Electronic excitations by chemical reactions on metal surfaces

Abstract

Dissipation of chemical energy released in exothermic reactions at metal surfaces may happen adiabatically by creation of phonons or non-adiabatically by excitation of the electronic system of the metal or the reactants. In the past decades, the only direct experimental evidence for such non-adiabatic reactions has been exoelectron emission into vacuum and surface chemiluminescence which are observed in a special class of very exothermic reactions. The creation of e–h pairs in the metal has been discussed in many theoretical models but it was only recently that a novel experimental approach using Schottky diodes with ultrathin metal films makes direct measurement of reaction-induced hot electrons and holes possible. The chemical reaction creates hot charge carriers which travel ballistically from the metal film surface toward the Schottky interface and are detected as a chemicurrent in the diode. By now, such currents have been observed during adsorption of atomic hydrogen and deuterium on Ag, Cu and Fe surfaces as well as chemisorption of atomic and molecular oxygen, of NO and NO₂ molecules and of certain hydrocarbons on Ag. This paper reviews briefly exoelectron and chemiluminescence experiments and the concept of the Nørskov–Newns–Lundqvist model. The major part is devoted to the detection of chemically induced e–h pairs with thin metal film Si Schottky diodes by discussing the different influences on the chemicurrent magnitude and presenting experimental results predominantly with hydrogen and deuterium atoms. The experiments introduce a new method to investigate surface reaction kinetics and dynamics by use of an electronic device. In addition, the diodes may be used as selective reactive gas sensors.

Introduction

Chemical reactions on surfaces are of fundamental interest as well as of enormous technological relevance. As Masel [1] pointed out, ‘90% of all chemicals are presently produced via a heterogeneously catalyzed process where a reaction occurs on the surface of a catalyst’. In addition, growth of thin films, evaporation, gas scattering including sputtering, tribology and corrosion inhibition are other applications where gas–surface interactions are involved. Surface reactions have been studied for more than two centuries [1] but considerable progress has been made after introducing ultrahigh vacuum (UHV) techniques in the 1960s which allow the preparation of well-defined systems without ambient atmosphere. Tremendous effort has been expended to achieve a detailed understanding of the kinetics and dynamics of surface reactions using a large variety of experimental and theoretical methods [1], [2], [3], [4], [5], [6], [303].

Reaction paths have been characterized by identifying precisely initial, intermediate and product states. However, the knowledge about the physical processes behind the transitions from one to the other state is not satisfactory and often speculative. One of the open questions is related to the energy-transfer problem how released chemical energy in exothermic reactions on surfaces is dissipated. Reactions are called exothermic if the enthalpy change is negative. The chemical energetics of many reactions are well known [7], [8]. Depending on the strength of the broken and formed chemical bonds on the surface, energies of typically a few electronvolts (eV) per reaction event are deposited.

The present study is devoted to a novel experimental approach to the energy-transfer problem with chemical reactions on metal surfaces. Here, the term chemical reaction is assumed to describe reactive scattering events on surfaces under following conditions:

• the gas beam impinging on the surface is thermal, i.e., the kinetic energy of the incident gas particles is well below 0.3 eV;

• the gas particles are neutral, i.e., ion–surface interactions are excluded;

• the chemical reaction leads to product formation, i.e., it causes bond breaking or bond formation at the surface.

Typical reactions of this type are atomic and molecular adsorption processes, dissociative chemisorption, abstraction reactions, i.e., the removal of adsorbates by reactions with particles from the gas phase, and catalytic reactions between different chemical species. Other gas–surface interaction like elastic and inelastic scattering, trapping-desorption, surface ionization or neutralization are not considered.

Exothermic reactions on metals transfer energy from the reaction complex into the nuclear and electronic degrees of freedom of the metal substrate. They may induce the following elementary excitations as schematically displayed in Fig. 1 for an adsorption process:

• Quantized lattice vibrations or phonons: their energies are typically in the 10 meV range [9] which may be two or even three orders of magnitude smaller than chemical energies. Consequently, the direct transfer of energy into the phonon system of the metal requires multiple excitation of phonons by the chemical reaction. This may occur in one step which is quantum-mechanically unfavored or in a cascade of subsequent excitation steps. As explained in Section 1.3, the direct energy transfer to phonons is called adiabatic.

• Electron–hole (e–h) pairs: a high density of low-lying excited electronic states exists in metals due to the zero-gap e–h pair continuum. The excitation of e–h pairs leads to an excited or hot electron with energy above the Fermi level E_F and to an excited or hot hole with energy below E_F. As pointed out in Section 1.3, this energy-transfer channel is expected under certain conditions from pure theoretical considerations like the Anderson theorem.

• Collective electronic excitations or plasmons: the excitation of plasmons by chemical reactions may be neglected in most cases since the deposited energy per reaction is typically smaller than the plasmon energy. The latter depends on the electron density and is usually well above 5 eV [10]. However, with certain gas–metal combinations with high exothermicity and small plasmon energies, e.g., with alkali metals, such excitations may become relevant.

Items 2 and 3 describe electronic excitations of the metal. The corresponding chemical processes on the surface are referred as non-adiabatic. For the given reasons, chemically induced plasmons are ignored furtheron and electronic excitations will be identified with e–h pairs only in this review.

Heretofore, it is unresolved for most exothermic surface reactions on metals whether electronic excitations are generated at all and, if so, whether phonon or e–h pair excitation is the dominating dissipation channel. Due to the lack of experimental evidence, many adsorption or reaction models use the adiabatic approximation (see Section 1.3) and neglect electronic excitations. They assume that creation of phonons is by far the most relevant process. The present work will present experiments which give direct evidence of chemically induced e–h pairs in metals. They may establish a growing database which can initiate theory to include non-adiabatic processes in their models.

The direct detection of excited electrons or holes in metals is challenging because—as it will be discussed in detail in 2 Exoelectron emission and surface chemiluminescence, 3 Direct detection of e–h pairs generated by chemical reactions on metal surfaces—they relax within 10⁻¹⁴ s by emitting phonons or, less likely, within 10⁻⁹ s by emitting photons. This is schematically depicted in Fig. 1. In a very short period of time, all electronic excitations are thermalized and have transferred their energy into the phonon system of the substrate if no excited electrons or photons leave the metal. Hence, reaching thermal equilibrium, the total released enthalpy of a surface reaction is expected to be converted into heat. This is the basis of calorimetry in which heats of reaction are determined by measuring the rise of the substrate temperature [2], [11]. The assumption is true unless work is involved. If chemical energy is transferred into work, e.g., by emission of particles like electrons, ions or photons the heat change is smaller than the released enthalpy.

Such situations are shown in Fig. 1. Excited electrons with sufficient energy larger than the metal work function may overcome the surface barrier leading to emission of the so-called chemically induced exoelectrons into vacuum. Generated photons may also leave the metal and this effect is called surface chemiluminescence. Exoelectron emission and surface chemiluminescence give direct evidence that a chemical reaction creates electronic excitations. Both phenomena have been observed in a special class of highly exothermic surface reactions which are briefly reviewed in Section 2. With this reaction type, calorimetric measurements must give erroneous results since the emitted particles carry away a part of the released chemical energy.

It has been unclear for a long time if exothermic reactions which do not lead to exoelectron or photon emission may generate electronic excitations in metals. Recently, a novel approach to detect chemically created hot electrons and hot holes has been presented. The framed inset in Fig. 2 shows the principle of hot electron detection using metal–semiconductor (Schottky) contacts with ultrathin metal films. The Fermi level, E_F, the conduction band minimum (CBM), and the valence band maximum (VBM), as well as the Schottky barrier Φ_n are labeled in the figure. When an e–h pair is generated on the metal surface, the excited electron may travel ballistically through the thin metal film and traverse the Schottky barrier if the kinetic energy of the electron is larger than the barrier height. The Schottky barrier works as a high-pass energy filter. Reaching the semiconductor, the electron is detected as a current in the device. This current is called chemicurrent furtheron. The details of this detection method and the design of such Schottky diodes will be discussed in Section 3.

Fig. 2 demonstrates that there is indeed a current response at a Ag/n-Si(1 1 1) diode with 75 Å of metal when the device is exposed to atomic hydrogen. At $\text{t=0}\text{s}$, the beam shutter is opened and at $\text{t=2900}\text{s}$, it is closed again. In between a chemicurrent is observed which decays exponentially from a maximum value of 720 pA to a steady-state current of approximately 100 pA. This transient reproduces the chemical kinetics of the surface reaction. So far, experiments were performed with Ag, Cu and Fe surfaces exposed to atomic hydrogen and deuterium as well as to molecular and atomic oxygen and NO or NO₂ molecules. Data of the studies will be presented and discussed in detail in Section 4.

This method to detect directly chemically induced e–h pairs on metals combines metal surface physics and semiconductor device technology. It may be used to monitor exothermic chemical reactions with an electronic device and may also be applied to exoelectron and chemiluminescent reaction systems where it is expected to be much more sensitive. Using p-type doped semiconductors, hot holes may be detected as well. The experimental approach is useful to observe e–h pairs created by other than chemical action, too. An outlook is given in Section 5.

A close relationship between electronic excitations and other gas–surface interactions has also been demonstrated in experiments like e–h pair creation by impingement of hyperthermal gas beams [12], [13], [14], [15], electron-induced desorption or reactions by injection of hot electrons with a scanning tunneling microscope or tunnel contacts [16], [17], [18], [304], [305], photochemistry at surfaces [19], [20], vibrational lifetimes of adsorbates [21], [22], [23], [24], [25], [26], [27] or electronic friction [28]. The discussion of these phenomena is beyond the scope of the present work and the reader is referred to the respective literature.

The dynamics of surface reactions is not exactly solvable due to the enormous number of degrees of freedom. Appropriate approximations are necessary. One of these is the common adiabatic or Born–Oppenheimer approximation which assumes a decoupling between nuclear and electronic motion. The nuclei appear static to the electrons and, hence, the electrons generate a potential which governs the nuclear motion [29], [30], [31]. The adiabatic approach neglects excitations of the electronic system by nuclear motion.

In mathematical notation, the general spinless Hamiltonian of the whole system with N nuclei of mass M and n electrons may be formally written as [30]

$$\text{H}\text{̂}\text{=}\text{T}\text{̂}{}_{\mathrm{<mtext>n</mtext>}}\text{(}\text{R}\text{)+}\text{H}\text{̂}{}_{\mathrm{<mtext>e</mtext>}}\text{=}\text{T}\text{̂}{}_{\mathrm{<mtext>n</mtext>}}\text{(}\text{R}\text{)+}\text{T}\text{̂}{}_{\mathrm{<mtext>e</mtext>}}\text{(}\text{r}\text{,}\text{R}\text{)+}\text{V}\text{̂}{}_{\mathrm{<mtext>e</mtext><mtext>–</mtext><mtext>e</mtext>}}\text{(}\text{r}\text{)+}\text{V}\text{̂}{}_{\mathrm{<mtext>e</mtext><mtext>–</mtext><mtext>n</mtext>}}\text{(}\text{r}\text{,}\text{R}\text{)+}\text{V}\text{̂}{}_{\mathrm{<mtext>n</mtext><mtext>–</mtext><mtext>n</mtext>}}\text{(}\text{R}\text{),}$$

where r, R represent the coordinates of all electrons and nuclei, respectively. $\text{T}\text{̂}{}_{\mathrm{<mtext>n</mtext>}}$ is the operator of the kinetic energy of the nuclei, i.e.,

and $\text{H}\text{̂}{}_{\mathrm{<mtext>e</mtext>}}$ denotes the electronic Hamiltonian for fixed nuclei positions. $\text{T}\text{̂}{}_{\mathrm{<mtext>e</mtext>}}$ is the operator of the kinetic energy of the electrons. The potentials $\text{V}\text{̂}{}_{\mathrm{<mtext>e</mtext><mtext>–</mtext><mtext>e</mtext>}}\text{,}\text{V}\text{̂}{}_{\mathrm{<mtext>e</mtext><mtext>–</mtext><mtext>n</mtext>}}\text{,}\text{and}\text{V}\text{̂}{}_{\mathrm{<mtext>n</mtext><mtext>–</mtext><mtext>n</mtext>}}$ describe the various Coulombic interactions between the charged particles. Solutions ψ(r, R, t) of the time-dependent Schrödinger equation may be expanded using a suitable basis set of electronic wavefunctions {φ_k(r, R)} according to

$$\text{ψ(}\text{r}\text{,}\text{R}\text{,t)=}\text{∑}\text{k}\text{χ}{}_{\mathrm{k}}\text{(}\text{R}\text{,t)φ}{}_{\mathrm{k}}\text{(}\text{r}\text{,}\text{R}\text{).}$$

The Schrödinger equation is then rearranged into a system of coupled equations of the form

$$\text{i}\text{ℏ}\text{∂}\text{∂t}\text{χ}{}_{\mathrm{k}}\text{=(}\text{T}\text{̂}{}_{\mathrm{<mtext>n</mtext>}}\text{+}\text{V}\text{̂}{}_{\mathrm{<mtext>n</mtext><mtext>–</mtext><mtext>n</mtext>}}\text{)χ}{}_{\mathrm{k}}\text{+}\text{∑}\text{j}\text{(〈φ}{}_{\mathrm{k}}\text{|}\text{T}\text{̂}{}_{\mathrm{<mtext>e</mtext>}}\text{+}\text{V}\text{̂}{}_{\mathrm{<mtext>e</mtext><mtext>–</mtext><mtext>e</mtext>}}\text{+}\text{V}\text{̂}{}_{\mathrm{<mtext>e</mtext><mtext>–</mtext><mtext>n</mtext>}}\text{|φ}{}_{\mathrm{j}}\text{〉+}\text{K}\text{̂}{}_{\mathrm{kj}}\text{)χ}{}_{\mathrm{j}}$$

with the coupling operators $\text{K}\text{̂}{}_{\mathrm{kj}}$ between nuclear and electronic motions

which depend on the velocities ℏ∇_RN/M of the nuclei and the derivative of the electronic states with respect to nuclear position.

In the adiabatic approximation these coupling terms are neglected. The φ_k are the eigenfunctions of the electronic Hamilton operator with static nuclei and depend functionally on r but parametrically on R [30]. The Schrödinger equation may be separated into a stationary electronic and a time-dependent nuclear part:

$$\text{(}\text{T}\text{̂}{}_{\mathrm{<mtext>e</mtext>}}\text{+}\text{V}\text{̂}{}_{\mathrm{<mtext>e</mtext><mtext>–</mtext><mtext>e</mtext>}}\text{+}\text{V}\text{̂}{}_{\mathrm{<mtext>e</mtext><mtext>–</mtext><mtext>n</mtext>}}\text{+}\text{V}\text{̂}{}_{\mathrm{<mtext>n</mtext><mtext>–</mtext><mtext>n</mtext>}}\text{)φ}{}_{\mathrm{k}}\text{(}\text{r}\text{,}\text{R}\text{)=ε}{}_{\mathrm{k}}\text{(}\text{R}\text{)φ}{}_{\mathrm{k}}\text{(}\text{r}\text{,}\text{R}\text{),}$$

$$\text{[}\text{T}\text{̂}{}_{\mathrm{<mtext>n</mtext>}}\text{+ε}{}_{\mathrm{k}}\text{(}\text{R}\text{)]χ}{}_{\mathrm{k}}\text{(}\text{R}\text{,t)=}\text{i}\text{ℏ}\text{∂}\text{∂t}\text{χ}{}_{\mathrm{k}}\text{(}\text{R}\text{,t).}$$

The electronic ground state energy ε_k(R) constitutes the multidimensional potential energy surface (PES) of the surface reaction. Nowadays, the PES may be calculated or modeled from first principles using density functional theory (DFT) [32], [33], [306]. As soon as a sufficiently accurate PES of the relevant nuclear degrees of freedom is obtained, the reaction dynamics may be studied. Various approaches have been developed from classical trajectories in molecular dynamics calculations [34] to fully quantum-mechanical treatments [33], [306]. The most impressive progress has been achieved in calculating the dissociation dynamics of hydrogen molecules on transition metals [33], [35], [36], [37], [38], [39], [40], [306], [307], [308]. The adsorption of H₂ on Pd(1 0 0) was the first model system on which Gross et al. [36], [37] applied six-dimensional quantum mechanics according to the six degrees of freedom of the H₂ molecule. The nuclei of the solid were assumed to be fixed. These investigations revealed the influence of surface corrugation on the reaction, dynamic steering and steric effects. Quantum-state- and energy-dependent sticking probabilities were determined. The theories are fully elastic, i.e., no energy transfer to metallic degrees of freedom is considered. Due to the low exothermicity of adsorption of hydrogen molecules on metal surfaces, electronic excitations are expected to play a minor role in the surface process. Recently, Brivio et al. [41], [309] derived quantum-mechanically the sticking coefficient for hydrogen molecules on Cu(1 1 1) including electronic excitations. They demonstrated that e–h pair creation may be indeed negligible for this system, but that dynamical polarization of the metal electrons contributes significantly to the sticking. For a detailed discussion of the various theoretical studies of surface reactions within the adiabatic approximation, the reader is referred to several excellent reviews on this topic [30], [32], [33], [42], [306].

According to Eq. (5), the coupling terms $\text{K}\text{̂}{}_{\mathrm{kj}}$ depend on the nuclear velocities. They may be neglected if the interaction potentials do not change rapidly during the surface reaction and if the coupling is much smaller than the spacing between the electronic energy levels [30]. The second condition is problematic in metals where the electronic level spacing is zero due to the e–h pair continuum. Therefore, the adiabatic approximation appears questionable with rapid and exothermic reactions on metal surfaces. This statement is supported by the fundamental Anderson orthogonality theorem [43]. It states that the ground state of a many-body Fermi system with infinite extension is orthogonal to the ground state of the same system in the presence of a localized scattering potential. It implies that an infinite Fermi system cannot stay in the ground state if a localized potential is suddenly switched on. In a metal, electronic (e–h pair) excitations are necessarily generated as a symmetry-breaking process [44].

On the background of this theorem, the response of electrons in a jellium metal to time-dependent perturbations has been theoretically studied by various groups [45], [46], [47], [48], [49], [50], [51], [311]. The initial investigations were motivated by X-ray absorption and X-ray photoemission experiments to explain the influence of the suddenly introduced core hole on the spectra. Müller-Hartmann et al. [48] performed calculations of localized dynamic perturbations in metals within the Tomonaga boson model which is exactly solvable and treats low-energy e–h pairs as bosons [310]. The results demonstrate that electronic excitations are created when a localized potential is turned on and off and respective excitation spectra were calculated depending on the time dependence of the potential.

Likewise, in gas–surface reactions on metals e–h pair excitations are expected. The non-adiabatic treatment of the interaction according to Eq. (4) is a formidable problem. A formal approach may use the diabatic representation [52], [53], [54], [312]. Since both terms, diabatic and non-adiabatic, are found in literature they are used here side-by-side. Diabatic states are introduced to describe the system in possible excited states. Their calculation is not straightforward and the choice of the diabatic basis set is not unique. Due to these difficulties, a diabatic description needs much empirical input in order to achieve good numerical results.

To visualize the adiabatic and diabatic description of a gas–surface interaction, one-dimensional PES (potential energy curves or PECs) are displayed in Fig. 3. Originally, such PES schemes were introduced in the famous paper of Lennard-Jones in 1932 [55] in which dissociative chemisorption is described. Diabatic PES were already used in 1935 by Ogg and Polanyi [56] to describe ionogenic gas reactions.

The curves in Fig. 3 give the total energy of the system as a function of the reaction coordinate which is the distance z of the particle from the metal surface. The diabatic PECs (1) and (2) in Fig. 3 belong to two different chemical situations. For example, curve (1) may represent a molecule–surface potential and curve (2) the atom–surface interaction. Then, the diagram would describe dissociative chemisorption. Alternatively, the interaction between a neutral gas particle and a metal atom follows curve (1), whereas curve (2) is the potential after a charge transfer between the approaching particle and the metal has occurred. This case will be considered in Section 2 to explain exoelectron emission. In both examples, the two diabatic PECs cross at a distance z_cr. This is the region where non-adiabatic processes may occur.

If the transition from (1) to (2) happens adiabatically, the crossing is avoided and the interaction follows the dashed line constituting the adiabatic PEC [30]. A precursor state with binding energy E_d is formed at z_p. An activation barrier E_a+E_d is established between the two potential minima in Fig. 3. If this barrier does not exist, the process happens spontaneously. In a non-adiabatic process, the system follows curve (1) beyond the crossing point and makes a sudden transition to the dash-dotted PEC which describes curve (2) plus an e–h pair excitation. Obviously, the construction of diabatic PECs is complicated since there is an infinite number of PECs which fill up the whole diagram due to the continuous e–h pair excitation spectrum.

The energy transfer between an impinging particle and the substrate by phonon or e–h pair excitation has been modeled by a variety of theoretical and phenomenological approaches to describe exoelectron emission and chemiluminescence [57], [58], [59], [60], [61], [62], the sticking of atoms or molecules on metal surfaces [63], [64], [65], [66], [67], [68], [69], [70], [71], [313], [314], [315], [316] and inelastic surface scattering events [53], [54], [72], [73], [74], [75], [76], [77], [78], [79], [312], especially of rare gas atoms. In the framework of gettering or sticking theory, the energy spectrum of substrate excitations may be estimated. It is an important input parameter to calculate the initial sticking coefficient s₀(ε) in a gas–surface scattering experiment. This number is the probability that a gas particle with kinetic energy ε gets trapped on the surface by exciting phonons or e–h pairs in the substrate. In a one-dimensional model and in the zero-temperature limit, it may be written as [30]

$$\text{s}{}_0\text{(ε)=}\text{∫}\text{ε}\text{∞}\text{d}\text{E}\text{P}{}_{\mathrm{\epsilon }}\text{(E),}$$

where P_ε(E) is the probability that the incident atom or molecule loses energy E to the substrate in a single collision. It describes the energy spectrum of the respective substrate excitation. Eq. (8) simplifies the interaction substantially since it considers single scattering events only. Stochastic methods were developed to describe a complete dissipative trajectory including multiple energy losses starting with the probability P_ε(E) [80].

The mechanical or adiabatic energy transfer to phonons has been extensively studied for gas–surface collisions under various conditions reviewed in, e.g., Refs. [72], [73], [81]. If the kinetic energy of the particle is much larger than the phonon energy, the scattering may be described by classical mechanics of binary collisions. This leads to the well-known Baule’s expression for the energy transfer [81]

$$\text{Δ}\text{E=}\text{4μ}\text{(1+μ)}{}^2\text{[ε+V}{}_0\text{],}$$

where μ=m/M is the mass ratio between the gas particle and the metal atom and V₀ the depth of the adiabatic PEC or potential well at the surface. Due to the surface potential, the atom or molecule is accelerated toward the surface which increases the kinetic energy.

The adiabatic interaction with a quantum lattice has been treated semiclassically in the forced oscillator model (FOM) as well as in fully quantum-mechanical models [30], [81]. As an example, P_ε(E) in the FOM is presented here. The particle is assumed to move on a classical trajectory governed by a model PEC and drives a bath of harmonic oscillators with N normal modes of frequency ω_q. Then the excitation spectrum may be written as [30]

where F(ω_q) represents the Fourier transform of the time-dependent force driving the oscillators. For E=0, Eq. (10) leads to the no-loss probability P_ε(E→0)=e^−2Wδ(E) which gives the intensity of elastically scattered particles. The quantity 2W is the well-known Debye–Waller factor. For thermal beams and depending on the assumptions on the driving force and the PEC, the excitation probability does not vanish in the energy region of the phonon band, i.e., in the lower millielectronvolt range. In general, it is found that phonon excitation by gas–surface scattering is more effective for heavy than light gas particles.

The non-adiabatic excitations of e–h pairs in metals by surface reactions may be described by applying the formalism of the above-mentioned time-dependent perturbation theory of Müller-Hartmann et al. [48], [74] for localized potentials in metals. The motion of the impinging gas particle is modeled classically and sets up a time-dependent perturbation potential. Schönhammer and Gunnarsson [69], [315], [316] considered the adsorption of a gas particle within the Anderson model and calculated the e–h pair excitation probability for a single reaction event as

In Eq. (11), ℏω_α represents the energy of a bosonized e–h pair and the coupling f_α is the Fourier transform of the time derivative of the interaction potential. The latter may be expressed by the time derivative of the instantaneous generalized phase shifts δ_EF(t) at the Fermi level which is essentially the rate of occurrence of new states below E_F, i.e.,

The energy and amount of excited e–h pairs is closely related to how rapid new electronic states are generated below E_F in agreement with the conclusions drawn from Eq. (5). Obviously, the FOM and the bosonized treatment of e–h pair excitations lead to the formally equal , for P_ε(E). Electron–hole pair excitation spectra according to Eq. (11) were calculated in the limits of strong and weak-coupling [69], [315], [316]. In the first an atomic or molecular electron affinity level crosses E_F, while approaching the surface representing a reaction system with possible exoelectron emission. The modeled e–h pair spectrum ranges between 0 and 1.5 eV with an average energy transfer of 0.52 eV per reaction event to the electronic system. In the weak-coupling limit where no level crossing occurs, e.g., in rare gas scattering, the energy of the e–h pair excitations are in the 0.1 eV range.

The results based on Eq. (11) strongly depend on the assumed dynamics of the process and may serve as a guideline only. In addition, the approximation to use bosonized e–h pairs is valid in the case of excitation energies which are much smaller than the Fermi energy. The classical trajectory approach is also questionable since Brivio’s and Grimley’s fully quantum-mechanical calculations [64], [65], [313], [314] of the sticking coefficient of hydrogen and deuterium atoms on metals reveal substantial differences to the semiclassical studies.

Unfortunately, first-principle calculations of chemically induced e–h pair excitations have not been performed yet due to the high complexity of the non-adiabatic processes. The theoretical investigations so far have pointed out in principal the high relevance of e–h pair excitation by rapid and exothermic chemical reactions on metal surfaces. The numerical results of the various calculations, however, are ambiguous due to the arbitrary choice of the unknown coupling parameters and the thin experimental database. For a long time, exoelectron emission and chemiluminescent systems have provided the only experimental evidence of chemically induced electronic excitations. Different semiclassical as well as phenomenological models, briefly described in Section 2, have been applied to explain the observed data. The new experimental approach using Schottky diodes to detect e–h pairs created by less exothermic reactions may initiate further theoretical efforts to achieve a better understanding and description of the physical origin of the electronic excitations.