanistan is a good example of how a middle power gets drawn into unwinnable conflicts at the behest of the mighty.

Poppies remind me that wars are fought by working people who are often discarded when their courage is no longer required. While every combat veteran is a hero, the same cannot be said for those who send them to war and arms manufacturers who profit from military strife.

Under the warrior’s code, soldiers have little choice regarding even the most dubious deployments. Rather than protest or refuse orders, the majority accept the risk of injury, death and the ugliness of killing. In the horror of battle; soldiers willingly die for their peers, as do their official enemies.

A newspaper editor once remarked that we all have the choice to join the military or seek political office. This statement assumes perfect equality of opportunity while ignoring the many socio-economic factors constraining career choices. It also suggests an uncomfortable question.

Why is military service so rare among Canada’s wealthy citizens and why is political success such a rarity among working people? Exceptions exist, but military service is primarily a means of establishing economic security or acquiring an education. Those born to wealth have little motive to risk their lives for socioeconomic benefit.

Government statements about respect for veterans are meaningless in the context of rampant PTSD, suicide, and homelessness. As well, Veterans Affairs remains understaffed while case officers struggle to properly serve their clients. If the government can afford to increase the number of highly-paid generals, it can certainly hire more VAC case managers and improve care for homeless veterans.


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Realtime generated VR application
with photogrammetric 3D data, artificial voice (loop 9'43"), ambient sound (loop 7'01")
first shown: Predigerkirche, Basel (ch), group show: "Wenn es ein Paradies gibt, kommt es in Brocken", June-Aug 2019

HTC Vive VR Headset, PC
proprietary software development
construction in painted MDF 400cm x 330cm x 330cm (h/w/l)

A fictitious, somewhat immature AI reflects on its paradoxical mental state, caused by the impossibility to define itself through a human body. To make up for this, it has acquired several spaces of our world for replacement. Using the headset, you can stand in the middle of these amorphous, moving spatial constellations and listen to the AI's desperate monologue.

The 3D spaces of the installation are generated using photogrammetry technique only, which uses hundreds of single camera shots to calculate a 3D model, and which can then be used in the VR software. For the first version of the installation, spatial situations have been taken from Predigerkirche Basel (the actual venue), a botanical gardens, a historic library (Stiftsbibliothek St. Gallen), a graffiti-painted youth center, a junkyard, and a museum of antique statues (Skulpturhalle).

The wooden construction (painted MDF) was conceived for Predigerkirche and can be adapted according to the spatial situation of the venue. The text of the voice over is be translated into different languages if necessary.


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Best answer: What direction is Saskatchewan to Toronto?

Saskatchewan is located nearly North West side to Toronto. The bearing degree from Toronto To Saskatchewan is 297 ° degree. The given North West direction from Toronto is only approximate.

Is Saskatchewan near Toronto?

The distance between Toronto and Saskatchewan is 2314 km. The road distance is 3046.7 km. … Saskatchewan is 1h behind Toronto.

In which direction is USA from Canada?

How far is Saskatchewan on a plane?

An average nonstop flight from the United States to Saskatchewan takes 12h 19m, covering a distance of 1412 miles. The most popular route is Newport News – Saskatoon with an average flight time of 11h 11m.

How long is the flight from Toronto to Saskatchewan?

Flight time from Toronto to Regina, Saskatchewan is 3 hours 19 minutes.

How many provinces are east of Saskatchewan?

Saskatchewan is part of the Western Provinces and is bounded on the west by Alberta, on the north by the Northwest Territories, on the north-east by Nunavut, on the east by Manitoba, and on the south by the U.S. states of Montana and North Dakota.

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Is Saskatchewan near Calgary?

Distance from Saskatchewan to Calgary is 565 kilometers. This air travel distance is equal to 351 miles. The air travel (bird fly) shortest distance between Saskatchewan and Calgary is 565 km= 351 miles.

How long is Canada from east to west?

Is US south or north of Canada?

What is the capital city of Canada?

Is Saskatchewan close to Alberta?

It is 564 km from Saskatchewan to Alberta. It is approximately 613 km to drive. … It takes approximately 2h 1m to get from Saskatchewan to Alberta, including transfers.

How far is Ontario to Toronto?

The distance between Ontario and Toronto is 3446 km. The road distance is 3996.9 km.

Is Saskatchewan a good place to live?

Saskatchewan is a great place to live and raise a family and to locate or invest in a business: Housing costs are lower in Saskatchewan than in most major cities in Canada, and owning a home is affordable and achievable for most people.

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Is Saskatchewan near Ontario?

The distance between Ontario and Saskatchewan is 2546 km. The road distance is 2813.9 km.

How many hours from Ontario to Saskatchewan?

How long is the drive from Ontario to Saskatchewan? The total driving time is 24 hours, 23 minutes.

Is Alberta near Toronto?

The distance between Toronto and Alberta is 2832 km. The road distance is 3558.8 km. … Alberta is 2h behind Toronto.


When did slavery end in Upper Canada?

The Slavery Abolition Act came into effect on 1 August 1834, abolishing slavery throughout the British Empire, including British North America. The Act made enslavement officially illegal in every province and freed the last remaining enslaved people in Canada.

When did Upper Canada abolish slavery?

A compromise was reached and on July 9, 1793 an Act was passed that prevented the further introduction of slaves into Upper Canada and allowed for the gradual abolition of slavery although no slaves already residing in the province were freed outright.

How long did slavery exist in Canada?

Canada’s slavery secret: The whitewashing of 200 years of enslavement. Why is it common knowledge that Canada was the terminal stop on the Underground Railroad for runaway slaves from the U.S., but few know that Blacks and Indigenous peoples were bought, sold and exploited right here? Contributor Kyle G.

When did slavery actually end in the North?

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How many slaves were there in Canada?

There are 6,500 slaves in Canada, nearly 46 million worldwide: charity – National | Globalnews.ca.

Was there slavery in Upper Canada?

By 1792 the slave population in Upper Canada was not large. … This law made Upper Canada “the first British colony to abolish slavery”. The Act remained in force until 1833 when the British Parliament’s Slavery Abolition Act abolished slavery in most parts of the British Empire.

When was Chloe Cooley born?

Born in Somers, Tolland, Connecticut, United States on 4 Jan 1759 to James Cooley and Ruth Parsons.

Who ended slavery in Canada?

Abolishment of slavery in Canada

In 1793, Governor John Graves Simcoe passed the Anti-slavery Act. This law freed enslaved people aged 25 and over and made it illegal to bring enslaved people into Upper Canada.

Why was there no slavery in Canada?

Those in what is now called Canada typically came from the American colonies, as no shiploads of human chattel went to Canada directly from Africa. There were no large plantations in Canada, and therefore no need for a large slave work force of the sort that existed in most European colonies in the Americas.

Who owned slaves in Canada?

Six out of the 16 members of the first Parliament of the Upper Canada Legislative Assembly (1792–96) were slave owners or had family members who owned slaves: John McDonell, Ephraim Jones, Hazelton Spencer, David William Smith, and François Baby all owned slaves, and Philip Dorland’s brother Thomas owned 20 slaves.

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What was the last state to free slaves?

Mississippi Becomes Last State to Ratify 13th Amendment

When did slavery end in Jamaica?

Who is the person who ended slavery?

It went on for three more years. On New Year’s morning of 1863, President Abraham Lincoln hosted a three-hour reception in the White House. That afternoon, Lincoln slipped into his office and — without fanfare — signed a document that changed America forever.

Who is considered black in Canada?

Black Canadians, or African Canadians, are people of African or Caribbean ancestry who live in Canada. According to the 2016 Canadian census, 1.2 million Canadians (3.5 per cent of the population) identified as being Black. This is a summary of Black history in Canada.

When was slavery abolished in Africa?

In January 1807, with a self-sustaining population of over four million enslaved people in the South, some Southern congressmen joined with the North in voting to abolish the African slave trade, an act that became effective January 1, 1808.

How many slaves are in the world today 2021?

Countries That Still Have Slavery 2021.

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Country Estimated Number of Slaves 2021 Population
North Korea 1,100,000 25,887,041