XPS

The general reference for this section is Woodruff & Delchar, Ch. 3, sections 1-3.

X-Ray Photoelectron Spectroscopy (XPS) is a method to characterize the surface region of materials by analyzing the the energy distribution of electrons ejected from the material when it is exposed to X-Rays of a well-defined energy. The method is also called ESCA (Electron Spectroscopy for Chemical Analysis) and it involves an X-Ray source, the sample and an electron energy spectrometer. Enhancements include the use of an X-Ray monochromator or, even better, synchrotron radiation

XPS can provide the following information:

identification of atomic species from KE, the kinetic energy of the photoelectron coming from an inner-shell with binding energy U (E_x is the X-ray energy).

KE = E_x - U

	Identification of the compound to which the atom belong, from the fine shifts of U with chemical composition.
	Atomic concentration, from the intensity of the photoelectron signal and empirically determined sensitivity factors.
	Depth composition, from the analysis of photoelectron intensity vs. angle of observation.
	Lateral composition or imaging, when using finely focused X-rays or special electron optics.
	Local structure in crystals, through photoelectron diffraction measured by changing the angle of observation.

Equipment

X-Ray source

The X-ray source consists of a hot filament at high voltage (10 - 15 kV) which emits electrons which are accelerated to an anode at ground potential. Inelastic electron-atom collisions in the anode produce an inner-shell ionization, which leads to the emission of either:

- an X-Ray when an electron from a higher level falls into the inner-shell vacancy (core hole)

- an Auger electron when the energy released when the hole is filled by the outer shell electron, is transferred to another electron (the Auger electron).

These emissions have characteristic energies determined fundamentally by U of the core level. The fraction of radiative (X-ray) decays is called the fluorescence yield, and is high for deep inner-shells (U more than a couple of hundred eV).

The atoms of the anode may emit different X-rays from the excitation of different shells. In some cases, the X-ray intensity is concentrated on radiation from a single shell. This is the case for Al and Mg, which give nearly monoenergetic (monochromatic) X-rays with E_x = 1486.6 eV and 1253.6 eV, respectively (DE ~ 1.3 and 1.1 eV). Since the use of two X-ray energies allow the elimination of ambiguities in the analysis, many XPS instruments have dual anodes (Al and Mg) that can be excited separately.

Unfortunately, the core hole can be filled by electrons from different shells. This means that there will be different X-ray energies. Usually there is one main X-ray line, corresponding to the minimum energy of an allowed transition, and weaker satellite lines. For instance, when exciting the K-shell (1s) of Al, the hole can be filled from the L₂ or L₃(2p) sub-shells, leading to K_a1 and K_a2 lines. The energy difference is so small that the lines are not separated. Electrons cannot come from the 2s shell, because a change in angular momentum is required in the quantum transition. The next shell with electrons is the valence band (n=3) that gives rise to the widely separated and weak K_b lines. The main satellite that is important in analysis corresponds to the case where the Al atom is doubly ionized when creating the core hole. These lines are the K_a₃ and K_a4 lines, and their consideration is important when doing XPS. The separation of the main satellites is 9.8 eV for Al and 8.4 eV for Mg, and their intensities relative to the main lines is 6% and 8%, respectively.

An additional complication is that the X-ray source also produces, in addition to the sharp lines, a continuum due to bremsstrahlung.

Why Use an X-Ray Monochromator?

Monochromators are expensive and decrease the X-ray flux, which means less longer measurement times (possibly leading to surface contamination) and less throughput. On the other hands there are many banefits, including:

	Better energy resolution that allows to separate photoelectron lines with close binding energies.
	Improved signal to background ratio by removing background caused by satellites and bremsstrahlung. This allows to obtain useful signals from elements present at small concentrations, or from small analysis areas.
	Minimizes sample damage from heat and unwanted radiation by separating X-ray source from sample.

Electron Spectrometers

Usual electron spectrometers (also called analyzers) are electrostatic, and operate on the principle that the electric field needed to deflect an electron on a define path is proportional to the kinetic energy of the electron. The most common analyzers are the spherical sector analyzer and the cylindrical mirror analyzer.

See analyzers.pdf for drawings.

The electron spectrometers need to be shielded from magnetic field, including that from the Earth. This is typically done by a shield made of high permeability magnetic material (mu-metal).

Calibration of Electron Spectrometers

The binding energy U is most commonly referred to the Fermi level of the sample. To do this from measured kinetic energies one needs to determine f_sp.the work function of the spectrometer (which is where the kinetic energy is measured). A good method uses an electron gun to produce a beam of electrons with well defined energy with respect to the Fermi level of the sample, equal to the acceleration voltage V_f plus an excess thermal energy E_th. The spectrometer is set to collect the electrons scattered elastically from the surface. Any type of electrostatic energy analyzer can be modelled as a retarding energy analyzer using a retarding voltage of V_sp. In a deflection type analyzer, this voltage is replaced by the inter-plate voltage times the analyzer constant plus the mean voltage between plates. The spectrometer is tuned to the elastic peak when the vacuum level of the retarding potential spectrometer is at the most probable energy of electrons from the electron source. The appropriate energy diagram (vertical axis) vs distance (horizontal axis) is shown schematically in the figure.

CALIBRAT.GIF (10959 bytes)

Thermionic electrons are emitted with a most probable energy E_thwith respect to the vacuum level, or f + E_th with respect to the Fermi level of the filament. For a tungsten filament at 2700 K, this energy is 4.8 eV to within about 0.1 eV. Therefore,

f + E_th + eV_f = eV_sp+ f_sp

or f_sp = 4.8 eV + e(V_f - V_sp)

To avoid errors due to a voltage drop in the filament the voltage should be measure to the mid point between the filament terminals, using a voltage divider.

Chemical Shifts in XPS

Reference level

In metals and semiconductors the Fermi level is the practical choice. If atom is inside the solid, shifts in work function due to chemical changes at the surface should not affect the local energies. For comparison of solids to free atoms, the vacuum level is the reference level to where the electron is removed when defining ionization potentials.

When there is an electric field inside the solid (insulators and semiconductors) the energy levels will be shifted because the energy of the bands are bent (energy-distance plot).

In particular, sample charging of insulators as a result of electron emission during X-ray irradiation can be a serious problem. In most cases, this positive charging can be circumvented by flooding the surface with low energy electrons. Self-regulation of a low charge occurs: if too many electrons go to to the surface it will start charging up negative and repel further electrons from arriving. In complex surfaces, differential charging may occur, which is harder to neutralize.

Point-Charge Electrostatic model of energies in solids

Transcribed from P. H. Citrin and T. D. Thomas, J. Chem. Phys. 57, 4446 (1972)

Fadley et al say two major terms contribute to the shift in the binding energy between a core electron in a compound from its value for the free atom:

1) there is a change in binding energy because of removal or addition of outer electrons to the atom. This is approximately equal to qe²/r, where q is the change in charge and r is the average radius from which electrons are removed (or to which they are added). The quantity e²/r ranges from about 10 eV for alkali metals to over 20 eV for carbon. More accurate values have been determined theoretically and, in some cases, experimental values are known.

2) there is a change in electron binding energy when the ion is placed into a crystal. The principal source of this change is the electrostatic interaction between an electron on the ion of interest and the other ions in the crystal, which are treated as point charges. There are additional corrections due to polarizability and compressibility, which we ignore for the moment. The shift in binding energy of an electron on the jth ion in the crystal is given by the expression

e² S^'_iq_i/R_ij, (1.1)

where the prime indicates summation over all the ions except the one of interest. The symbol q_i represents the charge (in units of e) on the ith ion and R_ij is the distance between the ith and jth ions. This expression can be rewritten in terms of the nearest cation-anion separation R, namely,

. (1.2)

The energy arising from this interaction is known as the Madelung energy because of the close connection between the constant F and the Madelung constant a_R. The relationship is

a_R = – S_jq_jF_j /2z², ( 1.3)

where the summation is taken over the ions in the stoichiometric unit and z is the highest common factor of the charges on the various ions in that unit.

Combining the two terms, we have for the binding energy of an electron on an ion in a crystal

E_x^pc = E_FA +qe²/r + Fe²/R. ( 1.4)

where E_x^pc and E_FA refer to the binding energy of an electron in the crystal composed of point charges and in the free atom, respectively. Since the first two terms on the right-hand side represent the binding energy of an electron in a free ion E_FI, we may rewrite this expression as

E_X^PC= E_FI+ Fe²/R. (1.5)

In a few cases E_FI is known from atomic spectroscopy. The third term can be calculated for any crystal geometry. We thus have an opportunity to make a test of this model using only the assumptions that the crystals are ionic, that the ions are point charges, and that we can neglect effects due to polarizability and compressibility.

We should mention that there has been some question about using the bulk value of F in calculating the Madelung energy. The electrons that leave the sample without energy loss originate from sites within less than 50 � of the surface. It has been suggested that the Madelung energy should vary from its bulk value for the transitions inside the crystal to half that value for those occurring at the surface. However, the surface Madelung constant computed in the (100) plane is 96 % of the bulk value for crystals with a sodium chloride structure. In the (110) planes in crystals with sodium chloride and cesium chloride structures, the surface Madelung constant is 86% and 90% respectively, of the bulk value. We are therefore justified in using the bulk Madelung constant (which, for crystals with the sodium or cesium chloride structure, is equal to F) in our calculation of the Madelung energy.

There are several ways to check the validity of Eq. (1.5). First, this expression should give the absolute value of the binding energy for various electrons in the crystal. Because of solid-state effects (discussed below) and because of possible charging of the crystal during the measurements, among other things, there is some question about how to make the comparison between experimental and theoretical values of the electron binding energies. Second, the model predicts that the binding energies of all the different electrons in a particular type of ion should be shifted the same amount (Fe²/R) from their values in the free ion. Third, Eq. (1.5) allows us to calculate energy differences between cation and anion binding energies in the crystal from the free-ion values. These last two tests are fairly reliable because they are free from most of the sources of error inherent in comparing absolute binding energies.

To see how we may use the third test, we let E_x^c(po) and E_x^c(pc) represent the binding energies of some particular electrons in the cation and anion of the crystal composed of point charges, and E_FI^C and E_FI^A represent the energies of the same electrons for the free ion. We then have

E_x^c(po) – E_x^c(pc)= (E_FI^C + F_Cee²/R) – (E_FI^A + F_Aee²/R) =

= (E_FI^C – E_FI^A) + (F_Cee²/R – F_Aee²/R) ( 1.6)

where F_A and F_C are the appropriate constants for the anion and cation, respectively. For a binary compound, the quantity (F_A – F_C) is equal to twice the Madelung constant for the crystal, divided by the charge Z on the most highly charged ion in the compound, and by the number N of such ions per stoichiometric unit: From Eq. (1.3) the Madelung constant a_R= – (N_cZ_cF_c– N_AZ_AF_A)/2z², where Z_c and Z_A are the absolute values of the charge of the cation and anion, respectively, and z is the highest common factor of Z_Cand Z_A. N_cand N_Aare the number of cations and anions per stoichiometric unit. Because of charge neutrality, N_cZ_c= N_AZ_A= N/Z and, therefore, a_R = NZ (F_c–F_A)/2z². Thus

E_x^c(po) – E_x^c(pc)= E_FI^C – E_FI^A– 2 a_R z²e²/NZR. (1.7)

This relationship has been used by Best in the analysis of x-ray spectra from several ionic solids.

Other XPS structure

Besides the main photoelectron peaks at KE=E_x-U, other structure, called shake-up satellites, appear in the electron energy spectrum. They should not be confused with the satellites in the incident X-Ray energy spectrum. Shake-up refers to the effect that the sudden creation of the core hole has on the other electrons in the atom. This shaking-up of the atom can excite plasmons, discrete outer levels, or electrons in the conduction band in metals.

Plasmon satellites appear at KE smaller than the main peak by amounts nE_b + mE_s where n and m are integers and E_b and E_s are the energy of a bulk and a surface plasmon, respectively. Besides the intrinsic plasmons created by the shake-up, the XPS spectra also contain extrinsic plasmons excited by the emitted photoelectron. Since the plasmon energy depends on the composition around the excited atom, the energy loss to plasmon excitation (energy difference to main photoelectron line) carries chemical information. Plasmons are seen clearly in few elements, most notably in Al, Mg, and Si.

In metals, the shake up excites a large number of electrons at the Fermi level. The number of excited electrons diverges near DE=0. The effect (thus called shake-up singularity) manifests in the tail added to the photoelectron peak towards low KE, which produces asymmetric line-shapes. The effect is absent in non-metals.

Quantification

The intensity of a given photoelectron line is proportional to the:

	X-ray flux
	Cross section for exciting the particular level
	n x L: Density of the particular atom in the lattice x the escape depth for electrons of the resulting kinetic energy
	Asymmetry factor in the angular distribution of the photoionization event
	Transmission of the analyzer, which includes the acceptance angle and area, and the efficiency of the electron detector.

in addition, there are several secondary factors, some of which depend on the matrix. There is no enough information on all the parameters to attempt to make an analysis from first principles.

The solution is to use standards to obtain sensitivity factors S_ifor a particular line i, which are proportional to the intensity of line i for pure elements. The proportionality factors are not needed since one can make them relative to the line of a particular element (say Si-2p), and since only ratios of factors are important. Dividing the intensity of the line i by the factor S_ione obtains R_i. Then, the concentration of element x is then obtained from:

C_x = R_i/SR_i

Updated October 17, 2000