Hydrogen atom collisions with a semiconductor efficiently promote electrons to the conduction band

The Born–Oppenheimer approximation is the keystone of modern computational chemistry and there is wide interest in understanding under what conditions it remains valid. Hydrogen atom scattering from insulator, semi-metal and metal surfaces has helped provide such information. The approximation is adequate for insulators and for metals it fails, but not severely. Here we present hydrogen atom scattering from a semiconductor surface: Ge(111)c(2 × 8). Experiments show bimodal energy-loss distributions revealing two channels. Molecular dynamics trajectories within the Born–Oppenheimer approximation reproduce one channel quantitatively. The second channel transfers much more energy and is absent in simulations. It grows with hydrogen atom incidence energy and exhibits an energy-loss onset equal to the Ge surface bandgap. This leads us to conclude that hydrogen atom collisions at the surface of a semiconductor are capable of promoting electrons from the valence to the conduction band with high efficiency. Our current understanding fails to explain these observations.

The Born-Oppenheimer approximation is the keystone of modern computational chemistry and there is wide interest in understanding under what conditions it remains valid. Hydrogen atom scattering from insulator, semi-metal and metal surfaces has helped provide such information. The approximation is adequate for insulators and for metals it fails, but not severely. Here we present hydrogen atom scattering from a semiconductor surface: Ge(111)c (2 × 8). Experiments show bimodal energy-loss distributions revealing two channels. Molecular dynamics trajectories within the Born-Oppenheimer approximation reproduce one channel quantitatively. The second channel transfers much more energy and is absent in simulations. It grows with hydrogen atom incidence energy and exhibits an energy-loss onset equal to the Ge surface bandgap. This leads us to conclude that hydrogen atom collisions at the surface of a semiconductor are capable of promoting electrons from the valence to the conduction band with high efficiency. Our current understanding fails to explain these observations. Atoms and molecules colliding at solid surfaces create time-varying electric fields that, due to their finite masses and associated low speeds, represent frequencies typically ≤10 13 Hz, whereas much lighter electrons in solids oscillate at frequencies one to two orders of magnitude higher than this. This separation of timescales is used to justify the Born-Oppenheimer approximation (BOA) 1 , the bedrock of computational surface chemistry 2 , where electronic quantum states rapidly adjust to the motion of nuclei. Inelastic H atom surface scattering experiments have provided excellent benchmarks against which theoretical methods can and have been tested and proved 3 . Using this approach, the BOA has been shown to be justified for H atom scattering from Xe, where molecular dynamics (MD) simulations using a full-dimensional potential energy surface (PES) quantitatively reproduced energy losses measured in high-resolution scattering experiments 4 . The validity of the BOA in that case is not surprising since the lowest energy electronic excitations in Xe exceeded the energies of that work. Similar energy-loss measurements from experiments scattering H and D from the semi-metal graphene, where low-energy electron-hole pair (EHP) excitations are possible, also showed no signs of BOA failure [5][6][7] . Despite these successes, there are reasons to question the validity of the BOA (refs. 8,9 ). For example, energetic H atoms colliding at metal surfaces always excite EHPs (refs. 10,11 ). However, theoretical methods could successfully treat this with a weak-coupling 'electronic-friction' approximation 12,13 , suggesting BOA failure is not severe and can be accounted for in a perturbative fashion. Article https://doi.org/10.1038/s41557-022-01085-x shows energy-loss distributions for three values of E i larger than the surface bandgap. In all three cases, the distributions are bimodal and the MD trajectories reproduce only the feature seen at low values of energy loss. Hereafter, we refer to this feature as the adiabatic channel. The second feature appearing at higher energy losses is absent in the adiabatic MD simulations, strongly suggesting that this channel involves conversion of H atom translational energy to electronic excitation of the Ge solid. This idea is further supported by the observation that the energy-loss onset of this feature is coincident (within experimental uncertainty) with the Ge surface bandgap of 0.49 eV at all values of E i . Furthermore, as expected for a channel involving BOA failure, this channel is strongly promoted by incidence translational energy, becoming about 90% of the observed scattering at the highest value of E i = 6.17 eV. For these reasons, we assign the high energy-loss feature to an electronically non-adiabatic process where the collision of the H atom at the surface promotes an electron above the bandgap of the Ge surface. We refer to this mechanism hereafter as the VB-CB channel.
Experiments with semiconductors present an opportunity to make predictions from our current understanding about a fundamentally different class of solids. This is true if semiconductors behave in some hybrid fashion, reflecting some intermediate between insulators and metals. However, let us consider semiconductors from the point of view of another kind of time-varying electric field. We know visible light with electric fields oscillating at ~10 14−15 Hz efficiently excites electrons from the valence band (VB) to the conduction band (CB), forming the basis for a large fraction of optical science and technology. This raises the question: if collisions of atoms and molecules with semiconductors could produce time-varying electric fields oscillating at similar frequencies, would they not also excite VB electrons to the CB and might this not provide important new avenues of research with the promise of new technology? If we were to adopt the physical picture derived from our study of metals, where electronic friction describes BOA failure, the answer to this question would certainly be 'no' or more precisely 'only weakly', as electronic-friction theories lead to hot EHP distributions that still favour low-energy excitation near the Fermi level 12 . Unfortunately, scattering experiments with semiconductors that test the validity of the BOA are rare. Transient currents were observed when Xe atoms with energies between 3 and 10 eV were scattered from surfaces of semiconductors [14][15][16] . However, this resulted from the creation of a local hot spot where initial phonon excitation subsequently transferred energy to EHPs. While these experiments provide us with clear evidence of BOA failure in a semiconductor, we can gain only little insight into the dynamics of the atom-surface collision. In fact, an electronically adiabatic model could describe the energy loss of scattered Xe atoms.
In the work presented in this article, we produce H atoms whose speeds are high enough to test the limits of the BOA directly by investigating the characteristics of their collisions with a semiconductor surface. The measured H atom energy-loss spectra and angular distributions reveal the excitations appearing in the solid on the sub-picosecond time scale. We find that, not only is VB-CB excitation possible, at sufficiently high energies it dominates the energy-transfer dynamics, showing that new physical mechanisms are at play. Specifically, we present translational energy-loss measurements on energetic H atoms scattered from a reconstructed Ge(111)c(2 × 8) surface along with first principles electronically adiabatic MD simulations, performed with a newly developed high-dimensional neural-network PES (NN-PES). When incidence energies are below the bandgap, only one scattering channel arises with small energy losses nearly identical to those seen in the MD simulations. These exhibit collision dynamics similar to those seen in H scattering from Xe. Surprisingly, at higher incidence energies, a second channel appears whose energy-loss onset is coincident with the semiconductor bandgap. This channel is absent in the MD simulations with and without electronic friction. The importance of this channel increases rapidly with H atom velocity-a signature of BOA failure-and accounts for ~90% probability at the highest H atom incidence energies of this work. Figure 1 shows experimental translational energy-loss distributions for H atoms scattered from Ge(111)c(2 × 8) 17 at incidence energies E i above and below the 0.49 eV surface bandgap 18 . We note that the given value for the surface bandgap was determined at a surface temperature of 30 K. However, a similar value is expected at room temperature since the reconstruction of the surface is unchanged. Also shown are the predictions of the electronically adiabatic MD trajectory calculations. Below the bandgap (Fig. 1a) only a single feature appears in the energy-loss distribution. The MD simulations reproduce the experimental result extremely well. MD simulations with electronic friction 19 at the level of local density friction approximation (LDFA) 20 fail to describe the energy-loss distributions (Extended Data Fig. 1). Analysis of adiabatic MD trajectories shows that H atoms interact with the Ge surface for only a few femtoseconds and that energy exchange is limited. Figure 1b Article https://doi.org/10.1038/s41557-022-01085-x Figure 2 shows differential properties from both experiment and theory for H atoms incident at three angles ϑ i and at E i = 0.99 eV. Here, polar plots display the final translational energy E f as a function of final scattering angle ϑ f . The black dotted lines show the expected minimal energy loss for excitation of an electron across the surface bandgap, which demarcates the adiabatic from the VB-CB channel. Experiment shows that the VB-CB channel exhibits a much narrower angular distribution (Table 1) than the adiabatic channel at all three incidence angles. The MD simulations yield similar differential scattering maps as seen in experiment for the adiabatic channel only. The energy loss agrees with experiment and even the experimentally observed dependency of the angular distribution on ϑ i is reproduced. The VB-CB channel is absent in the MD simulations. Figure 3 shows polar plot representations similar to Fig. 2 emphasizing the incidence energy dependence of the scattering. As before, the experimental results show bimodal scattering distributions with two well-resolved channels separated in energy space by the bandgap energy, marked as black dotted lines. The angular distributions of both channels broaden between E i = 0.99 and 1.92 eV, but the VB-CB channel broadens significantly more as it is narrower at E i = 0.99 eV ( Table 1). The adiabatic MD simulations (Fig. 3c,d) reproduce this effect for the adiabatic channel. c f

Experiment Simulation
Norm. H atom flux The average energy losses derived from the experiments are summarized in Table 2. Note that for the adiabatic channel, the average energy transferred to the surface <E i − E f > is a small and nearly constant fraction (10 ± 5%) of E i . The VB-CB channel behaves differently, as the fraction of incidence energy transferred to the solid goes up dramatically as E i is reduced. This is an influence of the surface bandgap, where the absolute of energy lost must exceed 0.49 eV, regardless of E i . Hence, at lower values of E i the fractional energy loss must sharply increase. Note also that the average energy lost decreases only slightly with increasing ϑ i for both channels.

Discussion
We start by highlighting some of the key observations just presented and their implications. First, Fig. 2 shows clearly that the most probable value of ϑ f depends on the chosen value of ϑ i , proving the scattered atoms did not thermalize with the solid. Thermalization occurs on the picosecond timescale. Thus, we conclude that the scattered atoms in both channels experience a sub-picosecond interaction time with the surface. Second, there is evidence of sticking, even though integrated scattering probabilities such as sticking probabilities cannot be easily obtained from in-plane differential scattering measurements, since the fraction of incident atoms that scatter out of the detection plane may also depend on incidence conditions and branching channel. We can nevertheless integrate the observed scattering at flux over E f and ϑ f . These integrals scaled to the experimentally observed adiabatic channel at E i = 0.99 eV and ϑ i = 45° appear as numbers next to each differential scattering diagram in Figs. 2 and 3. They are given as ratios that report the relative contributions of the two scattering channels. There is an overall loss of signal between E i = 1.92 and 0.99 eV. If we were to assume the out-of-plane scattering fraction was independent of E i , we would conclude that the sticking probability decreases with increasing incidence energy. A similar trend is seen in the MD simulations. Note also that the branching ratios shown in Fig. 3a,b are consistent with those of Fig. 1b,c, which represent the branching between the two scattering channels detected at ϑ f = 45° only. This agreement suggests that the branching seen in Fig. 1c (E i = 1.92 eV) is representative of other scattering angles.
The major outcome of this work is the observation that an H atom scattering from a semiconductor may experience one or the other of two types of interaction, either a mechanical interaction well described within the BOA or a strong non-adiabatic interaction capable of promoting an electron to energies above the bandgap. We emphasize that while there are similarities with past work, the behaviour seen here is qualitatively different from previous observations involving insulators, metals or semi-metals. For example, the adiabatic channel seen in Figs. 1-3 exhibits marked similarities to H atom scattering from insulating Xe. However, that system exhibited no BOA failure whatsoever. Conversely, H scattering trajectories describing collisions with metals simultaneously excite both phonons and EHPs (refs. [10][11][12][13] ), the two excitations being inextricably linked  The fact that H scattering from Ge exhibits branching behaviour between two distinct dynamical channels is consistent with a two-state picture. We envision that the H atom proceeds initially along the ground electronic state until it encounters a seam of crossing associated with a short-lived electronically excited state. (Note that the word state is used here loosely as many electronic states are involved in the VB and CB of the system.) We assume that this state rapidly decays into unoccupied electronic states within the CB. At low incidence energies, reaching the seam of crossing requires specific approach, but at higher energies other regions of the seam become accessible with reduced steric restrictions.
Evidence supporting this picture can be found in observations of this work, especially Fig. 2. Note that the VB-CB channel exhibits a narrow angular distribution, peaking near the specular scattering angle (arrows in Fig. 2). This shows that there is no preference for loss of incidence energy parallel or perpendicular to the surface when inducing electronic excitation. A narrow angular distribution is typical of scattering influenced by directional forces associated with atomic orbitals with preferred orientations, which is consistent with the suggested mechanism of a curve crossing, where H atom collisions must occur at specific surface sites (Ge atoms) and with specific approaching geometries. Figure 3 shows that at a higher energy these steric restrictions appear to be less severe and consequently the VB-CB scattering angular distribution broadens.
Contrasting this behaviour, the adiabatic channel exhibits a markedly broader angular distribution even at low incidence energies. This indicates a large corrugation of the PES experienced by the atoms passing through the adiabatic channel. Despite the many final scattering angles, the energy loss follows a hard-sphere line-of-centres binary collision model (black dashed lines). This indicates that the H atom scattered through the adiabatic channel is experiencing binary collisions with many impact parameters. It is not surprising, due to the complex surface structure of the Ge(111)c(2 × 8) surface, if the H atoms scattering through the adiabatic channel sample a large fraction of the surface unit cell.
Bimodal energy-loss distributions may be produced without electronic excitation. For example, H scattering from a graphene layer involves trajectories that either fail or succeed in surmounting a chemisorption barrier [5][6][7] . H atoms reflected from the barrier experience weak van der Waals interactions with little energy transferred, while H atoms surmounting the barrier couple strongly to in-plane phonons of the graphene layer 5 . In contrast to this behaviour, the electronically adiabatic MD simulations carried out in this work show no sign of bimodal distributions. This is consistent with the absence of a chemisorption barrier in the H/Ge system. The combined strength of the experimental and theoretical results supports our assignment of an electronically adiabatic and a non-adiabatic channel.
While it is common knowledge that absorption of photons in the bulk of a semiconductor excites electrons from the VB to the CB, this work shows that a colliding atom may efficiently promote electrons in a similar way in a purely surface-specific process. The probability to convert translational energy of the H atom to electronic excitation of the solid dramatically increases with incidence energy, as does the average excitation energy. The large excitation probability as well as the large energy loss is inconsistent with electronic-friction theories. Hence, this work stands as a challenge for new theories of electronically non-adiabatic surface chemistry. We hasten to add that the designation of this behaviour as VB-CB represents a simplified viewpoint. The precise nature of the excited electronic states involved is still unknown. Transient surface-localized excitations (even plasmons) might be important. Nevertheless, the observation that electronic excitation dominates the dynamics in collisions of a simple atom with a semiconductor opens new horizons for research into non-adiabatic effects in surface chemistry and chemical sensors.

Online content
Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41557-022-01085-x.  Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.