Inner shell ionization processes

The PE of energy E_p ejects an inner shell electron from an energy level E_i, leaving a vacancy in an inner shell energy level. The cross-section for this core level ionization process can be calculated using the formula given by Gryzinski (1965):

[7.2]

with G(U_i) a universal function depending only on the overvoltage parameter U_i = E_p/E_i. N_i is the number of electrons in the ionized shell. K shells contribute with two electrons and M₄₅ shells with six electrons. Examples of calculated cross-sections as a function of the PE energy are shown in Fig. 7.3. The two major characteristics of the distributions are:

CEL: plasmons and band transitions

Electrons located in outer energy bands can be excited either as collective density oscillations known as plasmon excitation, or as single electron inter-and intra-band transitions. The result is the creation of CEL having a well-defined energy ΔE generally in the range from a few eV up to about 40 eV. The PE loses this amount of kinetic energy and is scattered by a small angle as required by the conservation of energy and momentum.

Plasmon losses correspond to the eigenmodes of resonance of the electron gas forming the outer electron shell, valence, and conduction bands. The plasmon frequency for a metal with an ideal free electron gas, like aluminum, is given by

[7.3]

with e the electron charge, m the effective mass of the electrons, and n the electron density of the conduction electrons (Raether, 1980; Ferguson, 1989). The excitation of plasmons is not restricted to free electron gas, but also exists for insulators and semiconductors because the plasmon energy, commonly in the range 5–30 eV, is larger than the electron binding or gap energy (Raether, 1980, p15). The plasmon loss energy is ΔE = ω_p and is directly related to the density of state n and, therefore, to the chemical environment of the surface atoms. For instance, CEL of Al and Al₂O₃ are very different with plasmon loss energies of 15 and 23 eV respectively.

Plasmon excitations come in two forms, surface and volume plasmons. The surface plasmon ω_p,s corresponds to electron density fluctuations in the boundary surface and the loss energy is

[7.4]

for a free electron gas model. Plasmon losses are generally observed as multiple losses. The probability for an electron to suffer n plasmon losses depends on the ratio between the path length d traveled and the IMFP λ and is given by the Poisson distribution

[7.5]

as represented in Fig. 7.4. The no-loss probability P₀ decreases very rapidly even for small values of d/λ. For d = λ, P₀ is reduced by about 37% and equals P₁, the first loss peak. Even a layer thickness of 0.5 nm will cause the no-loss peak to decrease to 60% of its value. This is a sensitive method for measuring the thickness of deposits like a gas adsorbed on the surface. The ratio between intensities of multiple plasmon losses can be compared to give an estimate of d/λ. A plasmon excitation can also occur during the ionization-recombination process (intrinsic excitation). An atomic layer adsorbed on the surface will suffer characteristic energy losses even if the escape distance traveled is negligible compared with the IMFP. This process adds to the excitation of extrinsic losses occurring during travel through surface layers.

Band transitions are excitations of outer shell electrons. Ionization occurs when a valence or conduction electron is ejected, resulting in the creation of a vacancy. In contrast to optical absorption, the available momentum of the PE allows for direct and indirect band transitions. Band transition losses often occur in the same energy range as plasmons and overlap. The energy loss distribution is closely related to the optical properties of the surface. The energy loss function is given by the imaginary part of the complex dielectric constant (Raether, 1980, p35) and CEL distributions can be deduced from optical data. The strength of the energy losses is given by their IMFP which is the mean distance traveled by the electron between two CEL. The mean free path for a plasmon excitation is proportional to the electron kinetic energy, except in the low kinetic energy range (< 50 eV) where it increases. The IMFP shown for Si in Fig. 7.2 has a value of about 4 nm at 1800 eV and only 0.6 nm at about 100 eV. This is a large difference in escape depth for Auger or photoelectrons and is a major factor in the calculation of atom densities.

Continuous X-ray emission (bremsstrahlung)

Fast PE elastically scattered by nuclei in the crystal lattice are subject to strong acceleration and can emit X-ray photons of energy ranging up to the PE energy (Reimer, 1985, p158). The probability for this process is small and the process does not contribute significantly to the stopping power, but it generates a significant background continuum of X-rays. This background distribution adds to the characteristic X-ray lines and lowers the signal to noise ratio and the detection limit. The production rate Iv is given by Small et al. (1987)

[7.6]

with e the natural log base, Z the atomic number, and U = E_p/E_i the overvoltage parameter. The constants are M = 1.05 and B = 5.80 in the PE range 5 to 40 kV. The contribution increases almost linearly with Z and the detection of a low-Z element deposited on a high-Z substrate is more difficult than the other way around.

Experimental set-up for CL spectroscopy

The CL set-up was developed for use in electron microscopes and involves the imaging of the beam spot through a large aperture optical collector (Reimer, 1985, p210). CL designs must be modified for in situ applications to accept larger sample size and to increase the clearance required between the sample and the optical system. In practice, only a limited beam aperture is focused onto the detector. In contrast with electron microscope chambers that are extremely dark, growth chambers contain various sources of stray light and in addition the sample may radiate when heated during the growth. Optical filters, adapted to the emitted CL spectral range can filter out the parasite light outside the CL emission range. A more efficient suppression method is the modulation of the PE beam intensity, using beam blanking, and measuring the signal using a lock-in amplifier detection technique (Lee and Myers, 2007).

Application of CL to the measurement of the substrate temperature

GaN having a direct band gap is a good CL emitter and the spectral distribution shows a peak energy corresponding to the band gap energy (Lee and Myers, 2007). The position of the maximum is very temperature sensitive. The peak shifts toward lower energy as the sample temperature increases. The temperature measured by CL represents the actual temperature of the very surface layer and represents a way to calibrate sample temperature between different chambers. Once calibrated, CL is able to detect variations of the surface temperature more precisely than the usual thermocouple measurement. CL provides a way to cross-calibrate temperature measured in different GaN growth chambers.

Experimental set-up for RHEED-XRF in situ monitoring

The angular distribution of characteristic X-rays is basically isotropic (see Fig. 7.1), except in the range of very grazing angle of emission where the refraction effects become dominant. EDS detectors have a large sensitive area and accept radiation over a large solid angle. The acceptance solid angle must be reduced in order to block X-rays emitted from the chamber walls by X-ray fluorescence or BSE impact. A collimator system consisting of successive apertures is inserted between sample and detector. The Si(Li) detector crystal must be cooled in order to reduce the thermal background noise level. Cooling can use liquid nitrogen contained in a Dewar tank or, more simply, stacked Peltier cooling stages. Most detectors are sealed with a Be window in order to keep the crystal free of moisture condensation and contamination. In addition, the foil removes and blocks the light and BSE. Unfortunately, the Be window also acts as a filter absorbing the lower energy part of X-ray photons. The sensitivity of the detector is progressively reduced for photon energies below about 1 keV, cutting off, for instance, the oxygen Kα radiation. The Be foil can be replaced with lower Z materials, such as sapphire and C (in the form of polymer materials), or totally removed by carefully keeping the detector under controlled vacuum conditions. Because low Z window materials do not efficiently block fast BSE, a strong permanent magnetic can be used to dump the electrons before reaching the detector.

An additional requirement is to keep the detector crystal and the window foil free of material deposition. This is very important for quantitative analyses because any deposit will cause a nonlinear, selective absorption of X-rays and will selectively modify the intensities of measured peaks. A solution for materials with a low evaporation temperature is to use a heat control able to keep the foil clean during the process. This technique is used for elimination of the deposition of As during GaAs/AlGaAs by Pellegrino et al. (1998). Another approach is the use of an easily replaceable thin Be foil (Sun et al., 2009). In case the detector head cannot be easily accessed, moving a film like Mylar in front of the detector is another possible approach. Finally, X-ray energy dispersive detectors are not bakeable and must be placed far enough from the chamber wall or mounted on a mechanical retraction to move the detector far enough to stay at ambient temperature.

Quantification of characteristic X-ray line spectra

The signal intensity I_A(x) of an element A is given by general Formula 7.7. The matrix factor is given by the product

[7.11]

of the fluorescence yield ω_i for transition i, the backscattering factor B, the fluorescence factor F, and the attenuation length, corrected for the takeoff angle θ_d. The factor B becomes more significant when both incident and take off angles are small and is calculated by Monte Carlo simulations (CASINO). The standard method for quantitative calculation of atomic concentrations is described by Reimer (1985, p365) and referred to as the ZAF procedure. The method is based on the use of reference spectra from standards and followed by a linear combination of the standards to fit the measured signals. The accuracy of this simple method is much improved by introducing a correction factor for the Z dependence. It is assumed that the concentration is proportional to the ratio between the measured and the standard signal (corresponding to 100% concentration). Then the correction due to matrix effects, the ZAF factor, is introduced, taking into account variations of the BSE backscattering factor for different Z, of the absorption coefficient, and of the fluorescence factors between the actual sample and the standards. EDS-XRF combined with RHEED was used by Pellegrino et al. (1998) for quantitative monitoring of the surface composition of epitaxially grown InGaAs on GaAs. The stability of the signal over a long period of time is very reproducible and the accuracy of the mole fraction of In is < 0.1% after background correction. Quantitative analyses are performed by fitting Gaussian peaks for each element. The full width half maximum (FWHM) of the distribution is known to be the energy resolution of the detector and deconvolution of multiple, overlapping lines is therefore accurate and reliable (Hashimoto et al., 2009).

The surface sensitivity of EDS-XRF was tested by Ino et al. (1980) for the deposition of thin Ag layers on Si(111) surface. The detection limit is very good, less than 1% of a monolayer. The measurement of a high-Z material deposited on low-Z substrate is favorable for obtaining the highest detection limit because the bremsstrahlung background from the substrate is low and the PE backscattering and fluorescence effects are minimized.

Measurement of the critical angle in RHEED-TRAXS

The values for the critical angle are in the milliradian range and afford a high mechanical stability and accuracy of the positioning of the collimator unit. In principle, the take-off angle must be adjusted for each line when working under critical angle conditions. The critical angle for a compound is given by the simplified formula

[7.12]

for an X-ray of wavelength λ and a material of density ρ, mass number M, and atomic number Z. The critical angle depends both on the X-ray line energy and on the composition of the matrix. The angle is larger for lower X-ray energies (longer wavelength), for instance θ_c = 1.77° for Mg Kα (1254 eV) in MgO and only θ_c = 0.33° for Fe Kα (6403 eV) in BaFe₁₂O₁₉ (Sun et al., 2009). Accurate measurements of θ_c are given by Chandril et al. (2009) and Tompkins et al. (2006).

Measurement of layer thickness using attenuation by RHEED-TRAXS and in situ XPS

A different way to determine the thickness of a film during deposition is to measure the attenuation of a signal originating from the substrate. An example is given by Sun et al. (2009) for the deposition of MgO onto SiC. The relative intensity changes were observed under fixed RHEED electron energy (12.5 keV). Monitoring substrate Si Kα intensity decrease with film growth provides a real-time film thickness measurement. The film thickness is calibrated using in situ XPS measurements of the attenuation of the Si 2p3 photoelectron line at different angular incidence (angular resolved XPS).

Measurement of multilayer thickness using TRAXS and X-ray reflectivity

Chandrill et al. (2009) demonstrated that the angular dependence of XRF near the critical angle can be analyzed within the kinematic approach to yield useful structural information not only about a single thin film but also for a multilayered structure. Hence, it is possible to perform in situ quantitative structural characterization without the use of any reference samples. The X-ray reflectivity of a multilayer is measured ex situ using an X-ray beam of the same energy and scanned over the same angular range as the detected waves in TRAXS. This is like reversing the path of the X-ray waves and, according to the reciprocity theorem, the intensity of the X-rays emitted from a depth z inside a medium and observed at a grazing exit angle is proportional to the X-ray intensity, which is impinging at the same grazing incident angle and observed at the depth z inside the medium. Angular intensity profiles measured from multilayers of single layers of Mn and Y as well as bilayers containing Y on Mn and Mn on Y allow the determination of the layered structure and of the smoothness of the interface surfaces.

Experimental set-up for REELS analyses

A modified TEM (transmission electron microscope) energy filter for energy losses spectroscopy is used in reflection mode by Nikzad et al. (1992). A small pencil of diffracted or diffused beam is selected and enters the analyzer. The beam is energy filtered by a stigmatic imaging magnetic sector followed by a set of magnifying projection lenses. The focal plane contains a range of energies which are collected simultaneously. Another analyzer for REELS is a device that combines energy filtering and imaging. The full diffraction diagram is accepted and, by means of a set of electron lenses, is energy filtered and projected onto a fluorescent screen similar to the usual RHEED screen (Staib et al., 1999). The angular distribution is preserved and RHEED diagrams are energy filtered as shown in Fig. 7.8. The filtering progressively removes the inelastic BSE part and, at the cut off energy E_p, only the elastic diffracted spots remain and energy losses are filtered out. REELS distributions are achieved by measuring the intensity of a selected area of the diffraction diagram and lowering the energy filter voltage from above the elastic peak down to a few 100 eV loss energy. The signal is measured using a lock-in detection technique in order to improve the signal to noise ratio.

Examples of in situ REELS distributions

The surface sensitivity of REELS is demonstrated by Nikzad et al. (1992) for the deposition of Ge onto Si. The growth of the Ge L₂₃ ionization edge is recorded at a PE energy of 30 keV. A 0.15 nm deposited layer is clearly detected after normalization of the spectra. Weaker structures can be detected after differentiation of the signal. A more detailed discussion of REELS in MBE is given by Wang (1996, p334).

Figure 7.9 shows the REELS distribution of SrTiO₃ recorded at E_p = 14.5 kV measured using the imaging energy filter described by Staib et al. (1999). The energy loss distribution includes the elastic peak and multiple CEL features. The losses are strongly apparent without background subtraction. The electron binding energy levels, available from Sevier (1972) and updated by Williams (2006), are used to identify the loss structures. The structures (6) correspond to Ti 3s (58.7 eV), (4) to Ti 3p1/2 3p3/2 (32.6 eV), (3) to Sr 4p1/2 (21.6 eV) and Sr 4p3/2 (20.1 eV). Loss energy (5) corresponds to O 2s (41.6 eV) but is shifted to about 47 eV as a result of a chemical shift.

Use of RHEED-REELS for monitoring the surface growth and roughness

The ratio between surface and volume plasmon is used to characterize, in situ during growth, the surface roughness of a deposited Al film on sapphire (Strawbridge et al., 2006). The layer thickness was calibrated ex situ by Rutherford backscattering (RBS) and the surface roughness was measured by atomic force microscopy (AFM). The change of the energy loss distribution from the bare sapphire substrate to deposited Al layer is very sensitive to the Al atomic concentration. For thin layer deposits, only the surface plasmon is observed. For larger deposits in the range 3–14 nm, two behaviors are found; either the surface plasmon remains dominant correlating to a smooth surface deposit, or the volume plasmon dominate witnessing a rougher surface as confirmed by AFM scanning images. It is worth noticing that RHEELS data can be acquired in spite of the fact that sapphire is an excellent insulator. RHEELS is far less sensitive to charging effects than other analysis methods because the gain or loss in kinetic energy of the PE due to the surface charges compensates after backscattering. The PE enters and leaves the surface within a nanometer scale offset and the surface potential is homogeneous over this range. The same holds for the characteristic energy and ionization losses.

Monitoring the ionization loss for quantitative analyses

Quantitative analyses can be performed using the technique developed for transmission EELS as described by Leapman (1992). The intensity of the EEL structures is measured after background subtraction using a simple power law formula. The signal is then integrated over an energy width that includes the CEL region. A similar calculation can be used for reflection EELS, but an additional correcting factor is needed to account for backscattering effects (which are not present in transmission). The extraction of structures near the elastic peak, where ionization losses are superimposed on multiple CEL losses, requires a Gaussian background fitting.

Experimental set-up for RHEED-AES

For in situ operation, the energy analyzer must fulfill the specific requirements listed previously. These constraints rule out the classical spectrometer designs in favor of specially designed systems consisting of an electron optical lens system collecting the Auger electrons in front of the sample followed by an energy filter located further away from the sample, possibly behind the chamber wall. The angular position of the analyzer with respect to the surface is important. The analyzer should not be mounted at grazing take-off angle because the angular distribution of Auger electrons roughly follows Lambert’s law of a cosine distribution. The maximum peak intensity is normal to the sample surface; see Fig. 7.1. In contrast, the BSE peak toward the direction of specular reflection. Thus, an Auger analyzer mounted with its axis normal to the sample will collect most of the Auger electrons, less BSE, and thus have the best sensitivity. The normal position has the advantage of not being sensitive to crystalline channeling effects affecting the angular distribution of Auger electrons, especially marked for low energy lines. The azimuthal rotation of the sample during acquisition is then possible. An additional electron gun, positioned far from grazing incidence angle (about 45°) and able to work over a wide energy range, is useful for calibration purpose in quantitative analyses and for measuring REELS distributions in a lower beam energy range.

In situ monitoring of oxygen during ZnO oxide growth on GaN substrates

ZnO is grown on top of a GaN substrate using a radio frequency (RF) plasma source for oxygen deposition. The growth process can be followed in real time using a fast Auger probe analyzer mounted at normal incidence angle using the experimental set-up given by Staib (2011). The Auger electron lines of Ga LMM (1066 eV), oxygen O KLL (503 eV) and Zn LMM (990 eV) are monitored. The growth rate is about 10 ML/min and at an acquisition speed of 6 V/s, the measuring time for an Auger line is 3–10 s. The Ga signal abruptly vanishes and the Zn signal grows rapidly when the Zn shutter opens; see Fig. 7.11(a). The oxygen line is present on the surface, provided by the residual gas pressure in the chamber. The oxygen K LVV line grows further on opening the oxygen source shutter (see Fig. 7.11b), and reaches a stable value. The normalized intensity ratio of O KLL to Zn LMM is a measure of the ratio of atomic concentrations.

In situ monitoring of growth of MgO and of Cr_x Mo_(1–x) on MgO substates

Chambers et al., (1996) used RHEED combined with AES and in situ XPS to study the homoepitaxy growth of MgO on Mg0(001) substrates. The sample temperature is kept at 750 °C during deposition and oxygen is provided by an electron cyclotron resonance (ECR) plasma source. The Auger lines of Mg KLL and O KLL are converted into atomic densities by cross-calibration using in situ XPS intensities of the Mg 2p and O 1s photoelectron lines. The atomic percentages of Mg and O remain constant at 50 ± 2% during the growth. Heteroepitaxy of Cr, Mo alloy films on MgO can have a wide range of composition controlled by the atom fluxes. The composition of the films is measured during growth by monitoring the intensity of the Cr LMM and Mo MNN Auger lines. The calibration is performed by measuring the signal of the pure elements Cr and Mo substrate and a linear interpolation (ratio method) is used to quickly determine the film composition. The results are in good agreement with in situ XPS calibrations.

In situ growth control of lanthanide alloys

The Auger probe was used by Calley et al., (2011) to monitor the co-deposition of Fe, Dy and Tb on silicon substrates using the Auger spectrometer described by Staib (2011). The Auger spectra were measured at a primary beam energy of 10 kV and a beam current in the range of 3–10 μA. The intensities of the Dy and Tb MNN Auger peaks were much weaker than for the Fe lines because the Auger yield issued from the M shell ionization was distributed into a more complex multiplet structure extending over a wider energy range. The detection sensitivity was increased by using a lower energy resolution ΔE = 20 eV. The MNN lines shown in Fig. 7.12 correspond to pure Tb (100%) and pure Dy (100%). The quantification of the signals into atomic concentrations is possible using the peak heights, the area under the peaks, or the derivative signals and measuring the peak to peak amplitudes. These techniques are complicated in this example by the fact that the two Auger lines strongly overlap. The measured energy of an alloy Tb(70) Dy(30) is also shown. It shows that in spite of the overlap, there are energy regions marked by the lines a and b where the distributions vary markedly between the pure element. It is then possible to characterize a specific alloy composition calibrating the signals in this energy range as shown by Calley et al. (2011). A precision better than 2% for the atomic ratios could be demonstrated.

Chemical information from the Auger line shape and energy position

Auger lines provide multiple information about the composition and chemical state of the surface layer. All elements, except H, can be directly identified by their line energy and the concentration of elements can be deduced from the signal strength after calibration. In contrast with X-ray emission lines, the line shape and energy position can provide chemical information about the surface atoms.

The shape of the Auger lines provides useful information about the chemical environment and in-depth distribution of the elements as described by Ramaker (2003). The shape of the peak reflects the details of the transitions between core and valence-type band which depend on the density of states. In addition, the satellite structure of the Auger lines reflects the distribution of CEL that varies with the chemical environment of the atoms. The probability for the occurrence of a CEL depends on the position of the atom with respect to the surface. The line shape of atoms from deeper atomic layers show strong, multiple CEL structures, more visible in the N(E) mode than the dN(E)/dE mode. Auger peak energies are, in many cases, sensitive to the chemical bounding of the surface atoms. Chemical shifts, which are directly related to the changes in binding energy of core electron levels, are more common in XPS. Energy variations of an Auger peak are the result of transitions involving three energy levels which are all shifted by chemical bonding. In addition, the final state is a double ionized atom followed by a relaxation process as described by Grant (2003). The resulting shift is more complex than for XPS and some chemical bonding may not lead to noticeable energy shifts when all involved atomic levels are shifted by the same amount. However, a large number of chemical species result in changes in peak position and shape. The change in the energy of an Auger line was first accurately measured in XPS spectra. The chemical effects are measured using the energy difference between the Auger line and the photoemission line of the same element. The difference is constant if both lines shift with the same amount, but it will change if the Auger line shifts differently. The relation between the chemical shifts of the Auger and XPS peaks was described by Wagner (1972), introducing the notion of Auger parameters. A detailed description of the processes involved was given by Moretti (2003). A useful set of experimental data may be found in older AES reference books, such as from Wagner et al. (1979) and Moulder et al. (1992). The in situ during growth measurement of the Auger has a unique capability to show variations of chemical bonds of elements on the surface. An example of such behavior is given by Staib (2011) where the oxygen Auger peak shows a shoulder that corresponds to adsorbed oxygen on the surface and not incorporated into the oxide matrix.

The measurement of energy shifts can be complicated by the fact that the surface potential may vary as a result of charging up when the surface has a poor electrical conductivity. The energy position of the peak can be shifted by large amounts and, in a worst case, the signal becomes very unstable, making the measurement impossible. For moderate charging effects, the peaks will all be shifted by the same amount. The energy difference between peaks can then be used to measure the relative energy shifts between different Auger lines.

Control of the surface purity during the deposition process

Control of the surface purity during the deposition process is the most common application of AES, an obvious application for monitoring the atomic purity of the deposited layer. The surface composition can be monitored during the growth process. Although the vacuum chamber and deposition sources are most carefully prepared, experience shows that unexpected materials can be deposited on the surface. Figure 7.13 shows the sudden appearance of a phosphorus line when starting a deposition source. The P impurity is soon buried during growth, but the electrical properties of the deposited layer are likely strongly modified. Similar observations have been made on carbon, oxygen and chlorine. The systematic use of AES during growth is a convenient way to guarantee the chemical integrity of the material. This monitoring may become an important tool in performing purity control in real time throughout the deposition process.