User:Nathan Johnson/photoemission spectroscopy

Figure 1:Principle of angle resolved photoelectron spectroscopy

Photoemission Spectroscopy (PES), also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in a substance. The term refers to various techniques, depending on whether the ionization energy is provided by an X-ray photon, an ultraviolet photon, or an EUV photon. Regardless of the incident photon beam however, all photoelectron spectroscopy revolves around the general theme of surface analysis by measuring the ejected electrons.

History

X-ray photoelectron spectroscopy (XPS) was developed by Kai Siegbahn starting in 1957 and is used to study the energy levels of atomic core electrons, primarily in solids. Siegbahn referred to the technique as Electron Spectroscopy for Chemical Analysis (ESCA), since the core levels have small chemical shifts depending on the chemical environment of the atom which is ionized, allowing chemical structure to be determined. Siegbahn was awarded the Nobel Prize in 1981 for this work. XPS is sometimes referred to as PESIS (photoelectron spectroscopy for inner shells) whereas the lower energy radiation of uv-light is referred to as PESOS (outer shells) because it cannot excite core electrons.

Ultra-violet photoelectron spectroscopy (UPS) is used to study valence energy levels and chemical bonding; especially the bonding character of molecular orbitals. The method was developed originally for gas-phase molecules in 1962 by David W. Turner , and other early workers included David C.Frost, J.H.D. Eland and K. Kimura. Later, Richard Smalley modified the technique and used a UV laser to excite the sample, in order to measure the binding energy of electrons in gaseous molecular clusters.

In the ultraviolet region, the method is usually referred to as photoelectron spectroscopy for the study of gases, and photoemission spectroscopy for solid surfaces.

Extreme ultraviolet photoelectron spectroscopy (EUPS) lies in between UPS and XPS (between about 120 nm and 10 nm wavelength light). It is typically used to assess the valence band structure.5 Compared to XPS it gives better energy resolution, and compared to UPS the ejected electrons are faster, resulting in a better spectrum signal.

Basic Principles

PES is the study of photoelectrons that have been ejected from occupied molecular orbitals (MO) by short wavelength monochromatic light. The helium resonance line He I at 584 Å, which has an equivalent energy per photon of 21.22 electronvolts is the monochromatic light most commonly used to ionize the molecules of interest. Normal photoionization – ionization caused by energetic photons – involves the removal of a single electron from the neutral species without changing the quantum number of any other electrons (regardless of what orbital the electron is in). ⁴ Studying these electrons has the advantage that all such electrons have certain characteristics, such as energy, abundance and angular distribution, which link them to a specific MO. This means that the photoelectron spectrum is a direct representation of the molecular orbital energy diagram. Another useful characteristic of the spectrum is that it shows us the change in character of a particular orbital, by revealing geometric changes caused by the removal of one electron, which lets us determine whether or not the orbital is bonding, anti-bonding or non-bonding.

When an electron is ejected from an inner shell by photoionization, two other types of energy may be observed. The first of which, X-ray fluorescence, shown in Figure 2 produces radiation that may be observed in the X-ray region. An Auger electron is released from the outer shell of a molecule or atom after a valence electron relaxes to the hole created by the ejection of a photoelectron. One key thing to note about Auger electrons is that they are kinetically independent of the input photon, whereas the photoelectrons are kinetically dependent, allowing PES users to distinguish between Auger and photoelectrons. Photoionization has the advantage over electron impact ionization in that it is more likely to eject inner shell electrons at the same probability as outer shell electrons and that it consistently ejects only a single electron. Another benefit of PES is that incident photon beams are less destructive than electron bombardment of the sample, particularly when dealing with organic materials.

Koopmans' theorem is an approximation that tells us that the ionization potential (I_j), the most directly measured quantity in PES, is equal to the magnitude of an orbital energy, ε_j.

$I_{j}={\text{-ε}}_{j}$

(1)

A photoelectron spectrum is measured by varying the energy of the photoelectrons allowed to reach the detector and recording the rate at which the electrons of each energy arrive. The cation formed in the photoionization of the molecule has a total internal energy of the vibrational, electronic, and rotational ions. To compensate for additional energies, such as vibrational or rotational excitation caused by ionization, the following equation is used.

$KE=h\nu -I_{j}-E_{\text{(vib,rot)}}^{*}$

(2)

Two further approximations that make the relationship between the spectrum and the molecular electronic structure simple are: 1) that each band in the spectrum corresponds to ionization from a single MO and 2) that each occupied MO with a binding energy less than hν appears as a single band in the spectrum.

Explanation of a typical spectrum

Figure 3: A typical Photoelectron spectrum: The y-axis is the strength of the electron signal [electrons/second]. The x-axis is usually the Ionization energy [eV]. Reprinted with permission of John Wiley & Sons, Inc. ⁴

While absolute intensities are a product of experimental factors (and therefore irrelevant), the relative intensities are equal to the relative probabilities of photoionization to different states of a positive ion. The relative probabilities are a statistical weight of the ionic states produced, which is given by the equation 2J+1. This means that the ²P_3/2 state has a weight of 4 and the ²P_1/2 state has a weight of 2 (this 2:1 ratio is observed in electrons of rare gasses).

There are two types of spectra: differential and integral. The differential spectra are generated when electrons of only one energy at a time are able to reach the detector. The integral spectra are obtained when electrons from all energies can reach the detector simultaneously.

Because the timescale between ionization (10^-15s) and vibration (10^-3s) is so large, the internuclear distance remains essentially frozen during ionization. This effect (Franck-Condon principle) is true for electronic transitions in general.

A further important principle is that the vibration that corresponds most closely to the change in equilibrium molecular geometry caused by a particular excitation will be the one that is most strongly excited. If for instance, one electron in the lone pair of an ammonia molecule is removed, then the ammonia ion becomes planar. [It is this configuration change that causes the long progression of lines that show the excitation of the umbrella bending vibration]

The branching ratios in ionization are determined primarily by the following rule: The cross-sectional areas of bands in a photoelectron spectrum are approximately equivalent to the relative probabilities of ionization to the different ionic states. More explicitly this means that the partial cross-section for ionization from a given orbital is proportional to the number of equivalent electrons available to be ionized. This is especially true for closed shell orbitals. This means that the intensity of a band resulting from the ionization of an orbital with four electrons (for example a doubly degenerate π-orbital ) will be twice that of an orbital with two electrons; intensities from all orbitals with two electrons will therefore be approximately equivalent.

Other generalizations regarding relative intensities of ionization bands have also been made such as: the intensities are proportional to a statistical weight of the ionic state produced.

Other more specific factors must also be taken into account such as the light source used (wavelength) and on the molecular orbitals (more precisely the atomic orbitals that make up the MOs).

Common types of Line Splitting

Complexity in photoelectron spectra often arises because of physical and electronic interactions that lead to more than one final state. As mentioned earlier, every transition results in a line on the photoelectron spectrum. When multiple final states exist, transitions resulting from each of these can lead to unanticipated multiplets. ⁴ Three common types are splitting are listed below:

1) The Jahn-Teller theorem essentially states that an unequal number of electrons in degenerate levels (for example two electrons in a triply degenerate subshell) will cause the molecule to break the symmetry and make the orbitals non-degenerate. Splitting of this type happens when the ejection of a photoelectron causes the loss of a high degree of symmetry because the degenerate levels are now unequally filled.

2) When degeneracy is broken because of spin-orbit coupling, i.e. when an ion has a difference in the spin and orbital angular momenta, a multiplet may appear. The splitting occurs because of the transitions to newly formed non-degenerate states. These non-degenerate states have an energy difference that is characteristic of the subshell’s spin-orbit coupling constant.

3) The third type of splitting, multiplet splitting, occurs when an unpaired electron existing in any of a molecule’s incomplete shells interacts with an unpaired electron formed by photoelectron ejection.

Nitrogen as an example

There are three vibrational photoionizations at about 15.6, 17.0, and 18.8 eV respectively. These correspond to the three molecular orbitals that are highest in energy. On the MO diagram of N₂ it is obvious that these are the 2σ_u, π_u and 3σ_g orbitals.

When an electron is ejected from a non-bonding orbital, the resulting ion has essentially the same internuclear distance. This results in a single peak on the photoelectron spectrum. The ionization of an electron from a weakly antibonding orbital (3σ_g) can be observed as the single line at 15.6 eV. The bonding π_u orbital splits into the multiplet around 17.0 eV because the equilibrium bond distance changes when an electron is removed from a strongly bonding orbital.

Description of a photoelectron spectrometer

Figure 5: A photoelectron spectrometer. Reprinted with permission of John Wiley & Sons, Inc.⁴

The essential components of a photoelectron spectrometer are a lamp, and ionization chamber, an electron energy analyzer, an electron detector and a recorder. The light source is a crucial part of the photoelectron spectrometer because any deficit in quality here will be amplified throughout the rest of the experiment. A good quality light source should be of high intensity (to shorten the time it takes to complete an experiment), narrowness of the principal ionization line, and the absence of any other lines. The most frequently used light source is He Iα which gives a resonance line at 584Å The ionization chamber is designed to ionize the molecules at a defined electrical potential. Photoionization cross-sections are fairly small (10^-150 x 10^-18 cm²), therefore the high intensity of the resonance lamps is not sufficient to make photoelectron spectroscopy a very sensitive technique. The pressure in the chamber is usually about 10^-3 - 10^-1 torr and the amount of sample is on the order of milligrams. This means that high vapor pressures are required for samples that are not heated and that most samples will require some heating.

List of easy to read introductory sources

1) Ghosh’s Introduction to Photoelectron Spectroscopy is a good introductory text. It also provides plenty of primary references and literature review articles as a jumping off point.⁴

2) The 3-part series of Journal of Chemical Education articles by David M. Hercules provide a good general overview of the physical principles of electron spectroscopy as well as a comprehensive reference list.

3) Drago’s Physical Methods for Chemists only has a short section (16.10) but he clearly works out some basic examples.

4) Electronic Photoelectron Spectroscopy by Ellis, Feher, and Wright is an excellent source for some more complex examples.

See also

• Angle resolved photoemission spectroscopy
• Inverse photoemission spectroscopy
• Ultra high vacuum

External links

• Presentation on principle of ARPES