Electrons confined in solids do not spill out spontaneously. Some amount of energy, or work, has to be applied to liberate them out. The work function is the minimum energy required to take out one electron through the surface. It can be measured by analyzing the slowest electrons emitted from the substrate applied with excess energy.

From the time of Einstein [1], work function has been measured with the typical precision of 0.1 to 0.01 eV; reports with sub-0.01 eV precision are rare [2, 3]. In a recent publication [4], we showed that there is a way to narrow down the precision to sub-0.001 eV (sub-meV).

The key to improve the precision was to look into the direction of the slowest electrons emitted from the surface.

Imagine that there is a person who is going to roll a ball from the bottom of a slope. If the ball is to be rolled at the minimum speed to reach the top, toward which direction should the ball be rolled? The answer is: towards the steepest direction; otherwise, the ball will roll down before reaching the top.

Although this question appears trivial, applying this type of question to the electrons passing through the surface was the key. The Q & A illustrates that the slowest electrons that marginally emerged from the surface are directed along the surface normal. If the emission into the surface normal can be selected out, it becomes possible to see the clean signals of the slowest electrons that encode the work function.

Here, we applied angle-resolved photoemission spectroscopy (ARPES), by which the energy and angular distribution of the out-emitted photoelectrons can be detected. ARPES is often applied to the fast photoelectrons as their distribution replicates the electronic band structures of crystals [5]. 

Simple though it may seem, applying ARPES to the slowest electrons was a technical challenge. To drive the electrons into the analyzer located at ~34 mm away from the sample surface, we had to mind about the small electric field that remains in the spectrometer because the field can easily deflect the direction of the slow electrons. Besides, the electrons had to be emitted from a small point on the sample surface. To take control over the slowest electrons, we used the techniques of ARPES powered by lasers. The know-hows accumulated to detect the fairly slow electrons in laser ARPES [6, 7] was upgraded and applied to the slowest [4].

By using the upgraded laser APRES system, we successfully detected the genuine cutoff formed by the slowest electrons emitted into the surface normal. The slowest-end cutoff was sharper than the Fermi cutoff located on the fast end of the spectrum. The read of the slowest end is the work function and it stayed at φ = 5.5553 ± 0.0004 eV at least from 30 to 90 K; note, the precision is better than 1 meV.

With the sub-meV precision, we were able to discern the aging of the gold surface even though it can remain shiny over thousands of years. Just in half a day, the work function of the (111) surface of a gold crystal lowered by 0.0055 eV due to the degradation of the surface subjected to the gaseous molecules remaining in the ultrahigh vacuum chamber of the ARPES spectrometer.

Because the work function is a fundamental electronic property of the surface, our study would be of relevance to the field of surface science and engineering; it would be interesting to monitor the work function during catalytic interactions, across phase transitions, upon bending or when the surface is hit by a femtosecond light pulse. High-school students who have learnt Einstein’s theory of the photoelectric effect [1] are also the potential audience because the derivation of the electron trajectory is based on classical mechanics at the high-school level, as illustrated in the Q & A shown above.

This study was conducted under the ISSP-CCES Collaborative Program set by the two institutes, ISSP (The University of Tokyo, Japan) and CCES (Institute for Basic Science, Korea), and the fiber-laser ARPES system was set up in the joint research lab launched at Seoul National University [8].

1. Einstein, A. Ann. Phys. 5, 20 (1905); Einstein pointed out that light can behave as a particle by writing down ε = hν - φ, which relates the work function φ and maximum kinetic energy of the emitted photoelectrons ε to the frequency of light ν, or to the photon energy hν.
2. Cardona, M. & Ley, L. “Photoemission in Solids” (Springer-Verlag, Berlin, 1978).
3. Koitaya, T. et al., J. Chem. Phys. 136, 214705 (2012).
4. Ishida, Y. et al., Commun. Phys. 3, 158 (2020).
5. Reviews of modern ARPES: Yang, H. et al., Nat. Rev. Mater. 3, 341 (2018); Lv, B.-Q., Qian, T. & Ding, H. Nat. Rev. Phys. 1, 609 (2019); Sobota, J. A., He, Y. & Shen, Z.-X. arXiv:2008.02378 (2020).
6. Ishida, Y. et al., Rev. Sci. Instrum. 85, 123904 (2014).
7. Ishida, Y. et al., Rev. Sci. Instrum. 87, 123902 (2016).
8. Feder, T. Physics Today 72, 26 (2019).