Semiconductors are indispensable for solar cells and countless other technologies. What is crucial for this is their ability to change their electronic structure when excited by light or other energies: electrons in the semiconductor material leave their original position and create positively charged holes. The hole and electron then form pairs that behave like a new, independent particle. These quasiparticles formed by excitation – so-called excitons – play a key role in the generation of electricity through photovoltaics and the behavior of optoelectronic materials.
Wave function: Crucial but elusive
But a crucial feature of excitons has remained hidden until now: their wave function. This quantum physical state describes, among other things, the expansion, wave phase and internal structure of these quasiparticles and shapes their behavior: “The wave function of the exit zones determines their coupling, detachment and migration in the molecular lattice and therefore plays a central role,” explain Marcel Theilen from the University of Marburg and his colleagues. But measuring or mapping this wave function has so far been impossible.
That has now changed: “We have succeeded for the first time in experimentally reconstructing the spatial extent and temporal development of the wave function of an exciton in the first moments of its existence,” reports senior author Peter Puschnig from the University of Graz. The method they developed makes it possible for the first time to investigate the internal state of these important quasiparticles.
In time-resolved photoemission orbital tomography, a pump laser pulse (blue) creates a bound electron-hole pair (exciton) in the organic semiconductor material alpha-sexithiophene. The subsequent UV laser pulse shoots an electron from the exciton, whose energy and direction are measured. — © Andreas Windischbacher/University of Graz
This is how the measurement worked
The starting material for this breakthrough was alpha-sexithiophene (6T), a well-studied organic semiconductor often used in thin-film solar cells. “The samples are extremely thin, ordered films made of the rod-shaped molecule 6T, which were applied to a specially prepared copper surface,” explains co-author Monja Stettner from the Research Center Jülich. “The precise alignment of the molecules and their decoupling from the substrate are important in order to maintain the exciton long enough.”
In the experiment, the physicists first excited this semiconductor with light and thus generated the excitons. They then bombarded the sample with a strong laser pulse at different time intervals. This knocks the electrons out of the quasiparticles. “If you now measure the energy and direction of the electrons, you can use theoretical models to determine their quantum mechanical state,” explains Puschnig. This measurement method is called time-resolved photoemission orbital tomography (trPOT).
Excitons change their expansion
Through these measurements, the team was able to create snapshots of the quantum physical exciton state for the first time. Put together and combined with a model, a kind of video was created that reveals the spatial and temporal development of the exciton. “With our model, measured photoelectron images can be used to draw direct conclusions about the spatial shape and the inner quantum mechanical phase of the exciton wave function,” explains Theilen’s colleague Siegfried Kaidisch.
Specifically, it was shown, among other things, that the pairs of electron and hole are initially connected at a greater distance, but then move closer together in a fraction of a second. “The measurements show that the electron-hole pair is extended over about three molecules when it is formed,” reports Kaidisch. “Within the first 400 femtoseconds – quadrillionths of a second – their radius shrinks by around 25 percent.”
New insights into semiconductors
According to the physicists, their method opens up a way to measure and research the internal structure of excitons. “These results establish trPOT as a general and experimentally accessible approach to resolve exciton wave functions in a broad class of molecular and low-dimensional materials,” write Theilen and his colleagues. This could help optimize materials for organic solar cells and other photoelectric applications.
Source: Marcel Theilen (University of Marburg) et al., Physical Review X, 2026; doi: 10.1103/3zmg-276c