X-ray absorption spectroscopy (XAS)

Synchrotron radiation

Laboratory based conventional X-ray sources suffer from several drawbacks, namely limited photon flux, unpolarised radiation and lack of tunability of the photon intensity/energy. So, experiments which require high intensity, tunable and polarized X- rays, turn to synchrotron radiation sources. In synchrotrons, electrons are accelerated in a circular path by bending magnets to produce radiation. Synchrotron sources produce photons having a continuum of energy spanning from infrared to X-rays. For electrons moving with velocities close to that of light, the radiation is directed in the direction of the electron’s travel and the relativistic effect results in a collimated beam. The angular distribution (𝛥𝜙) of the emitted radiation is related to the Lorentz factor as

𝛥𝜙 ≈ 𝛾 − 1 ……….2.21

And γ = 1

√1 − 𝜈2

𝑐2

⁄ ……….2.22

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Figure 2.9 Schematic of a typical synchrotron facility with different components: electron gun, Linac, Booster ring, Storage ring, beamline and experimental station.

The primary components of a synchrotron radiation facility, namely the electron gun, linear accelerator (Linac), booster ring, storage ring, beamlines and experimental/end stations are shown in Figure 2.9. Electrons are emitted by a cathode and accelerated to energies ~120 MeV by the linear accelerator and injected into the booster ring in discrete bunches. The electromagnets in the booster ring accelerate the electrons and force them to travel around the ring. Variable magnetic fields guide the electron in a circular trajectory of constant radius while RF system boosts the energy of the electron beam. Electrons rotate in the booster ring until they achieve sufficient energy (2.3 GeV) to be injected into the storage ring. The booster ring feeds electrons into the storage ring, a many-sided donut shaped structure. The storage ring further ramps up the energy of the particles to 3 GeV and is maintained under vacuum to prevent deflection of electrons. Synchrotron radiation is produced when the bending magnets in the storage ring deflect the electron beam with each set of bending magnets being connected to a beamline. Precise focussing of the beam is undertaken with the help of the computer-controlled quadrupole and sextupole magnets. Undulators, wigglers and monochromators filter, intensify and modulate the beam to correspond to the various experimental requirements 184,185. Synchrotron-based studies (Chapter 3) in this project

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were undertaken at Stanford Synchrotron Radiation Lightsource, California. The storage ring at SLAC is named as SPEAR (Stanford Positron Electron Accumulator Ring) and was originally built for high energy physics research. Under normal conditions, the SPEAR stores up to 100 mA of current in its 234-meter circumference vacuum chamber.

XPS, though being highly surface-sensitive, provides information about the total density of states whereas NEXAFS is element-specific and probes the partial density of states of the concerned element. Near edge X-ray absorption fine structure (NEXAFS) was mainly developed in 1980s to study the structure of molecules bonded to the surface

186_{. Primarily it was aimed for low-Z molecules (where Z signifies the atomic number),}

but has ever since been used to understand the transitions during X-ray absorption and probe the nearest neighbour interactions, chemical structure, orientation of molecules and molecular fragments. Moreover, NEXAFS demonstrates channel selectivity when probing total and partial fluorescence yield.

X-rays incident on matter lose their intensity during transmission due to the interaction with matter. In addition to being transmitted and absorbed, some part of the incident X-ray also gets elastically, or inelasticity scattered. As a result, the incident intensity (I0) is observed to reduce exponentially. The transmitted intensity is also

affected by properties such as mass density (𝜌) and absorption coefficient (µ). X-ray absorption spectrum is a plot of the variation in absorption coefficient with incident photon energy. Sharp features known as absorption edges, corresponding to the transition of a core electron to the unoccupied density of states, are observed in a typical absorption spectrum and have energy values corresponding to the binding energy of the core electron. Figure 2.10 shows a typical C K-edge XAS spectrum demonstrating the pre-edge, absorption edge, NEXAFS and EXAFS regions.

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Figure 2.10 Typical C K-edge XAS spectrum showing the pre-edge, NEXAFS and EXAFS regions.

A NEXAFS spectrum is usually characterized by sharp resonance features in the energy region just below and up to ~50 eV 187 above the core level ionization threshold (absorption edge), arising due to transitions from the K-edge (the deepest core shell) of an atomic species into unoccupied bound or continuum levels. These transitions are governed by dipole selection rules (i.e. ∆𝑙 = ±1) and are sensitive to the local electronic structure, chemical configuration, oxidation state, molecular orientation and symmetry

186,188_.

Figure 2.11 Energy of K, L and M absorption edges as a function of atomic number Z. X-ray energies below 1 keV are referred to as soft X-rays and those above, as hard X- rays 189.

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Figure 2.11 presents the X-ray energies required to obtain excitation features at different absorption edges (K, L, and M edge). In this thesis, NEXAFS spectroscopy has been used extensively to reveal the electronic structure and bonding environment of different doped hole transport materials. Chapter 3 provides insight into the carbon and nitrogen

K-edge NEXAFS corresponding to the transitions from 1s→2p unoccupied states for

differentially doped hole transport materials spiro-OMeTAD, SFX-OMeTAD and SFX- TAD.

Theory of NEXAFS

Figure 2.12 shows the origin of the absorption features in NEXAFS spectra. In the figure, the potential distribution of a diatomic molecule is depicted along the X-axis with the corresponding K-shell absorption features. The anti-bonding π* and σ* levels are unoccupied states corresponding to the orbitals with π and σ symmetry, respectively. For a neutral molecule, the σ* orbitals have energy distribution above the ionization potential while the strong coulombic interaction between the excitons (electron-hole pairs) pulls down the π* orbitals below the vacuum level. The transitions from the core levels to the unoccupied π* and σ* levels give rise to the corresponding transitions wherein π* show sharper features and are easy to resolve and identify. In contrast, transitions to σ* orbitals are significantly broader due to life time broadening and vibrionic features. In addition to π* and σ* states, Rydberg resonances are often found just below the IP 188. The absorption cross section describes the probability of interaction of an electron with a photon. The X-ray absorption cross section (σx) is defined as the

number of electrons excited per unit time divided by the number of photons incident per unit time per unit area. A detailed quantum mechanical description about the absorption cross section has been presented by Stöhr in his book “NEXAFS Spectroscopy” 188_.

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Figure 2.12 Schematic potential (bottom) and corresponding NEXAFS K-shell spectrum (top) of a diatomic molecular (sub) group. In addition to Rydberg states and a continuum of empty states similar to those expected for atoms, unfilled molecular orbitals are present, which is reflected in the absorption spectrum 186.

According to Fermi’s Golden rule for initial and final state transitions, the

probability of transition from an initial state │i〉to a final state │f〉 driven by a

harmonic time dependent perturbation 𝑉(𝑡) = 𝑉𝑒−𝑖𝜔𝑡 is given by

𝑃_𝑖𝑗 = 2𝜋

ħ |˂𝑓|𝑉|𝑖˃| 2_𝜌

𝑓(𝐸) ………2.23

62 𝜎_𝑥= 4𝜋2ħ2 𝑚2 𝑒2 ħ𝑐 1 ħ𝜔|˂𝑓|𝑒. 𝑝|𝑖˃| 2_𝜌 𝑓(𝐸) ………...2.24

where ℏ𝜔 is the incident photon energy, 'e' is the electronic charge and 'm' is mass of electron, 𝜌𝑓(𝐸) represents the density of final states and ˂𝑓|𝑒. 𝑝|𝑖˃ is the dipole matrix

showing the interaction between the linear momentum operator ‘p’ with unit vector of

the electric field 'e' of a polarized incident light. This dipole matrix reveals the polarization dependence of the NEXAFS spectra. The transitions which involve change in angular momentum quantum number by Δl = ±1 are only allowed and this is reflected

in the NEXAFS spectra. The transitions between the molecular orbitals are governed by the dipole selection rules. For linearly polarized light, the dipole matrix can be written as˂𝑓|𝑝|𝑖˃ . The direction of this matrix element will be same as that of orientation of the orbital i.e. the vector O. The resonant features are most intense when the electric field vector has the same direction as that of the orbital orientation. On the other hand, if the electric field vector is perpendicular to the molecular orbital then the corresponding resonance features will be absent from the spectra.

Detection schemes

A tunable monochromatic soft X-ray source having photon energy less than 2000 eV is used for photoabsorption during NEXAFS measurements. The core hole thus created can be filled up by an electron either radiatively or non-radiatively. The radiative process results in the emission of florescence photon whereas the non-radiative process results in the emission of an Auger electron. There are two detection schemes for acquiring NEXAFS spectra. First is by measuring the secondary electrons, known as electron yield (EY) and second is by counting the florescence photons, known as fluorescence yield (FY). Total electron yield (TEY), Partial electron yield (PEY) or Auger electron yield (AEY) are the different ways in which electron yield measurements can be carried out. Electrons of all energies are collected in the TEY mode. The TEY

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signal usually has a strong intensity and low signal-to-noise ratio due to the dominance of secondary electrons. In TEY mode, spectra are recorded by measuring the current to the sample such that the sample remains electrically neutral after the photoionization process. The mean free path of the released electrons limits the sampling depth for the TEY detection scheme to about 10 nm of the surface. During the actual spectrum acquisition process, spectra for TEY is acquired by measuring the sample drain current (I0). The PEY signal is acquired by placing a retarding voltage in front of the electron

detector such that only electrons with low kinetic energies are allowed through to the detector known rendering this technique highly surface-sensitive. However, the electron yield methods are limited only to conducting samples. Auger electrons are measured by tuning the energy of the electron analyser to specific Auger transitions whereas fluorescence yield detection is carried out using a photodiode placed close to the sample. FY, on the other hand, is independent of the sample conductivity. The sampling length for FY mode depends on the attenuation length of the incident X-ray and the composition of the material under study and longer mean free path of photons reduce the surface sensitivity. In general, the sampling depth in FY mode being of the order of 100 nm for soft X-rays. The advantage for FY mode is the ease of sample preparation as the presence of surface oxides and contaminants can effectively be ignored. Both electron yield and florescence yield are normalized by dividing the signal by the incident photon flux measured at a gold grid placed upstream of the beam path (between the main chamber and the beamline optics).