Velocity Mapped Photoelectron Imaging

The Photoelectric Effect

Photoelectron imaging is an extension of photoelectron spectroscopy which in turn has its roots in the photoelectric effect. The photoelectric effect was first documented by Hertz in 1887[1] electrons are emited from a metal when illuminated. The expectations of classical physics is that as energy accumulates in the metal, it will eventually transfer to the electrons and allow them to escape. In this scenario there should be a time delay between illumination and emission, although increasing the radiation frequency should increase the rate of electron production. Also increasing the intensity of the radiation should ultimately lead to production of electrons regardless of the frequency. However, experimental observations (particularly by von Lennard [2]) showed that electrons are produced instantaneously, regardless of the intensity or frequency. The number of electrons produced is actually proportional to the intensity of the radiation. The energy of the outgoing electrons has no relationship to the light intensity, but is proportional to the frequency of the radiation. However, the rate of electron production is independent of the frequency except that below a certain value (specific to each particular metal) no electrons are produced, regardless of illumination time.

Einstein explained the photoelectric effect by invoking energy conservation but crucially introduced the idea that energy from the radiation occurred in discrete amounts.[3] The idea of packets of energy, which Einstein called "light quanta" and which G. N. Lewis later called "photons"[4] was a crucial step in the development of quantum mechanics. Einstein proposed that the energy of the light quanta was proportional to the frequency of the radiation (E = hν), and that this energy is all transferred to the electron. The energy transferred is used to overcome the forces holding the electron to the metal and any excess appears as the kinetic energy (KE) of the departing electron. Using energy conservation the relationship

    E = KEmax + Φ                 (1)

is obtained where Φ is known as the work function of the metal, the minimum amount of energy required to liberate the electron. Since each photon transfers its energy to a single electron, the more photons (greater intensity) the greater the number of electrons, whilst the increased frequency leads to there being greater energy in excess of the work function.

Photoelectron Spectroscopy

In photoelectron spectroscopy, atomic and molecular species are bombarded with photons, ejecting electrons. The kinetic energy distribution of these electrons (the photoelectron spectrum) is a measure of the internal energy states. Again this is the result of energy conservation, equation (1) being rewritten as

eKE = hν - eBE                 (2)

where eBE, the electron binding energy replaces the work function. The eBE is the energy required to leave the probed species in a particular energy state, or more completely, the energy difference between the starting and final energy level of the probed species. The example shown in fig. 1 is for the ejection of electrons from the superoxide (O2-) anion using 455 nm photons.[5] The different transitions in the spectrum reflect excitation to the vibrational levels associated with the two lowest energy electronic states of neutral O2.

Photoelectron Imaging

Photoelectron imaging records the position of each photoelectron at the instant of detection. Within an experiment, the probed species interact with the laser radiation within a finite volume and electrons are produced at a variety of starting locations. The velocity mapping technique effectively removes the ambiguity in starting point by imaging in momentum space.[6] Using a combination of open electrodes (e.g. fig.2 although there are many ways to do this) an inhomgeneous electric field can be applied to act as a momentum funnel. In practical terms, all electrons with the same momentum vector, regardless of where they are produced, are mapped onto the same point on the detector. Faster electrons are found further from the center of the detector, slower electrons are found closer to the center.

Fig. 3 shows the image from which the photoelectron spectrum of fig. 1 was obtained. This 455 nm image of O2-[7] was recorded using the high resolution photoelectron imaging spectrometer at Austalia National University by the group of Dr. Stephen Gibson.

The image itself is a two dimensional projection of the original three dimensional distribution of electron linear momenta. This leads to some information loss as only the components of the linear momentum in the plane of the detector are revealed. There are ways to circumvent this problem in charged particle imaging. We use a linearly polarized laser to produce the photoelectrons. This confers cylindrical symmetry on the three dimensional distribution, with the laser electric vector being the symmetry axis. We can then mathematically reconstruct the distribution from its projection using mathematical techniques such as inverse Abel transformation.

The radial distribution of the electrons corresponds to the photoelectron spectrum. This is extracted by integration of intensity at individual radii and Jacobian transformation from momentum to energy space. A side effect is that the energy resolution declines as the eKE increases. Each ring in the image (fig. 3) corresponds to a particular transition in the spectrum (fig. 1). Energy conservation means that smaller radii correspond higher binding energy transitions. Additionally, the distribution of electrons about a given ring in the image (the photoelectron angular distribution) is often non-uniform (anisotropic). These angular distributions have a rich information content, informing as to the nature of the original wavefunction as well as details of the coupling of the electronic and internal degrees of freedom and electron molecule interactions as the electron departs the molecule.


[1] H. Hertz; Ueber einen Einfluss des ultravioletten Lichtes auf die electrische Entladung. Annalen der Physik 267 983 (1887)
[2] P. Lenard; Ueber die lichtelektrische Wirkung. Annalen der Physik 313 149 (1902)
[3] A. Einstein Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Annalen der Physik 322 132 (1905)
[4] G.N. Lewis The Conservation of Photons Nature 118 874 (1926)
[5] M. Van Duzor, F. Mbaiwa, J. Wei, T. Singh, R. Mabbs, A. Sanov, S.T. Gibson, S. J. Cavanagh, B.R. Lewis, J.R. Gascooke Vibronic Coupling in the Superoxide Anion: The Vibrational Dependence of the Photoelectron Angular Distribution. Journal of Chemical Physics 133 177311 (2010)
[6] A. Eppink and D.H. Parker; Velocity Map Imaging of Ions and Electrons Using Electrostatic Lenses: Application in Photoelectron and Photofragment Ion Imaging of Molecular Oxygen. Rev. Sci. Instrum. 68, 3477 (1997)
[7] R. Mabbs, F. Mbaiwa, J. Wie, M. Van Duzor, S.T. Gibson, S. J. Cavanagh and B.R. Lewis Observation of Vibration-Dependent Electron Anisotropy In O2- Photodetachment. Physical Review A 82 011401 (2010)