Einstein‟s equation for the photoelectric effect was the initial theorem which was subsequently used by other researchers to develop the electron spectroscopy. Kai Siegbahn and his team in the late 1950s developed a high resolution beta-ray spectrometer, where each peak corresponded to a specific electron shell and chemical bonding effects could be derived [282]-[283]. The Electron Spectroscopy for Chemical Analysis subsequently developed by the same team [284], and along with the vacuum chambers advanced at that time it was developed into the X-ray photoelectron spectroscopy (XPS) device as known today.
XPS is used in semiconductor research in order to study chemical composition and bonding states. During the process, the sample‟s surface is irradiated with photons from a soft X-ray source or a synchrotron [285]. Poorly conductive materials readily become charged during XPS, resulting in meaningless results. An ion gun can be used to resolve this issue by neutralising the surface charge.
The equipment used is a FISONS VG Escalab MKII Scientific XPS, with Al Kα radiation as the X-ray source and photon energy of 1486.6 eV. For each sample a full survey scan was recorded over the binding energy (BE) range from 0 to 1286 eV, and then four extra scans were completed over the main core-level elements for Zn, O, Zr and C (the carbon is used for referencing). The step size was 0.1 eV, and the constant pass energy was 50 eV for the full scan and 20 eV for the individual elements scans.
Figure 34: Schematic of the XPS radiation and photoelectron excitation process.
During this process (Figure 34), the photon energy (hv) from the incident X-rays is absorbed by electrons from different inner shells and ionized, resulting in ejecting photoelectrons [286]. All measurements must be carried out in ultra-high vacuum (i.e. 10‒7 Pa) to prevent scattering by air molecules. The X-rays penetrate up to 1μm depth, but the electrons that are ejected from the sample are only coming from atoms closer to the surface (up to 10 nm) because electrons from deeper can‟t escape as they are inelastic scattered.
By assuming no loses in the process, the X-rays‟ photon energy (hv) is equal to the sum of the BE, the work function (Φ) and the kinetic energy (KE) of the ejected photoelectron measured by the detector (Equation 41). The binding energy is the
e
- 2p L 2s 1s K 3d M 3p 3s Conduction Band Vacuum level Fermi level Valence Band X-Rays Photoelectron DetectorThe BE is unique for each element, hence it is used to specify the composition and the atoms chemical bonding. The sample‟s work function, which is the energy up to the vacuum level, is aligned to the spectrometer work function (Φspec) and hence the latter energy is used. The BE can then be estimated by measuring the kinetic energy of the ejected electrons. The data obtained are in the form of peaks corresponding to BE of individual atoms. The peaks originating from each core levels may exhibit double peaks due to spin orbit splitting.
Equation 41
Photoelectrons in the solid may interact with other electrons, resulting in an electronic transition which causes energy loses to the photoelectrons [286]. The loss is known as inelastic scattering and it is shown as background noise. Inelastic scattering is one of the main issues of XPS as it limits the extraction information to only the top surface layer. In more detail, the photons from Al Kα have energy enough to insure accurate results only up to 2 nm deep in the film. However, the minimum path estimated without inelastic scattering is referred by the term inelastic mean free path (IMFP) estimated separately for each element [285]. The calculation of IMFP can be done theoretically with the use of Equation 42 [287], and experimentally with the use of elastic peak electron spectroscopy (EPES). The elastic electron backscattering ratio of intensities is used to calculate IMFP experimentally. The surface roughness has no effect on the IMFP [288].
Equation 42
The IMFP (Equation 42) is therefore related to the kinetic energy (KE) of a specific element. IMFP is converted into nm when is multiplied by the monolayer thickness (αm). To calculate the monolayer thickness in nm Equation 43 [287] is used.
Equation 43
where Aw is the atomic molecular weight, n is the number of atoms in the molecule, NA is Avogadro‟s number, and ρd is the bulk density in kg/m3. For the current ZnO films the value α is estimated as 0.23 nm.
The IMFP calculation is based on the assumption that the electrons signal travel in straight lines and the sample is atomically flat [287],[289]. This leads to a different approach, where the attenuation length (AL) is used instead of the IMFP, and it is relative to the atomic number (Z) of the elements by Equation 44 [289].
Equation 44 { ( ) }
IMFP or AL is used in the quantitative analysis, which can be completed by two methods. The first one is the comparison of each element‟s intensity by including standard sensitivity factors established by bulk materials. However, the method is not considered as the most accurate, due to the difference in contamination between the samples and the reference [290]. The second method is the comparison of intensities by using first principles, in which the photoelectron current is proportional to elements‟ concentration [290]
the use of independent parameters for each element, including IMFP (or AL) and the subshell photoionisation cross-sections established by Scofield (i.e. Scofield factor) [291]
. The atomic percentage could be then estimated by the peaks intensity of each element (I), the IMFP (λn), and by the Scofield factor (S) using Equation 45.
Equation 45
( )
(
) ( ) ( )
The limitation of this approach is that it assumes that the surface is uniform and that the scan is only from the top monolayer [290]. Therefore, the roughness of the surface layer may affect the quantitative results. This was first introduced by Fadley et al. [292]
, who examined the correlation of the photoelectron angular distribution and surface roughness, and found that the surface intensity is reduced by surface roughness, most probably by photoelectron scattering. Hence, this method had limited accuracy for rough surfaces, since photoelectron scattering increases when protrusion areas recapture the photoelectrons injected [288]. The roughness effect at different angle scans was the subject of several studies, where mainly it was specified that at low angles the surface topography affects the detected signal [293]. Therefore, it was suggested that X-ray beams remain perpendicular to the faces of the rough surface, so that the photoelectrons emitted in a relative angle to the X-rays will be less disrupted, providing more accurate results [294].
The photoelectron recapture effect may affect the XPS measurements in this study. Hence, although the dopant may be effectively deposited around the ZnO grains, the XPS may not be able to identify it due to the protrusion areas created by the grains
size and shape. In order to explain this, Figure 35 schematically illustrate how the incident X-rays reaches the surface and how the photoelectrons path is affected by the surface morphology. The image shows that the film with large grains and low surface roughness is causing less obstructing to the photoelectron path compared to the mixture of small and large grains. As the grains became narrower, the restricted photoelectron path is again affected, and thus it is possible to see lower XPS peak intensities. As a result, the morphology differences in the current data do not allow obtaining accurate composition of the films with XPS due to the photoelectron scattering effects.
Figure 35: Schematic of the photoelectron scattering effects for a) low roughness surface, b) high roughness surface, and c) for films with narrow grains. The red arrows indicate the incident X-rays and the green arrows the excited photoelectrons,