Examensarbete C i fysik, 15 hp
Institutionen för fysik och astronomi
Avdelningen för molekyl- och kondenserade materiens fysik
Datum
2019-12-13, Version 3.0
Utgivningsdatum
författare
Henrik Hansson Title (English)
Understanding interfaces in thin-film solar cells using photo electron spectroscopy.
Effect of post-deposition treatment on composition of the solar cell absorber.
Titel (Svenska) Nyckelord
solar cell, P-N junction, CIGS, PES, cross section Handläggare
Konstantin Simonov, Department of Physics and Astronomy, Uppsala University Examinator
Matthias Weiszflog, Department of Physics and Astronomy, Uppsala University Språk
English
Security
Abstract
The increasing demand of renewable energy is the big driving force for the research and development of more efficient solar energy conversion solutions. Solar cells, which use the
photovoltaic effect to convert the photon energy to electrical current, are an important solar energy conversion technique. One solar cell technology is thin-film solar cells. Thin-film solar cells use an absorption layer with a direct band gap. A direct band gap has the advantage that the photons will penetrate less deep until a photoexcitation occur compared to semiconductors with an indirect band gap (e.g. silicon). For this reason the thin-film solar cells can be made very thin.
CIGS is a common thin-film solar cell absorber material containing copper (Cu), indium (In), gallium (Ga) and selenium (Se). One objective of this work has been to determine element concentrations of CIGS absorption layers from sample measurements. The GGI ratio determines the band gap, which is an important factor for optimising the efficiency of the solar cell.1 The copper vacancy is the main acceptor dopant in CIGS. The Cu concentration has shown to be important for the efficiency and for other properties of the absorber [2].
The measuring technique used in this work has been photoelectron spectroscopy (PES). PES produces a spectrum showing distinct peaks corresponding to electron binding energy levels for specific element subshells. Measurements with different photon energies have been performed on samples with and without post deposition treatment (PDT). A great deal of the effort has been to calculate relative element concentrations based on the PES peak intensities. Two important parameters when performing the calculations are the photoionization cross section (including the angular dependence of the cross section) and the inelastic mean free path of the photoelectrons.
The results show that the GGI and the corresponding band gap will be almost the same with and without PDT except for close to the surface where PDT lowers the GGI.
The calculations showed that the copper concentration is lowest at the surface. Moreover, PDT with RbF results in lower copper concentration closer to the junction.
The results show a discrepancy of the GGI and CGI ratios when using the angular dependent cross sections in [10] and [11] compared to using the cross sections in [6] and [7].
Sammanfattning
Det ökande behovet av förnybar energi gör att forskning och utveckling av solenergilösningar är av största vikt. Solceller, vilka utnyttjar den fotovoltaiska effekten, är den vanligaste tekniken för omvandling av solenergi till elektricitet. Tunnfilmssolceller är en typ av solceller vars absorbent har ett direkt bandgap, till skillnad från kisel som har ett indirekt bandgap. Fördelen med ett direkt bandgap är att det ljusabsorberande materialet kan göras mycket tunt.
En vanlig tunnfilmssolcell är CIGS. Det är en komposit bestående av koppar (Cu), indium (In), gallium (Ga) och selen (Se). Ett syfte med detta självständiga arbete har varit att beräkna koncentrationerna
1 Higher band gap gives higher transmission losses and lower band gap gives higher thermalisation losses. Opti- mal band gap is achieved when minimising the sum of the thermalisation losses and the transmission losses.
av de ingående ämnena i halvledarskiktet av CIGS. GGI-kvoten
bestämmer bandgapet, vilket är en viktig faktor för solcellens verkningsgrad. Kopparvakansen är den huvudsakliga
halvledaracceptorn i CIGS. Kopparkoncentrationen har visat sig vara viktig för bl.a. solcellens verkningsgrad [2].
Mättekniken som används i detta arbete kallas fotoelektronspektroskopi (PES). PES-mätningar ger ett spektrum där spektrallinjerna representerar olika nivåer av elektroners bindningsenergi för olika grundämnen. Mätningar med olika fotonenergier, på prover med och utan ytbehandling (PDT), har utförts. En stor del av arbetet har varit att beräkna relativa koncentrationer av de olika grundämnena från spektrallinjerna i spektrumet. Viktiga parametrar som man behöver ta hänsyn till i uträkningarna är sannolikheten för en fotoemissionsprocess hos fotonerna, vinkelberoendet och den fria
medelväglängden hos fotoelektronerna.
Resultaten visar att GGI-kvot och bandgap blir nästan detsamma med eller utan PDT, förutom närmast ytan där PDT minskar GGI-kvoten.
Resultaten visar också att kopparkoncentrationen är lägst på ytan och att PDT med RbF minskar kopparkoncentrationen närmast ytan.
Resultaten visar att det blir skillnader mellan GGI- och CGI-kvoterna beroende på om beräkningarna baserats på vinkelberoende träffytor enligt [10] och [11] eller baserats på träffytor enligt [6] och [7].
T
ABLE OFC
ONTENTS1 Introduction ... 1
1.1 Background ... 1
1.2 Purpose ... 1
2 Theoretical basics ... 2
2.1 Quantum theory ... 2
2.2 Electronic structure of solids and light absorption ... 2
2.3 P-N junction ... 3
2.4 CIGS solar cells ... 5
2.5 Photoelectron Spectroscopy ... 8
3 Experimental ... 11
3.1 The samples ... 11
3.2 X-ray source and hemispherical spectrometer ... 11
3.3 Synchrotron and GALAXIES beamline ... 12
3.4 XPS setup ... 13
3.5 Peak fitting ... 14
3.6 Analysis of spectrum ... 14
4 Results ... 18
4.1 Results of XPS measurements with PHI Quantera II ... 18
4.2 Results of XPS measurements with HAXPES GALAXIES ... 21
4.3 Results summary ... 24
5 Discussions ... 28
6 Conclusions ... 30
References ... 31
1 Introduction 1.1 Background
Replacing fossil fuel energy with renewable energy is of paramount importance. One of the most important physical processes for renewable energy is the photovoltaic effect (PV).2 Absorber materials are used to absorb the light. By the PV-effect the photon energy is transferred to the electrons. This energy will excite the electrons from the valence band to the conduction band resulting in the formation of electron-hole pairs, which are free charge carriers. The charge carriers of opposite charge are separated in a PN-junction.
Extensive research is being done on different types of absorber materials. The driving force is to increase the efficiency and lowering the production cost of solar cells. Thin-films are the second generation absorber for solar cells. CIGS (Copper indium gallium (di)selenide) is the most used thin- films today. A lot of research on CIGS is currently ongoing.
Photoelectron Spectroscopy (PES) is one of the most accurate methods for measuring e.g. electron energy levels in atoms and molecules. This is essential for the determination of the structure and properties of the absorber material interfaces.
1.2 Purpose
The work aims to:
Demonstrate an understanding of the physical processes governing the power conversion in solar cell devices and CIGS-based thin-film solar cells in particular. The focus will be on the processes taking place at the absorber material interfaces.
Show how photoelectron spectroscopy can be used to study interfaces in thin-film solar cells.
Obtain and analyse PES data for CIGS absorbers with and without PDT (Post Deposition Treatment).
Analyse the effect of inelastic mean free path (IMFP) and photoionization cross section on the PES spectrum.
Calculate the relative concentration of CIGS elements (GGI and CGI ratios).
Give physical explanations to the measurement results.
2 In the end of 2018, PV contributed to 2.6% of the total electricity demand in the world [18].
2 Theoretical basics 2.1 Quantum theory
The earth receives about ~1361 W/ of solar energy (just outside the atmosphere) from the sun through electromagnetic radiation [19]. The radiation can be described as either a wave or a particle (photon) (the wave-particle duality) [1]. The spectrum received by the earth consists of wavelength between 0.15 and 4 μm. Einstein discovered that the radiated energy is quantized [1]. Each quanta (photon) has the energy of ΔE = hf (h = Planck’s constant and f = frequency). With this discovery Einstein could explain the physics behind the photoelectric effect. The photoelectric effect is the emission of a particle (e.g. electron) caused by the transfer of energy from radiation (photon).
Niels Bohr discovered that the electron that orbits around a simple hydrogen nucleus only can occupy distinct (quantized) stationary states [1]. Scientists after him made discoveries that extended the simple hydrogen model to explain the states for more complex atoms, molecules and condensed matter.
The electron states are described by quantum numbers. For atoms, the most important quantum numbers defining the electron states are the principal quantum number (n), the angular quantum number (ℓ), the magnetic quantum number (mℓ), the secondary spin quantum number (ms) and the spin quantum number (s=±½). These quantum numbers describe the properties of the electron and in a single electron picture the state is often referred to as an orbital. Linked to quantum numbers describing the orbital is also the total angular momentum number described as j = ℓ + s.
Each orbital (electron) can have spin up or down which doubles the degeneracy. The formula for degeneracy of quantum numbers (n, ) is ℓ . For the 2p subshell (n = 2, =1) the degeneracy is . For 3d (n= 3, =2) the degeneracy is . The s subshell ( =0) only has one spin up orbital and one spin down orbital.
The quantum mechanics and the quantum numbers define the electronic structure of all the atoms in the periodic table. Every atom in the periodic table has shells and subshells that are defined by the quantum numbers.
Electron excitation occurs when an electron from a shell (or subshell) with lower energy excites to a shell (or subshell) with higher energy and occupies a free position in that shell (or subshell). The required energy for excitation is the difference in energy levels (energy gap) between the two shells.
The opposite to excitation is sometimes referred to as relaxation. Then the electron occupies a shell with lower energy and energy is released.
2.2 Electronic structure of solids and light absorption
When two atoms are brought together their wavefunctions will overlap and the outermost energy level (quantum state) for each atom will split into two different energy levels (quantum states). In solids where the number of atoms is the number of split levels will be very large. One can regard the solid as having a continuous band of electronic energy levels [1].
For a stable material (e.g. at zero Kelvin) the outermost states electrons occupied is called the valence band. The structure of this band is the most important describing the properties of the material. For semiconductor materials outside of the valence band is the conduction band. When
electrons excite from the valence band to the conduction band the electrons will move freely (e.g.
diffuse or move in a direction of an electrical field). The difference in energy between the lowest energy state for a higher energy band (i.e. the conduction band) and the highest energy state for a lower energy band (i.e. the valence band) is called the band gap. Depending on the material the band gap will differ. Insulators have large band gaps 10 eV and semiconductors band gaps in the order of 1 eV. For metals there is no band gap as the valence band overlap with the conduction band.
The fact that matter is quantized at the atomic level plays a fundamental role in solid state physics.
When the photovoltaic effect shall be used for solar energy conversion it is important to match the photon energy quanta with the band gap. The materials which have the most suitable band gaps for the photovoltaic effect are the semiconductors, e.g. silicon with a band gap of = 1.1 eV. The band gap of semiconductors corresponds to wavelengths where the solar spectrum has a high intensity.
Photons with energies close to the band gap will have lower probability to be absorbed than photons with higher energies. The reason is that it is only the electrons at the edge of the valence band that can be absorbed when the photon energies are very close to the band gap. With increasing photon energy the number of energy states in the valence band for which photoexcitation are possible increases.
The energy states from single atoms splits when the atoms are formed in matter. All the interactions between the atoms results in a very large number of discrete energy levels. It can be described as a near-continuous band of energy levels. Still it exist a forbidden energy gap where no energy states are allowed. The Fermi level is an important thermodynamic concept for understanding solid-state physical properties. The energy level that has the probability of 50% to be occupied by an electron is called the Fermi level [2]. For intrinsic (no doping) semiconductors the Fermi level usually lies in the middle of the band gap, between the conduction band and the valence band. The energy difference between the conduction band and the Fermi level correlates to the density of charge carriers in the conduction (electrons) and valence (holes) bands. For an intrinsic semiconductor in room
temperature the density of charge carriers in the conduction band is quite low (> times less than for metals). For an N-doped semiconductor the Fermi level will be closer to the conduction band and the density of electrons in the conduction band is higher.
2.3 P-N junction
An important property of solar cells is its ability to avoid early electron-hole recombinations.
Recombination is when a conduction band electron occupies the hole created by the
photoexcitation. The solar cell shall be able to direct the excited electrons to the front contact and the holes to the back contacts (or vice versa). To accomplish this goal a P-N junction is used [2]. A P-N junction is created by contacting two semiconductor materials with different type of doping. Doping is a process that for example can be accomplished by mixing the semiconductor material with an element that has one electron more (N-doped) or one electron less (P-doped) in the valence band compared to the semiconductor itself. This means that the bonds at the N-side will have one electron extra and the bonds in the P-side will lack one electron (a hole). The almost free electrons at the N- side will diffuse and combine with the holes in the P-side (and vice versa for the holes). The result will be a negative charge accumulation at the P-side close to the junction and a positive charge
accumulation at the N-side close to the junction. This region becomes almost completely depleted of free carriers and is therefore called the depletion region. The result will be an electric field (built in
potential) that counteracts and balances the charge carrier separation caused by the diffusion of electrons and holes. See Figure 1 for the P-N junction.
Figure 1: P-N junction. Source: Wikipedia, article on the P-N junction.
To be able to explain the large scale distribution of electrons in energy states, statistical methods have to be used. The electrons belong to a group of particles called fermions [1]. Fermions have the property that only one particle can occupy a given quantum state (Pauli exclusion principle). Enrico Fermi discovered the Fermi-Dirac distribution which applies for fermions.
is the Fermi energy and the Boltzmann constant.
In thermal equilibrium and when there are no external processes there exists only one Fermi level.
However, outside of the equilibrium conditions, when electron-hole pairs are created as a result of photo absorption the physical conditions will be different. Two different processes will be in pace, the interband and the intraband processes. The interband process is the process when an electron from an occupied state in the valence band occupies an unoccupied state in the conduction band.
The intraband process is an electron-phonon3 (thermalization) process within the band. The intraband transition time is ~ 1000 times faster than the interband transition time [3]. The fast intraband processes create local equilibrium in each of the bands. To be able to describe the steady state distribution two different Fermi functions are used and they are called the quasi Fermi levels.
3 The lattice vibrations (or sonic waves) in solids have a quantized energy. The quantized lattice vibrations are called phonons [1].
One quasi Fermi level describes the distribution of holes in the valence band and one quasi Fermi level describes the electrons in the conduction band.
When photons are absorbed in the P-side of the junction, electrons in the valence band will excite to the conduction band. The electric field in the depletion region will cause the electrons (minority carriers) to migrate to the N-side of the junction. To be an efficient cell the charge separation shall dominate over the process of (early) recombination in the P-side region. The N-side is connected to a front contact and the P-side to a back contact (or vice versa). The potential difference and the current between the back and front contacts will depend on the impedance of the load. Maximum power is achieved when the product of U * I is maximized.
2.4 CIGS solar cells
2.4.1 Background
Crystalline silicon is the dominant material in solar cells. Silicon has several beneficial properties and one reason for its (relative) success is that more and more refined and efficient production processes have developed over the years [2]. However, silicon may not be the best choice for all solar cell applications. The silicon layer is required to be relatively thick (typically hundreds of µm) to be able to absorb a significant part of the sunlight. Silicon is also fragile and requires bulky and heavy glass- encapsulated solar panels.
The band gap is one of the main properties of a semiconductor. When a photon is absorbed in a semiconductor an electron excites from the valence band to the conduction band. For any transition to take place, both energy conservation and conservation of momentum have to be satisfied. For a direct band gap semiconductor where conduction band minimum and valance band maximum occurs at the same value of momentum, only a photon is needed to cause the transition. In the case of an indirect band gap semiconductor, a phonon (a quantum of the lattice vibration) is needed to
conserve the momentum. The involvement of the phonon makes the photoabsorption process much less likely to occur in a given span of time. The photons will therefore (statistically) penetrate more deeply before the excitation occurs in indirect band gap materials. Silicon is the most common example of an indirect band gap material.
Among this and other reasons a lot of research has been done with other types of solar cells. One important category is thin-film solar cells. A thin-film solar cell is composed of a micron-thick photon- absorbing material [2]. Already in the 1970s the first thin-film solar cells was introduced. A lot of research has been done to find the most promising combination of materials for the different layers.
2.4.2 Homo- and heterojunctions
P-N junctions can be divided in homo- and heterojunctions. In a homojunction both sides of the junction consists of the same material. Crystalline silicon, N-doped in one side and P-doped in the other side of the junction, is a typical example of a homojunction. For a heterojunction the two sides of the junction consist of different materials. There is a smooth transition between the energy bands on the interface in homojunctions. This is not often the case for heterojunctions. The two materials (often) have different band gaps but also different electron affinities and work functions. This often results in a discontinuity at the interface of the heterojunction. The difference in electron affinities
(which represent the energetic distance of the conduction band edge to the absolute vacuum level4) defines the magnitude of the discontinuity in the conduction band edge.
2.4.3 CIGS - general
For this work a common thin-film PV material has been chosen to be the solar cell absorber of study.
Its name is , abbreviated as CIGS [2]. CIGS is a compound semiconductor material composed of copper, indium, gallium, and selenium. The material is a solid solution of copper indium selenide and copper gallium selenide. It is a tetrahedrally bonded semiconductor, with the
chalcopyrite crystal structure [2].
CIGS has a band gap that can be controlled by adjusting the [Ga]/[Ga+In] ratio [2]. The value can be changed from around 1 eV for pure to around 1.65 eV for pure . This allows tuning the band gap to the optimal value. CIGS has a direct band gap which, as mentioned above, results in a high absorption coefficient. A layer thickness of 2 μm or less is sufficient to absorb almost all incident light of energy, equal or higher than the band gap.
In contrast to silicon when doping is usually an intentional process, CIGS layers are often naturally p- doped due to intrinsic defects. The main acceptor dopant is the copper vacancy, that can be found in most CIGS layers in concentrations of - [2]. The Cu concentration has shown to be important for the efficiency and for other properties of the absorber [2].
CIGS solar cells with efficiencies above 20% have been claimed by various research institutes [2].
2.4.4 CIGS band gap
CIGS solar cells utilize multi-layer heterojunctions, with p-type CIGS as the absorber layer [2]. A schematic band diagram for CIGS devices is presented in Figure 2. The local charge separation creates an electric field which is visualized as band bending in Figure 2. The dashed line is the Fermi level.
Photons with less energy than 2.42 eV will pass the ZnO- and CdS-layer to the absorption layer. In the absorption layer the photons with larger energy than the band gap will cause formation of electron- hole pairs. The photoelectrons drift to a lower potential energy (left in Figure 2) and the holes drift upwards to the right in Figure 2. This prevents early recombination so that the majority of the photoelectrons will drift to the front contact and the holes to the back contact.
An important property is the electron affinity which is the energy required to move an electron from the vacuum level to the bottom of the conduction band. The difference in electron affinity of the absorber layer and the buffer layer (see below) has an important role for band alignment and shaping the discontinuity of energy band at the buffer/absorber interface. The discontinuity of conduction band at the interface can be positive (spike) or negative (cliff). When using a CdS buffer, the conduction band discontinuity between the buffer and the absorber goes from a large spike for a CIS/CdS interface (gallium free absorber layer) to a large cliff for a CGS/CdS interface (indium free absorber layer). As large spikes have current blocking properties and cliffs tend to increase interface recombination, both effects should be avoided or minimized for solar cell applications.
4 The energy where an electron is at rest directly outside a material is called the vacuum level [4].
Figure 2: Schematic band diagram for a CIGS device. The CdS/CIGS interface has a cliff.
2.4.5 CIGS structure
The main layers for the most common device structure of CIGS solar cells are shown in Figure 3.
Soda-lime glass (SLG) of about of 1–3 mm thickness is commonly used as a substrate [2].
A molybdenum (Mo) metal layer with a thickness of around 0.5 µm is deposited (commonly by sputtering) on top of the SLG substrate. The Mo-layer acts as the back contact.
Above the Mo-layer we have the CIGS absorber layer. As described above CIGS has a variable band gap, which can be controlled by the [Ga]/[Ga+In] ratio. Most devices are produced by co-evaporation deposition. The result of this process is polycrystalline films, with a thickness of about 1.5-2.5 µm.
Above the absorber layer (at the n-side of the heterojunction) a cadmium sulphide (CdS) buffer layer is deposited. The role of the layer is to protect the absorption layer from the sputtering process of the layers above [2].
The top layer of most CIGS devices has very high conductivity as its role is to transport the current to the front contact. It also acts as a window. A commonly used material for this layer is aluminum- doped ZnO.
Energy (eV)
-2 -1 0 1
°
CdS ZnO
CIGS
photon
•
°
•
diffusion drift
Energy band diagram for a CIGS solar cell
0.15 0.05
Position (µm)
Figure 3: CIGS solar cell structure with main layers and typical thicknesses.
2.5 Photoelectron Spectroscopy
2.5.1 Techniques used to study the nanostructure of solar cells
There is a vast research around the world finding more efficient solar cells. Understanding of the structural and electronic properties of the absorption layer and interfaces are important for the development of efficient solar cells. Different techniques can be used to study different physical aspects of the molecule structure of an absorber. Some of these techniques are Scanning Tunnelling Microscope (STM) [21], Time-Resolved Laser Spectroscopy (TRLS) [20], Raman spectroscopy [22] and Photo Electron Spectroscopy (PES) [5].
For this work PES has been used as the technique to study samples of absorber materials. PES has several advantages. For this work the main reason for using PES is its excellent chemical sensitivity and ability to perform non-destructive studies of electronic properties of the interfaces. Two different type of instruments have been used, the SOLEIL synchrotron in Paris and a hemispherical spectrometer at the Ångström laboratories.
2.5.2 PES general
PES is an experimental technique used to study the electronic structure of material. For example, it provides information about quantitative composition of the sample. It can also give information about the character of atomic bonding, molecule geometry and layers thickness.
The basic principle of PES is that an electromagnetic beam is irradiated on the material under study.
The irradiated photons can be more or less energetic. From UV light with photon energies of a few eV to high energetic X-rays with photon energies above e.g. 6000 eV.
The photon will penetrate into the material and the photoelectric effect will liberate an electron that will escape out of the material. The electrons will be collected in a way such that the kinetic energy can be measured. A typical plot of the spectrum will have peaks at specific energies. These peaks
ZnO (0.5 µm)
CIGS (1.5-2.5 µm) CdS (0.05 µm)
Mo (~0.5 µm)
Glass substrate (1-3 mm)
correspond to specific binding energies of the electrons. Lower binding energies (high kinetic energies of the photoelectrons) correspond to electrons from an outer electronic shell (e.g. the valence band). Higher binding energies correspond to electrons from the core levels. The relation can be expressed as [4]:
where Ф is the work function5 of the material and and are the kinetic and binding energies of the photoelectron. is defined as being zero at the Fermi level. As and Ф are known, can be calculated from the measured .
The intensity of the peaks in the spectrum can give quantitative information (e.g. relative
concentrations of elements in a compound) while the positions of the peaks can give information of the chemical states of the material.
2.5.3 Using PES for studying solar cell materials
PES can be used for studying solar cell materials. Some typical properties that are important for solar cell materials and that can be studied by PES are [5]:
Measuring electron binding energies and work functions. This can be used to determine the position of the quasi Fermi levels. The energy difference of the quasi Fermi levels determines the band alignment at the P-N junction, which is an important factor in solar cells.
The stoichiometry of the sample, e.g. the proportion of indium and gallium in CIGS solar cells.
Depth profiling. The distribution of elements near the surface can be achieved by using different photon excitation energies to collect XPS spectra. Deeper depth can be analysed by sputter depth profiling.
Molecule geometry and orientations at the P-N junctions can be studied. This can be achieved by analysing the peak intensities for the different atoms in a molecule (higher intensities correspond to atoms oriented closer to the surface). Another method is to vary the angle of the incident X-ray beam.
2.5.4 Broadening and shift of the peaks
There are various factors that broaden and shift the observed position of the peaks in the spectrum.
Some of these factors are described below.
Electrons from higher states will eventually fill the hole created by the photoelectrons. The ionized states (the holes) will decay exponentially. This short lifetime of a photoexcited state give rise to an energy broadening and a peak with a Lorentzian shape [5]. The physical explanation is the
uncertainty principle which states that ΔE Δt > ћ.
The configuration of the electrons in the valence band will be different depending on the oxidation state. Depending on the oxidation state and the identity of the nearest neighbour of the atom a valence electron will give more or less screening effect (by the coulombic force) to the core electrons. The difference in screening effect will alter the binding energies of the core electrons, resulting in a broadening of the PES peaks [15]. Chemical shifts give information about chemical bonding in molecules.
5 The energy difference between the vacuum level and the Fermi level is defined as the work function.
Some photoelectrons lose kinetic energy by inelastic collisions on the way out of the material, e.g. by causing excitations of valence electrons. This will give rise to “inelastic tails” in the peaks.
The latter examples of broadening can be approximated by Gaussian distributions. The combined effect of the Lorentzian and the Gaussian shapes gives a Voigt function, which is the best
approximation of the shape of the peak [5].
2.5.5 Origin of the peaks in PES
The most common spectral features that can be identified in a PES spectrum are:
Photoelectron peaks. These peaks correspond to photoelectrons excited from specific subshells of an atom.
Auger peaks. When a photoelectron is excited a hole is created. This hole will eventually be occupied by an electron from a higher energy level (relaxation). The energy released by this relaxation can in turn initiate an Auger electron excitation or an emission of a photon.
Shake-up peak. Photoelectrons that excite valence electrons when leaving the atom causes shake-up peaks. The effect will be peaks with a few eV higher binding energy compared to the main peaks.
Spin-orbit coupling. When an electron moves in an electrical and magnetic field, the
magnetic moment of the electron will cause a perturbation of the energy levels of the atom [4]. This perturbation is called a spin-orbit coupling. The spin orbit coupling give rise (for all electron subshells except the s subshell, = 0) to a doublet (splitting) with the two different states having different binding energies.
Multiplet splitting. This is an effect created by the unpaired core electrons when the photoelectron has created a hole in the core level or by unpaired valence electrons created by relaxation [5]. Peak splitting (not derived from spin-orbit coupling) due to multiplet splitting can be observed in PES spectra.6
6 Multiplet splitting is in general more difficult to predict in the PES spectra than spin-orbit splitting.
3 Experimental 3.1 The samples
The samples investigated were Ag-doped CIGS (ACIGS). Some were Post Deposited Treated (PDT) with Caesium fluoride (CsF) or Rubidium fluoride (RbF) after the growth of ACIGS. The samples included the glass/Mo/ACIGS layers (i.e. not complete solar cells). Before the measurements the samples were prepared by dipping them into H2O just before introducing them into a UHV system (ultra high vacuum). The reason was to remove various fluoride residuals from the surface.
The samples were provided by SOLIBRO research AB.
3.2 X-ray source and hemispherical spectrometer
For this work the PHI Quantera II hemispherical spectrometer, residing in the Ångström laboratories, has been used. This section briefly describes the PHI Quantera II (although the text is common to hemispherical spectrometers).
An X-ray source is created by directing an energetic electron beam at a metallic solid (anode) [5]. A common used metal is aluminium. The electrons impinge on the Al-atoms and Al-1s core electrons with binding energies of 1559.6 eV will be ejected. The produced hole will be filled by electrons from the 2p level (binding energies of 73.0 eV for and 72.5 eV for ). The 1s – 2p energy
difference will create K X-ray emissions (and minor other emissions as well). This very low energy spread of 0.5 eV (73.0-72.5) is an important factor for the resolution of the PES spectra [5].
PHI Quantera II has an ellipsoidal quartz crystal monochromator. The electron beam from the anode will reflect on a quartz crystal. Braggs law implies that constructive interference will occur at a specific angle that depends on the wavelength. The relation between wavelength and reflected angle is defined by the crystal lattice spacing. At this specific angle a focused monochromatic X-ray beam will be impinged on the sample and photoelectrons will be ejected. A schematic figure of an X-ray spectrometer is shown in Figure 4 below.
Figure 4: Schematic of a hemispherical spectrometer
Before the photoelectrons enter the hemisphere they are accelerated or decelerated by electrostatic lenses to an energy window that will pass the hemisphere. The hemispherical spectrometer uses two hemispherical electrodes, the inner with a positive potential (attracting the electrons) and the outer with a negative potential (repulsive to electrons). The effect will be that only photoelectrons with kinetic energy close to the pass energy, will hit the detector. During a measurement session the pass energy will be held constant and the voltage of the lenses will vary in order to scan the energy band of interest. The resolution 7 of the energy analyzer will be:
where is the radius of the hemisphere, the pass energy and the width of the entrance slit.8 The number of photoelectrons hitting the detector will be counted for (in steps of ). These numbers will correspond to the intensities seen in the spectra.
One important condition is that the photoelectrons shall not be affected by an external electric or magnetic field. But the most important condition is that the photoelectrons move in vacuum to avoid a high number of collisions between photoelectrons and ambient gases. This condition requires a complicated arrangement where the pumping system is a key function [5].
3.3 Synchrotron and GALAXIES beamline
For this work the GALAXIES beamline in the SOLEIL synchrotron in Paris has been used.
7 The used resolution for PHI Quantera II was 1.0 eV for low and 0.2 eV for high resolution spectra.
8 The ultimate spatial resolution of the electron detector is determined by the size of the smallest analysis area.
Slit Slit
X-ray
monocromator
Electrostatic lenses
Hemispherical electrodes
Photon
Electron detector
Sample
A synchrotron consists of a closed orbit (called the electron storage ring) surrounded by adjustable bending magnets [4]. The electrons are first accelerated outside of the electron storage ring and then to relativistic speed inside of the ring. (The magnetic field of the bending magnets will be
synchronized to the increasing kinetic energy of the electrons.) The transverse acceleration caused by the bending magnets causes the electrons to emit radiation9. The higher magnetic field of the magnets the higher the energies will be of the emitted photons. The electrons are diverted, selected, and shaped by optic systems in experimental stations called beamlines.
The GALAXIES beamline in the SOLEIL synchrotron “is dedicated to inelastic x-ray scattering (IXS) and hard x-ray photoemission (HAXPES). These spectroscopic techniques are powerful probes to
characterize the electronic properties of materials. The beamline is optimized to operate in the 2.3 to 12 keV energy range with high resolution and micro beam” [13].
3.4 XPS setup
Three different samples have been used, both for the PHI Quantera II measurements and for the GALAXIES measurements. The first sample is a CIGS reference sample, the second a sample with rubidium fluoride PDT and the third a sample with caesium fluoride PDT. The three samples and the mounting plate for PHI Quantera II can be seen in figure 5 below:
Figure 5: PES samples and mounting plate for PHI Quantera II
The measurements by PHI Quantera II used K X-ray emissions (= 1486.6 eV).
The measurements from the GALAXIES beamline used HAXPES with electron energies of 2.3 keV and 10 keV.
9 Charged particles e.g. electrons that are accelerated (centripetal or in magnitude) emit electromagnetic radiation.
The used polarization of the X-rays and the angles between vectors (e.g. between beam and polarization vector) for PHI Quantera II and GALAXIES HAXPES is analysed in section 3.6.3.
The measurements differed by the used photon energies (1.487 keV, 2.3 keV and 10 keV) and resolution (high = 0.2 eV or low = 1.0 eV). An ID is used as a unique identifier of the combination of measurement and sample.
3.5 Peak fitting
The peaks were fitted using the XPSPEAK tool [8]. The procedure was as follows:
1) Create the input ASCII files by cutting off superfluous measurements.
2) Fit a background. The background was approximated with a linear function. This showed to be the simplest and most reliable method.
3) Locate the peaks. For peaks with doublets (due to spin orbit splitting) the built in fixed relation between the doublets was used.
4) Run the fitting procedure. In the peak fitting menu it is possible to fix different parameters.
Theses parameters are position (energy), FWHM (full width at half maximum), peak area, and the proportion of Lorentzian and Gaussian peak shapes. I did not set any of these parameters to a fixed value. Doing so gave the best fitting (although only by visual comparisons).
3.6 Analysis of spectrum
The most obvious factor that determines the relative intensities of the peaks are the density of occupied states for the subshells. The peak intensities are proportional to the number of electrons in the subshells (as each electron in a subshell has the same binding energy).
Several other factors determine the intensity (I) of a PES peak. These factors are the surface
concentration of the material under study (C), the photon flux (ø), the photoionization cross section of the process (σ), the angular distribution (f)10, the inelastic mean free path of the photoelectrons (λ), the area of the sample from where photoelectrons are detected (A) and the analyzer
transmission (T) [4]. The relation can be expressed as:
I f λ A T (1)
The higher the concentration of the element on the sample surface, the more intense the peak will be. Due to the surface sensitivity of PES, elements closer to the surface will also give a larger contribution to the peak.
When the objective is to calculate the relative concentrations of the elements it is only necessary to take into account those parameters that are different for different element subshells. For a single measurement sequence, the sample area (A), the photon flux ( ) and the analyzer transmission (T) are all constant in the first approximation. For this reason , T and A can be omitted when calculating relative element concentrations. The simplified formula for the concentration C will then be
dependent only on 1/f and 1/λ.
10 f in relation (1) symbolizes a general parameter. In section 3.6.3 several other parameters are used to describe the angular distribution of the cross sections.
3.6.1 Spin orbit splitting
The two peaks (doublets) due to spin orbit splitting will have specific area ratios based on the degeneracy of each state j. E.g. for the 2p subshell, where n = 2 and = 1, j will be 1/2 and 3/2. The area ratio for the two spin orbit peaks and will be 1:2 (corresponding to 2 electrons in the level and 4 electrons in the level). These ratios have to be taken into account when analyzing spectra of the p, d and f subshells.
3.6.2 Photoionization cross section
The photoionization cross sections (σ) “describe the likelihood for photoelectron production from a specific core level of a specific element under the irradiation of photons of a specific energy” [5]. It is usually given in units of barns [1 barn = ]. For other factors the photoionization cross sections remain constant, e.g. the chemical environment of the atom. This is a good thing as the intensities of the peaks in the PES-spectrum will be easier to draw conclusions from.
Hartree and Slater have analysed the wave function and developed an approximate model for the atomic potential, called the single potential Hartree-Slater atomic model [6]. Based on this model, together with the Hartree-Fock model for low Z element cross sections with high energies, Scofield calculated (relativistically) photoionization cross sections for different photon energies [6] and also specifically for Mg Kα and Al Kα X-rays [7]. These calculations are often referred to as the Scofield cross sections. I have not found any systematic study in the literature showing agreement of experimental data to the Scofields calculations of photoionization cross sections. However, experiments covering different subsets of cross sections have been done. These measurements generally show quite good agreement with Scofield’s calculations, see e.g. Kerur et. al. [9].
The Scofield cross sections in [6] and [7] are total cross sections, which mean that the cross sections have been integrated over all emission angles.
3.6.3 Angular distribution of photoelectrons
The intensity of photoelectrons differs depending on the emission collection angle. This effect is referred as the angular asymmetry factor [5]. The value of β is constant for a given subshell of a given atom. “Values of β vary from about 0.4 to 2 (the latter being the theoretical value for all s orbitals)”
[14].
It is common to consider the angular distribution of photoelectrons within the electric dipole approximation, Trzhaskovskaya et al. [11]. This dipole approximation uses the angular asymmetry parameter β. However it has been shown by several investigations that the angular distribution differs significantly from the calculated values using the dipole approximation. Expressions have been presented which adequately describe the angular distribution in various cases of photon polarization by the use of two additional nondipolar parameters and δ along with the dipole parameter β [11].
The photoelectron angular distribution for circular polarized and unpolarized photons may be written as [11]:
where Ω is the solid emission angle, is the photoionization cross section for the i:th atomic subshell, is the second order Legendre polynomial = and is the angle between
the incident photon and the photoelectron propagation. The PHI Quantera II in Ångström uses unpolarized X-rays.
For linearly polarized photons the angular distribution may be represented by:
where is the angle between the photoelectron propagation vector p and the photon polarization direction ε, the vector ε being coincident with the z axis; is the angle between the vector k and the plane passing through the z axis and the vector p. The HAXPES GALAXIES beamline uses linear polarized X-rays with . This gives:
3.6.4 Inelastic mean free path
For electrons with kinetic energies greater than ~100 eV, interaction probabilities follow an
exponential function. This means that the path length can be approximated using Beer Lambert law
11 [5].
The inelastic mean free path (IMFP or λ) “defines the average distance travelled by an electron of a specific energy within a particular single-layered homogenous amorphous solid between two successive inelastic scattering events” [5].
If the energy loss due to inelastic scattering is (at least) greater than the peak width, the signal will become part of the background. The reason is that this energy loss is typically of a non discrete nature.
The mean free path depends on the kinetic energy of the electron. This property is used when studying the samples with PES. For example when using higher photon energies the photoelectrons will get higher kinetic energies. This implies longer mean free path and will result in photo excitations deeper into the material.
Numerous empirical and semi-empirical formulas have been proposed to approximate the value of λ.
The most accurate formula developed as yet is the TPP-2M formula. TPP is short for Tauma, Penn and Powell, who developed this relation [5]. The formula is a modified form of the Bethe equation, taking into account the free electron effects that are responsible for the plasmon loss features [5].
QUASES [12] is an IMFP tool developed by S. Tougaard that is based on the TPP-2M formula. CIGS is a compound which means that all photoelectrons with a specific kinetic energy will, irrespective of which element the electron originates from, have the same inelastic mean free path. It is possible to add new materials in QUASES. The chemical formula for CIGS is . Using a
concentration of Ga and In with x=0.3 gives a mean atomic mass of 323. The number of valence electrons was set to 10 and the bulk density to 5.7 g/cm [12]. The IMFP will then only depend on the photoelectron energy. In figure 6 below an inelastic mean free path plot for CIGS is shown. The
11 The relation can be expressed as , where is the electron intensity and d the path length.
points in blue are the λ used in the PES measurements. The points in red are λ values plotted for arbitrarily kinetic energies using QUASES [12]12.
Figure 6: Inelastic mean free path for electrons in CIGS 3.6.5 Relative concentration of elements
Using the angular distribution function from [11] we can define the relative concentration of an element x compared to element y as where
(6)
subscript 1 and 2 are the two different energy levels due to spin orbital splitting.
12 The TPP2M formula from the papers by Tanuma, Powell and Penn is not valid for energies lower than 50 eV.
Inelastic mean free path for CIGS
Electron kinetic energy (eV)
In el ast ic me an f re e pa th (Å)
10
110
210
310
410
010
110
24 Results
4.1 Results of XPS measurements with PHI Quantera II
The XPS measurements, all with photon energies = 1.487 keV, were performed by using PHI Quantera II in Ångström 2019-03-19.
4.1.1 Survey spectra
An ACIGS low resolution survey spectra is shown below.
Figure 7: ACIGS low resolution survey spectra with no PDT (ID = 104). All major peaks are identified.
(A)= Auger lines.
4.1.2 High resolution fitting
An example of peak fitting of In3d is shown below. The analyzer data is the blue lines and the fitted peaks are colored red. The area of the peak is fitted based on the area of the peak (the ratio shall be 3:2). It appears that this fitting was not perfect as the asymmetric tails are not fully fitted.
Figure 8: Fitted In3d peaks (high resolution spectra with no PDT, ID = 107).
4.1.3 Parameter values
Table 1 below shows parameter values for β, and δ (see section 3.6.3 for a description of the parameters) derived from [11] for photon energies of 1500 eV. λ is calculated using QUASES [12]. The two parameter values due to spin orbital splitting are tabulated, e.g. for and for .
Peak (kb) (Å)
Ga2p ( , ) 29.5, 57.5 1.41, 1.44 0.48, 0.489 0.0359, 0.036 12.2, 12.8 In3d ( , ) 51.0, 74.1 1.22, 1.20 0.388, 0.394 0.0674, 0.0681 27.0, 27.1 In3p ( , ) 28.9, 57.9 1.60, 1.65 0.0224, 0.0222 0.00247, 0.00578 21.8, 22.6
Cu2p ( ) 53.0 1.42 0.521 0.0371 16.9
Table 1: Tabulated and calculated values for , β, , δ and λ for photon energies of 1500 eV13 For comparison concentration values were calculated without taking into account the angular asymmetry parameters. Scofield cross sections do not account for angular variations in the effective cross section. Therefore Scofield cross sections [7] were used, see Table 2 below:
13 The tabulated values are for 1500 eV but the actual photon energy was 1487 eV. As it is the relative concentration values that are of interest this difference will have almost no effect (the parameters for all elements changes in the same direction with changing photon energies).
455 450 445 440
60000 80000 100000 120000 140000
Fitted In3d peaks
Binding Energy (eV)
Peak (kb) Ga2p ( , ) 151, 291 In3d ( , ) 125, 181 In3p ( , ) 59.8, 121 Cu2p ( ) 228
Table 2: Tabulated Scofield values for for photon energies of 1487 keV 4.1.4 Calculations
Table 3 shows the areas of the fitted peaks and the FWHM, based on the XPS measurements in Ångström 2019-03-19. The peak areas correspond to the intensity I.
Peak ID PDT Resolution Peak(s) area FWHM
Ga2p 107 no high 36000 1.9
In3d 107 no high 229000 1.52
Cu2p3 107 no high 13100 1.32
Ag3d 107 no high 32000 1.13
Ga2p 105 RbF high 26000 1.69
In3d 105 RbF high 292000 1.54
Cu2p3 105 RbF high 4060 1.12
Ag3d 105 RbF high 24900 1.09
Ga2p 106 CsF high 35600 1.78
In3d 106 CsF high 293000 1.57
Cu2p3 106 CsF high 7000 1.06
Ag3d 106 CsF high 25200 1.13
Ga2p 107 no low 76700 1.7
In3p 107 no low 214000 3.63
In3d 107 no low 551000 1.85
Cu2p3 107 no low 36513 0.787
Table 3: Results based on XPS measurements 2019-03-19
have been calculated for Ga, In and Cu using formula (2) with values from Table 1 and using = 45° (it has been told us that the angle between the incident photon and the photoelectron propagation is 45° for the PHI Quantera II in Ångström). Concentration values have then been calculated using formula (6). The calculation of the concentration of indium based on In3d high resolution peaks is shown below (no PDT, high resolution, ID = 107).
= 3.91
= 5.71
The calculation of the concentration of gallium based on Ga3p high resolution peaks is shown below (no PDT, high resolution, ID = 107).
= 2.19
= 4.26
See section 4.3 for the summary of all results.
The relative angular dependence of the concentration between indium, gallium and copper when using formula (2) with = 45° from [11] compared to only using σ in Table 1 is very low (1-2%). This seems reasonable as the difference between the magic angle and is not very large (54.7° - 45° = 9.3°)14.
It would be interesting to compare concentration values for indium based on calculations from In3p peaks and from In3d peaks. As the high resolution measurements did not include In3p (or any other two different subshells of the same element) the low resolution (ΔE = 1 eV) survey spectrum with only a few samples for each peak was used. As a low resolution spectrum was used the calculated concentrations are assumed to be uncertain. The calculated Indium concentration using
Trzhaskovskaya asymmetry parameters based on the In3d peaks was 22% higher than the calculated concentration based on the In3p peaks (2117 versus 1730). Using Scofield cross sections indium concentration was 25% higher when using In3d than using In3p (66.5 versus 53.1). It is unclear which instrumental transmission corrections that were used in MultiPak (MultiPak is the processing
software we used for the PHI Quantera II measurements). The instrumental transmission corrections in MultiPak could be a reason for the differences.
4.2 Results of XPS measurements with HAXPES GALAXIES
The high energy XPS measurements (2.3 keV and 10 keV) were performed in the GALAXIES SOLEIL synchrotron.
4.2.1 Survey spectra
An ACIGS 10 keV low resolution survey spectra is shown below. The measured binding energies have an offset +17 eV. The reason for this offset is not effective grounding of the sample during the XPS measurements.
14 At the magic angle the dipole term vanishes in the differential cross section [10].
Figure 9: ACIGS 10 keV low resolution survey spectra with no PDT (ID = A5).
4.2.2 Parameter values
Table 5 below shows parameter values for and β derived from [10] for photon energies of 10 keV. λ is calculated using QUASES [12]. The two parameter values due to spin orbital splitting are tabulated, e.g. for and for .
Peak Photon
energy (keV)
(kb) (Å) Ga2p ( , ) 2.3 19.0, 28.9 1.34, 1.37 29.4, 29.9 In3p ( , ) 2.3 16.3, 31.8 1.58, 1.63 37.8, 38.5
Cu2p ( ) 2.3 25.4 1.34 33.5
Ga2p ( , ) 10 0.351, 0.638 0.837, 0.833 154, 155 In3p ( , ) 10 0.656, 1.13 1.23, 1.28 161, 162 In3d ( , ) 10 0.162, 0.223 0.656, 0.627 165, 165
Cu2p ( ) 10 0.474 0.772 158
Table 5: Tabulated and calculated values for , β and λ for photon energies of 2.3 and 10 keV15 For comparison, concentration values were calculated without taking into account the angular asymmetry parameters. Scofield cross sections [6] were used, see Table 6 below:
Peak Photon energy
(keV)
(kb) Ga2p ( , ) 2.3 38.0, 66.5 In3p ( , ) 2.3 29.8, 58.1
Cu2p ( ) 2.3 80.2
Ga2p ( , ) 10 0.524, 0.949
15 σ and β for photon energy = 2.3 keV are estimated by linear interpolation between 2.0 keV and 3.0 keV.
Peak Photon energy (keV)
(kb) In3p ( , ) 10 0.806, 1.38 In3d ( , ) 10 0.198, 0.272
Cu2p ( ) 10 0.668
Table 6: Tabulated Scofield values for for photon energies of 2.3 and 10 keV16 4.2.3 Calculations
Table 7 below shows the areas of the fitted peaks and the FWHM based on the HAXPES
measurements (2.3 keV and 10 keV) in the GALAXIES SOLEIL synchrotron. The peak areas correspond to the intensity I.
Peak ID Energy (keV) PDT Resolution Peak area FWHM
Ga2p A7 10 CsF high 266 2.07
In3p A7 10 CsF high 1208 3.52
Cu2p A7 10 CsF high 416 1.84
Ga2p A6 10 Rb high 269 1.76
In3p A6 10 Rb high 1301 3.63
Cu2p A6 10 Rb high 412 1.67
Ga2p A5 10 no high 281 1.81
In3p A5 10 no high 1237 3.5
Cu2p A5 10 no high 485 1.7
Ga2p A7 2.3 CsF high 430 1.25
In3p A7 2.3 CsF high 812 3.13
Cu2p A7 2.3 CsF high 512 0.976
Ga2p A6 2.3 RbF high 430 1.20
In3p A6 2.3 RbF high 833 2.89
Cu2p A6 2.3 RbF high 285 0.785
Ga2p A5 2.3 no high 403 1.11
In3p A5 2.3 no high 514 3
Cu2p A5 2.3 no high 460 0.837
Ga2p A5 10 no low 500 2.0
In3p A5 10 no low 1880 3.2
In3d A5 10 no low 390 1.68
Table 7: Results from the GALAXIES HAXPES measurements
As = 0° for the HAXPES GALAXIES beamline, was calculated using formula (4), with values from Table 4. As only one of the doublet peaks was measured in high resolution ( is assumed), it is only and that were used for the high resolution calculations. The concentration values have been calculated using formula (6). The calculation of the concentration of indium based on an In3p high resolution peak is shown below (10 keV, no PDT, high resolution, ID = A5).
16 σ for photon energy = 2.3 keV are estimated by linear interpolation between 2.0 keV and 3.0 keV.
The calculation of the concentration of gallium based on a Ga3p high resolution peak is shown below (10 keV, no PDT, high resolution, ID = A5).
To be able to calculate the indium concentration from the intensity of the In3p peaks and from the In3d peaks for 10 keV, the low resolution survey spectrum had to be used. The calculated indium concentration using Trzhaskovskaya asymmetry parameters based on the In3d peaks was 30% higher than the calculated concentration based on the In3p peaks (47.1 versus 36.2). Instead using Scofield cross sections gave 5.8% higher indium concentration when using In3p peaks than using In3d peaks (5.32 versus 5.03).
4.3 Results summary
The band gap can be calculated as [2]:
where x = GGI. Table 8 shows the GGI, CGI and band gap when taking into account the angular distribution of the cross sections.
Sample Energy (eV) GGI (eV) CGI
Reference, no PDT 1487 0.33 1.18 0.15
PDT = Rubidium fluoride 1487 0.22 1.12 0.042
PDT = Cesium fluoride 1487 0.28 1.15 0.067
Reference, no PDT 2.3k 0.55 1.31 0.65
PDT = Rubidium fluoride 2.3k 0.45 1.25 0.31
PDT = Cesium fluoride 2.3k 0.45 1.25 0.56
Reference, no PDT 10k 0.34 1.19 0.81
PDT = Rubidium fluoride 10k 0.32 1.18 0.67
PDT = Cesium fluoride 10k 0.34 1.18 0.72
Table 8: Ga/(Ga+In), Cu/(Ga+In) and band gap when taking into account the angular distribution of σ As the photon penetration depth is much greater than the inelastic mean free path the mean depth where the photoelectric effect will occur will be (approximately) equal to λ. The figures below show (in log scale) the dependence of depth on the relative gallium to indium concentration (GGI); and the dependence of depth on the concentration of copper relative to gallium and indium (CGI) when considering the angular distribution of cross sections. The used depths in the figures are the mean of Ga, In and Cu17.
17 Only the largest peaks for the elements are used for the estimation of depth in the figures. But to be exact the IMFP from all orbitals should be taken into account (in proportion to the peak intensities).
Figure 10: Ga/(Ga+In) ratios and band gaps in ACIGS samples using asymmetry parameters.
Figure 11: Cu/(Ga+In) ratios in ACIGS samples using asymmetry parameters.
50 100 150
0.20.30.40.50.6
Ga/(Ga+In) ratios and band gap in ACIGS samples considering the angular distribution
depth (Å)
GGI
Reference without PDT PDT = Rubidium fluoride PDT = Cesium fluoride
1.181.201.221.241.261.281.30 Band gap (eV)
20 50 100
0.050.100.200.501.00
CGI in ACIGS samples considering angular distribution
depth (Å)
CGI
Reference without PDT PDT = Rubidium fluoride PDT = Cesium fluoride
Table 9 shows the GGI, CGI and band gap when using Scofield cross sections.
Sample Energy (eV) GGI (eV) CGI
Reference, no PDT 1487 0.19 1.10 0.10
PDT = Rubidium fluoride 1487 0.12 1.07 0.027
PDT = Cesium fluoride 1487 0.15 1.08 0.043
Reference, no PDT 2.3k 0.47 1.26 0.39
PDT = Rubidium fluoride 2.3k 0.37 1.20 0.18
PDT = Cesium fluoride 2.3k 0.37 1.20 0.33
Reference, no PDT 10k 0.26 1.14 0.62
PDT = Rubidium fluoride 10k 0.24 1.13 0.51
PDT = Cesium fluoride 10k 0.25 1.14 0.55
Table 9: Ga/(Ga+In), Cu/(Ga+In) and band gap using Scofield cross sections
The figures below show (in log scale) the dependence of depth on the relative gallium to indium concentration (GGI); and the dependence of depth on the concentration of copper relative to gallium and indium (CGI), when using Scofield cross sections.
Figure 12: Ga/(Ga+In) ratios and band gaps in ACIGS samples using Scofield cross sections.
50 100 150
0.10.20.30.40.5
Ga/(Ga+In) ratios and band gap in ACIGS samples using Scofield cross sections
depth (Å)
GGI
Reference without PDT PDT = Rubidium fluoride PDT = Cesium fluoride
1.101.151.201.25 Band gap (eV)
Figure 13: Cu/(Ga+In) ratios in ACIGS samples using Scofield cross sections.
As can be seen in Table 5 and Table 6 the total cross sections (σ) in Trzhaskovskaya ([10] and [11]) are smaller than in Scofield ([6] and [7]). The differences decrease with increasing photoelectron energy.
It is the higher calculated indium concentration when using the Scofield cross sections compared to using the asymmetry parameters that is the main reason to the difference in GGI and CGI. The difference in GGI and CGI is ranging from 15% (GGI, 2.3 keV, no PDT) to 46% (GGI, 1487 eV, PDT=CsF).
It is unclear which sensitivity factors that were used in MultiPak (MultiPak is the processing software we used for the PHI Quantera II measurements). The sensitivity factors in MultiPak could be one reason for the difference between GGI and CGI for the PHI Quantera II measurements when using the Scofield cross sections, compared to using the Trzhaskovskaya asymmetry parameters.
20 50 100
0.050.100.200.50
CGI in ACIGS samples using Scofield cross sections
depth (Å)
CGI
Reference without PDT PDT = Rubidium fluoride PDT = Cesium fluoride
